Embed Size (px)
Citation preview
1
Contents CHAPTER 1: METHODOLOGICAL ISSUES IN ECONOMICS ................. 10
1. Differentiate between Micro-economics and Macro-economics. ........ 10
2. What do you mean by an economic model? What are the main features
of economic models? ................................................................................... 11
3. What are the criteria for determining the validity of a model? What are
the main limitations and uses of economic models?.................................... 12
4. What are the concepts used in building a model? Illustrate model
building with a particular example. ............................................................. 15
5. How do you choose models among many models?............................. 16
6. Write a short note on static equilibrium. ............................................. 17
7. What do you mean by dynamic equilibrium? ..................................... 18
8. Write a note on stationary state. .......................................................... 19
9. What is the difference between economic models and econometric
models?........................................................................................................ 19
10. Define the methodology in economics. .......................................... 21
11. Write short note on deduction. ........................................................ 21
12. Write short note on 'Induction'. ....................................................... 23
13. Differentiate between Inductive and Deductive methods. .............. 24
14. What do you mean by logical Positivism? ...................................... 25
15. How will you test a hypothesis in economics? What are the
difficulties on testing an economic hypothesis? .......................................... 26
16. What are the main assumptions in economics? What is the role of
assumption in economics? ........................................................................... 27
17. What is meant by scientific paradigm in economics? ..................... 28
18. What is Friedman and Lange's view on Economics? ...................... 28
19. Write a short note on empiricism in economics. ............................. 29
20. Is economics a science? .................................................................. 30
21. Analyze the role of value judgments in economics? ....................... 31
2
22. Critically analyze the Marxian methodology of economic analysis.
32
23. What do you mean by falsifiability criterion in economics? .......... 34
24. What are the main difficulties in falsifying the classical theories? . 34
25. Are the Neo-classical theories falsifiable? ...................................... 34
26. What are the limitations of Falsifiability criterion? ........................ 35
27. "Falsifiability criterion has helped to refute many established
theories and develop new theories instead" Justify with examples. ............ 36
CHAPTER 2: CARDINAL UTILITY ANALYSIS ......................................... 38
28. Explain about the consumer's equilibrium under cardinal utility
analysis. ....................................................................................................... 38
29. Derive the demand curves using the law of diminishing marginal
utility. 42
30. Derive a demand curve for an individual consumer for commodity X
by using equi-marginal principle. What will be the effect of change in price
of X on his purchase of another commodity Y? ........................................... 43
31. State the drawbacks of cardinal utility approach. ........................... 44
CHAPTER 3: ORDINAL UTILITY ANALYSIS .......................................... 46
32. Analyze the consumer's equilibrium under ordinal utility analysis?46
33. Derive the demand curve using ordinal utility analysis. ................. 50
34. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Normal good and price fall). ...................... 51
35. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Normal good and price rise). ..................... 55
36. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Inferior good and price fall). ...................... 55
37. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Inferior good and price rise). ..................... 56
38. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Giffen Goods good and price fall). ............ 56
39. Separate the substitution effect and income effect of a price change
in consumer’s equilibrium (for Giffen Goods good and price rise). ............ 57
40. Derive the ordinary and compensated demand for ordinary goods for
the fall in price of X. ................................................................................... 57
3
41. Derive the ordinary and compensated demand for ordinary goods for
the rise in price of x. .................................................................................... 60
42. Derive the ordinary and compensated demand curves for inferior
good X (Price fall). ...................................................................................... 60
43. Derive the ordinary and compensated demand curves for inferior
good X (Price rise) ...................................................................................... 62
44. Derive ordinary and compensated demand curve for Giffen good X
(Price fall). ................................................................................................... 63
45. Derive ordinary and compensated demand curve for Giffen good x
(Price rise). .................................................................................................. 64
46. Discuss the consumer's equilibrium under unusual shape of ICs. .. 65
CHAPTER 4: BEHAVIOURISTIC APPROACH AND OTHER DEMAND
MODELS ......................................................................................................... 69
47. Write a note on linear expenditure system (LES). .......................... 69
48. Write a note on empirical demand curves. ...................................... 71
49. Analyze the pragmatic Approach to demand theory. ...................... 72
50. Derive the demand theorem under Revealed preference approach. 74
51. Derive the indifference curve and prove its convexity under revealed
preference theory. ........................................................................................ 77
52. Critically appraise the revealed preference theory. ......................... 80
53. Describe about the Friedman-Savage hypothesis of the behavior of
consumers involving risk and uncertainty. .................................................. 81
54. Critically assess the Lancastrian demand theory. ........................... 84
55. Write short note on N-M utility index. ........................................... 88
CHAPTER 5: INTERTEMPORAL CHOICE.................................................. 92
56. Analyze the consumer’s equilibrium under intertemporal choice.
What are the effects of change in income and interest rate on such
equilibrium points? ...................................................................................... 92
CHAPTER 6: THEORY OF PRODUCTION AND TECHNOLOGICAL
CHANGE ......................................................................................................... 98
57. What do you mean by a production function? What are the main
features of production functions? Why is it necessary to study production
functions in economics? .............................................................................. 98
58. What is meant by a production process? ......................................... 99
4
59. Analyze how production is carried out under different decision
periods. 100
60. Write a note on elasticity of substitution. ..................................... 102
61. Write a note on short- run production function. ............................ 104
62. Explain the law of variable proportions and different stage of
production. In which stage does a rational producer operate? Where does the
producer operate in stage second? Where does the producer operate if price
of the variable factor is zero? .................................................................... 104
63. Explain the law of variable proportions using iso-quants. ............ 109
64. Write a note on log-run production function. ............................... 110
65. Define an iso-quant. What do you mean by the Marginal Rate of
Technical Substitution (MRTS). What are the different types of iso-quants?
111
66. Write a note on 'Ridge lines or economic zone of production'. .... 112
67. Discuss about the shape of product line. ....................................... 114
68. Explain the law of returns to scale. ............................................... 115
69. Analyze the producer's equilibrium. ............................................. 120
70. Write a note on profit maximization when the producer is free to
change the outlay as well as output. .......................................................... 125
71. Analyze the effects of change in outlay on producer’s equilibrium.
126
72. Analyse the effects of change in the price of factor on producer's
equilibrium. ............................................................................................... 129
73. Define and derive the production possibility curve (PPC) and
comment on its possible shapes and shifts in it. ........................................ 130
74. What do you mean by linearly homogeneous production function?
133
75. Write a short note on Cobb-Douglas production function. ........... 134
76. Write a short note on CES production function. ........................... 134
77. What is the role of technological change in production function? 135
78. What are the different types of production technical progress...... 136
79. Discuss the relationship between elasticity of substitution and
income distribution. ................................................................................... 137
5
80. What are the effects of technogical progress on income distribution.
138
81. What is cobb-Douglas production function? Why is it frequently
used in economics? How do we measure elasticities and marginal
productivities when such functions are used? ........................................... 139
82. Describe about the salient features of the two sector input output
model. 142
CHAPTER 7: THEORY OF COST ............................................................... 144
83. Write a short note on cost function. .............................................. 144
84. Derive the average fixed cost under traditional cost theory. ......... 144
85. Derive the short run average variable cost (SAVC) under traditional
theory of cost. ............................................................................................ 145
86. Derive the short run marginal cost (SMC) under traditional cost
theory. 146
87. What is the relationship between AFC, AVC, MC and ATC? ..... 147
88. Derive the long run average cost (LAC) and long run marginal cost
curve (LMC) with five alternative plants. ................................................. 149
89. Write a note on modern short run cost theory. .............................. 151
90. Write a note on long run cost under modern theory of cost. ......... 153
91. Derive the cost function from production function. ...................... 155
92. What is the significance of cost function in decision making? ..... 158
93. Analyze the economies of scale. ................................................... 160
94. Why is the short run average cost U-shaped? ............................... 161
95. Why is the long run average cost U-shaped? ................................ 162
96. Discuss about the empirical evidences on the shape of the cost
curves. 163
CHAPTER 8: PERFECT COMPETITION .............................................. 165
97. Define perfectly competitive market. What are the assumptions
underlying it? ............................................................................................. 165
98. Discuss the short run equilibrium of a perfectly competitive firm.166
99. Discuss the short run equilibrium of perfectly competitive industry.
169
100. Write a note on shut down point. .................................................. 170
6
101. Derive the short run supply curve of the firm. .............................. 170
102. Derive the Short run supply curve of perfect competition industry.
171
103. Analyze the long run equilibrium of perfectly competition firm. . 172
104. Analyze the long run equilibrium of perfectly competitive industry.
174
105. Predict the effects of increase in fixed cost in perfectly competitive
firm and industry. ...................................................................................... 174
106. Q.N. 10 Analyze the effects of change in variable cost. ............... 175
107. Predict the effects of imposition of lump sum tax. ....................... 176
108. Analyze the effects of profit tax on perfectly competitive firm. ... 177
109. Analyze the effects of the imposition of specific sales tax. .......... 178
110. Derive the long run supply curve of perfectly competitive industry?
179
CHAPTER 9: MONPOLY MARKET ........................................................... 183
111. Define monopoly market. ............................................................. 183
112. Analyze the short run equilibrium of a monopolist. ..................... 183
113. Q.N. 3. Why is the MC curve not the supply curve for monopolist?
185
114. Analyze the long run equilibrium of the monopolist. ................... 186
115. What are the effects of increase in fixed cost in monopoly market
structure? ................................................................................................... 188
116. Predict the effect of Lump sum tax. .............................................. 189
117. What are the effects of profit tax in monopoly? ........................... 189
118. Predict the effect of specific tax. .................................................. 190
119. What will be the effect of change in demand in monopoly
equilibrium? .............................................................................................. 191
120. Discuss the price and output determination under Multi plant
monopoly. .................................................................................................. 193
121. Analyze the price determination under bilateral monopoly. ......... 195
122. What is price discrimination? What are the conditions for applying
price discrimination? ................................................................................. 196
123. What do you mean by first degree price discrimination? ............. 197
7
124. Define the second degree price discrimination. ............................ 197
125. Define third degree price discrimination. ..................................... 198
126. What are the similarities and differences between monopoly and
perfect competition? .................................................................................. 201
CHAPTER 10: MONOPOLSTIC COMPETITION................................. 202
127. What do you mean by a monopolistic market structure? What are the
main assumptions underlying the Chamberlin model? .............................. 202
128. Explain the nature of cost and demand curves under Chamberlin's
large group model. ..................................................................................... 203
129. Discuss the short run equilibrium of monopolistic firm. .............. 204
130. Discuss the long run equilibrium under Chamberlin’s large group
model. 204
131. What is the main contribution of Chamberlin? Give a critique of
Chamberlin model. .................................................................................... 208
132. What are the similarities and differences between perfect
competition and monopolistic competition? .............................................. 208
133. What are the similarities and differences between monopoly and
monopolistic competition? ........................................................................ 209
134. Differentiate between monopolistic competition and imperfect
competition. ............................................................................................... 210
CHAPTER 11: OLIGOPOLY ................................................................... 212
135. Define Oligopoly. ......................................................................... 212
136. Discuss the Cournot model. .......................................................... 212
137. Discuss the Cournot model with the help of reaction functions. .. 215
138. Discuss the Bertrand model. ......................................................... 218
139. Analyze Chamberlin's small group model. ................................... 220
140. Discuss Stackelberg Duopoly Model. ........................................... 221
141. Analysis Kinked demand curve model. ........................................ 222
142. Define cartels. ............................................................................... 225
143. Write a note on cartel aiming at joint profit maximization. .......... 225
144. Explain the price determination under market sharing cartels. ..... 226
145. Write a note on low-cost price leadership. .................................... 228
8
146. Write a note on dominant firm price leadership model................. 229
147. Write a note on Barometric price leadership. ............................... 229
CHAPTER 12: OTHER MARKET MODELS ......................................... 231
148. Give a critique of neo-classical controversy. ................................ 231
149. Highlight the Hall and Hitch report. ............................................. 232
150. Critically present the representative model of average cost pricing
principle. .................................................................................................... 233
151. Discuss Bain’s Limit Pricing Theory. ........................................... 236
152. Discuss Baumol's Sales revenue maximizing model. ................... 238
CHAPTER 13: FACTOR PRICING .......................................................... 241
153. Differentiate between Rent and Quasi rent. .................................. 241
154. What are the main causes of wage differentials? .......................... 243
155. Derive the demand curve of labor for a market situation where the
factor market is perfectly competitive and the product market is
monopolistic. ............................................................................................. 244
156. Derive supply curve of labor. ....................................................... 247
157. Write a note on backward bending supply curve of labour? ......... 249
158. Write a note on monopolistic exploitation. ................................... 250
159. Analyze the price determination of factor in a scenario in which
there is monopolistic power in product market and monopsonistic power in
factor market.............................................................................................. 251
CHAPTER 14: GENARL EQUILIBRIUM ............................................... 254
160. Write note on interdependence of economy. ................................ 254
161. Distinguish between partial equilibrium and general equilibrium. 255
162. What do you mean by existence, stability and uniqueness of
equilibrium? .............................................................................................. 256
163. Differentiate between Marshallian and Walrasian conditions for
stability. ..................................................................................................... 260
164. Differentiate between Marshallian and Walrasian equilibrium
approaches. ................................................................................................ 262
165. Analyze the 2×2×2 general equilibrium model. ........................... 263
CHAPTER 15 : WELFARE ECONOMICS .............................................. 272
9
166. What do you mean by welfare economics? .................................. 272
167. Write a note on growth of GNP criterion of welfare. ................... 272
168. Write a note on Bentham's Criterion. ............................................ 272
169. Write a note on cardinalist criterion.............................................. 273
170. Explain the Kaldor-Hicks compensation criterion. ....................... 273
171. Clarify the Bergson's criterion. ..................................................... 274
172. State the Pareto Optimality criterion............................................. 275
173. Write a note on Scitovsky Paradox. .............................................. 278
174. Write a note on Scitovsky Double Criterion of social welfare. .... 279
175. Q.N.10 Write a note on ‘Pigovian Welfare Economics’. .............. 281
176. Write a note on 'point of bliss'. ..................................................... 282
177. Prove that perfect competition leads to maximization of social
welfare. ...................................................................................................... 285
178. What is market failure? How does it occur? ................................. 286
179. Write a note on the theory of second best. .................................... 289
10
CHAPTER 1: METHODOLOGICAL ISSUES IN ECONOMICS
1. Differentiate between Micro-economics and Macro-economics.
Microeconomics studies actions and behaviors of individual units of the
economy or about the different cells of an economic organism. Thus, it deals
with the equilibrium of the component of the economy or it may be called the
slicing method of the economy. It consists of looking at the economy through a
microscope as it were to see the millions of cells in a body.
According to K. E Boulding, “It is the study of particular firms, households,
industries, commodities, and wages.”
According to Maurice Dobb, “Microeconomics is the microscopic study of the
economy.”
On the other hand, Macroeconomics deals with the functioning of the economy
as a whole. It is the study of aggregates like aggregate production, employment
level and price level;
According to G. Ackley, “Macroeconomics is the study of forces that
determine the level of aggregate production, employment and prices in an
economy and their rates of change overtime.”
According to Edward Shapiro, “Macroeconomics is the study of economy’s
total output, employment and price level.”
The main points of difference between them can be summarized below:
Microeconomics Macroeconomics
It is the study of a particular component
of the economy e.g. firm, household,
industry,etc.
It is the study of the economy in
totality.
The objective is the analysis of
maximization of utility, profit, supply
etc.
The objective is full employment,
growth, BOP equilibrium, etc.
It concerns with:
How goods and services are
produced?
How are they distributed?
How efficiently are they
distributed?
It concerns with the economic
growth, macro theory of distribution,
general price level, theory of income
output and employment, etc.
It uses individual demand and supply as
tools of analysis.
It uses aggregate demand and supply
as tools of analysis.
11
It analyses the data of individual sector. It analyses aggregate level data.
It is not capable of solving the
problems like inflation, BOP, growth,
etc.
It is capable of solving such
problems.
Despite these differences, there is interdependence between these two. As
Samuelson argues, “There is really no opposition between microeconomics
and macroeconomics. Both are absolutely vital. You are less than half-
educated if you understand the one while being ignorant of the other.”
2. What do you mean by an economic model? What are the main
features of economic models?
The economic world is very much complex. So, we cannot analyze it as it is.
Rather, we use models which are the simplified representation of the real
situations for studying the economic processes and patterns. At heart, an
economic model is a means of simplifying the reality and making the
predictions. It does not matter whether it is a verbal description or a set of
mathematical equations or geometric diagrams. It tries to paint a simplified
picture of reality which allows meaningful economic predictions to be made. A
good analogy of model is a map which simplifies and predicts. Since maps
would be useless if all details are included; so are models. If a model were truly
realistic and comprehensive, it would be enormous and useless. So, they aim at
finding the right abstractions and making accurate predictions; they do not try
to be realistic.
According to David Hymen, “An economic model is a simplified way of
expressing how some sector of the economy functions. It contains assumptions
that establish relationship among variables. It uses logics, graphs and, maths
to determine the consequences of the assumptions.”
According to Oxford Dictionary of Economics, “A theoretical construct
designed to analyze the behavior of economic agents using quantitative and
logical methods. A model can be formulated verbally and/or in the form of
equations and/or diagrams, and is composed of a list of variables that
characterize the economic agents and the economic environment under
consideration, and a list of assumptions about their interaction…An economic
model is always a simplified representation of the real world.”
Samuelson and Nordhaus gave the definition of a model as a formal
framework for representing the basic features of a complex system by a few
central relationships. Models take the form of graphs, mathematical equations,
and computer programs.
12
Begg., Fischer, and Dornbusch observe that a model or theory makes a series
of simplifications from which it deduces how people will behave. It is a
deliberate simplification of reality.
Features:
An economic model shows the relationship between dependent and
independent variables.
To be a complete model, the number of equations must be equal to the
number of unknowns (variables).
It abstracts the real world and simplifies the reality.
It can be presented through symbols and equations.
It is not exact and rigid as in physical science.
It is built for the purpose of prediction and analysis.
Most economic models emphasize partial analysis.
Error of measurement cannot be heavily reduced. Box.1.1
3. What are the criteria for determining the validity of a model?
What are the main limitations and uses of economic models?
Economists are not in agreement on the criteria of measuring the validity of
the model. Some of the bases to evaluate the validity of the model are:
Predicative power.
Consistency and realism of assumptions.
Extent of the information provided by the model.
Generalizing capacity.
Simplicity.
Defining the Problem (Identifying the Variables)
Major Steps of Model Formulation
Formulating the Preliminary Model
Collection of Empirical Data
Estimation of the Parameters
Preliminary Test of the Model
Making Further Tests
Accepting or Revising the Model
13
According to the first criterion, a model is valid if it can make predictions about
the future happenings correctly. Similarly, according to the second criterion, a
model is valid if its assumptions are consistent and realistic. The third criterion
says that a model is valid if it provides sufficient information about economic
phenomena. The fourth criterion says that a model is valid if its conclusions can
be generalized and lastly the fifth criterion demands the simplicity nature of the
model for its validity.
The main limitations of Economic Models are:
i. They are not comprehensive but partial.
ii. Use of econometrics gives rise to the problem of identification and
random disturbance.
iii. Misspecification error is most likely to occur.
iv. Non-availability of data may give rise to the problem of testing the
model.
v. They may be destroyed by the fallacy of composition and post-hoc
fallacy.
vi. Pure theoretical models do not provide full explanation and prediction
of the phenomena under study.
Uses of Economic Model
Economic models are the simplified representation of reality. As
economic world is complex, it cannot be studied as it is. Thus, models are the
only means for studying how economic functions work. Prof. Mydral
observes, "The first virtue of economic model is that they can make explicit and
rigorous what might otherwise remain implicit, vague and self-contradictory.
Even if a model is totally unrealistic, it may have a therapeutic value."
Economists use the scientific approach to deal with economic problems, the
scientific approach starts from scientific observation (it can be the environment
or other fields of interest), after that they will build up a hypothesis, then they
will use the scientific experiment or existing theories to prove their hypothesis
and they will reach a conclusion that can be true of false (it depends on the
results from their experiment). Economists use this way when they think about
a particular issue in the economy; they try to simplify an economic issue in the
way that everyone will understand and be able to follow their thought; they try
to find a formula that can help them calculate the numerical issue; they try to
develop a new economic theory to explain the economic behavior in the real
world. They need a ‘model’ to fulfill these purposes.
To enlist, the main uses of economic models are:
Explaining an economic process
From Chinese proverb “A picture is worth a thousand words”, it is true that
a picture can express idea better than words or equations. Graphics help
14
economists in many specific purposes: some shows the relationship of
observed data; some shows how the economic process runs; some shows
the trend from historical data. Graphs and flow charts play the main role in
this purpose of using models.
Examining an economic issue
What do economists want to know from observed data? Not only do they
want to see how the system looks like or the relationship in the graphic
way, but they also want to see the trend or changes from observed data.
Economists use the wide range of mathematical models to examine the
economic issues: some simple formulas are used to calculate a new value
from given data or analyze it; some mathematical models are used in the
problem-solving process; some equations are used to estimate and forecast
the change in the economy.
Firstly, it is the best way to start with a simple mathematical equation
that is used to calculate and measure the change in the economy such
as the percentage change and the growth rate.
Secondly, a model is required in the problem-solving process. This
process can be divided into four steps: problem definition,
mathematical model, numerical or graphic result, and implementation.
Not only a mathematical model is used in the problem-solving
process, but also the graphics, statistics, etc. are used as the problem-
solving tools.
And thirdly, some models are used to estimate and forecast the future
trend. Economists have developed forecasting tools to help them
foresee changes in the economy. Forecasting models are built up by
the combination of mathematical models and historical data, as the
system of equations.
Developing a new economic theory
The good theories help economists measure the changes, see the new trend,
and predict the future result in the economy. To develop a new economic
theory, economists have to combine the scientific approach, the
mathematical knowledge, and historical economic data together. Then they
will use the problem-solving process to find the suitable model for the
particular problem, after that they have to test their model and if it is true
they can use it as a new theory. It sounds like an easy process but it is not
easy to simplify reality to a model. Most of economic theories are based on
or related to the existing theories (or models).
Simplify the reality for analysis and making predictions.
Help in making policy decisions.
Essential aids to clear thinking.
15
Quite useful in development planning and growth economics.
Helpful to understand the functioning of the economy.
Helpful for economic and econometric researches.
Static and dynamic models are quite useful in understanding
microeconomics and macroeconomics.
4. What are the concepts used in building a model? Illustrate model
building with a particular example.
The main concepts that are used in model building are:
i. Variable: A variable is something which may take differing
values over a period of analysis. e.g. demand, supply etc.
ii. Independent Variable: A variable whose value is predicted or
determined by another variable(s).
iii. Dependent Variable: A variable which determines the value of
another variable(s).
iv. Endogenous Variable: It is that variable whose value is
determined from within the model, e.g. demand, supply, NI,
consumption, saving, investment, etc.
v. Exogenous Variable: It is that variable whose value is determined
by external forces. e.g. price, exchange rate, exports, etc.
vi. Flow Variable: It is the quantity that can be measured in term of
specified period of the time. e.g. market demand and Supply,
income , expenditure, etc.
vii. Stock Variable: A stock variable is one which can be measured at
a specified point of time. For example: population, capital stock,
etc.
viii. Constant: It is something whose magnitude does not change.
ix. Parameter: It is a symbol which is constant for a problem/model
but may assume different values for different problems/models.
x. Definitional Equation: It is a relationship between two
alternatives having same meaning. E.g. = R – C
xi. Behavioral Equation: It specifies how a variable behaves in
response to change in other variable. E.g. Qd = 800-16p
xii. Equilibrium Condition: The equation that explains the
attainment of equilibrium is called equilibrium condition. For
market model, it is Qd = Qs.
Example: A Micro Static Market Model
The fundamental relations are
16
( )
( )
d
s
d s
Q f p
Q f p
Q Q
Assumptions:
Qd is a decreasing function of price.
Qs is an increasing function of price.
Qd and Qs are stock variables.
Market is in equilibrium when Qd= Qs.
Let the behavioral equations and equilibrium conditions are:
d
s
d s
Q a bp
Q c dp
Q Q
Solving, we get a b
Pc d
E.g. Qd= 800-200p and Qs= -100+100p, then300
900
100200
100800P
= Rs 3. Qd = Qs = 200.
Market Equilibrium
In figure 1.1, the demand and supply curves have intersected at point e where
Qd=Qs=200 and the equilibrium has been established at price level of Rs.3.
With the help of this economic model, we can analyze the behavior of price in
the market and as such predict the future price level.
5. How do you choose models among many models?
There is no hard and fast rule for choosing the best model among the many
ones. It depends on objective, circumstances, amount of data available, one's
own knowledge level, extent of precision required, etc. Freidman observes that
P
SD
e
P=3
S D
O QdQ=200
Fig.1.1
17
a model should be viewed as a filing system for organizing empirical material
and facilitating an understanding of it and the criteria which is to be judged are:
Are the categories of the model clearly and precisely defined?
Are they exhaustive?
Are the items we want to consider jointly filed together?
Does the filing system avoid elaborate references? etc
The minimum requirements of a model are:
It should be simple.
It should have wider applicability to real world situation.
It should be refutable by empirical evidence.
It should be valid, i.e. should do what it purports to do?
It should be reliable i.e. should be consistent in doing what it
purports to do.
The assumptions should be consistent, logical and clearly stated.
Choice of models depends on:
a) Objective of the Study: If the objective is to describe a relationship, a
model with real assumptions should be preferred and if the objective is to
predict, a model with strong predicative power is to be preferred.
b) A simpler model should be preferred if two models serve the same purpose.
c) A more valid model should be preferred.
d) Level of Sophistication: It depends on the investigator. If he can handle
sophisticated models, he can build and analyze difficult ones otherwise simple
models should be preferred.
e) Extent of Precision Required: A model with more precision should be
preferred.
f) Sometimes statistical values also help in choosing the model e.g. t, F, 2, R
2
and other tools. Given two regression models, a model with higher R2 is to be
preferred.
Thus, there is not any single criterion to separate good models from
bad ones. It all depends on objectives and many other factors.
6. Write a short note on static equilibrium.
Static equilibrium is that equilibrium which maintains itself outside the
period of time under consideration. It is a state of bliss which every firm,
industry or factor wants to attain and once reached would not like to leave. A
consumer is in equilibrium when he gets maximum satisfaction, given income,
prices of commodities and after reaching the equilibrium he has no incentive to
change his quantity of commodities. It has been illustrated in fig. 1.2 where the
18
demand and supply curves intersect at point e. This is static equilibrium
because all the variables refer to the same period of time.
Static Equilibrium
7. What do you mean by dynamic equilibrium?
A dynamic equilibrium is concerned with the process of change in the values
of the variable of interest in any time period. According to Prof. Mehta, "When
after a fixed period of time the equilibrium state is disturbed, it is called
dynamic equilibrium."
Consider fig. 1.3 where demand shifts rightward due to change in
tastes.
Dynamic Equilibrium
This will change the disposition of seller and buyers. Sellers raise their price to
p1. It induces the sellers to increase supply to oq1 but this is more than final
equilibrium quantity oq3. It reduces price to q1d. Now, producer would reduce
supply to oq2 but this is less than equilibrium oq3 quantity. Thus price will rise
to op4 which stimulates supply to oq3. Ultimately, equilibrium is established at
point g where price is op3 and quantity is oq3. This is dynamic equilibrium with
lagged adjustment.
P
SD
e
P
S D
O QdQ
Fig.1.2
D
D1
P,C
Qtyq
p2
q3
q1
q4
p3
p1p4
pa
O
Fig.1.3
g
S
q2
d
19
8. Write a note on stationary state.
It is a state of the economy in which the values of all variables do not change
overtime. The tastes, resources and techniques are constant. It is possible that
some economic phenomena may be changing from the microeconomic angle
but from macroeconomic angle, the phenomenon is constant. For example,
population remains constant in number, skill and composition but people
continue to born and die, though births equal deaths. It is a state in which
general conditions of production, consumption, distribution and exchange
remain constant. Method of production, total output and stock of capital goods
also remain the same. Goods continue to be produced and consumed at the
same rate which leads to constant price. The total quantity of money is constant
and there are neither saving nor investment, though individuals might be saving
and investing. Prof. Pigou observes, "Stationaryness does not mean frozen
fixity, individual drops composing the waterfall are continually in movement,
though the waterfall itself remains constant."
It is not a reality. Marshall calls it a fiction; an illusion because every
economic variable is changing overtime and influencing other variables. Taste,
technique, resources, population, capital etc are changing. Thus, relaxation of
the assumption of stationaryness brings us nearer to reality and helps in solving
a number of complex problems. Hicks is also very skeptical about its use. To
him, it has created more problems by impeding the development of economic
theories on realistic lines. We conclude with Prof. Water Eucken, "Obviously,
it has never been realized historically: large changes in data have been
constantly occurring, occasionally very small changes but never no change at
all."
9. What is the difference between economic models and econometric
models?
A model is a simplified representation of an actual phenomenon, such as an
actual system or process. The actual phenomenon is represented by the model
in order to explain it, to predict it, and to control it. Many different types of
models have been used in economics and other social and physical sciences.
Among the most important types are verbal/logical models, physical models,
geometric models, and algebraic models, involving alternative ways of
representing the real-world system.
Economic models establish the direct and exact relationship between
independent variables and dependent variable e.g.
C= a + bY
Where,
C = Consumption,
a = autonomous consumption, a>0
20
b = Marginal propensity to consume (0<b<1) and
Y = Income
Here, the relationship between C and Y is deterministic i.e. it assumes
a linear relationship which is exact and does not depend on any probabilistic
formula.
Mathematical Economic Models reveal the economic activity in the theoretical
relationship between various factors and use mathematical equations to
describe certain and exact relationship. For example, the production function
can be used to describe a production activity:
Q=f(T,K,L)
Q is output;
T is technology;
K is capital;
L is labor;
This function shows the relationship between the factors of production and
output that can be accurately realized.
This type of models, however, are not deemed appropriate from econometric
point of view because at a certain level of income, consumption may vary due
to other factors like property, family members, taste, price levels, seasons, etc.
similarly, output also may be affected by a large number of other factors . So, a
random disturbance term is included which makes it an econometric model. e.g.
C = a + bY + e
Where, e is a random variable or a random error term.
This relation does not accept the exact relationship but it depends on
probabilistic properties.
According to Michael D. Intrilligator, Econometric models are generally
algebraic models that are stochastic in including random variables (as
opposed to deterministic models which do not include random variables). The
random variables that are included, typically as additive stochastic disturbance
terms, account in part for the omission of relevant variables, incorrect
specification of the model, errors in measuring variables, etc. The general
econometric model with additive stochastic disturbance terms can be written as
the non -linear structural form system of g equations:
( , , )f Y X ……………………………………..(i)
Where, is a vector of stochastic disturbance terms, one for each equation, Y
is the vector of endogenous variables, X is the vector of exogenous variables
and is the vector of the parameters of the model.
From relation (i), it follows that the econometric model uniquely specifies not
the endogenous variables but rather the probability distribution of each of the
21
endogenous variables, given the values taken by all exogenous variables and
given the values of all parameters of the model. Each equation of the model,
other than definitions, equilibrium conditions, and identities, is generally
assumed to contain an additive stochastic disturbance term, which is an
unobservable random variable with certain assumed properties, e.g. mean,
variance, and covariance. The values taken by that variable are not known with
certainty; rather, they can be considered random drawings from a probability
distribution with certain assumed moments. The inclusion of such stochastic
disturbance terms in the econometric model is basic to the use of tools of
statistical inference to estimate parameters of the model.
Econometric models are either linear or non-linear. Early econometric models
and many current econometric models are linear in that they can be expressed
as models that are linear in the parameters.
10. Define the methodology in economics.
Methodology is the logical process of arriving at the truth. The methodology
of economics is the methodology of science. However, since strict physical
experimentation is not possible in economics, one should rely on intellectual
experimentation.
Economics uses two methods for the formation of its laws, principles
and theories: inductive and deductive methods. Inductive method mounts from
particular to the general. i.e. here, we begin with the observation of particular
facts and then proceed with the help of reasoning founded on experience so as
to formulate laws and theories. On the other hand deductive method descends
from the general to particular i.e. here, we start from certain principles which
are either self-evident or based on strict observation and carry them down as a
process of pure reasoning to the consequences which they implicitly contain.
There is a tearing controversy in selecting between the methods. The
classicals advocated deductive method and the historical school was firm in
inductive method. However, both were not extremists. This controversy went
on till Marshall, the great compromising genius, who regarded both methods
complementary to each other. Following Schmoller, he observed, "Inductive
and deductive methods are both needed for scientific thought as the right foot
and left foot are needed for walking."
11. Write short note on deduction.
Deduction means inference from general to particular. By analyzing the
indisputable facts about human nature, individual cases are predicted.
According to Bacon, "Deduction is a process in which we proceed from a
general principle to its consequences.” Also Willson Gee has observed, "By
deduction means reasoning from the general to particular or from universal to
individual."
22
For example deducing the of taxation from the law of diminishing marginal
utility
Supporters of this method are classical economists, Von Mises, Lionel
Robbins, Frank Night, etc.
Box.1.2
Merits
i. Simple: It is simple because it is analytical. It involves abstraction and
simplifies a complex problem.
ii. Use of logics and Mathematics: Here, theories can be deduced using
rigorous mathematical logic which can successfully explain economic
phenomena.
iii. Powerful: According to Cairness, it is the most powerful instrument
of discovery ever wielded (found) by human intelligence.
iv. Effective: It is effective if the premises or assumptions are true.
v. Real: “It is real because it is the method of intellectual experiments.”
Boulding.
vi. Certainly and Clarity: The use of sophisticated (standard)
mathematics brings accuracy, exactness and clarity in economic
principles.
vii. Universal: It helps us to draw universally valid conclusions because
these are based on general principles.
viii. Limited Scope of Experimentation: As economic phenomena are
affected by a multiplicity of forces, there is limited scope of
experimentation. Thus, it has a crucial importance in building-up of
economic principles.
Demerits
i. Highly Abstract and Requires Great Skill: It is highly abstract and
requires great skill in drawing inferences from various premises. Even
General Scheme
Exploration of the Problem
Specification of Assumptions
Logical Reasoning and
Hypothesis Formulation
Testing the validity of hypothesis
Verification of Theories.
23
experts feel difficulty due to complexity of certain economic
reasoning.
ii. Conclusions not Universally Applicable: The premises or
assumptions may not always hold good. In such a case, the
conclusions are not universally valid.
iii. Assumptions may Break down a Theory: If assumptions are
unrealistic, the theory breaks down.
iv. Highly Sophisticated Models with Little Practical Use: It develops
highly sophisticated theoretical models with little practical use. So,
they are just 'intellectual toys'.
12. Write short note on 'Induction'.
Induction is a process of reasoning from a part to the whole, from particular
to general or from the individual to universe. Bacon describes it as the
‘ascending process’ in which facts are collected, arranged and then general
conclusions are drawn.
It is called empirical method or historical method that derives
generalizations on the basis of experiences and observations. It can take two
forms:
1. Experimental: It is more popular in physical science as there is very
limited scope of experimentation in Economics.
2. Statistical: Here, conclusions are drawn from the collection and
analysis of data. It is more extensively used in economics.
The main profounders of this method are Roscher, Hilde Brand and
Schmoller.
Box.1.3
Merits
Dynamic: Changing economic phenomena can be analyzed on the
basis of experiences. So, it is dynamic.
General Scheme
Selecting of the Problem
Collection of Data
Observation of Facts
Generalization
24
Use of the Statistical Method: Use of statistics can analyze the
economic problems of wide range.
Realistic: It is realistic because it is based on facts and explains them
as they actually are.
i. Helps in Future Inquiries: Once a generalization is established on
the basis of observation, it becomes the starting point of future
inquiries.
ii. Possibility of Verification: Its proposition can be tested and verified
easily.
Demerits:
Difficult: It is difficult for a common man to collect data and derive
conclusions.
Time Consuming and Costly: Due to collection, classification,
analysis and interpretation of data, it is costly and time consuming.
Limited Scope of Experimentation: It has limited scope in
economics because strict experimentations in economics are not
possible.
Statistics cannot Prove a Hypothesis: It can only show that the
hypothesis is not consistent with the known facts.
It would not do a trick unless supplemented by deduction but
produce a help of unrelated and unconnected facts.
There is the serious risk of wrong conclusions being drawn upon an
inadequate number of facts particularly when the investigator lacks a
balanced and undiscriminating judgment.
13. Differentiate between Inductive and Deductive methods.
First, give a short introduction of induction and deduction as a method of
economic science.
The main differences between induction and deduction are summarized in the
table below:
Deduction Induction
Here, we move from general principle
to particular conclusions. So it is a
descending process.
Here, we move from particular to
general. So, it is an ascending process.
It was strongly advocated by the
classical school.
It was strongly advocated by the
German historical school.
It is a technique of abstract approach
to the problem of economic science.
It is a empirical and objective
technique to the problems of
economic science.
25
It is known as the analytical, abstract
or a-priori method.
It is known as historical and a
posteriori method.
Laws made by this method have
universal conclusions.
Laws here are only relative and thus
true to a particular situation only.
It is less time consuming. Large
number of deductions can be made in
a short time.
It is a complicated, time consuming
and expensive method of law making.
It is of more importance to economics
as there is limited scope of
experimentation.
The experimental induction is less
important but the statistical form is
very much vital.
The general scheme for this method
is:
The general scheme for this method
is:
Despite these differences, there is no sharp dichotomy between these two. Both
are absolutely vital. Induction with out the help of deduction would produce
meaningless heap of facts and deduction without induction would produce
highly abstract models with no practical use. Thus, we conclude with the
words of Marshall, "Induction and deduction are both needed for scientific
thought as the right foot and left foot are needed for walking."
14. What do you mean by logical Positivism?
It has been recognized that the furtherance of economic knowledge requires the
use of both empirical and analytical studies, each being necessary for the
success of another. Today, empirical studies undertaken through the inductive
method without an analytical framework to direct the selecting of relevant data
are completely futile. Analytical studies through deductive method without any
empirical content are deductive in logic without any possible usefulness.
The final methodological concept gaining popularity is logical
positivism. The positive economists agree that the basic axioms or assumptions
of theory are not subject to independent empirical verification but they consider
it both possible and desirable to test deduced hypothesis and thereby to test
Making Asumptions
Identify the Problem
Logical Deduction
Formulation of Hypothesis
Making Predictions and Test Them
Predictions are in Agrement with Facts
Modify Assumption
If in Conflict
Discarded
Data Collection
Identify the Problem
Data Processing
Deveop a Theory and Refine itthrough Satatistical Method
Making Predictions and Test Them
Predictions are in Agrement with Facts
Modify Assumption
If in Conflict
Discarded
26
indirectly the system of axioms. Thus, this middle approach between the
deductive logic and extreme empiricism is called logical positivism. It was first
named by Samuelson. To him, the premises cannot be verified but the
conclusions derived from them can and should be verified empirically. So, it is
related to the real analysis of economic world.
Merits:
Scientific: It is scientific as the conclusions are empirically
testable.
Practical: Because all premises may not be real but the
conclusions are real.
Middle Approach: It is the midway to extreme a-priorism and
ultra empiricism.
15. How will you test a hypothesis in economics? What are the
difficulties on testing an economic hypothesis?
A hypothesis is a testable statement of potential relationship between two or
more variables. It is the conjectural statement of relationship between two or
more variables. The procedure for testing a hypothesis is given below:
The main difficulties in testing a hypothesis are:
There is a high survival of economic theories. The old doctrine
continues to exist side by side; most of them can neither be
refuted nor proved.
There is sometimes a withdrawal into mere tautologies i.e.
expressing the same concept twice over different words.
Problem - Define Assumptions
Hypothesis Formulation
PredictionReformulationof Hypothesis
Generation of Data andTest of Hypothesis
YesNo
Rejection of Hypothesis Theory
27
There is danger of normative apologetics.
There is the difficulty of fiddling of assumptions. We assume
economic rationality, free enterprise economy and the like and
frequently modify our assumptions.
16. What are the main assumptions in economics? What is the role of
assumption in economics?
Economic laws depend on assumptions. They are the foundation for the
formulation of economic models. They simplify economic analysis and are of
two types: abstract and unrealistic. They become unrealistic when they are
overused. Some economists argue that they should be realistic while others
argue that they may not be so. To Friedman, they may not be like in physical
science since they are made merely to simplify the analysis.
Well-known assumptions in economics are:
Rationality.
Study of a normal man.
Aim of all is to attain equilibrium.
Ceteris paribus (other things remaining the same).
Self-interest.
Nature of economic organization.
However, the economic assumptions can be broadly classified under the
following categories.
i) Behavioral Assumptions: These are related to human behaviors as consumer
or producer.
ii) Institutional Assumptions: These relate to social, political and economic
institutions. Almost all economic theories have been developed on the
assumptions of capitalist economy where means are privately owned and used
for personal gain.
iii) Structural Assumptions: These relate to the nature, physical structure or
typography of the economy and state of technology.
Importance of Assumptions:
Simplification of economic theory- Friedman.
They are economical mode of describing and presenting a theory.
They facilitate indirect test of hypothesis by implications.
They are a convenient means of specifying the condition under which
the theory is expected to be valid.
Building explanatory theories- Earnest Nagel.
28
According to Friedman, the adequacy of theory must not be judged by
assessing the realism of assumptions but by examining the logical
consequences. He also emphasizes the explanatory function of theories in
addition to the predicative one.
17. What is meant by scientific paradigm in economics?
Scientific paradigm in economics means how economic science can be studied
through scientific method. It takes economics as a science and deals with how
theories are formulated and empirically tested. Friedman’s Falsifiability
criterion is related to scientific paradigm of economics.
To formulate a theory in economics, we need premises, axioms and
assumptions and all the conclusions and predictions depend on those axioms,
premises and assumptions. Assumptions must be compact, consistent, precise
and relevant.
Another most important aspect of scientific process is testability. Any
assumption or conclusion or predictions can be empirically tested on the basis
of observed data. But Friedman argues that assumption cannot be tested but
predictions can be. So, if predictions are consistent with the observed facts, the
theory can be accepted.
Scientific theory always incorporates truth from facts. But in
economics, there may not be the praise of truth but belief. But in modern time,
most economic theories are based on empirical facts based on scientific
paradigm.
18. What is Friedman and Lange's view on Economics?
Friedman published his essay on "Methodology of Positive Economics" in
1953 which started a new debate on methodological issue. According to him,
positive economics provides a system of generalizations that can be used to
make correct predictions about the consequences of any change in
circumstances.
The aim of economic science, to him, is to construct a theory which
can yield valid and meaningful predictions. A theory has two elements
i) language which facilitates logical reasoning and systematic analysis and
ii) hypothesis which abstracts the complex reality or set of substantive
empirical propositions but the second one is more important.
The validity of a theory, to him, is to be established not by the
descriptive realism of its premises or assumptions but by the accuracy of its
predictions with which it is concerned. Therefore, a hypothesis is rejected if its
predictions are contradicted. He insisted on predicative capacity as the sole
criterion of validity. So, a good economic theory must be so stated as to be
confirmed or contradicted by relevant facts at the time of test.
29
Thus, he relies on objective method of economics. The ultimate goal
of positive science, to him, is the development of a theory or hypothesis that
yields valid and meaningful predictions about phenomena not yet to be
observed. It studies the cause and effect relationship and eases (makes easier)
prediction. So, he emphasizes empiricism on economic analysis.
Lange's view is similar to Friedman. To him, theoretical economics
provides hypothesis or model based on generalization of observation and
subject to empirical test. Since economics is a science, the rejected theories
from the test are improved and old concepts are replaced by new and effective
concepts. Anyway, Lange emphasizes on empirical test of theories, analysis
through inductive method in economics.
19. Write a short note on empiricism in economics.
Empiricism in economics was initiated by the Chicago School of economics.
The most eminent economist among them is Prof. Milton Friedman.
Similarly, Prof. Klein of the University of Pennsylvania has emphasized it.
The classical and neo-classical economists formulated economic
principles by deductive method. So, they were far from reality. But empiricists
depend less on intuitive reasoning. Instead they collect data and study the
relationship among variables and predict through the relationship among
variables. Pragmatic demand curves, linear expenditure system (LES) models,
etc are the results of empirical approach in demand analysis.
Empiricism uses statistics, numbers and equations to evaluate
fictitiously constructed models. Under the cloak of empiricism; scientific
theory has pretended to be neutral.
Growth of empiricism in economics has been responsible at least for
two reasons.
To test existing theories and to examine their falsifiability in term of
factual evidence and
To build theories having empirical content and to make operational and
realistic generalizations.
The supporters of the empiricism are Hutchinson, Keynes, J.S. Mill, Hawley,
Friedman, Paul Samuelson, Gordon, etc. According to Lange, economics is
basically an empirical science. Its assumptions and postulates are approximate
generalizations of empirical observations. However, some inaccuracy in
approximation is accepted for the sake of greater simplicity. These theories in
turn are subject to a test by empirical observation.
However, strong empiricism requires cent percentage factual content
of a theory. So, it is the ideal one and never attained is reality. In fact, many
valuable theoretical outputs in economics would be demolished (destroyed) if
30
we accept the principle of strong empiricism. Non empirical concepts may
appear to be non-scientific but they still express a point of view and give
direction for scientific investigation.
However, the a-priori method and empirical method are not opposites
but they supplement each other. So, we can neither bury nor praise empiricism.
Taken alone, it is like a ship without any rudder. It is an aversion of truth that
theoretical pre-suppositions are arrived on the basis of presuppositionless
observation of facts. It is only with the help of a theory that we can determine
what the facts are. Thus, the empiricists must make use of theoretical tools.
20. Is economics a science?
A science is a systematized body of knowledge ascertainable by observation
and experimentation. It is a body of generalizations, principles, theories, or
laws which traces out a causal relationship between cause and effect. For any
discipline to be a science, it must have the following characteristics:
It must be a systematized body of knowledge.
It must have its own laws and theories.
The laws can be tested by observations and experimentations.
It can make predictions.
It is self-corrective in nature.
It must have universal validity.
Economics is a systematized body of knowledge in which economic
facts are studied and analyzed in a systematic way. It is divided into
consumption, production, exchange, distribution, and public finance which
have their own laws and theories. Also like any other science, there is a causal
relationship between two or more phenomena. For example, the law of demand
which tells us that, ceteris paribus, a fall in price leads to a rise in demand and
vice versa. Further, the laws of economics possess universal validity such as the
law of diminishing returns, the law of diminishing marginal utility, Gresham's
law etc.
Economics is self-corrective in nature too. It goes on revising its
conclusions in the light of new facts and circumstances. Economic theories or
principles are being revised in the fields of macroeconomics, monetary
economics, international economics, public finance and economic
development.
Some economists do not accord (agree) with the view that economics
is a science. To them, science is not merely a collection of facts by observation.
It also involves testing of facts by experimentation. Unlike natural sciences,
there is no scope for experimentation in economics because it is related to man
31
whose activities are bound by his tastes, habits and social and legal institutions
of the society in which he lives. Economics is thus concerned with human
beings who act irrationally and there is no scope for experimentation in
economics, even though economics possesses statistical, mathematical laws and
theories. As a result, exact quantitative prediction is not possible in economics.
But this does not mean that economics is not a science. As Marshall
said, "Economics aspires to a place in the group of science because though
measurements are seldom exact and never final, yet it is ever working to make
them more exact and thus to encourage the range of matter on which the
individual students may speak with the authority of his science. It is definitely a
science like any other science."
Further, there is a great debate on whether economics is a positive
science or normative science. A positive science is concerned with ‘what is?’
and the normative science is concerned with ‘what should be?’. Economists
like Marshall, Pigou, Hawtrey, Frazer, etc argue that economics is a
normative science which involves value judgments and they cannot be verified
to be true or false. Whereas the economists like Keynes, Robbins, Friedman,
etc take it to be a positive science. To them, the function of economists it to
explore, not to advocate and to condemn (disapprove).
In conclusion, we can say that the view that economics is only a
positive science is divorced (Far from) from reality. The science of economics
cannot be separated from normative aspect. Economics as a science is
concerned with human welfare and involves ethical considerations. Thus,
economics is a positive as well as a normative science.
21. Analyze the role of value judgments in economics?
All ethical judgments and statements which have suggestive or persuasive
effects are value judgments. There is a vital role of these judgments in
economics if it be a normative science. Economists like Marshall, Frazer,
Hawtrey, etc argue that subjectivity always enters in economics as it is related
to man and his problems. Boulding observes, "One must admit that the task of
making value judgment explicit is very important one."
The role of value judgments in economics can be presented below.
i) Economist is not an Armchair Academician: The economists cannot be
expected to be an armchair academician. He can comment and make policy
recommendations on efficiency distribution and equity grounds. Scitovsky
argues, "After all, it is the function of social science to make value judgment
and recommendation on the distribution of welfare and not only is the
economist a social scientist, he is probably the best qualified among social
scientists to deal with the subject."
ii) Basis of a Democratic Welfare State: Nowadays, all democratic countries
have an ideal of welfare state. Thus, the value judgments only can select the
32
various legislative measures like free education, heavy excise duty on wine,
compulsory national insurance, etc. Thus, in the absence of the value
judgments, the concept of welfare state can not even be imagined.
iii) Formulation of Economic Policies: The formulation of successful
economic policies is made by ethical norms. For example: Economics not only
says how to reduce high interest but also says which rate is justifiable.
iv) Welfare Economics Inseparable from Ethics: Welfare economics and
ethics are inseparable. Little argues, "Welfare economics and ethics cannot be
separated as the welfare terminology is a value terminology." Though
economists like Hicks, Scitovsky, Kaldor, etc tried to formulate value free
welfare economics but their very idea of compensation is not value free.
Samuelson and Arrow hold the view that no meaningful proposition can be
made without the introduction of value judgments. Boulding argues, "The
social fact is that we make interpersonal comparison all the time."
v) Economics as a Social Science: Since economics is a social science related
to man, subjectivity always enters. We may try hard to eliminate all value
judgments from our analysis but they enter through the back door. Gunnar
Mydral has said, "Our every concept is value loaded, then how can we possibly
make economics entirely neutral. Those who claim that their analysis is free of
any ethical norms are presuming too much."
Thus, whatever we think of modern welfare economics, there can be
no doubt that the desire to evaluate the performance of economic systems has
been the great driving force behind the development of economic thought and
the source of inspiration for almost every economist in the history of
economics.
22. Critically analyze the Marxian methodology of economic analysis.
The Marxist economics is a quite different school of thought in the area of
methodology and problem perception. It criticizes the orthodox economics and
argues that change is disruptive. Marx is the central figure of Marxist
economics.
Their main approaches can be summarized below:
i) Criticism of Orthodox Economics: The Marxists believe that the orthodox
economics is incapable of dealing with the problem of modern capitalist
system. The orthodox economics takes the existing system for granted as a
part of natural order of things and argues that any problem can be
ameliorated or resolved within the present institutional and ideological
framework. But the dominant characteristics of Marxist economics are
conflict of interests, disruptive forces and abrupt and violent changes.
ii) Mode of Production Determines the Social Processes of Life: The central
point in Marxism is the emphasis on the historical evolution of social,
33
political and economic institutions. To Marx, the mode of production in
material life determines the general character of the social, political and
spiritual processes of life.
iii) Aim of Political Economy: The task of political economy is to discover the
contradictions in the economic system which leads to conflict, movement and
change.
iv) Method: Marx argued that a scientific exposition of political economy must
follow proceeding from the abstract so as to reconstitute the concrete. The
concrete can't be understood without first being analyzed into the abstract
relationship which makes it up. The method must be genetico-evolutionary,
critical, materialistic and dialectical.
v) Marxian Philosophy of Change-Dialectical Materialism: To Marx,
change is nothing but development. An initial situation is called thesis, its
successor is antithesis and the third stage is synthesis and this process is
continuous, characterized by the following rules:
There is unity of opposites.
The rule of negation of negation. i.e. no system is permanent.
Rule of change of quantity into quality.
vi)Marx's Divergence from the Classical Economics: Marx differed from the
classical economists in two respects:
The classical economists regarded capitalism as permanent but he
treated it as a transitory phase in the long run evolution of society.
The former regarded economic laws as natural and universal but Marx
considers them as relative, valid only for a particular stage of
economic development.
vii) Marx's Basis on Classicism: Marx owes much to Ricardo. His labor
theory of value, treatment of unemployment problem, conflict between
wages and profit, his abstract deductive method, etc had been already
discussed by Ricardo. Even his theory of falling profit had already been
anticipated by the classical economists.
viii) Marxian Concept of Value: To Marx, labor is the source of all value and
is paid in wages. The value of a labor is the amount which is required to rear,
train and maintain labors. Capitalists employ workers for more hours than is
necessary to maintain them and takes the surplus value. He calls this the
exploitation of labor.
ix) Contradiction in Capitalism Leads to its Downfall: The aim of the
capitalists is to increase surplus value and they do it by accumulation of
capital. The employment of capital creates technological unemployment and
34
helps to keep wages down. But it benefits neither capitalists nor labors which
is the inherent contradiction in capitalism.
x) Trade Cycle Theory: This theory is explained by the conflict between the
effects of capitalistic mode of production and its aim.
The Marxists believe that society is gradually changing. i.e. from
feudalism to capitalism to socialism. No law is absolute rather it is relative.
Due to inherent contradiction in capitalist system, it will itself lead to another
phase of development i.e. socialism.
23. What do you mean by falsifiability criterion in economics?
Economists distinguish between good and bad economic theories on the test
of falsifiability. If a theory is capable of being proved contrary to facts or in
accordance which facts, it is a good theory. So, good economic theories must
be stated so as to be confirmed or contradicted by the gathering of relevant
facts in the future. This is popularly known as falsifiability criterion in
economics.
24. What are the main difficulties in falsifying the classical theories?
The main difficulties in falsifying classical theories are:
They are based on long-run analysis.
They are based on perfect competition.
Their standard defense is to attribute every contradiction to the
strength of counteracting tendencies.
They took certain variable that entered into their analysis as
exogenously determined e.g. role of technical improvement in
agriculture, disposition of the working entrepreneurship, etc.
Even Marx attributed all discrepancies between his theory and the fact
to the dialectical inner contradiction of capitalism.
25. Are the Neo-classical theories falsifiable?
It is easier to falsify neo-classical theories because.
Due to short run, marginal and partial analysis, data are easier to be
collected.
Based on more realistic form of market also i.e. imperfect
competition.
Difficulties
Argument was typically related to few continuous variables.
All the growth producing factors e.g. technical change, population
growth, expansion of wants, etc were kept in the box of ceteris
paribus.
35
The problem of achieving the equilibrium was passed over by the
method of comparative statics.
Indeterminacy of equilibrium was eliminated by excluding all
interdependence among utility and production functions.
The microeconomic character of the analysis made testing difficult in
view that most available data referred to aggregates.
They wrongly deemed taste, technology as exogenous variable. In fact
they are endogenous.
Ambitious propositions about the desirability of perfect competition
were laid down with insufficient scruples.
Illegitimate use of micro static theorems derived from timeless models
that excluded growth of resources and technical change to predict the
historical sequence of the events in the real world.
26. What are the limitations of Falsifiability criterion?
Empirical testing can be the heart of economics but it is only the heart. It is
not easy to make up one's mind whether particular economic theories are
falsifiable or not. It is even more difficult to know what to make of these
theories that are not falsifiable and so far as the ones that are indeed falsifiable.
It is still more difficult to think of appropriate method of putting them to the
test. The main difficulties are:
i) Strict Refutability of Theorem is Difficult: It is because it is very much
difficult to determine the condition or level which helps to accept/ refute a
theory. Further, if a theory is refuted, an alternative theory is needed.
ii) Statistical Tests are Arbitrary: They depend on significance levels.
iii) Testing a Theory cannot be Permanent: Economists are not unanimous
(have agreements) as to what degree of accuracy or inaccuracy is essential
for the acceptance or rejection of a theory. Often a theory cannot be
discarded (rejected) unless an alternative theory is built.
iv) Theories are sometimes mistakenly identified with Tautological
Proposition e.g. Say's law of markets. However, such propositions stimulate
theorizing.
v) According to Prof. Mark Blaugh, some so called theories which Leontief
called implicit theorizing have no empirical content and they serve merely as
a filing system for classifying information. To demand the removal for all
such heuristic devices and theories in the desire to prove the principle of
falsifiability is to proscribe (ban) further research in many branches of
economics. It is true that economists have deceived themselves and their
readers by presenting tautology in the guise of substantive contribution to
economic knowledge. But the remedy for this practice is clarification of
purpose, not radical and possibly premature surgery.
36
27. "Falsifiability criterion has helped to refute many established
theories and develop new theories instead" Justify with examples.
Falsifiability or refutability is the logical possibility that an assertion can be
contradicted by an observation or the outcome of a physical experiment. That
something is "falsifiable" does not mean that it is false; rather it implies that
such an assertion is capable of being approved or being disapproved by some
observation or experiments.
Economists distinguish good and bad economic theories on the test of
falsiability. If a theory is capable of being proved contrary to facts or in
accordance which facts, it is a good theory. So, good economic theories must
be stated so as to be confirmed or contradicted by the gathering of relevant
facts in the future. This is popularly known as falsiability criterion in
economics.
From the beginning of economic thoughts, economic theories are in
the continuous process of revisions, reformulations, and even replacements by
discarding the older theories. In other words, if the theory fails to explain the
events that exist in the prevailing circumstances, it is either revised on the light
of new facts, or reformulated or sometimes even discarded and replaced by a
totally new theory. If we browse the history of economic thought, we find
many examples of such reformulations, revisions and replacements. For
example: for a long period of time, the classical theory ruled the world but as it
could not explain the phenomenon of the Great Depression of 1930s, it was
replaced by a new theory of Keynesianism. The Keynesian theory also did not
accord with the real life circumstances in the 1970s and was replaced by a
newer theory of Monetarism by Friedman. Similarly, on the arena of money
demand function Friedman’s Reformulation of the Quantity Theory of Money
is the most enticing example of the reformulation of the economic theory. We
can cite many such examples in the field of market price and output
determination, theories of economic development, theories of interest rates,
theory of income and employment, theory of business cycles, theories of
international trade, etc. In these processes of revisions, reformulations and
replacements, the falsifiability criterion plays the central role. With the
falsifiability criterion, it is understood that the theory is not in accord with the
facts of real life. This discord of the theory arguments with the phenomena of
real life paves a way to the reformulation of the theory or its replacements.
Each science is an evolving science. As soon as a theory fails to
explain the real life situation or as long as the theory is not compatible with the
facts gathered by observation or experimentation, it takes the course of
reformulation. This process continues in each science. In economics too, the
theories are in the process of continuous revisions, reformulations and
37
replacements. All contribution for this goes to the falsifiability criterion. Thus,
falsifiability criterion has helped to refute many established theories and
develop new theories instead.
38
CHAPTER 2: CARDINAL UTILITY ANALYSIS
28. Explain about the consumer's equilibrium under cardinal utility
analysis.
This approach to the study of consumer behavior was put forward by Alfred
Marshall. It is based on the explicit assumption that the satisfaction obtained
from consuming a good/service can be measured objectively in cardinal
numbers. Marshall has used ‘the amount of money that one is ready to pay for
a good/service as a measure of utility from that good/service’.
Cardinal utility analysis is based on the following assumptions:
Rationality: Rationality implies that the consumer always aims at the
maximization of utility subject to the budget constraint.
Cardinal Utility: Cardinality of utility means that the utility from a
good can be measured in cardinal numbers with numerical
significance. The simplest way to measure utility from a good is the
amount of money that one is ready to pay for that commodity.
Constant Marginal Utility of Money: Marginal utility of money is
assumed to be constant. It implies that the value or significance of Rs.
1 remains constant for everyone, everywhere and every time. If
marginal utility of money changes as income changes, it cannot
measure the utility of money as a standard measurement rod.
Diminishing Marginal Utility: This assumption implies that the
utility gained from successive units of a commodity diminishes as the
consumer consumes more and more quantities of it.
The total utility depends on the quantities of the individual
commodities.
Equilibrium of the Consumer under Cardinal Utility Analysis
The equilibrium condition of the consumer means that he has reached the level
of maximum satisfaction and he does not want to reorganize his consumption.
Therefore, in equilibrium condition of the consumer, he does not want to
change the quantity of the commodities he is consuming.
We explain the equilibrium in three cases.
i) One-Commodity case.
Let the consumer is consuming only one commodity X and let the
utility function of the individual be U = f(X)
Where, U = utility
39
X = quantity of X commodity.
In cardinal utility analysis, utility is measured in monetary units so if
he buys X units, then his expenditure in monetary units is px.X. The utility or
the satisfaction from the consumption is given by the total amount of money
that the consumer is ready to pay for those particular units he is consuming.
Therefore, the consumer wants to maximize the difference between total utility
and expenditure. Then our problem can be formally written as:
Maximize Z = U - px.X
By using the calculus, the necessary condition for maximum is that the
partial derivative of the function Z with respect to X be equal to zero.
( . ) 0
0
x
x x x
p XZ U
X X X
Uor p MU p
X
Hence, the consumer is in equilibrium when marginal utility of commodity
equals its price i.e. MUx= px. The equilibrium condition has been shown in fig.
2.1.
Consumer's Equilibrium in one commodity case
In figure 2.1, the equilibrium has been established at the point ‘e;’ where the
equilibrium condition MUx= px has been fulfilled. At any point to the left of e,
MUx > px, so he increases the consumption of the commodity. Similarly, to the
right of the point ‘e’, MUx< px, so he reduces the quantity of commodity X.
ii) Two-commodity Case
To analyze the equilibrium in the two commodity case, let there be two
commodities, X and Y. and the utility function be given by U = f(X, Y). Again,
let px and py be the per unit price of X and Y respectively and M be the money
Px(MUM)Px
MUX
MU
XOFig.2.1
qx
e
40
income of the consumer. Then the consumer tries to maximize his utility
subject to the budget constraint.
Formally,
The problem is to maximize U= f(X, Y)
Subject to M= px.X+ py.Y
The combined Lagrange function is V = U+(M-px.X-py.Y)
The necessary condition for V to be maximum is that the partial derivatives of
V with respect to X,Y and be equal to zero.
Which is the condition for equilibrium. Here = marginal utility of money
expenditure which is assumed to be constant in Marshallian Cardinal Analysis.
MUx/Px is the marginal utility per rupee spent on X commodity and MUy/py is
the marginal utility per rupee spent on Y commodity. Thus, the consumer is in
equilibrium when the last rupee spent on both commodities yield (provides)
him the same utility and that is equal to the marginal utility of money (). That
is why it is called the law of equi-marginal utility. Equilibrium in a two
commodity case is shown in fig 2.2 where MUx/px and MUy/py are downward
sloping as MUx and MUy fall as the consumption increases. is the marginal
utility of money and is assumed to be constant.
Consumer's Equilibrium in two-commodity case
0 .......................( )
0 .......................( )
. . 0.......................( )
x x x
y y y
x y
V Up MU p i
X X
V Up MU p ii
Y Y
VM p X p Y iii
yx
x y
MUMUFrom (i) and (ii) =
p p
Fig.2.1
MUMPx
MU,P
XO
MUX
px
MUX
py
Loss
gain
G
F
H A B C
D
E
-
--- -------
-
-
--
-- -- --
+++ ++ ++ +
41
In fig. 2.2, the consumer is in equilibrium by consuming OA quantity of X-
commodity and OB of Y-commodity where the condition MUx/px = MUy/py=
is satisfied. If MUx/Px> MUy/py, he has to increase X but as his income is given,
he will increase the quantity of X and reduces the quantity of Y to equalize
MUx/px= MUy/py.
It is obvious that any combination other than OA of X and OB of Y
results in less utility. For example in terms of fig. 2.2, consider that price of
both X and Y is Rs. 1. Now, if he consumes one more unit of X and reduce one
of Y, then his gain in utility is the area BCDE and loss is AFGH which is larger
than BCDE. Hence, for utility maximization or equilibrium, it is necessary that
MUx/px= MUy/py= .
Effect of price change:
Suppose from the equilibrium situation, px decreases. Then, the
situation will be MUx/px> MUy/py= . Now to be in equilibrium, the consumer
must reduce MUx/px. It is because increasing MUy/py will not lead to
equilibrium as the value of remains constant. For this, he will have to
purchase more X but he cannot reduce Y because then MUy/py>. Hence, when
px decreases, it causes quantity of X to increase but the quantity of Y remains
unaffected.
iii) n-Commodity Case (generalization)
If there are n commodities say x1,x2………..xn, with their prices
p1,p2……….pn. We have the problem as
Max U = f (x1, x2, ……….,xn)
Subject to the budget constraint n
i i
i 1
M p x
The combined Lagrange function is
V= f (x1, x2……….,xn)+ (M-pixi)
The first order conditions are
Solving these, we get the equilibrium condition as:
Thus, in case of n-commodities, the consumer will be in equilibrium when he
has equlisied the ratio of MU and price of every commodity to the MU of
money.
0 0i
V V
x
1 2
1 2
......... ( )n
n
MUxMUx MUxMUM
p p p
42
29. Derive the demand curves using the law of diminishing marginal
utility.
Demand curves can be directly derived from the axiom of diminishing
marginal utility. The assumptions underlying our analysis are:
Marginal utility is measured cardinally in terms of money.
Diminishing marginal utility.
Marginal utility of money remains constant.
Geometrically, marginal utility is the slope of total utility curve
U=f(X). The total utility increases but at a diminishing rate up to quantity X' in
fig. 2.3(a) and starts declining. As a result, MU declines up to X' and then
becomes negative. In fig 2.3(b). Thus, we have for x1<x2<x3, MU1>MU2>MU3.
Derivation of demand curve by using the law of diminishing marginal utility
For equilibrium of the consumer, in fig. 2.3(b), we have MU1=P1 at
point e1 and in this situation the consumer demands OX1 quantity of X to
maximize his utility. If price falls to p2, the equilibrium is at the point e2 where
MU2= p2 and he demands oX2 quantity. Clearly, this shows the inverse
relationship between price and quantity demanded. The demand curve has been
derived in fig. 2.3(c).
Thus, if Marginal utility is measured in monetary units, the demand
curves for the commodity is identical to the positive segment of MU curve. The
negative segment of the marginal utility curve does not make any sense in
economics as a segment of the demand curve because there is no use in trying
to ask, ‘where will be the consumer’s equilibrium if price of X is negative?’.
UX
XX
TU
O
Fig.2.3(a)
XX2
MU
O
Fig.2.3(b)
MU3
MU2
MU1
e1
e2
e3
MUx
X
P
O
Fig.2.3(c)
X1
X3
X1
X2
X3
P1
P2
P3
demand curve
43
30. Derive a demand curve for an individual consumer for commodity
X by using equi-marginal principle. What will be the effect of
change in price of X on his purchase of another commodity Y?
According to law of equi-marginal utility or the law of substitution , the
consumer is in equilibrium when he is buying the quantity of the goods in such
a way that ratio of marginal utility and price for each good are equal and these
ratios are equal to the marginal utility of money. For a two commodity case of
X and Y, we have the following equilibrium condition according to this law:
MUx/px=MUy/py=
Where, is the marginal utility of money which is assumed to be constant.
To derive the demand curve for commodity X, the following
assumptions underlie our analysis:
MUM does not change.
No account is taken of the increase in real income due to fall in px.
Utility function of commodities are independent of each other s.t. U
=Ux+Uy; so the relationship of substitution and complementarity is
ruled out.
Consider the equilibrium situation in fig. 2.4 panel A where we have measured
X and Y commodity on positive axes.
44
Derivation of Demand Curve using the law of equi-marginal utility
Let initial price be px1. The consumer is in equilibrium purchasing OX1
of X and OY1 of Y commodity. When price of X falls, the equilibrium condition
is disturbed. It is assumed in cardinal analysis that MUM does not change as a
result of change in the price of one good. So, the consumer must increase his
quantity of X to reestablish the equality MUx/px=MUy/py=. Thus, as price of X
falls, MUx/px1 shifts to MUx/px2 and quantity of X increases to OX2 from OX1.
In the lower Panenl of the diagram, we have measured quantity of X along X-
axis and price of X along the vertical axis. At price px1, the consumer demands
OX1. Thus, A(Px1,OX1) is a point on the demand curve. Similarly at reduced
price P2, B(Px2,OX2) is another point on the demand curve. Joining such points,
we get a demand curve as in shown in fig. 2.4 panel B which is downward
sloping indicating the inverse relationship between price of commodity and
quantity demanded, ceteris paribus.
31. State the drawbacks of cardinal utility approach.
The main drawbacks of cardinal utility approach are:
MUM
O
MUX
px1
MUX
py
MUX
px2
X1
X2
Y1
Y X
X1
X2
PX2
PX1
d
d
A
B
Fig.2.4
(A)
(B)
PX
45
The very assumption of cardinal utility is unrealistic because utility is
a subjective concept and thus cannot be measured objectively.
The assumption of constant marginal utility of money is unrealistic.
The assumption of independent utilities is unrealistic.
The axiom of diminishing marginal utility has been established from
introspection and has no empirical validity.
Derivation of demand curve on the ceteris paribus assumption (other
things remaining the same) is unrealistic. Thus, it ignores the income
and substitution effects.
It cannot explain Giffen paradox.
"Marshallion demand theorem cannot genuinely be derived except in
a one-commodity case" JR Hicks and Tapas Majumdar.
46
CHAPTER 3: ORDINAL UTILITY ANALYSIS
32. Analyze the consumer's equilibrium under ordinal utility analysis?
A consumer is in equilibrium when he has maximized satisfaction/ utility
subject to the budget constraint. So, to analyze a consumer’s equilibrium, we
should search for a point of consumption that will maximize the consumer’s
satisfaction. We below analyze the consumers’ equilibrium under ordinal
utility analysis.
The following assumptions underlie our analysis:
Rationality: The consumer is rational in the sense that he always aims
at the maximization of utility, given his income and market prices.
Consistency: The consumer behaves consistently. It means if he
prefers (likes) commodity A to commodity B in one situation, then he
won’t prefer B to A provided both are available. i. e. If A >B then B
A.
Ordinal Utility: Here utility is ordinal in the sense that it cannot be
measured quantitatively in numbers but the consumer is able to rank
his preferences according to the satisfaction of each basket.
Transitivity: It implies transitivity in choices i.e. if he prefers bundle
A to B and B to C then he prefers A to C . i.e. if A>B and B>C then
A>C.
Diminishing Marginal Rate of Substitution: The diminishing
marginal rate of substitution implies that the rate of substitution along
the indifference cure goes on diminishing as we move from the right-
up to right-down and thus the indifference curves are assumed to be
convex everywhere.
For simplicity of analysis, we restrict our case to two commodities
only: X and Y. However this can be generalized to n commodities.
Tools for Analysis
i) Indifferences Curves:
For two commodities X and Y, the indifference curve is the locus of
combinations of X and Y that yield same level of satisfaction to the consumer.
It means that each point on the IC gives same level of satisfaction. The negative
of the slope of IC is called marginal rate of substitution between X and Y i.e.
MRSxy= -dY/dX. This is the rate at which the consumer substitutes Y
commodity by X as he moves to the right-down along the IC. This rate goes on
diminishing. A particular IC is shown in fig.3.1.
47
Indifference curve
The collection of ICs is called indifference map.
The ICs have the following properties in general.
They slope downwards to the right.
They are convex to the origin.
They never intersect each other.
Each higher IC shows a higher level of satisfaction.
ii) The Budget Line:
The budget line shows the maximum amount of X and Y that he can
buy if he spends all his income. Let, his total income be M. Then from fig. 3.2,
we can see that if he wholly spends it in purchasing X, he can buy M/px of X
commodity and if on Y, he can buy M/py of Y-commodity. By joining the
points A and B, we get the budget line.
Budget Line
Algebraically,
The price line or the budget line can be written as:M=px.X+py.Y
XOFig.3.1
IC
Y
Y
X
XOFig.3.2
Y
M/Py
M/Px
M=Px.X+Py.Y
slope=-Px
Py
A
B
48
If X = 0, he can buy M/py of Y as shown by point A in fig. 3.2 and if Y= 0, he
can buyM/px as shown by point B in fig. 3.2. From the equation of the budget
line,
Y = M/py- px/py. X where, dY/dX= -px/py is the slope of the budget line.
Equilibrium Conditions for the Consumer
By superimposing (drawing together) the consumer's indifference
curves on budget line, we see in fig. 3.3 that the maximum utility level he can
reach by spending his total income is the utility level U2. Level U3 is desirable
but he cannot attain it due to income constraint ( he cannot buy any point that
lies out of the budget line).
Graphically, the equilibrium conditions can be summarized as:
Necessary Condition
The necessary condition is that the indifference curve must be tangent
to the budget line. This condition is fulfilled at point e in fig. 3.3. Thus, the
necessary condition for equilibrium can also be written as:
Slope of IC= Slope of budget line.
Consumer's equilibrium
At equilibrium, the consumer consumes OX* of X commodity and
OY* of Y commodity. Also at point ‘f’, slope of IC>Slope of price line i.e.
MUx/MUy> px/py and at point ‘g’, slope of IC< slope of budget line i.e.
MUx/MUy< px/py.
Sufficient Condition:
The sufficient condition for the equilibrium is that at the point of
tangency the IC must be convex to the origin. In fig. 3.4, at point e1, the
necessary condition is fulfilled but the IC is concave and utility is not
maximized. Both the conditions are fulfilled at point e2. So, e2 is the point of
equilibrium, not e1; though it is also a tangency point.
O
B
A
U1
g
e
f
Y*
Y
XX*
U2
U3
Fig.3.3
49
Sufficient Condition for consumer's Equilibrium
Mathematically,
Our problem is to maximize U= f(X,Y)
Subject to the budget constraint M= px.X+py.Y
The combined Lagrange function is V=U+(M-px.X-py.Y)
The first order condition/ necessary condition for V to be maximum is
that the partial derivatives of V with respect to X, Y, be equal to zero i.e.
0..........( )
0..........( )
. . 0..........( )
/( ) ( ) .........( )
/
/ / ,
x x
y y
x y
x
y
x y
V UV p i
X X
V UV p ii
Y Y
VV M p X p Y iii
pU Xfrom i and ii iv
U Y p
here U X MU and U Y MU
Thus, relationship (iv) becomes MUx/ MUy = px/py
So the necessary condition is that the ratio of marginal utility of two
commodities must be equal to the ratio of their prices.
The second order condition or the sufficient condition requires that the
Boardered Hessian Determinant must be positive i.e.
>0 also implies the strict convexity of indifference curves.
O
B
A
Y
X
Fig.3.4
e1
e2
U1
U2
U3
H
0
x y
x xx xy
y yx yy
o p p
H p V V
p V V
H
50
From the above analysis, the conditions for consumer's equilibrium can be
summarized as:
The necessary condition is that the IC must be tangent to the budget
line i.e. MUx/MUy=px/py which implies that slope of the IC must be
equal to the slope of budget line.
The sufficient condition is that the IC must be convex to the origin at
the point of tangency.
33. Derive the demand curve using ordinal utility analysis.
The consumer’s equilibrium in ordinal analysis in two-commodity case is
established at the point of tangency between indifference curve and budget line.
As the price of one commodity, say X, falls, other things remaining the same,
the budget line rotates rightwards. Now, the consumer can purchase more
quantity of commodity X. The new budget line is tangent to a higher
indifference curve. The new equilibrium occurs to the right of the original
equilibrium (note that this only happens in case X is a normal good only). If we
let the price of X fall continuously, we get new equilibrium points as e1, e2, e3
and so on. (fig.3.5). By joining such equilibrium points, we get the price
consumption curve. From the price consumption curve (PCC), demand curve
for X-commodity can be derived.
Derivation of Demand Curve using IC Analysis
PCC
IC1
IC3
IC2
e2
e3
e1
B
L1 L1L X
Y
x1 x2x3O
OX
Fig.3.5
x1x2 x3
P1
P2
P3
demand curve
Px
51
At point e1, the consumer is consuming OX1 quantity, say at a price OP1. As
price of X reduces to OP2, OP3, etc, (OP3<OP2<OP1), his purchase of X-
commodity will increase to OX2, OX3, etc respectively.
The demand curve has been derived in the lower part of fig. 3.5.
Clearly, it shows that as price of X falls, more of it is purchased, other things
remaining the same.
We can derive the demand curve in a formal way too from the first order
condition of utility maximization.
For that let the utility function be U= XY, then
From first-order condition for equilibrium
MUx/MUy= Px/Py
or,
Substituting relation (1) in the budget constraint of the consumer, we get
M= px.X+py.Y
M= px.X+py.px/py .X
M=2px.X
X=M/2px which is the demand function for the commodity X implying
that quantity of X commodity demanded is directly related to income and
indirectly related to its own price.
34. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Normal good and price fall).
Effect of price change on consumer’s equilibrium is called total price effect
which can be decomposed (divided) into income effect and substitution effect.
When the price of a commodity falls, it affects consumer’s equilibrium position
in two ways: one the one hand, it increases consumer’s real income and on the
other hand it makes the commodity whose price has fallen relatively cheaper.
The effect of the increased real income in consumption is called income effect
and the effect through the fall in relative price of X commodity is called
1
2
1 1
2 2x
U UMU Y and X
X Y
1
21
2. .
....................................................(1)
x
y
x y
x
y
Y p
pX
X p Y p
pY X
p
, MUY=
52
substitution effect. Thus, the effect of any price change can be separated into
income effect and substitution effect.
There are two methods of separating these effects: Hicksian Method and
Slutsky Method.
Hicksian Method
In this method, we adjust the change in real income due to the fall in
the price of a commodity in such a way that the consumer’s satisfaction level is
unchanged. In other words, increase/decrease in purchasing power is so
adjusted that the consumer remains on the same indifference curve. This
method is known as the method of compensating variation in income.
Let from the initial equilibrium point ‘e’ in fig.3.6, price of X falls as
such budget line rotates outward. After the fall in price, his purchasing power
increases. So, he can buy more of X. Thus, his final equilibrium is at e3 where
he consumes OX3 of X. This movement from e1 to e3 is called the total price
effect which can be decomposed into income effect and substitution effect.
To decompose price effect, we draw an imaginary budget line CD, so
that it is tangent to the original IC and parallel to the budget line AB'. This
imaginary budget line is drawn so as to keep the consumer compensated from
the increase in real income.
Separation the Substitution effect and Income effect using Hicksian Method.
After compensating the consumer for the price fall, he is in equilibrium at e2
where he consumes OX2 quantity of X. Here, the consumer has increased
consumption of X from OX1 to OX2 exclusively due to change in relative price
of X because the effect of increase in real income has been nullified or removed
x3x2x1
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
SE IE
Fig.3.6
(Normal goods)
53
by drawing compensated CD budget line. So, the movement from e1to e2 or
X1X2 is substitution effect.
If we give the snatched (taken away) income back to the consumer, he
will consume OX3 quantity of X. So, the movement from e2 to e3 or X2X3 is due
to the effect of increase in real income and is called income effect.
Symbolically,
Price effect (e1 to e3)= SE (e1 to e2) +IE (e2 to e3)
In case of normal goods, the negative income effect of price change
reinforces the negative substitution effect so that price effect is negative.(Note
that, the income effect in normal goods is positive but income effect of price change is
negative. It is because here the income effect caused by price fall increases the quantity
consumed So, price and the resultant change in consumption due to price induced
income effect are inversely related in case of normal goods So, income effect of price
change is negative. See Koutsoyiannis for details.)
Slutsky's Method
In this method, income after the price change is so adjusted that it
offsets the change in purchasing power i.e. his purchasing power is kept
constant after the change in the price of a commodity or commodities. After
adjusting for the change in purchasing power, the consumer can consume the
original bundle if he so likes. This method is known as cost difference
method. The amount of income to be changed (increased or decreased) is given
by M= Px1Qx1 - Px2Qx1
Where M = Change in income. Qx1= original quantity
Px1= Original price Px2= Price after reduction.
For example, let the consumer is consuming 10 units of X at the price level
Rs.5. Suppose, price of x falls to Rs. 2.5 per unit. Then the amount of money
income to be taken away for keeping the purchasing power constant can be
found as:
M= Rs. 5×10- Rs. 2.5×10=Rs. 25
Now, to separate the effects graphically, let the original equilibrium be
at the point e1 in the fig3.7 where the consumer is consuming OX1 of X
commodity. Let price of X falls. This results in the outward rotation of the
budget line from AB to AB'. Due to the fall in px, his purchasing power
increases. To offset the change in purchasing power, we draw an imaginary
budget line CD through the point e1 and parallel to AB'. Drawing the new
compensated budget line through the point e1 implies that his purchasing power
has been kept constant and he can consume the original bundle if he so likes.
Now, unlike in Hicksian method, the equilibrium will be on a higher IC (IC2)
where he is enjoying higher level of satisfaction.
54
Separation the Substitution effect and Income effect using Slutsky Method
In terms of fig3.7, movement from e1 to e2 (x1x2) is substitution effect
because it is the effect in consumption due to change in relative prices of the
commodities only when the change in purchasing power has been nullified or
removed. Now, if we give him the snatched income back, he will move to the
point e3 on IC3 where he consumes OX3 quantity of X-commodity and reaches
a higher level of satisfaction. Thus, movement from e2 to e3 (X2X3) is income
effect.
Symbolically,
PE (e1 to e3) = SE (e1to e2) + IE(e2 to e3)
Comparison between Hicksian Method and Slutsky Method
Hicksian Method Slutsky Method
Compensating variation method. Cost-difference method.
SE in Hicksian Method <SE in
Slutsky Method.
SE in Slutsky Method > SE in
Hicksian method.
IE>IE in Slutsky method. IE<IE in Hicksian method.
Highly persuasive solution. It is intuitively less satisfying.
IE and SE cannot be known
without the knowledge of
consumer IC map.
IE and SE can be obtained from
directly observed facts.
More convenient to measure SE. Easy to handle IE.
x3x2x1
IC1
IC2
e1
e2e3
B B1
A
C
D
Y
XO
SE IE
Fig.3.7
IC3
(Normal goods)
55
35. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Normal good and price
rise).
The explanation in this case is similar to the one in Q. N. 3 above. So, it has
been left as an exercise to the readers
36. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Inferior good and price fall).
The explanation in this case is similar to the one in Q. N. 3 above. So, it has
been left as an exercise. In case of Inferior goods, the substitution effect and
income effect work in opposite direction but magnitude of SE is more than the
magnitude of income effect that is why SE more than offsets the income effect
and the end result is a negative price effect.
x3x2x1
IC1IC2
e1
e2e3
BB1
A
C
D
Y
XO
Fig.4.15(Hicksian method)
IE SE
x3x2x1
IC1
IC2e1
e2
e3
BB1
A
C
D XO
Fig.3.9(Slutsky method)
IC3
IE SE
NormalgoodNormal good
x3 x2x1
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
IE
Fig.3.10(Hicksian Method)
SE
x3 x2x1
IC1 IC2
e1
e2
e3
B B1
A
C
D
Y
XO
SE
IE
Fig.3.11(Slutsky Method)
IC3
Inferior goodInferior good
56
37. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Inferior good and price
rise).
The explanation in this case is similar to the one in Q. N. 3 above. So, it has
been left as an exercise. In case of Inferior goods, the substitution effect and
income effect work in opposite direction but magnitude of SE is more than the
magnitude of income effect that is why SE more than offsets the income effect
and the end result is a negative price effect.
38. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Giffen Goods good and price
fall).
The explanation in this case is similar to the one in Q. N. 3. In case of Giffen
goods, the substitution effect and income effect work in opposite direction but
the magnitude of income effect is more than the magnitude of substitution
effect. That is why IE more than offsets the SE and end result is a positive price
effect.
x3x2 x1
IC1
IC2
e1
e2
e3
BB1
A
C
D
Y
XO
IESE
Fig.3.12(Hicksian Method)
x3x2x1
IC1
IC2
e1
e2
e3
BB1
A
C
D
Y
XO
Fig.3.13(Slutsky Method)
IC3IE
SE
Inferior good Inferior good
57
39. Separate the substitution effect and income effect of a price
change in consumer’s equilibrium (for Giffen Goods good and price
rise).
The explanation in this case is similar to the one in Q. N. 3. In case of Giffen
goods, the substitution effect and income effect work in opposite direction but
the magnitude of income effect is more than the magnitude of substitution
effect. That is why IE more than offsets the SE and end result is a positive price
effect.
40. Derive the ordinary and compensated demand for ordinary goods
for the fall in price of X.
The ordinary demand curve or Marshallian demand curve shows the quantity
of commodity purchased as a function of money income and price when no
action is taken for the adjustment in the change in real income of the consumer
x3 x2x1
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
Fig.3.14(Hicksian method)
x3 x2x1
IC1 IC2
e1
e2
e3
B B1
A
C
D
Y
XO
SE
IE
Fig.3.15(Slutsky method)
IC3
IESE
Giffen goodGiffen good
x3x2x1
IC1
IC2e1
e2
e3
BB1
A
C
D
Y
XO
Fig.3.17(Slustky Method)
IC3
SE
IE
x3x2 x1
IC1
IC2
e1
e2
e3
BB1
A
C
D
Y
XO
Fig.3.16(Hicksian Method)
IESE
Giffen good Giffen good
58
but compensated demand curve shows the relationship between price and
quantity purchased of a commodity, when he is compelled to remain on the
same indifference curve or when adjustments are made in the real income or
the consumer is compensated for the change in real income. The ordinary
demand curve is also called the demand curve that keeps money income
constant and the compensated demand curve is also called the demand curve
that keeps real income constant.
To derive the ordinary and compensated demand curves for a normal
good, consider the original equilibrium of the consumer at the point e1, in fig.
3.18 under usual assumptions, where he is purchasing OX1 quantity of X
commodity. Let price of X falls. This results in the outward rotation of the
budget line to the right. Due to increase in purchasing power, the consumer can
purchase more of X and his equilibrium is at the point e3 where he is enjoying
higher level of satisfaction by consuming more quantity of X i.e. OX3. From
this relationship, we can get two points of the ordinary demand curve (P1,OX1)
and (P2,OX2). By joining these two points, we get the ordinary demand curve as
dodo in lower panel of fig 3.18 which is downward sloping.
59
Derivation of Demand curve (Ordinary and Compensated in case of normal goods)
To derive the compensated demand curve, compensate the increase in
purchasing power by drawing as imaginary budget line CD parallel to AB'(fig.
3.18) and tangent to IC1. We now see that after compensating the consumer’s
increase in real income, he is in equilibrium at point e2. After he is compelled
to remain on the same IC, he will consume only OX2 quantity of X. From this,
we get the two points of the compensated demand curve as (OP1, OX1) and
(OP2, OX2). Graphically, it is derived in the lower panel of fig.3.18 as dcdc
which is also downward sloping but steeper than ordinary demand curve.
In case of normal goods, the income effect of the price change for
normal goods is negative (Koutsoyiannis) and it reinforces the negative
substitution effect. So, both demand curves are negatively sloped. Here, as
price falls, quantity of X demanded will increase and as income increases,
quantity of X demanded will increase.
x1 x2 x3
x3x2x1
P1
P2
Px
X
dc
dc
do
do
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
O
SE IE
Fig.3.18
Normal good
Normal good
60
41. Derive the ordinary and compensated demand for ordinary goods
for the rise in price of x.
The analysis in this case is similar to that of Q. N. 9.
Derivation of Demand curve (Ordinary and Compensated in case of normal goods)
42. Derive the ordinary and compensated demand curves for inferior
good X (Price fall).
In the first paragraph, introduce ordinary and compensated demand curves as
done in the answer of Q.N. 9.
To derive the demand curves, let X be the inferior good and let the
original equilibrium be at point e1 where the consumer is purchasing OX1
quantity of X commodity which is an inferior commodity. Let price of X falls,
then the budget line rotates outwards and the new equilibrium will be
established at a higher indifference curve. To compensate the increase in
x1x2
x3
x3x2x1
P1
P2
Px
X
dc
dc
do
do
IC1IC2
e1
e2e3
BB1
A
C
D
Y
XO
O
SEIE
Fig.3.19 Normal good
Normal good
61
purchasing power due to the fall in the price of X, we draw an imaginary budget
line CD parallel to AB' and tangent to IC1. In case of inferior goods, the
substitution effect is negative as usual whereas the income effect of price
change is positive but the negative substitution effect will more than offset the
positive income effect of price change so that the total price effect will be
negative(Koutsoyiannis).
Derivation of Demand curve (Ordinary and Compensated in case of Inferior goods)
From fig.3.20, we have,
PE (e1 to e3) = SE(e1to e2) +IE(e2 to e3)
Consequently, the ordinary demand curve and the compensated
demand curve both are negatively sloped but the latter is less steeper then the
former. In fig, dodo is the ordinary demand curve and dcdc is the compensated
demand curve. There is an obvious reason for the negative slope of the
compensated demand curve which is the negative substitution effect in all
cases. In case of inferior goods, the price effect also becomes negative, despite
x1x2x3
x3 x2x1
P1
P2
Px
X
dc
dc
do
do
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
O
SE
IE
Fig.3.20
Inferior good
Inferior good
62
the income effect going in the opposite direction due to the fact that
substitution effect more than offsets the income effect, which makes the
ordinary demand curve also downward sloping.
Here, as income increases, quantity demanded decreases and as price decreases,
quantity demanded increases.
43. Derive the ordinary and compensated demand curves for inferior
good X (Price rise)
Analysis is same as in the previous question. This has been left as an
exercise.
Derivation of Demand curve (Ordinary and Compensated in case of Inferior goods)
x1x2 x3
x3x2 x1
P1
P2
Px
X
dc
dc
do
do
IC1
IC2
e1
e2
e3
BB1
A
C
D
Y
XO
O
SEIE
Fig.3.21
Inferior good
Inferior good
63
44. Derive ordinary and compensated demand curve for Giffen good
X (Price fall).
In the first paragraph, introduce ordinary and compensated demand curves as
done in the answer of Q.N. 9.
To derive the demand curves for the Giffen good, let X be the Giffen
good and let the original equilibrium of the consumer be at point e1 in fig 3.22,
where the consumer is consuming OX1 quantity of X commodity. Again, let
price of X falls. Then the budget line rotates outward to AB' from AB. Now, he
can purchase more quantity of both commodities. To compensate the consumer
due to the increase in purchasing power, we draw an imaginary budget line CD
so that it becomes tangent to IC1 and parallel to AB'. The consumer's new
equilibrium is e2 where he consumes OX2 of X. In case of Giffen good the
income effect of price change more than offsets the negative substitution effect
so that in final equilibrium the quantity demand of X falls to OX3.
Derivation of Demand curve (Ordinary and Compensated in case of Giffen goods)
x1 x2x3
x3 x2x1
P1
P2
Px
X
dc
dc
do
do
IC1
IC2
e1
e2
e3
B B1
A
C
D
Y
XO
O
SEIE
Fig.3.22
Giffen good
Giffen good
64
From fig.3.22
PE (X1X3)= SE (X1X2)+IE (X2X3)
In the fig 3.22, the ordinary demand curve dodo is upward sloping. This
is due to the fact that in case of Giffen goods, the income effect working in
opposite direction is so strong that it more than offsets the SE. As a result, the
total price effect becomes positive. However the compensated demand curve is
still downward sloping because SE is always negative.
Here as Px rises, quantity demanded of X will rise and if the income level rises,
the quantity demanded falls.
45. Derive ordinary and compensated demand curve for Giffen good
x (Price rise).
In the first paragraph, introduce ordinary and compensated demand curves as
done in the answer of Q.N. 9. The further analysis is similar as in previous
question.
Derivation of Demand curve (Ordinary and Compensated in case of Giffen goods)
x1x2 x3
x3x2 x1
P1
P2
Px
X
dc
dc
do
do
IC1
IC2
e1
e2
e3
BB1
A
C
D
Y
XO
O
SE
IE
Fig.3.23 Giffen good
Giffen good
65
46. Discuss the consumer's equilibrium under unusual shape of ICs.
In case of downward sloping and convex indifference curves, we see in the
above analyses that the consumer will be in equilibrium at the point of
tangency. But this condition does not lead to the maximization of satisfaction in
case of ICs that have other than the downward sloping convex shapes. Some
such exceptional equilibrium cases are analyzed below in brief:
Concave IC: The concavity of IC implies the increasing MRSxy
between the commodities. It occurs when consumer have a distaste for
variety and diversification in consumption. Here corner solution
occurs as shown in fig.3.24.
Corner Solution in case of concave ICs
We see in the figure that in case of concave IC, if the consumer wants to
remain on the point of tangency N, his satisfaction will be lower. Rather, he
will get higher satisfaction by moving to the corner point B.
Convex IC with Corner Equilibrium: Even though the IC is convex,
if price of a commodity is very high in relation to the price of other
commodity; it may result in corner equilibrium where the consumer
does not consume the very much expensive commodity. It is shown in
fig.3.25where price of X is very high.
Y
XO
A
B
e
Fig.3.24
IC3
IC2
IC1
N
Y
XO
A
B
Fig.3.25
IC2
IC3
IC1
e
66
Corner Solution in case of convex ICs.
Straight Line IC: It occurs in case of perfect substitutability between
goods. It results in corner solution but three cases may arise.
i) If slope of budget line is greater than slope of IC, the consumer consumes Y
commodity only (fig3.26(a))
ii) If slope of budget line is less than slop of IC the consumer consumes X
commodity only (fig3.26(b))
iii) If slope are equal there are infinite equilibrium. (fig3.26(c))
Corner solution in case of straight line ICs
Right-angled IC: It occurs in case of perfect complementarity (means
we have to increase the quantity of both together to have a gain in
utility e.g. pen and ink) between goods.
Corner solution in Right angled ICs
Neutral and Bad Commodities: In these both cases, there is corner
solution and the consumer consumes one commodity only ( Fig
3.28(a) and 3.28(b)).
Y
XO
A
B
Fig.3.26(a)
IC2IC3
IC1
Y
XO
A
B
Fig.3.26(b)
IC2IC3IC1 XO
A
B
Fig.3.26(c)
IC2 IC3IC1
Y
e
e
Ic coincideswith the budget line.
XO
A
B
Fig.3.27
Y
IC1
IC2
IC3
e
67
Corner solution in case of Bad and Neutral Goods.
Q.N. 16 Critically Evaluation of IC Analysis:
IC analysis has been a major advance in the field of consumer behavior/
demand. Its assumptions are less stringent than cardinal utility analysis. Only
ordinality of preference is required and the assumption of constant MUM is
dropped out.
Uses:
It provides a framework for the measurement of consumer's surplus
which is important in welfare economics and designing government
policy.
It establishes a better criterion for the classification of goods into
substitutes and complements.
Helps to analyze the effect of taxes and subsidies.
Helps in determining the wage-offer curves.
Weaknesses:
The main weakness of this theory is its axiomatic assumption of the
existence and convexity of ICs. It does not establish either the
existence or shape of IC.
It is questionable whether the consumer is able to order his preference
as precisely as the theory implies.
It has retained most of the weaknesses of cardinalist school with
strong assumption of rationality and the concept of marginal utility
implicit in the definition of MRS.
It does not analyze the effect of advertising of past behavior of stocks
of their interdependence of the consumer which lead to the behavior
that would be considered irrational and hence is ruled out by the
theory.
XO
A
B
Fig.3.28(a)
Y
IC1
IC2
IC3
e
Bad
GoodXO
A
B
Fig.3.28(b)
Y
IC1 IC2IC3
e
Neutral
Normal
68
Speculative demand and random behavior are ruled out but these
factors are very important for the pricing and output decisions of the
firm.
It cannot deal with consumer behavior under uncertainty.
69
CHAPTER 4: BEHAVIOURISTIC APPROACH AND OTHER DEMAND MODELS
47. Write a note on linear expenditure system (LES).
Linear Expenditure System (LES) models are a specific type of models to
analyze the consumer behavior. These models are concerned with the groups
of commodities rather than individual commodities. Here total consumer
expenditure consists of such groups. So, LES models are of great interest in
aggregate econometric models. These models are usually formulated on the
basis of utility function in the normal way as in the IC analysis by
maximization of utility function subject to budget constraint. Thus, LES model
are same as IC system but differ in two ways:
The IC analysis deals with individual commodities while LES deals
with groups of commodities.
In IC analysis, goods are substitutable but in LES substitution between
groups is ruled out but substitution within the group is allowed.
The following assumptions underlie the analysis under LES models:
Substitution is allowed within group but not between groups.
Each group of commodity includes all substitutes and complements.
The income of the consumer is given.
The consumer acts rationally.
Utility function is additive which implies that the total utility of the
consumer is the sum total of the utilities from different groups. If we
suppose that there are five groups, namely: a-Food and beverages, b-
Clothing, c-Consumer durables, d-household operational expenditures
and e-services, then U = Ua + Ub +Uc + Ud + Ue. Additively implies the
independence of utilities of groups.
The consumer buys some minimum quantities of commodities from
each group irrespective of their prices. These are called subsistence
quantities and money spent on them is called subsistence income. The
remaining income called supernumerary income is then allocated
among the various groups of commodities on the basis of their prices.
Since no substitution is allowed between the groups, Indifference curves for
LES models are right angled as shown in fig 4.1.
70
Indifference Curves
We can illustrate the LES models with the help of the LES model as formulated
by R. Stone in 1954 for the first time:
Let the utility function be
1
log( )n
i i ii
U b q
Where, i= minimum quantity from group i,
qi= quantity purchased from group i,
bi= marginal budget shares for group i.
Clearly, the above utility function is additive in logarithms.
Assumptions:
Rationality of consumers.
Additivity
0<bi<1
i0 i.e. there is no negative minimum quantity.
qi - i > 0 i.e. some quantity above the minimum is purchased.
Total income is spent.
The consumer wants to maximize the utility function subject to the total income
constraint i.e.
Max U = bi log (qi-i)+………+bnlog(qn-n)
Subject to Y=piqi
The combined Lagrange function is
1 1
log( ) ( )n n
i i i i ii i
V b q Y p q
First order conditions for maximization of utility are:
O
Fig.4.1
B Group
IC1
IC2
IC3
71
1
...............( ) 1, 2,.......( )
i
i
i i in
i ii
bVp i i n
q q
V Y p q
Solving the above n+ 1 equations, we get
ii
i
i
iiPY
P
bP
piqi=pii+bi(Y-pii)
where, piqi=expenditure of group i
pii= Subsistence expenditure on group i.
Y-pii= Super-numerary expenditure on group i.
It can be easily verified the second order condition is satisfied for such utility
function.
48. Write a note on empirical demand curves.
Since the general demand function has little empirical significance, a
particular functional form of the demand function need to be specified. This
purpose is fulfilled by empirical demand curves. Empirical demand curves
determine the relationship between demand and the variables affecting it and
express the relationship in numerical form. Even if taste variable cannot be
measured directly, it may be expressed as a variable of time. Dummy variables
and error terms are also included.
The two commonly used functional forms are:
i) Linear: It can be written as Q= +p+po+Y+ at + bD+
Where, Q = Quantity demanded, p= price level,
po= price of other commodities, Y=income,
t=time variable, D= Dummy variable and
is a random error term.
If data are available, each of the coefficients can be estimated by using
multiple linear regression analysis.
ii) Exponential (Log linear): Here the estimated elasticities are
assumed to remain constant over the entire range of data. It is also
assumed that tastes remain constant. It can be written as.
log Q = log p+log po+logY+ Ut
Where, Ut is a random error term.
It can be estimated by using multiple regression giving direct estimates of the
different elasticity of demand.
72
49. Analyze the pragmatic Approach to demand theory.
The general demand function Qx=f(px, py, ...I,T…..), where I =
income, T= taste, etc have little meaning in the practical application of the
concept of demand function to the complex problem of the real world because
it does not tell the form of relation between demand and the variables affecting
it. Nonetheless, it provides a starting point for the statistical estimation of
demand function both from static and dynamic angles. Thus, many writers have
followed a pragmatic approach to the theory of demand. They accept the
fundamental law of demand on trust and have formulated demand functions
directly on the basis of market data without reference to the theory of utility
and the behavior of the individual consumer. They have formulated
multivariate demand functions in which the demand for a commodity is a
function of many variables rather than the price of the commodity only. So,
such demand functions are concentrated on market demand. Moreover, some
demand functions deal with various groups of commodities such as food,
durables, etc. These demand functions are estimated with various econometric
methods. Some such functions are:
The Constant Elasticity of Demand Function: It is based on a very
simple assumption about the relation between demand and its
determinants e.g. price, price of other related commodities, income of
the consumer, etc. It assumes the price of related commodities and
income of the consumer to be constant. On this basis, the price
quantity relationship in the demand function is isolated. The curve is
fitted on the basis of statistical data. So it is just an approximation.
The most commonly used from is
Qx = b0pxb1
pob2
Yb3
eb4t
………………..(i)
Where, Qx= Quantity demand of commodity X.
Difficulties in Estimation
Problem of aggregation.
Problem of estimating when several variables change
simultaneously.
Multiple regressions provide a good fit which may be poor.
Problem of identification.
The estimated coefficients are correct only when
assumptions about the error term are valid.
73
px= price of X.
Po= price of other commodities.
Y= consumer's income
eb4t
= a trend factor for tastes
b1=price elasticity of demand.
b2 = cross elasticity of demand.
b3 = Income elasticity of demand.
Relation (i) is called the Constant Elasticity Demand (CED) function
because its coefficients b1, b2 and b3 are assumed to remain constant and they
show different elasticities.
Taking log on both sides,
log Qx= log bo + b1log px+b2 log po+b3 logY
The term eb4t
is ignored for simplicity.
Price elasticity of demand
=Proportionate Change in Quantity Demanded
Proportionate Change in Price
=1 1
log log
log log
x x
x x
Q pb b
p p
Cross elasticity of demand= 2 2
log log
log log
x o
o o
Q pb b
P p
Income elasticity of demand=3 3
log log
log log
xQ Y
b bY Y
The CED function is graphically presented in fig 4.2. as fitted to a hypothetical
set of data represented by the cluster of points. Thus the D curve depicts CED
function.
Estimated CED function
QXO
Fig.4.2
PX
D
74
Dynamic demand functions: These functions include lagged values
of the quantity demand and of income as separate variables
influencing the demand in any particular period. Dynamization of
demand function expresses the generally accepted idea that current
purchasing decisions are affected by past behavior.
The most common assumption in this respect is that the current
consumption behavior depends on past level of income and demand. If the
commodity is durable, the past purchases constitute a stock which clearly
affects the current and future purchases. If the commodity is non durable, past
purchase reflects a habit and thus it influences the current patterns of demand.
Another usual assumption concerning the way in which past behavior affects
the present is that the more recent of past level of income or demand has a
greater influence on present consumption pattern than the more remote ones.
Models including lagged values of demand, income, etc. are called
distributed lag models. In general the models can be expressed as
Qx,t=f(px, px(t-1),…………, Qx(t-1), Qx(t-2) ….,Yt. Yt-1…
The number of lags depends on the particular relationship being
studied.
Examples:
Durable Goods Case:
This is also called Nerlove's stock adjustment principle and is given by
Qt= a1Yt + a2 Qt-1
Where Qt=quantity demanded at time period t.
Qt-1= quantity demanded at time period t-1
Yt= income at time period t
Non-Durable Goods Case: Here demand depends on the change in variables
like price, income etc. The Houthaker and Taylor's dynamic model is
Qt=a0+a1pt+a2 pt+a3xt+a4 yt +a5Qt-1
Where yt=yt-yt-1= change in income.
pt= pt-pt-1 = change in price.
In this way, we can estimate the demand functions for durable as well as non-
durable goods case in a pragmatic way.
50. Derive the demand theorem under Revealed preference approach.
Both cardinal and Hicks-Allen analysis provide the psychological
explanation of consumers’ demand. In sharp contrast to these, Samuelson's
Revealed Preference Theory is a behaviorist explanation of consumer's
demand. It is an analysis of the behavior of the consumers in the market in
various price-income situations. Thus, the two basic features of the theory are:
It applies behaviorist method.
75
It uses the concept of ordinal utility.
This theory is a landmark, a major breakthrough in the development of
the theory of demand because it releases the consumer's choice from
psychological implications and makes possible the establishment of the
law of demand directly on the basis of the revealed preference axiom
without the use of indifference curves and the restrictive assumptions and
finally, the existence and convexity of indifference curve can be
established.
This theory is based on the following assumptions:
Rationality: Rationality in theory implies that the consumer
is rational in the Pareto sense that he prefers more quantity of
any commodity without reducing the quantity of other
commodities.
Consistency: consistency assumption implies the consistency
in the behavior of the consumer i.e. if he chooses bundle A in
one situation in which bundle B was also available then, he
won’t choose bundle B in any other situation provided A is
available i.e. If A>B then B A.
Transitivity: It implies that in any particular situation if A>B
and B>C then A>C.
The Revealed Preference Axiom: This is the most
important assumption in the theory. It implies that the
consumer chooses a bundle among the different bundles that
he can buy and prefers that bundle over all other bundles and
that bundle only maximizes the satisfaction of the consumer.
This axiom can be put into index number from. Let Po be the vector of
prices po1,p
o2…..p
on and q
o=q
o1,q
o2………q
on and q' = q'1q'2…………q'n be the
vectors of quantities, then qo is said to be revealed preferred to q' as qo is
selected by the consumer under poq'≤p
oq
o i.e. q
o is at least as expensive as q'.
Samuelson has preference hypothesis as the basis of his theory of
demand. Further his theory is based upon a very strong axiom of preference
hypothesis in which relation of indifference between various alternative
combinations is ruled out.
Derivation of Demand Curve:
Revealed preference hypothesis can be utilized to derive the demand
theorem. Samuelson proceeds to establish the inverse relationship between
price and quantity demanded assuming that income elasticity of demand is
positive. He states the demand theorem which he calls the fundamental
theorem of consumption theory as "Any good that is known to increase in
76
demand when money income alone rises must definitely shrink in demand when
price alone rises."
To derive the demand curve, consider the initial price income situation
as represented by the budget line AB in fig4.3. Let the consumer chooses
bundle Z. Assume that price of X falls. As a result, the budget line rotates to
AB'. We make an adjustment to the change in real income due to a fall in price
of X by drawing a budget line CD through Z and parallel to AB'.
Derivation of demand curve
The consumer can not choose any point on CZ because if he chooses
that way, his choices would be inconsistent. He thus chooses either Z or any
point on the segment ZD. The choice on ZD won’t be inconsistent because
those bundles were not previously available. Let he chooses the bundle W.
Clearly, W includes a higher quantity of X. Secondly, if we give back the
reduction in income; he will choose some point say N to the right of W,
provided the income elasticity of demand for good X is positive.
From this relation, we can derive the demand curve as shown in the
lower panel of fig. 4.3. At initial price say OP1, the consumer chooses OX1
P1
Fig.4.3
X
X
A
C
Z
W N
DB B1O Y
X1
X2
X3
d
X1 X
3
demand curve
O
d
Px
P2
77
quantity of X commodity. At reduced price OP2<OP1, he chooses more
quantity of X commodity i.e. OX3>OX1. Obviously, this is the inverse
relationship between the price level and the amount of goods demanded.
Thus, in the reveled preference theory, we can derive the demand curve by
observing the market behavior of the consumers on the basis of revealed
preference axiom. There is no need of using the indifference curves in
analyzing the demand curves as in the Hicks-Allen analysis. Here, demand
curve is derived directly from the study of market behavior of the consumer.
51. Derive the indifference curve and prove its convexity under
revealed preference theory.
Both cardinal and Hicks-Allen analysis provide the psychological
explanation of consumer behavior. In Samuelson’s revealed preference theory ,
the consumer need not rank his preferences or to give any other information
about his tastes as in the indifference curve analysis. The theory helps us to
construct the indifference map of the consumer just by observing his behavior
at various market prices. The following assumptions underlie our analysis:
His choices are consistent.
He is rational in Pareto sense and
His tastes do not change.
For deriving the indifference curve from the revealed preference
theory, assume the initial budget situation as shown in fig4.4 Initially, let the
consumer chooses Z bundle which implies that Z is preferred to all other
bundles lying within the triangle OAB. The bundles on the area CZD are
preferred to Z because it consists more quantity of at least one commodity as
compared to the point Z.
Then the indifference curve through the point Z must pass through the
ignorance zones as shown in the figure. To determine the exact location of IC,
Y
X
Z
C
D
A
O
perferred batches
Ignorance zone
Ignorance zoneInferior batch
BFig.4.4
78
we can narrow down the ignorance zones by making changes in price of the
goods and then observing consumer's choice bhavior.
Let price of X falls (and that of Y rises) so that price line becomes EF,
which passes below Z. (fig 4.5). The consumer, in the new budget line, will
choose either bundle G or a point on GF since points on EG would be
inconsistent. Assume that he chooses G, then, we have
Using transitivity assumption,
Z>G (original budget situation)
G >GBF(New budget situation)
Hence, Z>GBF (Transitivity)
Thus, all the batches in GBF are inferior to Z bundle in the sense that
they provide less satisfaction to the consumer than the bundle Z and the IC
through Z cannot pass through GBF. We may repeat this procedure by drawing
budget lines below Z and may reduce the lower ignorance zone to find out the
area that provides as much satisfaction as the Z bundle.
Similarly, we may reduce the upper ignorance zone. For this, let Price
of X rise and the new budget line LK passes through the Z bundle (fig4.6). The
consumer will either stay at Z or choose a point such as U on the budget line
KL.
Y
X
A
B
E
F
Z
C
D
G
OFig.4.5
79
Using the assumption of rationality, we get,
MUN>U (MUN consists more quantity of at least one commodity
without reducing the quantity of the other)
From revealed preference principle, U>Z,(because the consumer has
chosen the point U rather than Z in the new budget situation)
Thus, MUN>Z (from transitivity)
This shows that all the bundles in the area MUN are superior Z and the
indifference curve through Z cannot pass through the area MUN. We may
repeat this reasoning to narrow down the upper ignorance zone until we get the
area that provides satisfaction equal to that of Z bundle.
Shape of Indifference curve:
To determine the possible shape of the indifference curve, let us
redraw the original budget situation in fig.4.7 The IC through Z bundle must lie
in the ignorance zones and must be convex because it cannot have any other
shape. First, the IC cannot be a straight line such as AB because the consumer
by choosing the Z bundle has considered all the bundles on AB as inferior
bundles. So, other bundles on AB cannot provide satisfaction equal to that of Z
bundle. It cannot be a curve or line cutting AB at Z like IJ because points below
Z would be inferior to him and points above Z would be superior. Finally, the
IC cannot be a concave through Z because all points on the area OAB have
already been ranked as inferior to Z.
Y
X
M
U N
C
Z D
A
B
K
LO Fig.4.6
80
Possible shape of IC
Thus, it follows that the only possible shape of IC is convex and downward
sloping like the curve EF in fig. 4.7.
52. Critically appraise the revealed preference theory.
Samuelsson’s revealed preference theorem is a major advancement
over the earlier theories of demand as it gives up the dubious assumptions
underlying them. It has many advantages over the Marshallian Cardinal Utility
Analysis and Hicks-Allen IC Analysis. Some are:
It provides a direct way to the derivation of demand curves which does
not require the concept of utility or indifference curve.
It can prove the existence and the convexity of IC under weaker
assumptions than the earlier theories.
It can provide the basis for the construction of index numbers and their
uses for judging change in consumer welfare in situation where price
changes.
This theory is first to apply the behaviouristic method to derive
demand theorem from observed consumer behavior. Samuelson
thinks that his theory casts away (removes) the last vestiges of the
psychological analysis in the explanation of consumer behavior. It has
been argued that it is more scientific method. Prof. Tapas Majumdar
observes, "Behaviorist method has great advantages of treating only
observed ground, it can't go wrong."
Ignorance zone
Ignorance zone
Y
X
A
B
C
D
O
E
F
G
H
I
J
Z
Fig.4.7
81
But this theory is not free from flaws, some weaknesses are:
Indifference relation is methodologically inadmissible to his theory
but it clearly emerges if the existence of preference or otherwise is to
be judged from a sufficiently large number of observations.
Mr. Armostrong has argued that there are points of indifference on
every side of a given chosen point. If this contention is granted, his
theory breaks down.
It does not recognize the Hicksian type of Substitution Effect which is
the operational consequence of non observable indifference hypothesis
It cannot enunciate (Provide) the demand theorem when income
elasticity is negative. So, it cannot account for Giffen paradox.
It is applicable to single consumer only.
Choice does not necessarily reveal preference.
As the theory assumes, a consumer may not buy every commodity
available.
However, these weaknesses do not reduce the superiority of the theory over
other psychological theories of consumers’ demand.
53. Describe about the Friedman-Savage hypothesis of the behavior of
consumers involving risk and uncertainty.
This is an extension of the N-M utility index. N-M index is based on
the expected value of utilities and provides a method to measure the marginal
utility of money in cardinal terms under the situation of risk and uncertainty.
But it does not tell whether MUM increases or decreases. Prior to this
hypothesis, Bernoulli resolved the St. Petersberg paradox arguing that
marginal utility of money income falls thus any person does not take part in
gambling. But in reality, people indulge in both avoiding risk and loving risk.
The answer to this phenomenon has been provided by Friedman and Savage
in their article. The Utility Analysis of Choices Involving Risk(1949). They
observe, "It seems highly unlikely that there is a sharp difference between the
people who gamble and who take insurance. It seems much more likely that
many do both or would be doing so at any rate."
They advanced a hypothesis that for most people the marginal utility
of money income diminishes when income is below some particular level,
increases for income between that level and some higher level and diminishes
again for the higher level of income. Their conclusion was that people become
82
risk averter i.e. buy insurance when marginal utility of money (MUM) is
decreasing and they become risk lovers when MUM is increasing.
According to them, the function describing the utility of money
income has in general the following properties.
Utility rises with income i.e. MUM is everywhere positive.
The total utility curve is concave below some income level, convex
between that income and some higher income and concave for all
higher income levels.
The hypothesis can be illustrated with help of fig. 4.8.
Friedman Savage Hypothesis
In the fig.4.8, income is measured on X-axis and utility of income is
measured on Y-axis. Clearly the U(I) curve has three distinct shapes: first
concave, then convex and again concave.
Suppose a person's income is I5 with I5F utility without a fire. Now, he
buys an insurance to avoid risk from a fire. If his house is burnt down by fire,
his income is reduced to I0 with utility I0A. By joining A and F, we get utility
points between these two uncertain income situations. Let his expected income
be I4 with probability of no fire P and fire (1-P), calculated on the basis of N-M
utility index i.e. I=P.I5+(1-P).I0
Fig.4.8
U(I)
H
G
A
B
C DE
F
TU
Money income(I)I0
I1
I2 I
3 I4
I5 I
6 I7
O
83
Now assume that the insurance premium is equal to I3I5. Thus the
person’s assured income with insurance is I3 which gives him greater utility I3D
than I4E utility from expected income I4. Thus, he will buy the insurance to
avoid risk and have the assured income I3.
With the left income I3, he decides to buy a lottery which cost I1I3. If
he wins, his income would be I7 and if he loses his income would be I1. Let his
expected income be I2 calculated by the N-M utility index: I1=.I1+(1-)I7
where = probability of not winning. Here, I2 income level gives him more
utility I2C than I3D which he would get if he had not bought the ticket. Thus, he
will also buy the ticket along with the insurance against fire.
If his expected income was I6, again the utility after buying the lottery
ticket will be higher. In the last stage, when the expected income of the person
is more than I7, MUM declines and he is not willing to undertake risk except at
favorable odds. This region explains St. Petersberg's paradox.
Thus, a generalization follows from the hypothesis that when marginal
utility of money income diminishes or the utility function is concave, people
become risk averters and when MUM is rising or the utility function is convex,
they become risk lovers.
Friedman and Savage tentatively believe that the three segments of the
curve are descriptive of the attitude of people in different socioeconomic
groups. They recognize the multitude of differences from one person to another
in the same socioeconomic group. Some persons are inveterate gamblers, other
avoid all possible risks. Still, they think that the curve describes the
propensities of broad classes. The middle group with the increasing marginal
utility of money income are those who have eager to take risks to improve
themselves. The expectation of more money means much to this group. If their
efforts succeed, they lift themselves into the higher socio-economic group.
They not only want more consumer goods but want to rise in the social scale to
change the patterns of their lives.
Critical Appraisal
In the modern utility analysis, this hypothesis contains an added
element to the N-M utility index. It attempts to explain the shape of the utility
curves of money income. However, it is not complete. It seems to have dropped
the neo-classical assumption that MUM diminishes for all ranges of income.
Further, there is confusion whether it measures utility cardinally or cordially. In
addition, Markowitz has found this hypothesis contrary to common
observations. He has modified it by relating the MUM to the change in the
present level of income.
84
Despite these some weaknesses, the hypothesis is a brilliant
contribution to the modern theory of utility analysis.
54. Critically assess the Lancastrian demand theory.
This new approach lays stress on the attributes or characteristics
possessed by goods rather than the product themselves. The traditional theories
of demand i.e. Marshallian demand theory, IC analysis and revealed preference
theory suffer from various shortcomings which have failed to explain why
consumers prefer brand A to brand B. They cannot explain the effect of
improvements in a product or introduction of new product. K. Lancaster
developed a new approach to demand in 1966. According to him,
characteristics are relevant for making choices and they must be incorporated
explicitly in the demand analysis of goods and services. It is assumed that the
interest of the consumer is in characteristics and not in goods per se. Any
preference for a collection of goods is because of preferences for the
characteristics. He observes, "Goods as such are not the immediate objects of
preference or utility or welfare but have associated with them characteristics
which are directly relevant to the consumer, the consumer is assumed to have a
preference ordering over the set of all possible characteristics subject to the
constraint of the situation, the consumer demand for goods arises from the fact
that goods are required to obtain characteristics and is a derived demand".
Thus the novelty of the approach is the notion that attributes of goods
provide utility to individuals and that goods themselves provide utility only to
the extent that they contain desirable attributes.
Assumptions:
There are three varieties of fruit say A,B and C.
They have only two characteristics: Vitamin and Protein.
The attributes can be measured objectively in cardinal numbers.
The price of each variety is different from others.
The income of the consumer is given.
The consumer aims at maximizing his utility with a mixed bundle of
attributes.
The usual assumptions of complex quasi-ordering of preferences,
transitivity of preferences, completeness, convexity, non-satiation etc
are the standard requirements of consumer theory are applicable here
also.
Consumer's equilibrium:
85
A consumer is in equilibrium when he maximizes his satisfaction. We
analyze it with the help of indifference curves of attributes and efficiency
frontier( Budget constraint).
IC of Attributes:
It is the locus of combinations of attributes that provide same level of
satisfaction. To explain how one will choose a combination of two attributes,
an important concept called product ray is introduced. In fig.4.9, point M
shows that the consumption of OM units of A yield OV1 amount of vitamin and
OP1 amount of Protein. Similarly, other product rays OB and OC have been
drawn for other type of fruit.
IC of Attributes and Efficiency Frontier
The Budget Constraint
The budget constraint presents the various alternative combination of
the maximum amount of two attributes provided by various products which our
consumer, given his income and prices of products, can buy. In fig.4.10, if the
consumer spends his entire income on fruit A, he can purchase OM amount of
A, if on B, he can buy ON units of B and if on C, he can buy OP amount of C.
By joining the points M,N and P, we get the efficiency frontier or the budget
constraint.
Maximization of Satisfaction (Equilibrium of the Consumer)
As in other approaches to consumer behavior, here also the consumer's
equilibrium is defined by the point of tangency between the indifference curve
and efficiency frontier. However, there may be two cases:
Case I: Corner equilibrium:
As shown in fig. 4.11, the IC is tangent to the budget constraint at point N,
which implies that the consumer is getting maximum satisfaction by consuming
ON units of fruit B.
Protein
VitaminO
P1
M
A
B
IC1
C
V1 Fig.4.9
efficiency frontier
A
B
C
M N
P
O
Protein
VitaminFig.4.10
86
Consumer Equilibrium with Corner Solution
Case II: Non-corner solution
The consumer may consume a combination of two fruit to get the maximum
satisfaction. In fig. 4.2, the efficiency frontier is tangent to IC at point R. To get
the amount of two fruit consumed by him, we draw RX parallel to OC and RY
parallel to OB and obtain the units of fruit B as OX units and that of C as OY
units.
Consumer Equilibrium with non corner solution
It can be easily shown that if he consumes all three fruit, he won’t be
maximizing satisfaction.
Mathematically, his choice problem under the regular budget
constraint will be
Max U (Z)
A
M
B
C
IC1
N
P
Fig.4.11 Vitamin
Protein
O
IC2
IC3
Protein
VitaminO
M
XP
A
B
C
IC3
IC2
IC1
R
N
Y
Fig.4.12
87
Subject to Z=B.X
PX≤ y
X ≥ 0
Where Zi=bij.Xj i=1,2……………r and
B=bij is the consumption technology matrix.
P is the vector of prices
Y is income and X is the vector of goods.
We cannot say that it is similar to simple utility maximization. Thus,
all the first order conditions of traditional utility maximization model cannot be
satisfied. A complex technique of non-linear programming is needed to tackle
with it.
Derivation of Demand Curve
Derivation of Demand Curve
As in other models of consumer demand, here also demand curve can be easily
derived. Suppose, in fig.4.13(a), the original equilibrium is at the point R and
price of fruit B decreases which shifts the budget constraint MNP to MN'P.
Consequently, the equilibrium point will be on a higher IC at point R' where he
is consuming OX' of fruit B. It is obvious that due to fall in price of B, its
consumption has increased form OX to OX'. This inverse relationship has been
shown in fig. 4.13(b) which is the representation of famous negatively sloped
demand curve.
Critical Appraisal:
Lancaster’s theory of demand is not only superior but improvement
over the Marshallian demand theory, IC analysis and revealed preference
theory because:
It emphasizes demand for attributes rather than individual
commodities.
It explains that the consumer wants variety.
It explains why an individual prefers one brand to another.
Fig.4.13(b)O Vitamin
Protein A
B
M N
P
N1
C
IC1
IC2
R
R1
X
YY
1
X1
Protein
Vitamin
P1
P2
d
d
demand curve
x x1
88
It provides a practical tool for companies and market researchers to
identify the attributes needed for new brand of product.
It provides the new insights into the concepts of substitutes and
complements.
It deepens the understanding of marginal utility i.e. MU of a
commodity = sum of MUs of its constituent attributes.
However the theory has following weaknesses:
Weaknesses:
Measuring of attributes is entirely subjective.
The weaknesses of IC analysis are also present here.
Consumer pay for the quantity purchased not for the attributes
contained in them.
When different consumer think about same brand having attributes in
different ratios, then slopes of product rays become different making it
impossible to compare and measure such variations in attributes.
Conclusion:
Despite these weaknesses, this theory is a landmark in the theory of
demand. It gives a better explanation of how a new product is successfully
introduced in the market, the concept of product differentiation, the concept of
substitutes and complements, in addition to establishing the law of demand. It
is important to note that it is not the rival of the theories of cardinal utility,
ordinal utility and revealed preference. Instead by focusing on attributes, it
supplements them.
55. Write short note on N-M utility index.
The traditional theory of consumer behavior does not include an
analysis of uncertain situation. So, it is unrealistic in the sense that particular
action on the part of the consumer is followed by particular determinate
consequences which are known in advance. J. Von Newman and Oscar
Morgenstern gave a method of cardinally measuring expected utility form
risky choices that are found in gambling, lottery tickets etc. By making use of
the idea of Bernoulli that under risky and uncertain situations as in betting,
gambling, purchasing lottery tickets, a rational individual would go by the
expected utilities rather than expected money values. For this, they constructed
a utility index which is called the N-M utility index. They showed that it is
possible to construct a set of numbers for a particular consumer that can be
used to predict his choice in uncertain situations.
Assumptions
89
i) Complete Ordering Axiom: The consumer is not assumed to be faced with
indecision. For two alternatives A and B, one of the following must be true
a) he prefers A to B b) he prefers B to A c) he is indifferent between A and
B. It also implies transitivity of choices i.e. if he prefers A to B and B to C,
then he prefers A to C.
ii) Continuity Axiom: Assume that A> Band B> C. This axiom asserts that
there exists some probability 0<<1 such that the consumer is indifferent
between outcomes B with certainty and lottery ticket offering the outcomes
A and C with probabilities and 1- respectively.
iii) Independence Axiom: Suppose AB and C be any other outcome
whatsover. If one lottery L1 offers A and C with probability and 1- and
another lottery L2 provides B and C with and 1-, then L1L2 i.e. the
relative preferences between A and B is not affected by the third outcome.
iv) Unequal Probability Axiom: Assume that A>B. If two lottery tickets
L1and L2 both offer the outcomes A and B, then he prefers L2 only if the
probability of getting A is greater for L2 than for L1.
v) Axiom of Complexity or Expected Return Maximization: It asserts that
consumer preference under uncertainty is dependent in expected return rather
than complexity or simplicity of the situation.
vi) Uncertainty or risk does not have any utility or disutility of its own.
Construction of Utility Index:
Based on the above assumptions, to construct the utility index, assume
three outcomes such that A>B>C. Suppose B is certain outcome, and A and C
are uncertain outcomes. Then by continuity axiom.
BP.A +(1-P).C
We can thus write UB=P.UA+(1-P).UC
To construct a utility index, we have to assign utility values to A and C
arbitrarily s.t. UA>UC. Suppose P=0.6, UA=500 UC=2 then UB = 0.6×500+0.4×2
= 300.8
Proceeding in this way, we can construct a complete utility index for
UA, UB, UC…… starting from two arbitrary situations:
Situation UB UA UC
1 300.8 500 2
2 271.6 450 4
3 332.2 550 8
4 184.0 300 10
5 242.4 400 6
By using this index, we can find the utility numbers for all
possible quantities and combinations of all commodities. Hence, a complete
utility index can be derived by taking arbitrary points and successively
90
confronting the consumer with various choice situations involving probabilities
or risk.
Measurement of Marginal Utility of Money:
Assume that a lottery gives Rs 5000 if one wins and gets Rs 10 only if
he loses. If the odds are 60:40, then expected value is
E= .w + (1-).F
Where w = won amount F=amount in case one loses
=probability of winning
In our example E= 0.6×5000+0.4×10
=3004
We can write expected utility =.Uw +(1-).UF
Or E(U) =.U(Rs5000)+(1-).U(Rs 10)
=0.6×500+0.4×1
= 300.4
Where, utility of Rs.5000=500 and utility of Rs.10= 1 units are taken arbitrarily
such that Uw > Uf
Now, we seek the certainty equivalent of this lottery. Let the consumer
is indifferent between Rs 3000 with certainty and the lottery. Then utility of
3000 = utility of the lottery.
Thus, utility of 3000 = 300.4 utils.
Then, Amount Rs 10 Rs 5000 Rs 3000
Expected utility 1util 500 utils 300.4 utils
Critical Appraisal
The utility index of N-M analysis is cardinal in restricted sense.
Expected utility is unique except for linear transformation. Even then the
interpersonal comparison of utility is still impossible. However, the
construction of N-M utility index permits:
The complete ordering of utility differences by virtue of cardinal
property.
The complete ranking of alternative situations characterized by
uncertainty.
The calculation of expected utility and thus making it possible to deal
with the consumer behavior under uncertain situations.
The N-M index provides conceptual measurement of cardinal utility
under risky choices. It is meant to be used for making predictions about two or
more alternatives relating to gambling, lottery tickets, etc. Further it provides a
measure of marginal utility of money. It permits the cardinal measurement of
relative preferences of risky choices.
The N-M method is not the same thing as neo-classical cardinal
measurement of utility. This method does not measure the pleasure from goods
91
and services; it is intended to measure the utility of money with respect to
predicting how an individual will make choice in risky and uncertain situations
Criticisms
It does not measure the change in marginal utility of money.
It is cardinal in restricted sense. Henderson and Quandt claim that
the inferences from this are valid until the consumer wants to
maximize the expected utility. Here, the consumer is given to compare
between two mutually exclusive choices. So, by analyzing the
individual utilities of A and B, the combined utility cannot be
predicted.
92
CHAPTER 5: INTERTEMPORAL CHOICE
56. Analyze the consumer’s equilibrium under intertemporal choice.
What are the effects of change in income and interest rate on
such equilibrium points?
When the consumer faces the problem of consuming today or tomorrow or
at present or in the future, he has to select the consumption and saving patterns
over time so as to maximize his utility subject to the budget constraint. These
types of choices are called intertemporal choices.
In intertemporal choice, the problem of the consumer is to decide:
Consumption today, say C1,
Consumption tomorrow, say C2 and
Savings between today and tomorrow.
Here also, the consumer’s equilibrium is analyzed with the help of budget
constraint and indifference curves.
Budget Constraint
Let the consumer’s income be Y1 in period 1 and Y2 in period 2, consumption
be C1 in period 1 and C2 in period 2 and let price of each unit of C1 and C2 be
one unit. Then the flow budget constraints are:
C1 = Y1-S1………………..……….……..(i)
C2 = Y2+ (1+r).S1……………….………..(ii)
Where, r = interest rate
Equation (i) shows that consumption in period 1 equals income of period 1
minus saving of period 1 and equation (ii) shows that consumption in period 2
equals income of period 2 plus saving from period 1 plus the amount of interest
earned on such savings. These equations are true when there is no possibility of
borrowing.
Equation (ii) can be written as:
C2 = Y2 + (1+r) (Y1-C1)…..…………………….(iii) ∵S1=Y1-C1
Now, if the consumer can borrow money, his consumption in period 1
may be greater than his income in period 1. If this happens, he must pay the
borrowed money back with interest which reduces his consumption in period 2.
In this case, his consumption in period 2 will be:
C2 = Y2 – r×B-B
Where, B= borrowed amount in period 1 which equals C1-Y1.
Or, C2= Y2-r (C1-Y1)-(C1-Y1)
Or, C2 = Y2 + (1+r) (Y1-C1)……………………….(iv)
93
Equation (iii) and (iv) can be rearranged as:
1 2 1 2(1 ) + C = (1+r)Y + Y .........................................( )
Value of Future Value of
Consumption Income
r C v
Future
Equation (v) represents the budget constraint in terms of future value and
equation (vi) represents the budget constraint in terms of present value.
We can show the budget constraint graphically. For that:
If C1 = 0, C2= (1+r) Y1 + Y2 and
If C2= 0, C1 = Y1 + Y2/ (1+r).
In fig. 5.1, by joining the two points A and B, we get the budget constraint that
passes through the point E (Y1, Y2). Such a point E where the consumer neither
borrows nor saves is called Polonius point.
Budget Constraint
The budget constraint in fig. 5.1 shows all combinations of C1 and C2 that
exhausts (completely uses) the consumer’s resources.
The slope of the budget constraint is given by –(1+r) which can be derived
from equation (vi) as:
2 21 1
C Y + = Y + .........................................( )
(1+r) (1+r) Present Value of Present Value of Consumption Income
C vi
(1+r)Y1+Y2
Y1+Y2/(1+r)
(Y1,Y2)Y2
Y1O
C2
C1
Consumption pointwhen all saving inPeriod 1
Consumption pointwhen the consumerdoesnot consume in period 2
Consumption pointwhen no saving andnoborrowing
E
Fig.5.1
94
The slope being –(1+r) implies that if the consumer increases his consumption
in period 1 by one unit (or reduces savings by one unit), he has to sacrifice
consumption in period 2 by 1+r units.
Consumer’s Equilibrium
In this analysis also, the consumer’s equilibrium will be realized at the point of
tangency between the budget constraint and the IC. Formally, the problem is:
Maximize U= U (C1, C2)
Subject to the budget constraint
The equilibrium will be established at the point where:
Slope of IC = Slope of Budget Constraint
Or,
This condition is known as Euler’s Equation.
Graphically, the equilibrium condition has been shown in fig. 5.2 below.
Consumer's Equilibrium (Saver)
2 21 1
1 2 1 2
2 1 2 1
2
1
C Y + = Y +
(1+r) (1+r)
Rewriting as, C (1+r)+C =Y (1+r)+Y Taking L.C.M.
or, C = Y (1+r)+Y (1 )
C of Budget Line = (1 )
C
C
C r
Slope r
2 21 1
C Y + = Y +
(1+r) (1+r)C
1 2
1
2
UC
=1+r = Intertemporal Price U
C
c cMRS
C2
C1
E
(1+r)Y1+Y2
Y1+Y2/(1+r)Y1
Y2
C2
C1O
e
Fig.5.2
Original endowment
IC
95
In fig. 5.2, point e is the equilibrium point where the condition for equilibrium
has been satisfied. The consumer saves S1 amount in period 1 and spends it in
period 2 so as to maximize his utility. That is why in fig. 5.2, C1<Y1 and
C2>Y2. This is a specific example of a consumer’s equilibrium where the
consumer is a saver and not a borrower. In case the consumer is a borrower, his
equilibrium would be e’ point as shown in fig. 5.3 where he would consume
more in period 1 than his income i.e. C1>Y1 and C2<Y2.
Equilibrium of Consumer ( Borrower)
Effect of increase in Income
If there is a permanent increase in income, the budget constraint shifts outwards
parallely and the consumer’s equilibrium will be on a higher IC as shown in
fig. 5.4 below.
Effect of rise in interest Rate on saver costumer
C2
C1
E
(1+r)Y1+Y2
Y1+Y2/(1+r)Y1
Y2
C2
C1O
e
Fig.5.3
Original endowment
IC
Fig.5.4
C2
C1
E
(1+r)Y1+Y2
Y1+Y2/(1+r)Y1
Y2
C2
C1O
e
e1
E1
C1
2
C1
1Y1
1
Y1
2
IC2
IC1
{C2
Y2
C1 Y1
Original endowment
endowment afterincrease in income
96
Effects of Change in Interest rate
We analyze the effects of change in interest rate in the following two cases:
Case(i)
If the consumer is a lender/ saver initially (C1<Y1), he will remain a saver if
there occurs a rise in interest rate.
With the increase in interest rate, say from r to r1, the slope of the budget line
increases in absolute terms making it steeper. But, again the budget line passes
through the point (Y1, Y2) because whatever is the interest rate, if the consumer
does not want to save or borrow, he can always purchase the point (Y1, Y2).
Now, a consumer who is initially a saver will be a saver. By doing so, he will
gain extra utility. If he becomes a borrower in such a case, clearly, his utility
will fall (fig. 5.5).
Effect of rise in interest Rate on saver costumer
Case (ii)
If the consumer is initially a borrower, even after the fall in interest rate, he will
remain a borrower because if he becomes a lender/saver in this case, his
satisfaction will be reduced (fig. 5.6).
C2
C1
E
(1+r)Y1+Y2
Y1+Y2/(1+r)Y1
Y2
O
e
Fig.5.5
Original endowmente1
IC1
IC2
Original budget constraint
New budget constraintafter rise in interest rate
97
Effect of fall in interest Rate on borrower costumer
Finally, in the following two cases, nothing can be said with conformity about
the consumer behavior:
When the consumer is a saver and interest rate decreases.
When the consumer is a borrower and the interest rate increases.
C2
C1
E
(1+r)Y1+Y2
Y1+Y2/(1+r)Y1
Y2
O
e
Fig.5.6
Original endowment
e1
IC1
IC2
Original budget constraint
New budget constraintafter fall in interest rate
98
CHAPTER 6: THEORY OF PRODUCTION AND TECHNOLOGICAL CHANGE
57. What do you mean by a production function? What are the main
features of production functions? Why is it necessary to study
production functions in economics?
The production function is the basic physical relationship between inputs or
factors of production and output of the product. Since it shows the physical or
technical relationship between the factors of production and the output
produced, the inputs and output are measured in physical units, not in monetary
units. It is an embodiment of technology which yields maximum amount of
output from a given set of inputs. It defines the firms’ technical production
possibilities. It is a mathematical equation showing the maximum amount of
output that can be produced from a given set of inputs, given the existing
technology. According to Stigler, "The production function is the name given
to the relation between the rates of inputs of productive services and the rate of
output of the product. It is economists’ summary of technological knowledge."
Symbolically, the production function can be written as,
Q = f(X1, X2……..Xn)
Where, Q = Output and Xi's are factors of production or inputs.
To put it in a more convenient term, we can express the production function as:
Q = f(L, K, Ld, T,…………………)
Where, Q stands for output produced, L stands for labor, K stands for capital,
Ld stands for land, T stands for Technology, etc,.
Some well known production functions are:
i) Cobb-Douglas Production Function: It is given by Q=AKL
Where,
Q is output, K is capital, L is labor, A is efficiency parameter, and are
output elasticities.
ii) CES Production Function: It is given by
Q=A [K-
+(1-) L-
]-1/
,
Where, A=technology parameter = Substitution parameter and is
the distribution parameter.
iii) Multiple Linear Production Function: It is given by.
Q = a+b1x1+b2x2+………bnxn where bi= Q/xi= MPPx is the marginal
product of xith
factor of production.
99
iv)Spillman's Production Function: It is given by
Y= A(1-Rx)x (1-Rz)
z
Where, A= technology, Y = output, X and Z are inputs and Rx and Rz
are the ratios by which MPP of X and Z factors decline with their increased
application respectively.
v) Input-output Production Function: it is given by
Q = min(X1/c1 , X2/c2)
Where X1 and X2 are inputs and ci = amount of input i to produce one
unit of output.
The main features of production function are:
i) It depicts only the physical or technical relationship between inputs and
output.
ii) Production function is monotonic.
iii) It is not necessary that all inputs are variable.
iv) The production process is not influenced by externalities.
v) It is continuous i.e. Xi's and Q are divisible.
vi) It includes only those inputs for which some price is paid.
vii) It is specified in relation to a given period of time.
viii) It is specified for a given technology and design of the product.
Why Study Production Function?
Production function enables economists to analyze a variety of problems such
as determination of factor income, shares of factors of production, the nature of
technological unemployment, etc. Even in production theory, it helps us to
determine:
i) To what extent will the output of production process change while the
quantity of some fixed inputs is held constant and the quantity of some
variable inputs is increased?
ii) What will be the change in output if quantity of one input is decreased and
that of another is increased?
iii) To what extent will the total output change if the firm increases the quantity
of all inputs in equal proportion?
Due to these reasons, the study of production function is an integral part to the
study of economics, especially microeconomics.
58. What is meant by a production process?
A production process means a method of production. It is a method of
production where various combinations of inputs are determined to produce
one unit of output. For example, suppose that one unit of commodity X can be
produced by any of the following processes.
100
Process I Process II Process II
Capital 2 3 1
Labor 3 2 4
In first method, two units of capital and three units of labor are required to
produce one unit of output. Similarly, in process II, three units of capital and
two units of labor are required to produce one unit of output and if we follow
process III, one unit of capital and four units of labor are required to produce
one unit of output.
All these methods are considered technically efficient. However, ultimate
choice depends on the cost factors of each method/process. If there are two
processes to produce one unit of commodity X given as:
A B
Capital 2 3
Labor 3 3
Then, clearly, process A is more technically and economically efficient than
process B as this can produce the same output of one unit as process B but with
less capital (with one unit less of capital).
Production process can either be labor-intensive or capital-intensive
depending on the technique used. In the labor-intensive production process,
relatively more units of labor are used as compared to capital and conversely, in
capital–intensive production process, relatively more units of capital are used
as compared to labor to produce one unit of output.
59. Analyze how production is carried out under different decision
periods.
A producer behaves differently in the use of the factors of production along
with the time span of production. This behavior depends on the time span of the
production process from the point of view of increasing the quantity of the
factors of production. We can divide the behavior of producer in the following
four categories according to his behavior shown along with the time span of
production:
i) Very Short Run/ Momentary Period: It is very short run period of time. All
inputs and hence production level is fixed. From the point of view of
understanding producer’s behavior, this time period is not relevant as quantity
of inputs and output are invariant (constant).
ii) Short-run: It is a period in which the size of the plant and equipment
remains unchanged (quantity is fixed) and only some factors of production are
variable factors. So, production process is carried out with the fixed and
variable factors. The variable inputs and fixed inputs are combined in variable
101
or changing proportion. Agricultural production is an example. The period of
short run may be a few month, a year, etc, depending on the nature of
production. The flows of factors defined for short run are subject to three
restrictions.
a) It must be so short period that the firm should be unable to change all the
factors of production.
b) It must be sufficiently short so as to leave no room for technological
improvements. In other words, it should not be such a long time where
technology can improve.
c) Yet, it must be long enough to allow the combination of necessary inputs and
completion of the production process. In other words, it should not be such
a short time period so that the production cannot be done.
Fixed factors are those whose quantities cannot be changed readily
when market demands an immediate change in output because the cost of such
immediate change in their quantity may be exorbitant (very much costly) that
the entrepreneur may not deem it appropriate to undertake the same. Factory,
farm and building, major pieces of machinery and managerial personnel are
generally treated as fixed inputs. On other hand, a variable input is one which
can be readily changed almost instantaneously (with in a moment or
immediately) in response to a desired change in output.
Thus, in the short run, the producer operates with a given production
function and increases the amount of production by increasing the quantity of
variable factors and keeping constant the amount of fixed factors.
iii) Long-run: In the long run, producer can build new plants and has to decide
at what plant he should produce given the framework of known production
possibilities. All the factors of production, except technology, are variable in
the long run. So, production is carried out by changing all the factors of
production in the same proportion or in various proportions. Since
technology does not change in the long-run, the production function is stable.
iv) The Very Long-run: In the very long run, new techniques may be
introduced. It means all the factors and technology are variable as such the
production function is not stable. Technological improvements may bring to
light more efficient and less costly methods of production for producing
commodities.
The nature of efficiency improvement may assume several forms like:
a) A new production function may use the same amount of resources to
combine in a different way to produce more output than before.
b) It may utilize same types of inputs to produce the same types of output but
require a smaller quantity of one or several inputs and no more of the
remaining inputs to produce the same quantity of output as before.
c) It may require inputs of the type not heretofore (until now) used.
102
Technological changes that are less efficient than those already known
can safely be ignored. Thus, in the very long run, the producer increases the
quantity of the factors of production in line with the changing technology to
continue the production activity. In this process, he switches to the most
efficient technique of production if the resource availability allows him to do
so.
60. Write a note on elasticity of substitution.
The elasticity of substitution is a concept introduced to measure the degree
of substitutability between the factors of production. Marginal rate of technical
substitution (MRTS) is a simple measure to tell something about the rate of
substitution between the factors of production but it suffers from a serious
defect in the sense that it depends on units of measurement of the inputs
involved in the production.
A better measure in this regard is elasticity of substitution which is
unit less. It is denoted by ‘’ which is a pure number defined as the rate of
percentage change in input ratio and percentage change on MRTS. i.e.
= Proportionate change in the ratio of inputs
Proportionate change in MRTS
LK LK
L K L K
d(K/L) K/Lor,
dMRTS /MTRTS
d(K/L) K/Lor,
d(f / f )/ f / f
Where, MRTSLK = fL / fK where fL = MPPL and fK = MPPK
Further, solving this, we can write as
2 2
( )
(2 )
L K L K
L K KL L KK K LL
f f Lf Kf
LK f f f f f f f
In case of perfect competition and in equilibrium,
is a positive pure number i.e. ≥ 0 because both numerators and
denominator increase/decrease in the same direction. To show this, suppose w/r
increases. If w/r increases, labor is relatively more expensive than capital. So,
the firm reduces the use of labor as such K/L increases. Similarly, if w/r
decreases, labor becomes relatively cheaper and as such the use of labor
increases and K/L also decreases.
is a pure number that measures the rate at which substitution
between inputs takes place. It varies from point to point on the production
function. Higher the value of , the greater the possibility of substitution
between the inputs. ranges from 0 to .
( / ) / // in equilibrium
( / ) / /LK
d K L K LMRTS w r
d w r w r
103
i) If =0, it means zero substitution between the inputs which implies that all
the factors must be increased to increase production. In this case, the iso-
quants will be right angled(See fig.6.9).
ii) If = , then inputs are perfect substitutes of each other. Here, the iso-
quants will be straight lines with negative slope (See fig.6.8)
iii) If 0<<, then factors can be substituted to some extent only. Here, the iso-
quants are convex to the origin and negatively sloped (See fig.6.10.)
In this way, the magnitude of varies inversely with the curvature of
the iso-quant.
can be also measured as below.
Elasticity of Substitution
At point A, K/L ratio is K1/L1 = Slope of the ray OA
At point A, MRTSLK = Slope of tangent t1t1
At point B, K/L ratio is K2/L2 = Slope of the ray OB
At point B, MRTSLK = Slope of tangent t2t2
Then can be defined as
=Proportionate change in the slope of rays
Proportionate change in slope of tangents
In equilibrium MRTS= w/r and the formula with w/r is more helpful in
its application because information regarding prices are more easily available
than the information regarding MRTS.
Importance:
It occupies an important place in the theory of distribution. According to neo-
classical theory of distribution, the relative factor share depends on the
elasticity of substitution.
O
Y
X
K1
K2
L2
L1
A
Bt1
t2
Fig.6.1
104
61. Write a note on short- run production function.
In the short run, production function indicates the output obtainable from
combining various amount of variable inputs with given amount of fixed
inputs. Thus, the short run production function shows the relationship between
the output and inputs when the production is operated by changing the quantity
of the variable inputs and keeping the quantity of fixed inputs constant. Thus,
the short run production function can be expressed as:
Q = f(X1, X2/X3……..Xn)
Here, the vertical bar indicates that inputs to the right of it are held constant and
left to it are variable as such X1 and X2 are the decision variable or variable
inputs and a producer optimizes the use of X1 and X2 to produce a good in
question. For the sake of simplicity, Let us take a production function with two
inputs only. i.e.
Q = f (L,K ), Where L is the variable factor and K is the fixed factor.
This short run production function is defined under three restrictions.
a) The time period should be short enough so that the firm is unable to change
all the factors of production.
b) It must be sufficiently short so as to leave no room for technological
improvements.
c) Yet, the time must be long enough to allow the combination of necessary
inputs and completion of the production process.
It must, however be kept in mind that both fixed and variable factors
are necessary in the short run. Only the short run production function is
characterized by variable returns with respect to a variable factor.
62. Explain the law of variable proportions and different stage of
production. In which stage does a rational producer operate?
Where does the producer operate in stage second? Where does
the producer operate if price of the variable factor is zero?
It refers to the input-output relationship when output is increased by varying
the quantity of one input, keeping the quantity of others fixed during the short
run. When the quantity of one input is varied, keeping the quantity of other
factors constant, the proportion between the variable factor and fixed factor is
altered (changed). Since we study the effect of variations in factor proportions
on output, this is known as the law of variable proportions.
105
The law of variable proportions says that once we increase the
quantity of one factor of production, keeping other factors constant, the output
will first increase at an increasing rate up to a certain point. However after
reaching this point, the total output will increase at a diminishing rate and
after reaching a maximum point, the total output will decline. In other words,
the total product curve will first rise rapidly and then begins to taper off until it
finally reaches a maximum and then begins to decline.
The law is based on the following assumptions:
i) The state of technology is given.
ii) There exits at least one factor variable.
iii) There is possibility of variation in factor proportion.
To illustrate the law, let us take a hypothetical production function as
Q=5KL+5/2(L2K
2)-1/8(K
3L
3)
Let us fix capital at 2 units then,
Q= f (L,K)= 10L+10L2- L
3 (Putting K=2)
Then average physical product (APL) = Q/L = 10+10L-L2
and
marginal physical product=L
Q
= 10+20L-3L
2 but for discrete change we use
MPL= TPL-TPL-1 in the following table.
The responses of TPL, APL to successive doses of variable factor labor
is shown in the following table.
Table 3.1
Law of Variable Proportions
Labor
units(L)
Capital
units(K)
L/K
ratio
APL=
10+10L-
L2
MPL=TPL-
TPL-1
TPL Stage
1 2 1/2 19 19 19 Stage I
2 2 2/2 26 33 52
3 2 3/2 31 41 93
4 2 4/2 34 43 136
5 2 5/2 35 39 175
6 2 6/2 34 29 204 Stage II
7 2 7/2 31 13 217
8 2 8/2 26 -9 208 Stage
III 9 2 9/2 19 -37 171
10 2 10/2 10 -71 100
106
As we said before, TPL first rises rapidly up to 4 units of labor and
then increases at diminishing rate up to 7 units of labor and then decreases.
Similarly, MPL increases and reaches maximum 43 at 4th
unit of labor and
decreases to zero and becomes negative. Also APL rises and reaches maximum
of 35 at 5th and then decreases continuously. Clearly there are three stages as
separated in the table.
The above three stages can be made clear with the help of following
diagram (Fig. 6.2 )
Three Stages of Production in the Short run.
A
B
C
TPL
L
TPL
O L1
L2 L
3
L1
L2
APL
MPLFig.6.2
O
MPL
APL
L
Stage I Stage II Stage III
Point of inflection
L3
107
In fig 6.2, TPL curve first rises rapidly up to the point A. After point A,
it increases at a diminishing rate up to point C and then decreases. A is the
point of inflection where MPL is maximum. The point of inflection is that point
at which the curve changes its shape from convex to concave.
The nature of APL, MPL and TPL under different stages are given
below.
Three Stages of Production:
Stage I: It starts from the origin and ends where APL is maximum. Here:
TPL increases at an increasing rate up to point A and then increases at
a diminishing rate.
MPL increases, reaches the highest point at L1 units of labor and then
declines.
APL increases and reaches maximum at the end of the stage.
Causes of stage I
The fixed factor is abundant in relation to the variable factor.
The efficiency of variable factor increases when more and more units
are applied due to specialization and division of labor.
Stage II:
It is also known as the stage of diminishing returns. It starts from the point of
extensive margin (Max APL) of labor and ends at the point of intensive margin
of labor (MPL=0).Here,
TPL increases at a diminishing rate and reaches maximum at the end.
MPL and APL are decreasing but they remain positive.
MPL<APL
Causes of stage II
Scarcity of the fixed factor in relation to the variable factor.
Indivisibility of fixed factor.
There may be the point where the proportion of the factors is
optimum. Beyond that point the wrong proportion will lead to fall in
APL and MPL.
Stage III : It is called the stage of negative returns. It starts from the point of
intensive margin (MPL=0). Here,
TPL is declining as such TPL curves slopes downward.
APL is decreasing but positive.
MPL is negative.
Causes of Stage III
Excessive amount of variable factor. The proverb ‘Too many cooks
spoil the broth’ applies here.
108
Stage of Operation:
It is interesting that there is symmetry between the stages i.e. stage
first for labor is the third stage for capital and stage III of labor is the stage I for
capital. Thus, in stage I,MPL>0 but MPK <0. It means that capital has not been
utilized fully. So the producer increases the amount of labor at least until
MPK>0. Stage III for labor is obviously irrational because the pay off of an
extra labor unit is negative. Thus, it is the stage II only where both MPL and
MPK are positive, fixed factor is fully utilized and where business decisions
have to be taken.
It is apparent that stage II is the best from the stand point of cost and
efficiency. The exact point of operation depends on the price of variable
factors.
Exact Point of Operation:
To define the exact point of operation, let us take the production
function as Q = f(L,K) and Total cost C= wL +F
Where F is fixed cost and wL is the variable cost of using labor used with the
available fixed input.
Further assume the market to be perfectly competitive so that wage
rate w and price of X (px) are given.
The firm's aim is to maximize profit () = TR-TC
Or, = Px.Qx-w.L-F
The first order condition for profit () maximization is that the first derivative
of with respect to L is zero.
wL
QPOr
wL
QPOr
L
F
L
Lw
L
QP
L
xx
xx
xx
.,
0.,
0
Here, Qx/L= MPL
Px.MPL=w or VMPL=w Px×MPL=VMPL
Where, VMPL= value of marginal product of labor given by MPL times price of
X.
Let us reproduce fig. 6.2 below and plot VMPL on the same diagram.
109
Extra point of Operation
VMPL lies right to MPL because VMPL= MPL× Px and Px> 0. Only if Px= 1 unit,
VMPL coincides with MPL.
In the fig 6.3, the condition VMPL=w is satisfied at le unit of labor. Thus,
producer operates at le units because by employing that much labor, he is
maximizing the profit or he reaches the equilibrium point.
Point of Operation If Labor is Free
If labor is free, wage rate (w) = 0, thus the equilibrium condition is
VMPL=0 or Px × MPL=0.
Thus the producer operates at l3 units where both MPL and VMPL are
zero.
63. Explain the law of variable proportions using iso-quants.
To show the law of variable proportion with the help of iso-quants, we have
shown the economic region of production (please, read the answer of Q.N. 10.
first to know about the economic region of production and its features) in fig.
6.5 where beyond OA, MPK<0 and beyond OB, MPL< 0. Let us fix capital at
K. Now the producer can expand along KK only due to capital constraint.
For simplicity, we take product multiple level of iso-quants with equal increase
in output every time, say 100, 200, 300 etc.
L1
L2 L
3
APL
MPLFig.6.3
O
MPL
APL
L
Stage I Stage II Stage III
e
VMPL
Le
w w
110
Law of Variable Proportion
Up to point M, less and less units of labors are needed to increase
output by 100. Also out of OA, MPK<0. Thus KM is the Stage I.
From M to N, increase in output by 100 units needs increasing
amount of labor. Also between OA and OB, both MPL and MPK are
positive. So, it is the second stage of production.
After point N, if we increase labor, it results in a decline in TP. Also,
beyond OB, MPL < 0. Thus, it is stage III of production.
64. Write a note on log-run production function.
In the long run, all factors, except technology, are variable. The long run
production function shows the nature of output when more than one variable
factor changes in the long run in the same proportion or at varying proportions.
The general long run production function can be written as:
Q = f(X1,X2……….Xn/T)
Where, Q is output, X1, X2, …Xn are the factors of production, T is
technology. The bar shows that the variable T after it is a fixed factor of
production. In practice, we take only two factors of production L and K in
analysis so that we can graphically treat the analysis using iso-quants. Then,
our function can be written as:
Q = f (L, K)
M N
K
L
K
O
600
500
400
3002 0 0
100
Fig.6.5
A
B
K
111
The function Q = f (L, K) can be represented by an iso-quant.
It technology is variable, we will have very long-run analysis.
65. Define an iso-quant. What do you mean by the Marginal Rate of
Technical Substitution (MRTS). What are the different types of
iso-quants?
An iso-quant is a graphical visualization of the three variable long-run
production function. In case two variable factors, an iso-quant is the locus of
combination of the two factors that yield the same level of output. A typical iso-
quant is shown in fig.6.6.
Iso-quant
In fig. 6.6, the curve named IQ is the iso-quant. Every point lying on the iso-
quant, like A and B gives same level of production. That is why; it is also
called an equal product curve.
As we see in the figure, when we move from one point of the iso-quant down
to another point, we are giving up (sacrificing) some quantity of capital for
some quantity of labor. For example, in fig.6.6, as we move from point A to
point B, we are reducing K1K2 amount of capital and replace it by L1L2 amount
of labor. The rate at which one factor of production can be substituted for
another along an iso-quant is called the marginal rate of technical substitution
(MRTS). It can be measured as:
O L
K1
K2
L2
L1
A
B
Fig.6.6
IQ
K
LK
KMRTS
L
112
The value of MRTS gives us the slope of the production function or
slope of the iso-quant.
MRTS goes on diminishing as we move downwards right along the iso-quant.
It is because as we increase the use of labor, MPL falls and as such less and less
units of capital are needed to replace for one unit of labor if production is to be
kept constant.
The collection of iso-quants is called an iso-quant map.
Types:
Linear Iso-quant: It assumes perfect substitutability of factors of
production. Here, iso-quant is negatively sloped straight line. (fig. 6.8)
Input-Output Iso-quant: It assumes strict complementary i.e. zero
substitution between factors of production. Here, iso-quants are right
angled. (fig. 6.9)
Kinked Iso-quant: It assumes limited substitutability between the
factors of production. There are limited methods for producing a
commodity and substitutability is possible only at the kinks. Such an
iso-quant is also called activity analysis iso-quant or linear
programming iso-quant. (fig. 6.7)
Convex Iso-quant: It assumes continuous substitutability between the
factors of production. It is smooth, convex and negatively sloped.
(fig6.10)
The main properties of iso-quants in the economic zone of production are:
They are negatively sloped i.e. dK/dL<0.
They never intersect each other.
Higher iso-quant represents higher level of output.
They are convex to the origin i.e. d2K/dL
2>0.
66. Write a note on 'Ridge lines or economic zone of production'.
The general shape of the iso-quant is oval (slope like egg) but why we regard
only negative sloped and convex part is that the other portion than this
represents economically foolish resource combination because at other
portions, marginal products of at least one factor is negative. The theory of
production concentrates only one the economic zone where marginal products
O
IQ
L
K P1
P2
P3
Fig.6.7 O IQ L
K
Fig.6.8O
IQ
L
K
Fig.6.9O
IQ
L
K
Fig.6.10
113
of all factors are positive but declining. It corresponds to the segment of iso-
quant where they are convex and negatively sloped.
Ridge Lines
Consider fig 6.11 where at a0, MPK= 0 and if we increase capital beyond K1,
MPK< 0. Thus, the iso-quant bend back up to themselves. On the positively
sloped part, no rational producer would use capital as MPK < 0. Similarly at a1
and a2 also, MPK = 0. Thus, a1, a2, a3 etc, are the points of intensive margin for
capital beyond which MPK will be negative. Also at those points, MRTSLK=
as MPK =0.
Joining such points, we get the upper ridge line as OA. On the other
hand at b0, b1, b2 etc MPL is zero and beyond them MPL is negative. So, no
rational producer would use labor beyond these points. These are the intensive
margin for labor where MRTSLK = 0 because MPL =0. Beyond those points, the
iso-quants bend back upon themselves. Joining the points b0,b1,b2 etc, we get
the lower ridge line as OB.
The region bounded by the upper ridgeline OA and lower ridge OB is
called the economic zone of production where both MPL and MPK are positive.
On the economic zone, MRTSLK lies between 0 and i.e. 0<MRTSLK <, and
iso-quants are convex to the origin and negatively sloped.
The well behaved production function e.g. Cob-Douglas production
function, CES production function, etc have no economic regions because APL
K
LO
a0
a1
a2
b0
b1
b2
MPL>0
MPL<0
MPK<0
MPK>0
MPK>0
MPL>0
Slope =MP
K
MPL =
K1
K2
L1
L2
Slope =MP
K
MPL = 0
Fig.6.11
economic zoneQ
2
Q1
Q0
A
B
114
and MPL in such case are positive and diminishing everywhere monotonically.
So, there is neither stage I nor stage III.
67. Discuss about the shape of product line.
A product line shows the physical movement from one iso-quant to another
as we change one or both the factors of production. It does not depend on the
price of factors of production and does not imply any actual choice of
expansion. In other words, a product line does not necessarily show the way of
expanding the output with minimum cost. It describes only the technically
alternative paths of expanding output. So, it’s just one possible way, among the
thousand ones, along which output can be increased, whether that is a least cost
way or not.
Product Line in the Short Run: If there is only one variable factor, keeping
the other constant, we cannot increase both the factors of production in the way
we like because the fixed factor cannot be increased in the short run. Thus, we
are forced to increase the amount of variable factor only to increase the output.
In such a case, product lines are parallel to the axis on which we measure the
variable factor. It is shown in fig 6.12. The capital labor ratio declines along
such product line.
Product Line in the Short-run
Product Line in Long run: Long run is a period of time sufficient to allow
change in all fixed factors of production. So, in the long run, we can walk in the
way we like to increase the output if we neglect the cost of production along a
particular path. That is why there is no any restriction on the shape of long run
product line.
Fig.6.12
Q2
Q1
K K
O
Product line
L
K
115
Among all the possible product lines of particular interest are the so
called isoclines. An iso-cline is the locus of points of different iso-quants at
which the MRTS of factors is constant.
If the production function is homogeneous, the isoclines are straight
lines through the origin. Also, along such an iso-cline, the capital-labor ratio is
constant. It is shown in fig 6.13 In case the production function is non-
homogeneous, then the iso-cline will not be a straight line but its shape will be
twiddly (having bends). The capital labor ratio changes along each iso-cline
which is shown in fig. 6.14.
Product line (homogenous production function) / Product line (non-homogenous production function)
68. Explain the law of returns to scale.
The law of returns to scale deals with the input-output relationships over a
time span sufficiently long to allow changes in all inputs; especially those
inputs such as plant, space, major pieces of capital equipment and managerial
capability which are typically fixed in the short run. So, it refers to the effect of
scale relationship. In the long run, output may be increased by changing all
factors in the same proportion or in different proportions. However, traditional
theory of production concentrates on the effects of equi-proportionate change in
all inputs.
Thus, the laws of returns to scale seek to analyze the response of
output when inputs are increased by a fixed proportion. In such a case, output
may change more than proportionately, less than proportionately or equi-
proportionately. Accordingly, we have three types of returns to scale:
Increasing Returns to Scale (IRS).
Diminishing Returns to Scale (DRS).
Constant Returns to Scale (CRS).
The following assumptions underlie our analysis:
All factors are variable.
Technological changes are absent.
There is perfect competition.
Fig.6.13
Q2
Q1
O
Product line
L
K
Q3
Fig.6.14
Q2
Q1
O
Product line
L
K
Q3
A A
116
Output is measured in quantity.
For simplicity, we use multiple product level of iso-quants assuming
homogeneous production function i.e. with linear expansion path. The returns
to scale thus may be shown graphically by the distance between iso-quants that
show the level of output which are multiples of some base level e.g. X, 2X, 3X
etc.
i) Constant Returns to Scale (CRS): CRS refers to the phenomenon in which
inputs and output change in the same proportion i.e. a proportionate change
in the variable inputs leads to an equi-proportionate change in output. If
doubling or trebling of all factors causes a doubling or trebling of output,
returns to scale are said to be constant. For example, if the inputs labor and
capital are increased by 20% per period of time, and output increases by
20%, the production function is said to possess CRS.
Formally, If Q = f(L,K) and if we increase inputs by times and the output
also increases by times, there is said to exist the constant returns to scale.
i.e.,
Q= f (L,K)
This type of production function is called a linearly homogeneous production
function.
For example:
Labor Capital Output.
1L 1K X
2L 2K 2X
3L 3K 3X
Graphically, along an isocline, the successive multiple product levels of
iso-quants will be equidistant to each other. i.e. increase in quantity every
time by X units requires equal increase in labor and capital. In fig 6.15 oa
= ab = bc
Constant returns to scale Output curve
In this case, the output curve is a straight line and upward sloping
(fig.6.16).
Fig.6.15Fig.6.17
O L
K
1K
2K
3K
1L 3L2L
X
2X
3X
O 1K 2K 3K1L
3L2L
X
2X
3X
Output
K,L
Output curve
A
a
b
c
117
Causes of CRS:
When the factors of production are perfectly divisible,
substitutable, homogeneous and their supply are perfectly elastic
at given price.
When external diseconomies and external economies cancel each
other.
When internal economies and internal diseconomies balance each
other.
ii) Increasing Returns to Scale (IRS): Production function is said to possess
IRS if output increases in a greater proportion than the proportion of
increase in inputs. That is if increase in inputs by a given proportion leads
to a more than proportionate increase in output, it is called IRS. For
example, if labor and capital are increased by 20% per period of time and
output increases by 30%, the production function is said to possess IRS.
Formally specking if inputs are increased by fold and output increases by
more than fold i.e. if Q = f(L, K) and f(L, K) = rQ where r >1, the
production function is said to possess IRS.
Illustration:
Labor Capital Output.
1L 1K X
2L 2K 3X
3L 3K 6X
Graphically, along an isocline, the distance between the successive
multiple product levels of iso-quants decreases implying that that by
doubling the inputs output is more than doubled. In fig. 6.17 oa > ab> bc.
Increasing returns to scale Out put curve
Fig.6.17
O L
K
1K
2K
3K
1L 3L2L
X
3X
6X
2X
Fig.6.18O 1K 2K 3K1L 3L2L
X
3X
6X
Output
K,L
Output curve
a
b
c
A
118
Here the response of change in output by change in inputs is more. So,
the slope of output curve increases with every increase in input level and
thes, it becomes convex. (fig.6.18)
Causes of IRS
Indivisibility of fixed factor.
Greater possibilities of specialization of labor and machinery
which increases productivity.
External economies that are obtained from skilled labor, transport
and credit facilities, subsidiary industries, etc.
Trade journal, research and trading centers which also help in the
cost effective and more efficient production method.
Economies of space and marketing.
Dimensional economies.
iii) Decreasing Returns to Scale (DRS): Returns to scale are said to be
decreasing if proportionate change in output is smaller than a given
proportionate change in inputs. In other words, if an increase in all inputs
by fixed proportion leads to a less than proportionate increase in output
there is said to exist DRS. Here, if we double the inputs, output is less than
doubled.
Speaking formally, given that Q = f(L, K) and if f(L, K)= rQ
where r<1, the production function exhibits DRS.
Illustration:
Labor Capital Output.
1L 1K X
2L 2K 1.5X
3L 3K 2X
Graphically, the distance between the multiple product levels of iso-quant
along an isocline goes on increasing. In fig.6.19 oa <ab.
Decreasing Returns to Scale and Product curve
Fig.6.19
O L
K
1K
2K
3K
1L 3L2L
X
1.5X
2X
A
Fig.6.20
O L,K1K 2K 3K1L, 3L,2L,
X
2X
1.5X
Outut curve
Out put
a
b
119
Here, the product curve is positively sloped but its slope diminishes with
increase in the level of inputs as such it becomes concave. (Fig.6.20)
Causes of DRS:
Diminishing returns to management: Though there is a larger number
of management techniques developed to make the management more
efficient, beyond a certain level of the firm size, management fails to
coordinate and management diseconomies starts.
In case of exhaustible (that goes on diminishing in quantity if used)
natural resources, DRS are likely to exist. For example, doubling the
fishing fleet (fish catchers) may not lead to the doubling the catch of
fish, trebling the persons who are collecting Yarsagumba may not
raise the collection by three times or more, etc.
Problem of supervision and co-ordination.
Difficulties of control and rigidities by large management
Indivisible factors may become less efficient after an optimum level.
External diseconomies.
Transport and marketing difficulties.
Conclusion:
Though returns to scale are assumed to be same everywhere on the
production surface i.e. the same returns along all expansion product lines, in
reality, the technological conditions of production may be such that return to
scale may be different over different ranges of output. Over some ranges of
output, we may have constant returns to scale while over another we may have
increasing or decreasing returns to scale. In fig. 6.21, we see CRS unto 4x level
for output and beyond that there is DRS.
Different Returns on the Production Surface
Fig.6.21O L
X1X
K
2X
5X
6X
3X
4X
120
69. Analyze the producer's equilibrium.
A producer is in equilibrium when he has achieved his goals and does not
want to change the use of inputs and accordingly the output produced. The
traditional theory of firm assumes that the firm has the single goal of profit
maximization. Thus, a producer’s equilibrium point is that point which
maximizes the profit of the firm. For achieving this single goal, there are two
alternative ways: either to get maximum output using the fixed resources or to
get fixed output at minimum cost.
We analyse his equilibrium with the help of iso-quants and iso-cost
line.
Iso-cost line: An iso-cost line is the locus of combination of two inputs, say,
labor and capital that can be purchased by a firm with a fixed outlay
(expenditure) and given the price of inputs.
Algebraically, it can be written as:
C = wL +rK
where C = fixed outlay
w = per unit price of labor (wage rate)
r = per unit price of capital (rental)
Slope of the iso-cost line = -w/r
X-intercept = C/w, Y-intercept = C/r
A typical iso-cost line is shown is fig 6.22
Iso-cost Line
The following assumptions under lie our analysis:
a) The goal of the firm is profit maximization.
b) A single commodity X is produced.
K
O L
slope = -wr
C= wL+rK
Isocost line
Fig.6.22
A
B
Cr
Cw
121
c) There exists perfect competition in product and factor market as such px, w, r
are given.
We follow the following two approaches:
Constrained output maximization.
Constrained cost minimization.
Constrained Output Maximization:
In this approach the firm seeks to maximize his output given the resources
(outlay). His aim is to get maximum profit. His profit is =R-C
Or =px.Qx-C
Since Px and C are given, the only way to increase is by making
Qx bigger and thus making the gap between revenue and cost higher. So, profit
maximization in this case is achieved by making Q maximum.
Thus, our problem is to
Maximize Q = f (L, K)
Subject to C = wL + rK
Graphically,
The necessary condition for maximization of output is that the iso-quant must
be tangent to the iso-cost line. It is obvious from the fig. 6.23 that among the
points on the iso-cost line d, e and f, the maximum output is given by the point
e where the iso-quant Q2 is tangent to the iso-cost line. Symbolically, the
condition for maximum profit or producer’s equilibrium is:
Slope of iso-quant = slope of iso-cost line
MPL/MPK = -w/r
Producer's Equilibrium
Fig.6.23
K
O L
C= wL+rK
Q3
Q2
Q1
d
f
e
122
At point d, MPL/w> MPK/r, which implies that labor is more productive than
capital. So, the producer uses more labor and reduces the use of capital and
moves towards point e.
At point f, MPL/w< MPK/r, which implies that capital is more productive than
labor. So, the producer reduces the use of labor and increases the use of capital
and moves towards point e.
The fulfillment of the above discussed condition does not necessarily
lead to the maximization of profit. It is only a necessary condition and not a
sufficient condition. The sufficient condition is that the iso-quant must be
convex at the point of tangency. If the iso-quant is concave at the point of
tangency, such a tangency point does not maximize profits.
Mathematically
Our problem is,
Maximize Q = f(L,K)
Subject toC= wL+rK
Combining the objective function with the cost constraint with the help of
Lagrange multiplier, we get,
V= f(L,K)+(C-wL-rK); >0
The first order condition for maximum profits is
)(00
)(00
)(00
iiirKwLCV
iirfK
V
iwfL
V
K
L
From (i) and (ii) we get
r
f
w
f KL
Here, is the marginal product of money expenditure. Thus the above
condition implies that the marginal productivity of RS 1 in purchasing labor
must be equal to that of capital. Manipulating further, we have
LK
K
L
K
L MRTSr
w
MP
MPor
r
w
f
f
WhereKKLL
MPK
Qf,MP
L
Qf
and MRTSLK=Absolute
slope of iso-quant or the marginal rate of technical substitution.
The second order condition is that the bordered Hessian determinant
H must be positive i.e. H>0
123
KL
LL
KK
LK
KKKL
LKLL
KKKL
LKLL
fr
fwr
fr
fww
ff
ff
ffr
ffw
rw
H
)()(0
0
= 0+w(-wfKK+rfLK)-r(-wfLK+rfLL) ∵fKL=fLK
=-w2fKK+rwfLK+rwfLK-r
2fLL
=2rwfLK-w2fKK-r
2fLL>0
Theoretically, the positivity of Hessian determinant implies convexity
of iso-quants.
ii) Cost Minimization:
Producer sometimes may have a fixed output in mind. In such a case,
the only way to maximize profit is to minimize cost. Thus, here our problem is
Minimize C= wL+rK
Subject to Q0=f(L,K); where, Q0 = fixed output.
Graphically,
a) The necessary condition for cost minimization and accordingly profit
maximization is that the iso-quant must be tangent to the iso-cost. In fig 6.24,
the fixed output Qo can be produced with many cost level C1, C2, C3,etc.
Among them, we see that the minimum possible cost level is C1 which cost line
is tangent to the iso-quant Q0. Thus, again the necessary condition for the
maximization of profits is the tangency condition.
Producer's Equilibrium
The sufficient condition is that the iso-quant must be convex to the origin.
Fig.6.24
K
O L
Q0
e
C1= wL
1+rK
1
C0= wL
0+rK
0
C3= wL
3+rK
3
C2= wL
2+rK
2
124
Mathematically,
Our problem is to minimize C = wL+rK
Subject to Q0= f(L,K)
The combined Lagrange function is
V= wL+ rK+(Q0-f(L,K) >0
The first order condition for minimizing V is
)iiii...(....................0)K,L(fQ0V
)ii...(....................0fr0K
V
)i...(....................0fw0L
V
0
K
L
From (i) and (ii)
LK
K
L
K
L
K
L
MRTSMP
MP
f
f
r
w,or
1
f
f
r
w
The interpretation of this first order condition is the same as in the case of
above maximization problem. Here, = marginal cost of production (dC/dQ).
The second order condition requires that the Bordered Hessian
determinant must be negative i.e. H<0.
0
fff
fff
ff0
H
KKKLK
LKLLL
KL
Putting fL=w/ and fK=r/ from first order condition, we get:
0
ff/r
ff/w/r/w0
H
KKKL
LKLL
Dividing row 2 and row 3 by -
0
ff/r
ff/w/r/w0
H
KKKL2
LKLL22
Multiplying col. 1 by 2 and row 1 by -,
LL LK
KL KK
0 w r1
H w f f 0
r f f
0
ffr
ffwrw01
H
KKKL
LKLL
Since 0
ffr
ffwrw0
KKKL
LKLL
125
Thus, H <0 also implies the convexity of iso-quant. (why?)
Thus, to sum up, for producer's equilibrium, the two conditions are:
The necessary condition is that the iso-quant must be tangent to the
iso-cost line
The sufficient condition is that the iso-quant must be convex to the
origin.
70. Write a note on profit maximization when the producer is free to
change the outlay as well as output.
When the producer can change his expenditure and his output level, there is
neither cost constraint nor the output constraint. The entrepreneur is free to
vary the levels of output and cost level to get his aim of profit maximization.
Symbolically, his aim is
Maximize profit () = R-C
Or, =Px. Qx- wL - rK
Given Px, w and r, the problem depends on choosing the variable L and K. Thus
applying the necessary and sufficient conditions for maximization, we get:
The first order condition is that,
)ii(....................0rf.PK
)i(....................0wf.PL
KxK
LxL
From (i) and (ii)
Px. fL = w and Px .fK = r
Here, KKLL MPPK
QfandMPP
L
Qf
Thus our conditions are
Px.MPPL=w PX.MPPK = r
Further, MPPL multiplied by Px gives the value of marginal product of
labor (VMPL) and px multiplied by MPPK gives value of marginal product of
capital (VMPK). Thus, our conditions are:
VMPL = w and VMPK = r.
This implies that for profit maximization, the entrepreneur will
employ each input up to that point at which price of the input is equal to the
value of marginal product of the inputs.
The second order condition is that the principle minor of bordered Hessian
determinant be alternating in sign starting with a negative sign i.e.
126
LL<0, KK<0, and
We have,
0.
0.
KKXKK
LLXL
LL
fPL
fPL
And KL = LK=Px.fLK
Thus ,
The second order condition is fulfilled because in economic region of
production, fL, fK>0. fLL, fKK<0
Thus, in case of no constraints on outlay and output, the producer will use the
inputs at a level at which their marginal product valued at market price (VMP)
equals the price of the respective input.
71. Analyze the effects of change in outlay on producer’s equilibrium.
When outlay increases, price of labor and capital remaining constant, the iso-
cost line parallely shifts upwards and touches a higher iso-quant. This shift
continues further with the increase in outlay and thus the outward shifting iso-
cost line becomes tangent to higher and higher iso-quants. If we join the
equilibrium points, we get a curve which is called expansion path. It is the
locus of tangential points between iso-quant and iso-cost which serves to
describe the least-cost combination of labor and capital to produce different
level of outputs. It is also called scale line because it shows how the
entrepreneur will change the quantities of the two factors when he increases the
level of output. A rational entrepreneur always seeks to produce at one point or
another on the expansion path.
Expansion Path in the Short run:
In the short run, one factor say capital is fixed. So the firm is not able to
maximize profit due to capital constraint and cannot equalize MRTS (Slope of
iso-quant) and w/r(Slope of iso-cost). So. he is compelled to expand along a
straight line parallel to the axis on which we measure the variable factor labor.
In fig 6.25, the optimal expansion path would be OA, if it were possible to
increase capital. Given the capital fixed atK, the firm can increase output
0LL LK
KL KK
0
0 , 0
LL LK
KL KK
x LL x LK LL LK
x
x KL X KK KL KK
P f P f f for P
P f P f f f
2
127
along the lineKK by increasing the units of labor only. So the product line
KK is the short run expansion path.
Short run Expansion Path
Expansion Path in the Long run:
In the long run, all the factors are variable and there is no capital constraint as
such the firm can increase the amount of both the factors of production to
maximize profit. That is why the expansion path in the long run will be the cost
minimizing or profit maximizing expansion path. All the points lying on the
long run expansion path will maximize profits. Thus, an expansion path in the
long run is the locus of equilibrium points of the producer as he expands his
level of output. It goes through the point of tangency between the iso-costs and
iso-quants showing the optimal or best way to expand the output level for the
Producer. (see fig.6.26)
Expansion path in the short run
Fig.6.25
K
O L
Q3
Q2
Q1
A
KK
128
Long run Expansion Path
Further, the expansion path may be a straight line or a curve with many bends.
It depends on whether the production function is homogeneous or not. We
below discuss the two cases:
If the production function is homogeneous, the expansion path will be
a straight line starting from the origin whose slope depends on factor
price. If the factor price ratio (w/r) increases, the expansion path
becomes flatter. In fig. 6.27, the expansion path OB is flatter than OA
because w'/r'> w/r.
In case of non-homogeneous production function, the expansion path
will not be a straight line. This case is shown in fig 6.28.
Expansion Path (Homogeneous production Function) and (Non homogeneous Production Function)
An illustration:
An expansion path can be derived from the first order condition of
maximization. The first order condition is r
w
MP
MP
K
L
In case Q=AKL (Cobb Douglas production function)
Fig.6.26
K
O L
Q3
Q2Q1
K
A
Long run expansion path
Q4
e1
e2
e3
e4
Fig.6.27
K
O L
Q3
Q2
Q1
B
K
A
Long run expansion path
Fig.6.28
K
O L
Q3
Q2
Q1K
A
Long run expansion path
129
L
K
MP
MP
K
L
Thus we have, Lr
wK,or
r
w
L
K
Which gives us a linear expansion path.
72. Analyse the effects of change in the price of factor on producer's
equilibrium.
When price of an input changes, the total outlay and price of other factor
remaining constant, the producer's equilibrium position changes. For simplicity,
let's suppose that price of labor falls, other things remaining the same. It makes
labor relatively cheaper and the iso-cost line rotates outwards and the producer
will be producing a higher output remaining on a higher iso-quant. Consider
fig. 6.29, where original equilibrium is at e1, at which the producer is producing
Q1 output with L1 units of labor. Let price of labor falls, other things remaining
the same, his iso-cost line rotates outwards to AB' and his equilibrium will be
on a higher iso-quant Q2; where he is using OL3 amount of labor. The
movement from e1 to e3 or increase in the use of labor by L1L3 is called total
effect which can be decomposed (divided) into substitution effect and output
effect. The substitution effect shows the change in input use that is due to the
sole effect of the changes in relative price of inputs, output remaining constant.
It is always negative in the sense that a fall in the price of an input leads to
increase in its usage. The output effect is the change in the use of input use if
output is let to increase, input prices being constant.
To separate these effects, we draw an iso-cost line CD parallel to the
iso-cost line AB' and tangent to Q1 in fig 6.29. This is for finding the change in
input use due to change in relative price of labor only, output remaining
constant. The new equilibrium will be at point e2. Thus, the movement from e1
to e2 is called substitution effect because the producer has substituted capital by
L1L2 amount of labor for producing the same level of output. The reason is that
labor has now become relatively cheaper due to a fall in its price. Further, the
movement from e2 to e3 is output effect which comes from the change in output
by keeping the relative prices constant.
Thus when the price of inputs change, it changes the output level and
the use of the inputs. The total effect brought by the fall in the price of an input
can be divided into substitution effect and output effect.
130
In fig 6.29, we have
Total effect (e1to e3)= Substitution effect(e1to e2)+ output effect(e2 to e3).
Thus, change in the price of an input changes the input use as well as
output.
73. Define and derive the production possibility curve (PPC) and
comment on its possible shapes and shifts in it.
To understand the concept of production possibility curve, we assume a case
of two goods and two factors of production. In such a case, a production
possibility curve (PPC) is the locus of combinations of two commodities: say X
and Y that can be produced by the firm, given the resources and state of
technology. It shows all the efficient possible combinations of the goods that
can be produced with the given technology and with the available amounts of
labor and capital.
PPC is derived from Edgeworth Box of production.
The following assumptions underlie our analysis.
There are two inputs labor and capital.
The firm produces only two commodities.
The production function are X= f (L,K) and Y = f (L,K).
Technology is given.
The resources L and K are given.
Each production function can be represented by a set of iso-quants.
Consider the fig.6.30, where the iso-quants for X- commodity are placed by
Removed in new syllabus.
K
LO
A
B1
C
DBL1
L2
L3
e1
e2
e3
SE OE
Fig.6.29
Q2
Q1
131
taking Ox as origin and the iso-quants for Y-commodity are placed by taking
Oy as origin. This box type diagram is also known as Edgworth box of
production diagram.
Edge worth box Diagram of Production
Each point on the box shows six variables: quantities of X and Y, and use of
labor and capital in producing X and Y. However, not all the points are
efficient. As we analyze some of the points, we see that only the points lying on
the contract curve which is made up of the tangency points of iso-quants are
efficient. The points that lie out of the contract curve are inefficient in the sense
that by moving from a point out of the contract curve to a point on the contract
curve, production of at least one commodity can be increased without reducing
the quantity of another commodity and by moving from a point on the contract
curve to a point out of it, there is no way to increase the quantity of one
commodity without reducing the quantity of another. For example, points z is
inefficient because by moving from z to u, production of X remains the same
but production of Y increases to Y4 (y4>y3). Similarly, if we move from z to v,
the production of Y remains the same but production of X is increases. If we
move to a point lying between u and v, production of both commodities will
increase as compared to the point z.
Thus, the Edge worth contract curve shows the Pareto efficient points
for the joint-production of the two commodities. If we plot all the efficient
points of the Edgeworth contract curve in a output space graph on which we
measure the quantity of X-commodity on X-axis and quantity of Y-commodity
on Y-axis, we get a curve which is called the production possibility curve. By
plotting the points of Edgeworth contract curve on an output space in fig 6.31,
OY
OX
y6
y5
y4
y3
y2
y1
x1
x2
x3
x4
x5
x6
K
L
a
b
c
d
u
v
zK1
L1
Fig.6.30
Edgeworth contract curve
132
we get the PPC whose points a', b', u', v', c' and d' correspond to a, b, u, v, c and
d on the contract curve.
Production Possibility Curve
This curve is called PPC because it shows the possible efficient combinations
of two commodities that can be produced with the given technology and the
input levels. It is also called the product transformation curve because by
moving from one point to another on it, one is just transferring the resources
from the production of one commodity to the production of another. The rate at
which one product is transformed into another; resources remaining unchanged,
is called the marginal rate of product transformation (MRPTxy). As the sacrifice
of Y for an additional production of X goes on increasing, MRPT increases and
it makes the PPC concave to the origin.
y6
y5
y4
y3
y2
y1
x6
x5
x4
x3
x2x
1
a’
b’
u’
v’
c’
d’
production possbility curve
Fig.6.31
X
Y
133
Shift in PPC due to Increase in Labor and Capital or Technological Improvement.
The PPC shifts outwards or inwards due to change in the amount of labor and
capital resources available and improvement in the technical progress because
with these increases, it is possible to increase the production of both
commodities together or with a fall in resources, one is compelled to produce a
lower amount of both commodities. It is not necessary that the shift resulting
from these factors is parallel. It depends on the nature of technological
progress: whether it is capital deepening, labor deepening or a neutral one.
74. What do you mean by linearly homogeneous production function?
A production function Q = f( L,K) is called linearly homogeneous
production function if it shows constant returns to scale. Speaking formally, if
we increase the inputs by -fold and the output also increases by -fold, such a
production function is said to be linearly homogeneous production function.
i.e. given the production function, Q = f ( L,K) if Q = f(L, K), the
production function is linearly homogeneous.
Properties:
It shows constant returns to scale.
It satisfies Euler’s theorem i.e. Q = L.MPPL+K.MPPK.
It can be expressed as a function of K/L ratio.
APPL, APPK, MPPL and MPPK also can be expressed as a function of
K/L ratio.
For example the function Q = AKL
1- which is the famous Cobb-Douglas
production function is a linearly homogeneous production function.
Y
O XFig.6.32
P
P P1
P1
134
75. Write a short note on Cobb-Douglas production function.
The Cobb-Douglas production function is one of the intensively used
production function in economics and econometric researches. It was
formulated by the American Economists C. W Cobb and P.H. Douglas on the
basis of US empirical data.
The simplest form is in case of two inputs given by
Q=AKL
Where, Q= output,
A= efficiency or technology parameter
and are output elasticities.
Properties:
It is log linear.
Both factors are indispensable.
Marginal products are positive.
Iso-quants are negatively sloped.
Iso-quants are convex to the origin.
MRTS is given by K/L
Elasticity of substitution is unity.
Euler's theorem is satisfied.
The exponents and show output elasticities and share of inputs in
total production (under perfect competition).
The expansion path is linear.
Marginal products are declining but positive. In other words, it is a
well behaved production function.
Merits:
It is used to determine the relative share of labor and capital.
It is used to prove Euler's theorem.
Its parameter and represent elasticity coefficients that are used for
inter-sector comparison.
It shows constant returns to scale.
Even non-linear function can be made linear.
It describes the type of technology.
o If / > 1 Capital Intensive Technology.
o If / < 1 Labor Intensive Technology.
76. Write a short note on CES production function.
It was derived by Arrow, Chenery, Minhas and Solow. The linearly
homogeneous form is given by:
135
Q = A[ K-
+(1-)L-
]-1/
Where Q= output
A= Technology parameters A>0
= distribution parameter 0< <1 (=Alpha)
= substitution parameter >-1 (= Rho)
Properties:
It is linearly homogeneous.
Iso-quants are negatively sloped.
Iso-quants are convex to the origin.
Elasticity of substitution is 1/1+
Marginal products are positive.
It is a well-behaved production function.
Cobb-Douglas Production function is a special case of CES function.
Merits:
Prediction is easy.
Elasticity of substitution is not unity.
It includes three types of parameters.
77. What is the role of technological change in production function?
Technological changes can take pace with the invention in production
technique, new products, new raw materials, etc. With technological progress,
knowledge of new and more efficient method of production becomes available.
As a result, the productivity of the factors of production rises and there is more
efficiency in the methods of production. The development and application of
scientific knowledge leads to both more efficient methods of production and
utilization of better quality inputs. Not only better machine and inputs, there
may be improvement in the training and overall quality of workers and in the
organization over time under technical progress. It causes a shift in the
production function showing the increase in the productivity of the factors of
production,
Graphically, in case of singe variable factor labor TPL shifts upward
with the same quantity of variable factor labor implying that production of
more output is possible with the same amount of inputs. Similarly, in case of
two factor labor and capital the iso-quant shifts downwards implying that the
same production can be produced with a less quantity of both inputs. The effect
of technological improvement in production function are shown in fig 6.33 and
6.34.
136
Technological change in production when capital is constant
78. What are the different types of production technical progress.
Prof. J. R. Hicks has distinguished three types of technical progress.
i) Labor Deepening Technological Progress:
Technological change is labor deepening if along an isocline through
the origin along which K/L ratio is constant, the MRTSLK increases. It implies
that technical progress increase MPPL faster than MPPK because MRTSLK
increase means increase in MPPL/MPPK. In such a case the downward shifting
iso-quants becomes steeper along the isocline
Labor Deepening Technical Progress.
ii) Capital Depending Technical Progress:
Technological progress is capital depending if along an iso-cline with
constant K/L ratio MRTSLK decreases. It implies MPPK rises faster than MPPL.
In such a case, the downward shifting iso-quant becomes less steeper.
O L
X
Fig.6.33L
1
X1=f(L)X1
X X=f(L)
O L
K
Fig.6.34
L1L
0
K0
K1
Q0
Q10
O L
K
Fig.6.35
Q3
Q2
Q1
Q0
K
137
Capital Deepening Technical Progress
iii) Neutral Technical Progress:
Technological progress is neutral if along an iso-cline with constant
K/L ratio, MRTSLK remain unchanged. It implies that technological change
raises both MPPK and MPPL by the same percentage. In such a case, the
downward shifting iso-quant becomes parallel to each other.
Natural Technical progress.
79. Discuss the relationship between elasticity of substitution and
income distribution.
As discuss in Q.N. 4,elasticity of substitution is defined as:
LKLKMTRTS/dMRTS
L/K)L/K(d
In case of perfect factor market and in producer's equilibrium MRTSLK=w/r
r
wr
wd
L/K)L/K(d
Fig.6.36O L
Isocline
Q0
Q1
Q2
Q3
A
O L
K
Fig.6.37
Q3
Q2
Q1
Q0
A
Isocline
138
The value of lies between zero and infinity ie. 0<<
<1= inelastic substituability.
=1= Unitary substitutability.
>1= elastic substitutability.
On the other hand, the share of factor is given by,
Share of labor= X
L.w
output
wages
Share of labor= X
K.r
output
rental
The relative factor share is LK
rw
XrK
XwL
ShareofK
ShareofL
Now, we can establish the relationship between elasticity of substitution and
income distribution.
When <1, a give percentage increase in w/r ratio results in a smaller
percentage increase in K/L ratio. This increase the share of labor
relative to the share of capital because relative share is given by LK
rw
.
When =1, a given percentage increase in w/r results in equal
percentage increase in K/L as such the relative share of labor remains
constant.
When >1, given percentage increase in w/r results in larger
percentage increase in K/L as such the relative share of labor
decreases.
Thus in summary, the relative share of labor increases if <1, remains constant
if =1 and decreases if >1.
80. What are the effects of technogical progress on income
distribution.
For the nature of technical progress see the answer of Q.N.22. We
below summarise the effects of each type of technical progress on income
distribution:
If technological progress is neutral both MPPL and MPPK increase at
the same rate so that MRTSLK=w/r remains constant. Also K/L ratio
will be unchanged. As such the relative factor share remain constant.
In case of labor depening technical progress MPPL rises faster than
MPPK as such the relative share of labor will increase and the relative
share of capital will fall.
139
Finally, if the technical progress is capital depending MPPK rise
faster thann MPPL as such the relative share of capital will increase
and the relative share of labor will fall.
81. What is cobb-Douglas production function? Why is it frequently
used in economics? How do we measure elasticities and marginal
productivities when such functions are used?
The Cobb-Douglas Production function is one of the most widely used
production function in economis. It was formulated by C.W cobb and P.H
Douglas and first time estimated by them with the monufacturing industry data.
They found that about 75% of the increase in manfacturing production was due
to labor and the remaining 25% was due to the capital input. It can be written
as:
Q=AKL
1- , A>0, 0<<1
Where Q= output
K and L are inputs
and 1- are the partial output elasticties and they also show the
relative factor shares in case of perfectly competitive market.
A= technology/efficiency parameter.
This production function is extensively used in economics because:
It is simpler than other type production functions to estimate.
It can be made liner with log transformation.
It shows constant returns to scale.
It can be used in case of increasing / decreasing returns to scale too
by replacing 1- by a new parameter .
Is satisfies Euler's theorem.
Its parameters and 1- show the partial output elasticities with
respect to capital and labor respectively.
The parameters and 1- also show the relative factor share of
capital and labor respectively in case of perfect competitive market.
Measurement of Elasticities and Marginal Productivities
Marginal product of labor can be derive as:
L
LAK
L
LAK
L
Q
MPL
Qor
L
Q
11
L
= AK(1-)L
-
140
L
KA)1(
L
KA)1(
Similarly, Marginal Product of capital can be derived as:
K
KAL
K
LAK
K
Q
MPK
Qor
K
Q
11
K
= AL1-K
-1
1
1
1
K
LA
K
LA
Partial elasticity of output with respect to labor is given by:
eQL= Proportionate change in Output
Proportionate change in labor
LMP
Q
L
L
Q
Q
LL
Q
Q
LL
L
L
KA)1(
LAK
Le
1QL
1LAK
LAK)1(
1
1
Partial elasticity of output with respect to capital is given by:
EQL= Proportionate change in Output
Proportionate change in Capital
KMP
Q
K
K
Q
Q
KK
Q
Q
KK
K
141
1
1
1QLK
LA
LAK
KE
KAL
KAL1
1
Finally, elasticity of substitution can be derived as:
Elasticity of substitution()=
LK
LK
MRTSMRTSd
LK
LKd
1
K
L
LK
K
LA
L
KA)1(
MP
MPMRTS
11 K.LA
L.K)1(A
L.L
K.K.
11
1
L
K.
1
MRTSLK L
K.
1
L
K.
1L
K.
1d
L
KL
Kd
=
L
K.
1d
L
K.
1
LK
LKd
L
Kd.
1L
K.
1
LK
LKd
=1
Thus, For Cobb Douglas production function elasticity of substitution is unitary
which implies that the relative factor share remains constant for any changes in
the amount of capital and labor.
142
82. Describe about the salient features of the two sector input output
model.
Hint: Input output analysis is a technique invented by Prof. W.W Leontief in
1951. It is used to analyze the inter-industry relationship to understand the inter
dependence and complexities of the economy and thus, the conditions for
maintaining equilibrium between demand and supply. This is a technique to
explain the general equilibrium of the economy. It is also known as inter-
industry analysis.
For simplicity if we consider that there are only two sectors only as
agriculture sector and manufacturing sector in the economy, the basic structure
of the input-output model can be presented as below:
Let out of agriculture sector (Industry I) = X1
Output of manufacturing sector (Industry II) = X2
Since the input output model is concerned with finding the output
level that leads to the general equilibrium or equilibrium in all the sectors in the
economy, the basic equations are demand equals supply in each sector i.e.
For Industry I,
Demand for X1= Supply of X1
Demand for X1 as input in industry I(X11)+ demand of output X1 as
input in industry II (X12)+ final demand of X1 for consumption(d1) = Total
supply of X1
Similarly,
For Industry II,
Demand for X2= Supply of X2
Demand for X2 as input in industry I(X21)+ demand for output X2 as
input in industry II(X22)+ final demand for X2 for consumption(d2) = Total
supply of X2
In the form of equations:
X11+X12+d1=X1…………....……………………… (i)
X21+X22+d2=X2…………………………………… (ii)
If we define a relationship as aij=Xij/Xj, we can interpret aij as the
amount of output produced by the ith industry that is being used as the input in
jth industry. So aij can be called input coefficients. We have,
a11=X11/X1 which implies X11=a11X1
a12=X12/X2 which implies X12=a12X2
a21=X21/X1 which implies X21=a21X1and
a22=X22/X2 which implies X22=a22X2
Now, substituting these values in equation (i) and (ii) we get
a11X1+a12X2+d1=X1
a21X1+a22X2+d2=X2
143
The above two equations can be solved for finding the equilibrium
outputs by the two industries as:
where, is the vector ofequilibrium quantities,
called the Leotief matrix , is
called the input c
1
1 11 12 1
2 21 22 2
1
2
11 12 11 12
21 22 21 22
X 1 a a d
X a 1 a d
X
X
1 a a a ais
a 1 a a a
oefficient matrix and is the final demand vector.
1
2
d
d
The main features of such two sector model are:
It is used to find the correct level of output to be produced by the sectors in
order to keep the economy in equilibrium.
The value of the determinant of the Leontief matrix must be positive for the
meaningful solution to exist and the values of the diagonal elements of the
input coefficient matrix like a11, a22 must not exceed unity.
Concerned with Production only: It is concerned with production only and does
not consider what determines final demand for goods. It is thus only a
technological problem.
It based on Empirical facts: It is based on only empirical facts. Estimates of the
quantities of variable inputs and output of industries are made on the basis of
empirical data. Thus, it differs from general equilibrium theory propounded by
Walrus which is purely analysis and theoretical.
Based on General Equilibrium Analysis: It gives practical shape to the
theoretical framework of general equilibrium analysis.
It shows the interrelationships among the industries. Since the output of one
industry is used as an input of another industry, it shows the interrelation
among the industries.
144
CHAPTER 7: THEORY OF COST
83. Write a short note on cost function.
The relationship between the cost incurred in the production process and its
determinants is called the cost function. In a cost function, cost appears as
dependent variable and the determinants of cost like factor prices, technology,
level of output, etc appear as independent variables. Cost function is derived
function. It is derived from production function as it is the type of production
process that determines the cost of production.
The cost in the short run and in the long run depends on a lot of
factors. So, it is a multivariate function. Symbolically we can write the long run
cost function as
C= f(X, T, pf) and the short run cost function as C=f(X, T, pf,K)
Where, C= total cost
X= Output
T= technology
Pf = price of factors.
K= fixed factor.
For graphical simplicity, we present the cost function in a two
dimensional diagram by taking the level of output as the single independent
variable and keep other things constant. Such curves imply that cost is a
function of output C=f(X), ceteris paribus. The change in other factors is shown
by a shift in the cost function.
84. Derive the average fixed cost under traditional cost theory.
Traditional cost theory has divided the total cost into fixed costs and variable
costs. Fixed costs are those costs whose quantity cannot be changed in the short
run as the market demands an increase in output. On the other hand, variable
costs are those costs whose quantities can be changed immediately as the
market demands an immediate increase in output.
Average fixed cost is derived total fixed cost. Total fixed cost consists of:
Salaries of administrative staff.
Depreciation of machinery.
Expenses for building depreciation and repairs.
Expenses for depreciation and maintenance of land (if any)
Graphically, total fixed cost is a horizontal straight line parallel to X-axis as
shown in fig 7.1 implying that the total fixed cost remains the same for
whatever level of output. The average fixed cost (AFC) is found by dividing
TFC by the level of output.
i.e. AFC= TFC/X
145
Graphically, the average fixed cost at some level of output is given by the slope
of ray from origin to the point on the TFC curve. In fig.7.1, as the slope of ray
goes on decreasing continuously the AFC also falls continuously. Its shape is a
rectangular hyperbola which is asymptote to both the axes.
Derivation of Average Fixed Cost
For very large levels of outputs, the AFC becomes very small but it never
reaches zero. That is why, the AFC curve never touches the X-axis.
85. Derive the short run average variable cost (SAVC) under
traditional theory of cost.
SAVC is derived from total variable cost. Under traditional theory, total
variable cost includes:
Raw materials
Cost of direct labor
The running expenses of the fixed capital such as fuel, ordinary repairs
and routine maintenance.
O X
C
Fig.7.1
ATFC
B C
AFC
AFC
O XX1 X2 X3
X1X2 X3
146
Average variable cost is found by dividing total variable cost (TVC) by the
level of output i.e. AVC=TVC/X. Graphically, AVC at some level of output is
given by the slope of the ray from origin to TVC curve at that level of output.
Derivation of Short run Average Variable Cost
In fig. 7.2, the slope of the ray on TVC goes on decreasing until point
C and increases thereafter. Thus, SAVC also decreases up to point C and then
increases. As shown in panel B of fig 7.2, SAVC is U-shaped showing the law
of variable proportions.
86. Derive the short run marginal cost (SMC) under traditional cost
theory.
Marginal cost is defined as the change in total cost which results from a unit
change in output. It is the cost of production of one extra unit or marginal unit.
Mathematically, the marginal cost is the first derivative of the total cost
function. Symbolically MC= C/X
AVC
O
C
Fig.7.2
TVC
O
ab
c
d
x1 x3 x4x2
a
b
c dSAVC
X
X
(A)
(B)
147
Derivation of Short-Run Marginal Cost
Graphically, MC is the slope of TC curve. The slope of a curve at any
point is the slope of tangent at that point. With an inverse S-shaped TC curve,
the MC will be U shaped as shown in fig 7.3(A). The slope of the tangent to the
total cost curve declines gradually up to X3 level of output at which the slope is
minimum. After X3 level of output, the slope of tangent again rises.
Consequently, SMC falls up to X3 level of output, becomes minimum at X3
level of output and then rises thereafter.
87. What is the relationship between AFC, AVC, MC and ATC?
The SAVC is a part of SATC, given SATC= SAFC+SAVC. Both SATC and
SAVC are U-shaped, following the law of variable proportions. However, the
minimum point of SATC occurs to the right of the minimum point of the
SAVC. This is because SATC includes AFC and AFC falls continuously with
OMC
C
Fig.7.3
TC
O x1 x3x4x2
a
b
cd
SMC
X
X
(A)
(B)
148
increase in output. Even after the SAVC has reached its lowest point and has
started rising, the rate of change in the rise in SAVC is slower initially which is
offset by the rate of fall in AFC so that SATC is falling even after SAVC rises
slowly. However, after a point, the rate of increase in SAVC becomes rapid
which more than offsets the fall in AFC as such SATC starts rising. The
distance between SAVC and SATC goes on diminishing as they both rise but
they never meet each other. Thus, SAVC approaches the SATC asymptotically
as X increases. The reason behind this is the continuously falling AFC.
In the fig 7.4, the minimum point of SAVC is reached at X1 level of output
while the SATC is at its minimum point at X2 level of output. Between X1 and
X2, the fall in AFC is greater than the rise in SAVC so that SATC is falling.
After X2 level of output, the rise in SAVC wins the fall in AFC so that SATC
itself rises. On the rising part, SAVC rises more rapidly than the SATC curve
and SATC and SAVC becomes closer and closer but they never meet each
other.
Relationship between MC. AVC and ATC.
The SMC cuts SATC and SAVC at their lowest points. To show this:
Consider,
AC= TC/X
Or, AC.X = TC
Or, TC = AC.X
Or, dTC/dX= AC.(dX/dX)+X.d(AC/dX) (Product Rule)
Or, MC = AC+X.dAC/dX
Or, MC= AC+X.slope of AC.
C
XO
SAVC
SMC
SATC
AFC
Fig.7.4
x1 x2
149
If AC is falling, slope of AC is negative, then MC<AC.
If AC is at minimum, slope of AC is zero, then MC=AC.
If AC is rising, slope of AC is positive, then MC>AC.
88. Derive the long run average cost (LAC) and long run marginal
cost curve (LMC) with five alternative plants.
The long run average cost curve(LAC) is derived from the short run cost
curves. Each Pont on LAC corresponds to a point on the short run cost curves
which is tangent to LAC at that point.
Suppose that the available technology has five alternative sizes of
plants represented by SAC1, SAC2, SAC3, SAC4 and SAC5 in fig. 7.5. If the
producer wants to produce output X1, he produces with plant I. If the market
demand is OX2, he can produce with either plant: I or II but if he expects that
market demand goes beyond OX2, he will install the second plant because if he
produced from first pant any output larger than OX2, per unit cost will be
higher. Similar considerations will be taken if he expects that market demand
goes on increasing.
Derivation of Long-Run Average Cost
In fig 7.5, the curve SAC2 is lower than SAC1, implying internal economies of
scale and traditional theory of the firm assumes that economies of scale exists
only up to a certain size of plant (SAC3 in fig 7.5). After the optimum plant is
reached, there are diseconomies of scale arising from managerial inefficiencies.
C
XO
LAC
Fig.7.5
x1 x2
SAC1
SAC2
SAC3
SAC4
SAC5
x3 x4 x5x6
x7 x9x8
150
Given the five plants only, the LAC is the discontinuous curve with
scallops as shown by the bold faced curve. But it is assumed in traditional cost
theory that each plant is designed to produce optimally a single level of output.
So, there are an infinite number of plants each producing optimally a single
level of output and as there exists such infinite SACs. In such a case, the LAC
is a smooth continuous curve touching the all SACs at a single point only.
It can be seen in the figure that below the output X5, the SACs are
tangent to LAC at their falling portions implying economies of scale. Similarly
after OX5 level of output, the SACs are tangent to LAC at their rising potion
implying diseconomies of scale and at the optimum plant size; the minimum
point of SAC is tangent to LAC.
Any point below LAC is economically desirable because it implies a
lower unit cost but it is not attainable in current state of technology and with
the prevailing market price of factors of production. Any point above the LAC
is inefficient in the sense that it shows a higher cost for producing the
corresponding level of output.
Finally, the LAC curve is the panning curve of the firm and serves as a
guide to the entrepreneur in his planning to expand production in the future.
The long run Marginal cost (LRMC) is also derived from short run
marginal cost curves but it does not envelope the latter as in the LAC. The
LRMC goes from the points of intersection of short run marginal cost curves
with vertical lines drawn from the point of tangency of the corresponding SAC
curve to LAC. The LMC must equal the SMC at the output at which LAC is
tangent to the corresponding SAC. This is shown in fig.7.6.
Derivation of Long-Run Marginal Cost
C
O
LAC
Fig.7.6
x1
SMC2
SMC4
SMC3
x2 x4
SAC2
SAC4SAC3
LMC
SMC1
SAC1
SMC5
SAC5
x3 x5
ab c
d
e
151
At X1 level of output, SAC1 is tangent to the LAC. The point ‘a’ is the point of
intersection of the vertical line from the point of tangency and SMC. So, point
‘a’ is a point of the LMC. Similarly, at X2 level of output, point b is the point of
the LMC and at X3 level of output; point c is the point of LMC. By generating
and joining such points, we get the LMC curve as shown in fig.7.6.
It is obvious that the curve is below LAC for output less than X3,equal to LAC
for output X3 and greater than LAC for output larger than X3. Thus, the
properties of LMC are similar to that of SMC: when LAC is falling, it lies
below LAC, when LAC is at minimum, LAC equals LMC and when LAC is
rising, LMC lies above LAC. At the minimum point LAC, the following
condition is fulfilled.
SAC3=SMC3=LAC=LMC.
89. Write a note on modern short run cost theory.
In modern theory also, short-run costs are divided into fixed and variable
cost.
i.e. ATC= AFC+AVC
Average fixed cost includes:
Salaries and other expenses of the administrative staff.
Salaries of the staff directly involved in production but paid on fixed
term basis.
Wear and tear of machinery.
Expenses for building depreciation and repairs.
Expenses for land depreciation and maintenance
Unlike in traditional theory, here it is assumed that firms choose a
plant with flexible capacity i.e. a plant with built in reserve capacity. The firm
wants reserve capacity for the following reasons:
To meet the seasonal increase in demand.
To avoid loss of production due to breakdown and repairs.
To allow minor changes in product.
In this case, the firms will not necessarily choose the plant which will give
them today the lowest cost but rather that equipment which will allow them the
greater possible flexibility for minor changes in their product.
Due to reserve capacity, the AFC will be as shown in fig 7.7. The firm
has some largest capacity units of machinery which sets an absolute limit to the
short-run expansion of output which is boundary B in fig 7.7. The firm has also
some small unit machinery which sets a limit to expansion. (Boundary A in fig
7.7). This however is not an absolute boundary because the firm can increase
its output in the short run until the absolute limit B is encountered either by
playing overtime to direct labor for working longer hours (in this case the AFC
is shown by the dotted line in fig 7.7) or by buying some additional small unit
152
type of machinery ( in this case the AFC curve shifts upwards and starts falling
again as shown by the dashed line ad in fig 7.7).
AFC in Modern Cost Theory
Average variable cost includes:
Direct labor.
Raw materials
Running expenses of the machinery.
The SAVC in modern theory has a saucer-shaped curve that is broadly
U shaped but has a flat stretch over a range of output. The flat stretch
corresponds to the built in reserve capacity of the plant. Over this stretch, the
SAVC is equal to MC, both being constant per unit of output. To the left of the
flat stretch the MC lies below the SAVC. The falling part of the SAVC shows
the reduction in cost due to the better utilization of the plant and rising
productivity of the variable factor labor. The increasing part of the SAVC
reflects reduction in labor productivity due to the longer hour of work, the
increase in the cost of labor due to overtime payment, the wastes in raw
materials and the more frequent breakdown of machinery as the firm operates
with overtime or with more shifts.
Average Total Cost: The SATC is obtained by adding AFC and AVC at each
level of output. The ATC falls continuously up to the level of output XA
(Fig7.8) at which the reverse capacity is over. After that level of output, ATC
will start rising. The MC will intersect the ATC at its minimum point. The
SATC is shown in fig 7.8 below.
Fig.7.7
O X
CA B
xA xB
AFC
153
SATC in Modern Cost Theory
90. Write a note on long run cost under modern theory of cost.
Modern theory of cost has a different view about the shape of the long run
costs than the traditional theory. According to modern theory, the long run
costs are not U-shaped, rather they are roughly L-shaped. It implies that the
average cost in the long run falls continuously and may remain constant for a
large level of output but it never rises. The total costs are divided into
production costs and managerial costs. The production cost falls in the
beginning but continuously with increase in output. On the other hand,
managerial cost also falls but at very larger scale of outputs, managerial cost
may rise but the fall in production cost more than offsets the increase in
managerial cost. So, the total average cost falls continuously.
The production cost falls steeply in the beginning and then gradually due to
technical economies of larger scale production. In the beginning, such
economies exist in large amount but after a certain level of output is reached all
or most of such economies are attained and the firm is said to have reached the
minimum optimal scale, given the technology of the industry. If new method of
production is innovated for producing even larger output and they are more
efficient, the LAC falls forever. Such economies are realized in the form of:
Economies from further decentralization and improvement in skill.
Lower repair costs may be attained if the firm reaches a certain size.
O X
C
xA xBFig.7.8
MC
SAVC
SATC
AFC
154
The firm may produce some of the raw materials or equipment which
it needs by itself.
Managerial cost falls in the beginning but may rise at very larger scale of
output but very slowly.
In summary, production cost falls smoothly at very large scale while
managerial cost may rise only slowly at very large scale but the fall in technical
cost more than offsets the probable rise of managerial cost so that the LRAC
curve falls smoothly or remain constant at vary larger scale of output.
Derivation of LAC:
In modern theory also, the LAC is derived from the SACs but here the
LAC does not envelope the SACs. Rather the LAC intersects the SACs at their
load factor points. The load factor point is the operation level of the whole
capacity. For example, the load factor point of ½ implies that the plant is
operating at half of its total capacity level. Taking the typical load point of
each plant as two third of its full capacity (which is taken as the most general
case in business), the LAC has been derived in fig.7.9 below. In the figure, the
SACs have met the LAC at their load factor point of 2/3.
LAC in modern theory has the following characteristics:
It does not rise even at very large scale of output.
It does not envelope the SATC curves rather intersect them at the
point defined by the typical load factor point of each plant.
LAC in modern Cost Theory
Now, two cases are likely to appear about the shape of LAC and LMC in
modern theory.
If LAC falls continuously and smoothly at large scale of output; the
LMC will lie below the LAC at all scales. (fig. 7.10).
O X
C
Fig.7.9
LAC23
23
23
23
155
If LAC remains constant after a certain large level of output, the LMC
lies below LAC until the minimum optimal scale is reached and equals
LAC thereafter (fig7.11)
91. Derive the cost function from production function.
“The behavior of the cost function is derived from that of production
function.” Discuss.
The cost of production per unit of the commodity is determined by the
production function under which the commodity is being produced. Thus,
information about per unit cost can be obtained from the production function.
That is why, cost functions are derived functions. They are derived from
production functions. We below derive the cost function graphically as well as
mathematically.
Graphical Derivation
Graphically, cost curve is determined by points of tangency of
successive iso-cost line with higher iso quants.
The following assumptions underlie our analysis:
The production function shows constant returns to scale.
Price of labor hour is Rs. 5.
Price of capital /machine hour is Rs 10.
Assume that the following three methods of production only are available
under the given technology.
XXO O
LAC
LAC
LMC
LMC
X
CC
Fig.7.10 Fig.7.11
Labour hours
Capital hours
P1
1
2
P3
2
1
P2
2
3
156
Clearly, among the three methods, the least cost method is process 3 which will
be chosen by a rational entrepreneur. The product expansion path is shown in
fig 7.12 which is formed of the points of tangency. The TC may be drawn from
the information provided by the points of tangency. For example,
At point a, X=5 and TC= 100
At point b, X=10 and TC= 200
At point c, X=20 and TC= 400, etc
By plotting the information from fig. 7.12 in a graph on which we measure
output and total cost on X and Y axes respectively, we get a straight line total
cost function as derived in fig. 7.12.
Mathematical Derivation
To derive the cost function from production function, we need two
tools: production function and iso-cost line. Assume that the production
function Q = f(L,K) and isocost line is C=wL+rK
The Procedure
Step 1 Maximize the production subject to cost constraint.
ie. Maximize Q = f(L,K)
Subject to C=wL+rK
Step 2 From first order condition of maximization find input demand function
in the form:
L=L(w,r,C)
K=K(w,r,C)
Step 3 Substitute the value of L and K in the production function and solve for
C to get, C=(Q,w,r)
Total cost
Labour cost
Capital cost
P1
5
2025
P3
10
1020
P2
10
3040
K
O L
400
300
600
700
800
900
1000
510
15
20
25
30
35
40
100 200
500
45
50
Fig.7.12
Output
TC
a
b
c
d
5 10 15 20 25
100
200
300
500
400
TC
Fig.7.13
O
157
One concrete example:
Let Q= AKL ; A>0, , >0 are parameters.
Then, our statement of the problem is
Maximise Q = AKL
Subject to C=wL+rK
The combined Lagrange function is
V= AKL+ (C-wL-rK)
The first order conditions for maximization are:
)......(....................0
)......(....................0
)......(....................0
1
1
iiirKwLCV
iirLKAL
V
iwLAKL
V
From (i) and (ii) on division.
).......(**..........Kw
rL,And)........(*..........L
r
wK
wLrKr
w
L
K
Substituting (*) in (iii), we get,
01wLC,or
0Lr
w.rwLC
)iv.........(.....................w
CL,or
CwL,or
Which is labor demand function.
Similarly substituting relation (**) in eqn (iii).
rC rK w. K 0
w
or,C rK 1 0
or, rK C
Cor,K . .............................(v)
r
Which is capital demand function.
158
Substituting relation (iv) and (v) in the production function,
Q= AKL we get,
C CQ A . . .
r w
1 1or,Q AC . . .
r w
Raising both sides to the power1/(+), we get.
.A.r.w.QC,or
...w.r.Q
A
1C,or
.w
1..
r
1Q
A
1C,or
.w
1..
r
1CAQ,or
11
1
1
1
1
11
Putting + = R( Returns to scale) we get,
R1
R
1
RRR
1
ARK,Let
R.A.r.w.QC,or
we have, C=KQ1/R
.w/R
.r/R
or, C=(Q,w,r) which is the required cost function. This cost function shows
that the total cost of production depends on the amount of output produced and
the prices of factors of production: wag rate and interest rate or rental of
capital. But if we assume perfect competition, the prices of factors of
production are given. Thus, we can write the cost function as C=f(Q).
92. What is the significance of cost function in decision making?
The shape and position of the cost function plays a vital role in business
decision making and even for the government regulation. The primary
importance lies in the price and output determination of the business units and
the long term planning for the growth of the firm in the long run.
In summing up, the importance of the shape of the cost curve can be
summarized as below:
Cost and Price Output Decisions: The shape of the cost function is
very much important in the price and output determination in all
market forms. In perfectly competitive market, it is necessary that the
159
curve must be U-shaped otherwise the output level cannot be
determined. Similarly, in other forms of market like monopoly,
monopolistic competition, oligopoly, etc, the equilibrium condition
MR=MC is used explicitly in the price and output determination and
the MC must be upward sloping. In collusive oligopoly, the position
of the cost function determines the bargaining power for quotas and
even in non-collusive market; cost function is used explicitly in price
determination. Similarly, in all other market price output
determination models that are recently developed, the shape and
position of the cost curve plays a vital role for the price and output
determination.
Cost and Barriers to Entry: The shape and position of the cost curve
is one of the most important determinants of the price level that
effectively prevents the entry of new firms to the market. If a firm has
lower cost, it can prevent the entry by keeping the price level low.
Therefore, the lower the cost level, higher is the power to create the
barriers to entry.
Cost and Market Structure: The structure of the market also
depends on the shape of the cost function to a large extent. If the size
of the market is fixed and the firms can enjoy large economies of scale
as they expand their output, only few firms are likely to exist in the
market and the market is most likely to be an oligopolistic one. On the
contrary, if the economies of scale are not so much important, a large
number of firms will exist in the market and it is likely to be a
monopolistic one.
Cost and Growth Policy of the Firm: The shape of the cost curve
determines the growth policy of the firm too. Since LAC is the
planning curve of the firm, the long run investment depends on the
shape of the LAC. Therefore, the cost curve is the most significant
determinant for determining where to invest how much by the firm.
Cost and the Regulation of Industry:
The knowledge of the cost curve helps the policy makers and
government regulatory agencies in the regulation of the firm. The
regulatory authorities may merge small firms into a large one or may
decompose a large firm into a number of small firms. One of the most
important factors that helps in this decision making is the shape and
position of the cost curves. If there are too many small firms in an
industry in which economies of scale can be obtained in large amount
only when the output size is large, the government can merge the
160
small firms to make large ones. On the other hand, if economies of
scale are not so much obtainable, the government may decide to adopt
polices aiming at the reduction of the size of firm.
93. Analyze the economies of scale.
The benefits (reduction in per unit cost) which a firm gets as it expands its
plant size or as it increases the level of production are called economies of
scale. Such economies are obtained in the form of increase in the efficiency of
the factors of productions, cheaper raw materials, different marketing
economies, etc. The economies may occur to the firm from within it or from
external sources. The former are called internal economies and the latter are
called external economies. However, for simplicity purpose, economies of scale
are distinguished into real economies and strictly pecuniary economies of scale.
i) Real Economies: Real economies are associated with the reduction in the
physical quantity of inputs, raw materials; various types of capital for
producing one unit of output as the production expands .The following types
may be distinguished:
Production Economies.
Selling and Advertising Economies.
Managerial Economies
Transport and Storage Economies.
a) Production Economies: It arises from labor capital and inventory.
Labor Economies: It consists:
Division of labor.
Automation of the production process.
Time saving
Cumulative volume economies
Technical Economies: it arises from:
Specialization and indivisibilities of capital
Set up costs.
Initial fixed cost
Research capacity requirements
Technical volume input relation between cost and output.
b) Selling and Marketing Economies:
These economies are associated with the distribution of the product.
The main types of such economies are:
Advertising economies
Model change economies
Economies from special arrangements with exclusive dealers.
Spread of overhead cost is smaller e.g. R/D for changing model.
c) Managerial Economies:
161
Managerial economies come partly from production cost and partly
from selling cost. Managerial economies come from:
Specialization of management (e.g. Finance manager, production
manager, etc.)
Mechanization of managerial function: (Through telephone, fax,
T.V. screens, computer, etc).
d) Transport and Storage Economies:
If production is in large quantity, per unit transport and storage cost
will fall continuously.
ii) Pecuniary Economies of Scale:
Pecuniary economies are realized by paying lower prices for factors
used in the production and distribution of the product due to buying in large
amount as its firm size increases. These arise from:
Lower price of raw material (Due to special discounts)
Lower cost of external finance: Banks usually offer loans to larger
corporation at a lower rate of interest and other favorable terms.
Lower advertising cost
Lower transport cost
Lower wages to the workers: Often large firms have monopolistic
power or due to prestige associated with the employment by a large
well known firms.
94. Why is the short run average cost U-shaped?
In the short run, all the factors of production cannot be changed: there are
some fixed factors which are combined with the variable factors of production
to produce the output. This leads to the operation of the law of variable
proportion in the short run which is the cause of the U shape of the SATC in
the short run. We know that among the three stages of production, average
productivity of the variable factor increases in the first stage which implies that
the per unit cost decreases continuously because less amount of labor is
required to produce one unit of output. When the APL is at the maximum point,
the ATC reaches its minimum point. As productivity of the variable factor
starts falling, the ATC starts rising. That is why the shape of AVC and ATC is
U-shaped in the short run. The relation between APL and ATC has been
explained in the fig7.14 below.
162
95. Why is the long run average cost U-shaped?
In the long run, all the factors of production are variable and the firm
can install the desired plant depending on the market size. As the firm expands
output by increasing all the factors of production, it may gain internal and
external economies of scale. Economies of scale are the benefits in terms of the
reduction in per unit costs as the firm increases the size of output. According to
the traditional theory of cost, the firm enjoys economies of scale until the
optimum plant size is reached. Due to these economies of scale, the LAC falls
initially until the optimum plant size is reached. The optimum plant size is the
one which has the lowest per unit cost of production. We may classify this
phenomenon as the law of increasing returns to scale also. Thus, the reason
behind the fall in the LAC in the initial stage is the economies of scale or the
operation of the increasing returns to scale. But after the minimum optimal
plant is reached, the diseconomies of scale appear. Due to the diseconomies,
per unit cost rises and the LAC rises upwards. This phenomenon may be called
the diminishing returns to scale. The U-shaped LAC has been shown in fig.
7.15
X1 Q
SAC
O
Fig.7.14
Q
AP
O
SAC
AP
Rising AP
Ecomonic ofScale or IRS
Disecomonic ofScale or DRS
Optimal Plant Size
X1 Q
LAC
O
LAC
Fig.7.15
163
Thus, it is the appearance of the economies and diseconomies of scale
that creep in the long run production process which gives rise to the U-shaped
LAC.
96. Discuss about the empirical evidences on the shape of the cost
curves.
A number of studies have been carried out to know about the shape of the
cost curves in the short run and long run. Most of the studies have found that
the total variable cost in the short run is a positively sloped straight line. The
reason for this is that is that the average cost (AC) and marginal cost (MC)
remain constant over a range of output. Similarly, they have found the long run
average cost curve to be roughly L-shaped; falling steeply in the beginning and
remaining constant after a certain level of output. We can below summarize the
empirical studies:
(a) Statistical Cost Studies:
In these studies, the cost curves are found with the help of statistical
data collection and estimation. For example:
C = b1x+u
Where, C = Total variable cost (TVC)
x =Level of output
u = random error term
To estimate this cost function, first data relating to the output level and
TVC is collected and the cost function is estimated with the help of regression
analysis. The AVC and MC remain constant in this case.
AVC = C/x= b1
MC =dC/dx= b1
This type of cost studies have been criticized on the basis of lack of data,
selection of appropriate variables, problem of interpretation, etc.
(b) Studies Based on Questionnaires
Among these cost studies, the study by Eliteman and Guthrie is very
remarkable. They asked different firms about the shape of the cost
curves and concluded that the total cost curve does not rise in the long
run rather it remains constant. However, this has been also criticized
from different perspectives.
(c) Statistical Production Functions
These studies have estimated the production functions and found that
the production follows constant returns to scale which also implies
that cost remains constant during the certain range of output. These
studies have also been criticized from different angles.
164
(d) Engineering Cost Studies
These studies have first estimated the production functions and then
derived the cost functions therefrom. Cookenboo has concluded on such a
basis that the long run cost falls continuously. But these types of studies
have covered the production cost only and other types of costs like selling
costs, administrative and managerial costs, etc have been ignored.
(e) Studies using the Survivor Technique
The pioneer for this technique is George Stigler. This technique is
based on the Darwinian principle of ‘Survival of the Fittest’ according
to which the low cost firms only exist in the long run.
Stigler’s study shows that the long run cost remains constant during a certain
range of output.
This technique is based on the following assumptions:
All firms have same objective.
Factor prices and technology are given.
Perfectly competitive market
All firms operate in the same environment
The long run cost curve as estimated by Stigler with the data from steel
industry in US is presented in fig…… below.
This technique has also been criticized on different grounds.
Thus none of the empirical study supports the view of the traditional theory
that the long run cost rises in the long run to produce the U-shaped cost curves.
Size of firm (% of industry capacity)
O
AC
Fig.7.16
LAC
5 25
165
CHAPTER 8: PERFECT COMPETITION
97. Define perfectly competitive market. What are the assumptions
underlying it?
Perfect competition is a market structure defined by complete absence of
rivalry among the individual firms. According to Brigham, "Perfect
competition market structure is characterized by a large number of sellers and
buyers each of whose transactions is so small in relation to total industry
output that they can not affect the price of the production."
In reality, perfect competition never exists because the real world is
characterized by imperfect competitions. For the time being, we can assume
that the market of basis essentials like rice, wheat could be perfectly
competitive but when we probe into them, we find heavy imperfections in those
markets. Therefore, this form of market structure can never be realized. For this
reason, some economists have called it a myth.
Even then, study of it is necessary because:
If furnishes us with a simple and logical starting point for economic
analysis.
A high degree of such competition exists in the real world.
It provides a norm against which actual performance of the economy
can be evaluated.
It helps us to understand the working of non-competitive market and
establishes a benchmark for regulator which function in a non-
competitive market.
The model of perfect competition is based on the following assumptions.
Larger Number of Buyers and Sellers: There are a large numbers of
buyers and sellers in the market. That is why a firm's output is very
small share of the total market and as such it cannot affect market
price. Thus, price level is given for a firm.
Product Homogeneity: Product homogeneity implies that the
products of all firms in the market are identical in technical respects
like weight, size, ingredients, taste, etc as well as the services related
to the selling and delivery of the products. Therefore, product
differentiation is not allowed here.
Free Entry and Exit: The firms in this type of market are free to
leave the market if they incur losses and new firms are free to enter the
166
market if they want. However, entry or exit happens in the long run
only.
Profit Maximization: The only goal of the firm is profit
maximization.
No Government Intervention: The government does not intervene
the market in the form of regulation like tariffs, subsidies, rationing of
the production and rationing of demand and so on.
Perfect Mobility of Factors of Production: There is perfect
competition in the factor market. Factor of production can move freely
between firms, industries, raw materials and other factors are not
monopolized.
Perfect knowledge: This is the most unrealistic assumption. It implies
that buyers and seller have complete information about the present and
future conditions of the market. There is no uncertainty.
Thus, perfectly competitive market is a market where there are a large numbers
of buyers and sellers, the sellers sell homogenous product, there is no
intervention from the government and both parties of the market have perfect
knowledge about the present and future conditions of the market.
98. Discuss the short run equilibrium of a perfectly competitive firm.
First define perfect competition and write the assumptions in one paragraph
in brief.
The firm is in equilibrium when it maximizes profit. Profit is defined as the
difference between revenue and cost i.e, = R-C
The equilibrium of the firm can be analyzed under two approaches:
TR/TC approach:
The firm is in equilibrium when the output level is such that the profit of the
firm is maximum. In other words, when the profit earned (gap between revenue
and cost) is maximum, the firm is said to be equilibrium. The TR curve here is
a straight line through origin implying that the firm are only price takers. The
TC curve is inverted S-shaped reflecting the law of variable proportions.
The firm's equilibrium is at output level Xe, where the vertical
distance between TR and TC is maximum at which profits are maximum as
shown by the profit curve in fig. 8.1. Geometrically, it happens when the slope
of TR and TC are equal however it is not sufficient condition.
167
Short-Run Equilibrium
MR/MC approach:
The AR curve or price curve is a horizontal straight line because in this type of
market price is given for a firm. Thus, marginal revenue, average revenue and
price are identical i.e. MR=P=AR. The short run cost curves are U-shaped
reflecting the law of variable proportion.
Graphically,
The necessary condition for equilibrium is that marginal revenue must equal
marginal cost. In fig. 8.2, MR = MC condition is fulfilled at point e where
equilibrium output is Xe and firms profit is PABe. Before Xe output, MR>MC.
in such a case the firm will increase the level of output because by doing so the
profit will increase. Similarly, after Xe, MC>MR and the firm reduces the
output level.
TR
TCTC TR
Maximum gap between TR and TC
Output
OutputX1
Xe
X2
X1
Xe
X2
O
O
Fig.8.1
168
Short-Run Equilibrium
The sufficient condition or the second order condition is that MC must be rising
i.e. slope of MC must be greater than slope of MR. In fig. 8.3 the necessary
condition is satisfied at two points e and e' but at e' the sufficient condition is
not satisfied as MC is falling. Thus, profit can be increased by moving beyond
X'e.
Mathematically,
The firms aim is to maximize = R-C, R=f(x) and C=f(x)
The first order condition for maximization of profit is that the first derivative of
with respect to x be zero.
P,C
P
A
X
MR
SMC
SAC
e
B
O Xe
Fig.8.2
MR,MC
P
X
MR
SMC
SAC
e
O Xe
Fig.8.3
e1
X1e
169
0 0R C
x x x
Where X
R
= slope of TR curve= MR and
X
C
= slope of TC curve =MC
Thus, the first order condition is MR=MC
The second order condition requires that the second derivative of
with respect to x be negative implying that profit curve is concave i.e.
2
2
2
2
2
2
x
C
x
R
x
<0
Or, slope of MR-slope of MC < 0
Or, slope of MR< Slope of MC.
Since MR is a horizontal straight line parallel to X-axis, slope of
MR=0. Thus, the second order condition reduces to slope of MC>0 i.e. MC
must be rising.
However, the firm in short equilibrium does not mean that it is earning
abnormal profits, it may incur losses also but its losses are not more than the
fixed costs.
99. Discuss the short run equilibrium of perfectly competitive industry.
The short run equilibrium of industry is achieved through the equality of
demand and supply force where the price is determined and that price clears the
market that is there is neither excess demand nor excess supply. It is important
to note that during short run, firms can not adjust themselves so as to produce at
their minimum cost. So, there may be the firms earning abnormal profit or
incurring losses even if the industry is in equilibrium.
For full equilibrium, all firms must be earning normal profit. But this
is by sheer accident, and we take only the condition that at equilibrium quantity
demand must be equal to quantity supplied whatever may be the case of an
individual firm. In fig 8.4, the equilibrium of the industry and the possible
states of individual firms is presented.
Industry Equilibrium in Perfect Competition
X
e
O
D
S
XO
XO
XO
LossProfit
SMC SAC
SMCSAC
SMC SAC
ee
e
N
P
M
P
AB
P,C P,C P,C P,C
Fig.8.4(a) (b) (c) (d)
170
100. Write a note on shut down point.
The perfectly competitive firm in the short run equilibrium does not
necessarily imply that it is earning excess profits. It may be incurring losses
also depending on the positions of its cost curves. But if the losses are so
substantial(large) that it is unable to cover its AVC, it closes production even in
the short run to minimize its losses. Such a point at which the firm closes down
in the short run is called shut down point. It can be made clear with the help of
fig. 8.5
Shut-down Point
In fig. 8.5, if the price is P2, the firm’s equilibrium is at the point e2 where the
firm is making losses. Despite the losses, the firm will continue producing
hoping to earn normal profits in the long run because by doing so the firm will
cover at least variable costs. If price falls below P1, the firm closes production
because it is not able to cover even its variable costs. Thus, by closing
production in the short run, it can minimize its losses and its losses will be
equal to the total fixed costs. That is why the last point of production, point e1
in fig.8.5.is called the shut down point of the firm.
101. Derive the short run supply curve of the firm.
The supply curve of the firm in the short run can be derived from the points
of intersections of MC curves with successive demand (=MR) curves.
Supposing that the market price rises gradually leading to an upward shift in
demand curve which cuts MC to a point to the right of the pervious point. This
implies that the firm increases its supply as the price rises. Given its SMC and
AVC, the firm will not produce if price falls such that it is not covering even its
MR2
MR1P1
P2
XX2X1
SAVC
SATC
SMC
P,C
Fig.8.5
O
e2e
1
171
AVC. In such a case, supply drops to zero. The derivation of supply curve is
presented in fig. 8.6 and 8.7 below.
Derivation of Short-run Supply Curve
Below the price P1, the firm's output falls to zero as it will close down to
minimize its losses. At price P1, the firm supplies OX1 output which defines a
point S1(X1, P1) of the supply curve. Similarly, at price P2, the firm supplies
OX2 which defines point S2(X2, P2) of the supply curve. Generating such points
for higher price levels and joining them, we get the short run supply curve of
the firm as shown by boldly inscribed curve in fig. 8.7. It indicates the quantity
of output per period of time that the profit maximizing firm would supply at
various prices. The supply curve coincides with its marginal cost curve for all
levels of output equal to or greater than the output at which AVC is minimum.
Thus, the MC curve above the minimum point of AVC serves as the short-run
supply curve in perfectly competitive market situation. The firms supply would
drop to zero at any price below minimum AVC.
Here in our analysis, we assume that as price increases, the resource
prices will not increase. This assumption is valid because a firm in perfect
competition is an insignificant part of the total market demand and its increased
demand for inputs will not have any effect on their prices.
102. Derive the Short run supply curve of perfect competition industry.
Under the assumption of given factor prices and technology, the short run
supply curve of a competitive industry can be derived by the lateral (horizontal)
summation of the supply curves of the individual firms. Since the number of
firms is very large, the industry supply at some price is equal to the sum of
quantity supplied by all firms at that price.
Supposing that all 1000 firms in the industry are alike in the cost
structure, the supply curve of the industry would be 1000 times the supply of an
P1
P2
XX2X1
SAVC
SAC
SMC
P,C
Fig.8.6
O
P3
P2
P1
P2
P3
P2
e1
e2
e3
e4
S1(P1,X1)
S2(P2,X2)
S3(P3,X3)
S4(P4,X4)
X1 X2X3 X4X3 X4
Fig.8.7
P
O X
172
individual firm. From fig. 8.8 and 8.9, we see that at price P1, supply of the firm
is OM1. Thus, supply of industry at price P1= 1000×OM1=N1. At price level P2,
industry supply will be 1000×OM2= N2 etc. Since individual supply curve (MC
curve) is positively sloped, the industry supply curve will also be positively
sloped.
However, if as a result of expansion, the input prices rise, the industry
supply curve cannot be obtained by simply horizontal summation of individual
supply curve because as input prices change, MC curve shifts each time.
i) If the prices of variable factors increase, the industry supply will be more
steeply sloped than had input prices remained constant.
ii) If prices of variable factors decrease, the industry supply curve will be less
steeply sloped than had the input prices remained constant.
Whatever the change in price, it is certain that the industry supply
curve will be positively sloped. However, its slope depended on the change in
price of the variable factors which indeed determine the MC curves.
Firms Supply Curve Industry Supply Curve
103. Analyze the long run equilibrium of perfectly competition firm.
In the long run, the equilibrium of the perfectly competitive firm will be on
the minimum point of the LAC curve and the firm can thus earn normal profits
only. Thus, the firms in the long run adjust their plant size to the minimum
point of LAC and at equilibrium point the LAC is tangent to their demand
curves defined by market price. The only reason for the normal profit in the
long run is the freedom of entry and exit in the long run. If the firms are making
excess profits, new firms will be attracted in the industry which will lead to a
fall in price and upward shift of the cost curve due to increase in the price of
factor as industry expands. This downward shift of the demand curve and the
upward shift of the cost curve will continue until the LAC is tangent to the
MR2
MR1P1
P2
XM2M1
SAVC
SAC
SMC
P,C
Fig.8.8
O
MR3P
3
P1
P2
P3
N1
(1000×m1)
Fig.8.9
short run industry supply curve
N2
(1000×m2)N3
(1000×m3)
P
XO
173
demand curve defined by the market price. If the firms are making losses in the
long run, some of them will leave the industry as a result of which price will
rise and cost may fall as the industry contracts until the remaining firms in the
industry cover their total cost inclusive of the normal rate of profit.
The adjustment to long run equilibrium is presented in fig 8.10(a) and
(b). If price is P1, the firm is making excess profit working with the plant
represented by SAC1. It will thus expand its plant size further because by doing
so, it will face with falling costs. At the same time, being attracted from the
excess profits, new firms enter the industry. The result of these actions is an
increase in production and a rightward shift of the supply curve resulting into a
fall in price. This process will continue until the price falls to P1 where the
excess profits disappear and the firm is said to reach the long run equilibrium.
The LAC in fig. 8.10(b) is the final cost curve including any increase in the
prices of factors that may have taken place as the industry expanded.
Long run Equilibrium of Firm
Thus, the condition for the long run equilibrium of the firm is that marginal
cost must be equal to the price and LAC i.e.
LMC=LAC=P
The firm in the long run equilibrium will produce at the minimum
LAC, given the technology and prices of factors of production. At equilibrium
the short run marginal cost is equal the LRMC and SAC is equal to the LAC.
Thus, the long run equilibrium condition of the firm is,
SMC=LMC=SAC=LAC=P=MR
XO
D
S
XO
SMC
SACe
P1 M
P,C P,C
(a) Industry
S1
LMCLAC
PMR1
MRSAC1
(b) firm
Xe
Fig.8.10
P1
P
174
Thus, in the long run equilibrium, all firms produce at the minimum LAC,
working their plant at optimal capacity and earn just normal profits.
104. Analyze the long run equilibrium of perfectly competitive industry.
An industry is in equilibrium when there is no tendency for the industrial
output to vary. The conditions for industry equilibrium are:
All the firms must be in equilibrium in the long run i.e. they must be
making just normal profits producing at the minimum LAC.
The number of firms should be equilibrium i.e. there should be no
tendency for the firms to enter or exit the industry.
The long run equilibrium of the industry is shown in fig.8.11 (a) and
(b) where, given the market price P, the firms are producing at their minimum
LAC earning just normal profits. The firm is in long run equilibrium at point e
because at that point, LMC=SMC=LAC=SAC=P=MR
At the price P, the industry is in equilibrium because profit is normal
and there is neither entry nor exit with all firms in the industry being in
equilibrium and with no entry and exit, the industry supply remains stable,
given the market demand and the price P is a long run equilibrium price.
Long Run Equilibrium of Perfect competitive market
105. Predict the effects of increase in fixed cost in perfectly competitive
firm and industry.
An increase in fixed cost will have no effects on the price and output
of the perfectly competitive firm in the short run because it will not affect the
MC curves. But increase in fixed cost will reduce the amount of excess profits
enjoyed by the firms. To analyze this, let us assume that fixed cost increases
which will shift both the ATC and AFC curves upwards. But it cannot affect
X
e
O
D1
S1
XO
SMCSAC
e
P,C P,C
Fig.8.11(a) Industry (b) firm
LMC
LAC
X
D
S
175
the AVC and MC curves. That is why the short run equilibrium of the firm will
not be affected by a rise in fixed cost. The same output will be produced and
market supply and price will not change in the short run.
We know that condition for equilibrium is MR=MC.
Assuming fixed cost increases by FC, we have,
Profit () = R-TVC-(TFC+FC)
Thus, for profit maximization
dx
FCTFCd
dx
dTVC
dx
dR
dx
d )(0
Or, MR-MC=0
Or, MR=MC
So, even after the change in fixed cost, equilibrium position remains
unaffected.
However, if the firm before the change in fixed cost was just earning
normal profits, it will not cover its higher average total cost and will go out of
the business in the long run. Consequently, in the long run, the market supply
will shift upwards, the price level will rise and there will be fewer firms in the
industry. This case has been presented in fig 8.12 (a) and (b) below.
Effects of Rise in Fixed Cost
106. Q.N. 10 Analyze the effects of change in variable cost.
In case of increase in variable cost, the MC will be directly affected as such
the equilibrium price rises and the equilibrium quantity falls. To analyze this,
assume that variable cost e.g. market wages rise. This will shift AVC, the ATC
and MC upwards to the left. As a consequence of this, even in the short run,
given the market demand, prices will rise. In the new market equilibrium, the
P,C
XO
SAVC
SMC
SATC
AFC
Fig.8.12
AFC1
SATC1
P
D1
D
S1
S1
S
S
e
e1P1P1
P
(a) (b)
P
X
176
number of firms will be the same but the quantity will be lower and price
higher as compared to the initial equilibrium. This has been shown in fig.8.13
also.
Effects of Rise in Variable Cost
Formally speaking, assume that the initial cost was TC= a+bx
Where a =TFC, b= AVC=MC
Let AVC increases by c units, then TC=a+bx+cx
For equilibrium, 0dx
d ; where = R-a-bx-cx
00, cbdx
dRor
Or, MR=b+c
Or, MR=MC+c
Thus, clearly, we have higher price for equilibrium.
107. Predict the effects of imposition of lump sum tax.
The effects of lump sum tax are same as the effects of the increase in fixed
cost as it is just like an increase in fixed cost. That is why imposition of lump
sum tax will not affect the AVC and MC and thus the price and output of the
firm remains unaffected in the short run. However, if the firm was just earning
normal profit prior to the tax, it won’t be covering its ATC at the going market
price and will close down in the long run. Thus, in the long run the market
supply curve will shift upwards left as firms leave the industry. In such a case,
the output will be lower and the price will be higher as compared to pre-tax
equilibrium.
Assume that the lump sum tax is Rs. T
The after tax profit is say *= -T
Fig.8.13
D1
D
S1
S1
S
S
e
e1P1
P
(b)
P
XX1 X2X1
X2
P,C
O
O O(a) X
MC1
MC
P1
P
177
Or, *= R-C-T
For profit maximization,
00*
MCMRdx
d
Or, MR=MC
Supposing that the Second order Condition for equilibrium is satisfied, we have
the same condition of equilibrium as in the case of no tax. So long as * =-
T>0, the firm is not likely to leave the industry. The lump sum tax will only
reduce the excess profit in the short run as shown in fig. 8.14 whereas the
output produced by the firm remains the same at Xe.
Effects of Lump Sum Tax
108. Analyze the effects of profit tax on perfectly competitive firm.
The profit tax is levied on the profits earned by the firm. The effects of such
a tax are same as in the case of lump sum tax. It also reduces the profit earned
by the firm but doesn’t affect the MC of the firm and hence the price and output
of the firm. However, if the firms were earning just normal profits before tax,
they will leave the industry in the long run. The long run supply would shift to
the left and a new equilibrium will be reached with a higher price, a lower
quantity produced and a smaller number of firms.
Suppose, the tax rate is t% .Then, the after tax profit will be,
**=R-C-t
Or, **=-t
Or, **= (1-t)
Or, **= (1-t) (TR-TC)
For maximum profits, dx
d ** = 0 = (1-t)(MR-MC)=0
Since (1-t)0, we must have MR-MC=0 or, MR=MC
Fig.8.14O
Before tax profit
After tax profit
ddx
=0
X
d *dx
=0
xe
178
Thus, the equilibrium is not affected in the short run. But in the long
run, it may increase price and reduce quantity produced.
109. Analyze the effects of the imposition of specific sales tax.
This tax is imposed on per unit of the commodity sold. That is why it clearly
affects the AVC, MC and ATC. If this type of tax is imposed, the MC curve
will shift upwards left and the short run supply curve will also shift leftwards.
As a result, the market price will increase and the equilibrium quantity will fall.
To analyze this, let ‘e’ be the tax per unit on output sold, then the
after-tax-profit will be,
= TR-TC-e.x
The first order condition for profit maximization requires that,
d/dx=0
0dx
exTCTRd,or
or, MR-MC-e=0
or, MR=MC+e
Assuming that the second order condition is fulfilled, with the
imposition of tax Rs. ‘e’ per unit output, the firm has higher price level and
lower quantity of output produced.
One important question is ‘how much the price will increase’. This
depends on the price elasticity of supply, given the market demand. The less
steep the supply curve, the higher the proportion of the tax that the consumer
will bear and less the burden to the firm from the specific tax. Broadly, we can
divide it into three cases:
i) If the market supply curve is positively sloped, the tax will be paid partly by
the buyer and partly by the firm. The burden of tax will be smaller for the
consumers for the steeper supply curve. It is clear from fig. 8.15(a) and 8.15(b).
Effect of Special Tax(Upward Sloping Supply Curve)
Fig.124
O X
P
P
P} tax per unit
S1
P1
S
S
D
D
X2 X1
a
b
O X
P
P
P } tax per unit
S1
S1
S
S
D
D
X2 X1
P1
b
a
(a) (b)
179
Clearly, ab tax per unit >P in both cases whereas the rise in price is higher in
panel (b) where the supply curve is less steper.
ii) If the supply curve is infinitely elastic, price will increase by the full amount
of the tax. In this case, the whole burden of the tax goes to the consumers. In
fig.8.16, P = ab i.e change in price is equal to per unit tax.
Effects of Spicific Tax(Horrizontal Supply Curve)
iii) If the supply curve is negatively sloped, the price will increase by more than
the tax amount per unit. In this case, consumers have to bear more than the tax
burden. It is shown in fig. 8.17 where the tax per unit ab < P.
Effects of Specific Tax (Downward slopping Supply Curve)
110. Derive the long run supply curve of perfectly competitive industry?
The short run supply curve of the industry is positively sloped but it may not
be so in the long run. In the long run, the industry supply curve may be
positively sloped, negatively sloped or horizontal straight line depending on the
Fig.8.16
O X
P
P
P }
tax per unit
S1
S
D
D
X2 X1
P1 a
b
S1
S
Fig.8.17
O X
P
P
P }tax per unit
S1
P1
S
S
D
D
X2 X1
a
b
180
change in factor prices as the industry output increases. We below discuss the
above three possible cases.
i) Constant Cost Industry or Horizontal Long-run Supply
Curve:
An industry is said to be a constant cost industry if the prices of factors of
production employed by it remain constant as the industry output increases
in the long run. This case has been presented in fig. 8.18(a) and 8.18(b).
Horizontal Long-run Supply Curve
We start with the initial long run equilibrium where at price P, the firms are
enjoying the normal profits and the firms are producing at the minimum point
of their LAC curve. Suppose that the demand curve shifts to D'D'. Due to this
shift, the short run price increases to P' and the existing firms increase the
output operating their plant above full capacity. The increase in quantity is
shown by a movement along supply curve SS. But in the long run, abnormal
profits due to the rise in the price level will attract new firms to the industry. As
a result, the demand for factors of production will also rise but it is assumed in
this case that the prices of the factors will not rise as a result of the increase in
their demand. That is why the LAC curve does not shift upwards. It implies that
the new firms also will produce under the same LAC curve as already
established firm. The new entry means more output which shifts the supply
curve rightwards and as such the price level begins to fall. This process will
continue until the excess profits disappear and the price level returns to the
original level of OP and the shifted supply curve S'S' intersects the shifted
demand curve at the price level OP. The long run supply curve can be drawn by
joining the points like ‘a’ and ‘b’ and the supply curve in the long run will be
parallel to the quantity axis at the initial price level.
ii) Decreasing Cost Industry or Downward sloping Long run Supply Curve:
Fig.8.18
O X
P
P
S1
P1
S
S
D
D
X2X1
a b
D1
D1
S1
Industry
LMC
SMC
LAC
SAC
FirmX
P
P1
Long-runsupply surve
O
P,C
(a) (b)
181
An industry is said to be a decreasing cost industry if the prices of factors of
production decline as the market expands output and the long run supply curve
has a negative slope.
The process of adjustment in such a case is shown in fig. 8.19(a) and
8.19(b). From the initial long run equilibrium at price P, as the market demand
shifts from DD to D'D', the price level will increase in the short run to P2 and
new firms will be attracted due to excess profits. The increase in the demand
for the factors of production due to new entry is assumed to lead to a further
fall in the prices of the factors of production. The reason for such a fall in the
prices of factors of production is specialization and innovation of new
techniques of production. As a result, the LAC will shift downwards as shown
in fig 8.19(b)
Downward sloping Long-run Supply Curve
The increased output due to new entry will shift the supply curve
rightwards. This process will continue until the excess profits disappear and the
industry equilibrium will be on a lower price with a larger quantity produced by
each firm. By joining the equilibrium points like a and b, we get a downward
sloping long run supply curve as shown in fig. 8.19(a)
iii) Increasing Cost Industry or Upward Sloping Long Run Supply Curve:
An industry is said to be an increasing cost industry if the prices of the factors
of production increase as the industry output increases in the long run and the
long run industry supply curve is positively sloped.
Such a case has been illustrated in fig.8.20(a) and 8.20(b). As the
market demand shifts from DD to D'D', price will increase in the short run to
P1. Due to the price rise, the existing firms increase the level of output by using
the plant beyond the optimal one and the new firms are also attracted to the
market. This will cause a rightward shift in the supply curve of the industry.
In this case, it is assumed that as the firms demand more inputs, their
price will rise leading to a shift in the LAC upwards. This upward shift in the
Fig.8.19
O X
P
P
S1
P1
S
S
D
D
X2X1
a
b
D1
D1
S1
(a) Industry
LMC1
SMC1
LAC2
SAC1
(b) FirmX
P
Long runsupply surve
O
P,C
SMC2
LMC2
SAC2
LAC1
P2
X1
1
P2
P1
182
LAC and the downward shift in the supply curve will continue until a new
equilibrium with normal profits is achieved at price P1 in fig. 8.20. By joining
the equilibrium points like a and b, we get the upward sloping long run supply
curve as ab in fig8.20(b)
Upward sloping Long-run Supply Curve
Thus, in an increasing cost industry, output can be increased in the
long run with an increasing supply price only.
Thus, there is no certainty as regards the slope of the long run supply curve of
the perfectly competitive industry. It may be horizontal, downward sloping or
even upward sloping depending on whether the prices of the inputs remain
constant, fall or increase with the rise in their demand as the industry output
expands in the long run.
(b) FirmFig.8.20
O X
P
P
S1
S
S
D
D
X2X1
a
b
D1
D1
S1
(a) Industry
LMC1
SMC1
LAC1SAC2
X
P
P1
Long runsupply surve
O
P,C
SMC2
LMC2
SAC1
LAC2
P2
X1
1
P2
P1
183
CHAPTER 9: MONPOLY MARKET
111. Define monopoly market.
Monopoly is a market structure in which there is a single seller and there
are no close substitutes for the commodity it produces and there are strong
barriers to entry. Thus, in a monopoly market, a single seller supplies the total
output demanded and thus has power to determine the price of the product.
Further, no substitutes are available and no firms are allowed to enter the
industry.
Reasons for a Monopoly:
Ownership of key raw materials or exclusive knowledge of production
techniques so that no other firms keeps courage to produce the output.
Patent right for product or production method will not allow any firm
to produce the output produced by the firm.
Government licensing creates barriers to entry of foreign firms which
would not encourage competition.
Natural monopoly i.e. the size of the market allows only one firm of
optimal size to operate.
Firms limit pricing policy, which creates barriers to entry usually
combined with other limiting policies such heavy advertising or
continuous product differentiation.
112. Analyze the short run equilibrium of a monopolist.
A monopolist is in equilibrium when he has maximized profit. And his profit
would be maximum when the following two conditions are met.
i) MC = MR i.e. MC equals MR.
ii) The slope of the MC is greater than slope of MR at the point of intersection.
The equilibrium condition is same as in perfect competition but here
MR does not equal the price and is always less than price.
The equilibrium of the monopoly firm has been shown in fig. 9.1
below where the equilibrium has been established at point e which satisfies
both of the above conditions required for equilibrium. This has determined the
equilibrium price as Pm and equilibrium quantity is Xm. The monopolist earns
abnormal profits as shown by the shaded area ABCPm. Unlike in perfect
184
competition, the monopolist faces two decisions i.e. he faces two policy
variables: price and output. But he cannot determine both simultaneously.
Short run Equilibrium of Monopoly
He will either fix the price level and sell the amount that the market
will buy at that price or he will produce the output defined by the intersection
of MR and MC which will he sold at corresponding price Pm. Thus, the
monopolist cannot decide both the policy variables independently and
simultaneously. The necessary condition for the equilibrium of the firm or for
the profit maximization of the firm is the equality of his MR and MC provided
that MC cuts the MR from below.
The short run equilibrium of the monopoly firm can be analyzed with the help
of calculus. For this, let the demand curve for the product of the firm be x =f(P)
which may be solved for P as P=f(x) and let the cost function be C=f(x)
Since the goal of the firm is profit maximization, we have to maximize =R-C
Where = profit R= revenue=f(x) and C= cost =f(x)
The first order condition for maximum requires that,
d0
dx
dR dCie. 0
dx dx
Here dx
dR slope of TR= MR and
dx
dCslope of TC=MC,
Thus, the condition becomes MR=MC
The second order condition requires that the second derivative of
with respect to x be negative i.e.
Fig.9.1O X
P,C
D
MR
SACSMC
Xm
A B
CPm
e
185
0
dX
Cd
dX
Rd,or
0dX
d
2
2
2
2
2
2
2 2
2 2
d R d Cor,
dx dx
d dor, (MR) MC
dx dx
Slope of MR< Slope of MC
This implies that MC curve must intersect the MR curve from below. 2
2
d0
dx
also, this implies concavity of profit curve.
113. Q.N. 3. Why is the MC curve not the supply curve for monopolist?
In case of perfect competition, the upward sloping MC curve above the
minimum AVC itself is the short-run supply curve. But in case of monopoly,
this is not necessarily so. This is because there is no unique relation between
the MC curve and the amount supplied. The monopolist firm can sell different
amounts of output at the same price, given his MC and on the other hand, it can
sell the same quantity of output at different prices, given his MC, depending on
the price elasticity of demand curve. That is why, no unique relationship can be
derived about the price and quantity supplied from the nature of MC. In fig 9.2,
the quantity X will be sold at price P1 when demand is D1 and will be sold at
price P2 when the demand is D2
. Fig.9.2
O X
P,C
SMC
P2
D2
MR2
MR1
D1
P1
x
186
Similarly, given his MC, the monopolist can sell various quantities at
the same price. It is shown in fig. 9.3. The cost condition is represented by
SMC. Given the MC, the monopolist would supply OX1 quantity if market
demand is D1 and at the same price will supply OX2 if the market demand is
D2.
Thus, the monopolist's MC need not give the supply curve of the monopolist as
this depends on the elasticity of demand.
114. Analyze the long run equilibrium of the monopolist.
In the long run, the monopolist has choice to expand his plant or to use his
existing plant at any level to maximize his profit. With entry blocked he may
not reach the optimal scale i.e. to expand his plant size until he reaches the
minimum point of LAC. Neither is there any guarantee that he will use his
plant at optimum capacity. These all decisions depend on market demand. But
if he makes losses in the long run he will closed down. He will most probably
earn supernormal profit even in the long run, given the entry is barred.
However, he may reach the optimal scale remain on a sub optimal scale (falling
LAC) or go beyond the optimum scale, i.e. expand beyond the minimum LAC
depending on the market condition.
i) Underutilization of Capacity:
If the market size is not so large as to support the production that occurs when
the firm produces by operating at the minimum point of LAC, the long run
equilibrium of the firm will be on the falling part of LAC where the firm uses a
non-optimal plant and underutilize it. This case has been depicted in fig. 9.4.
Fig.9.3
O X
P,C
SMC
MR2
MR1
D1
D2
e1 e2
P
x1
187
Under Utilization of Capacity
ii) Over Utilization of Capacity:
If the market size is so large that the firm must build a plant larger than the
minimum LAC, the SRAC will be tangent to the rising part of LAC. Thus, in
case of high market demand, the firm in the long run may install a more than
optimal size plant and overutilise it. This is often the case faced by public
utility companies operating at the national level. Such a long run equilibrium
situation has been presented in fig. 9.5 below.
Over Utilization of Capacity
iii) Optimum Utilization:
Sometimes the market size will be just sufficient to make the firm reach the
optimal size plant. In such a case, the firm will produce with the optimal plant
size, and in this case the plant will be fully and optimally utilized. In this case,
the long run equilibrium of the monopoly firm will be established on the
minimum point of the LAC curve. This case has been depicted in fig. 9.6
Fig.9.4O X
P,C
D
MR
P
e
A B
CSMC
SAC
LMCLAC
X
ExcessProfit
Fig.9.5O X
P,C
D
MR
P
eA
B
C
SMCLMC
SAC
X
ExcessProfit LAC
188
Optimum Utilization of Capacity
Thus, it is obvious that any of the three cases may arise in the long run
depending on the size of market demand, given the technology. There is no
certainty to reach the optimal scale as in pure competition. Here, the firm may
be in the long run equilibrium on the falling LAC, on the minimum point of
LAC or even on the rising part of LAC. This all depends on the size of market
demand.
115. What are the effects of increase in fixed cost in monopoly market
structure?
In case of monopoly market structure also, an increase in fixed cost cannot
affect the short run equilibrium of the firm because it cannot affect the variable
cost as well as marginal cost. This result is the same as in the case of perfect
competition. But in the long run, if the increase in fixed costs are not covered
by the amount of excess profits earned by the firms, the firm will close down
because in that case the demand curve of the firm lies above the SATC curve so
that the firm has to suffer losses at all levels of output. Thus, the increase in
fixed cost does not have any impact on the short run equilibrium, it only
reduces the amount of excess profits but in the long run it may compel the firm
to close the production.
Q.N. 6. What are the effects of increase in variable costs in monopoly?
An increase in variable cost clearly affects the marginal cost of the firm and
thus the short run equilibrium of the firm is clearly affected. An increase in
variable cost shifts the MC curve upwards and thus the equilibrium price will
rise with a reduction in equilibrium quantity. This effect is also same as in
perfect competition but the change in price and output will be greater in pure
competition than in monopoly. The reason behind this is the fact that in perfect
O X
P,C
D
MR
P
eA
B
SMC
SAC
LMC
LAC
X
ExcessProfit
Fig.9.6
189
competition, AR=MR=Price=MC and in monopoly MC=MR<AR. This has
been illustrated in fig. 9.7 and 9.8.
Effects of Rise in Variable Cost
Clearly, PC>PM and XC>XM. So, we can conclude that the price and
employment changes caused by change in variable costs will be higher in
perfect competition than in pure monopoly, given the market demand.
116. Predict the effect of Lump sum tax.
The imposition of lump sum tax is something like increase in fixed cost.
Thus, in case of imposition of such type of tax, the short run as well as long run
equilibrium of the firm is not affected. It only reduces the amount of excess
profit of the firm. But if the tax amount exceeds the excess profits, the firm
closes down in the long run.
Formally,
Assume the amount of lump sum tax = Rs T.
Thus, after tax profit is = R-C-T
The first order condition for profit maximization,
00 dx
dT
dx
dC
dx
dR
dx
d
Or, MR=MC
Which is same condition as the before tax case. Thus, the equilibrium
conditions do not change so long as the tax does not exceed the supernormal
profit of the firm.
117. What are the effects of profit tax in monopoly?
The effects of profit tax are same as in the case of lump sum tax. Profit tax
takes away some part of the excess profit of the monopolist and does not affect
the marginal cost. That is why profit tax also has no effect on the equilibrium
Fig.9.7
O X
P
PC
XC
P2
P1
X1
X2
DS2
S2
S1
S1
Fig.9.8
O X
P
D
MR
Xm
Pm
P2
P1
X2
X1
MC1
MC2
190
of the firm. But if the profit tax is imposed on such a way that the monopolist
cannot earn even normal profit, the firm will close down.
To illustrate this fact, assume that tax is t % of the profit. Then, after tax profit
is =(1-t)(R-C)
For maximization, 0)1(0
dx
dC
dx
dRt
dx
d
Or, (1-t)(MR-MC) = 0
Since (1-t)0, so MR-MC=0 or, MR=MC, Which is same as initial equilibrium
condition with no profit tax.
118. Predict the effect of specific tax.
As in the case of perfect competition, the specific tax increases the total
variable cost as well as marginal cost and accordingly the MC curve shifts
upwards. This results in a rise in the equilibrium price level and equilibrium
quantity. Further, as in the case of perfect competition, price rise may be lower,
equal to or higher than the tax imposed per unit.
To illustrate this fact formally, assume that per unit tax is Rs. s.
Then, after tax profit is = R-C-s.x
For maximization, the first order condition is
00
dx
dxs
dx
dC
dx
dR
dx
d
Or, MR-MC-s =0
Or, MR=MC+s
Thus, after the imposition of tax, the firm has to equate MR with a
higher MC than before, thus price rises and quantity decreases. We below
discuss the three possible cases:
Case I: Horizontal MC
If the MC of the monopolist is horizontal, the monopolist firm can raise the
price but not by the full amount of the tax. Thus, the monopolist has less power
than the perfectly competitive firm to raise the price level due to tax imposition,
whereas a perfectly competitive firm can raise price by the full amount of the
tax in this case. This case has been illustrated in fig. 9.9 where, ∆P< tax per unit
‘ab’.
191
Case II: Positively Sloped MC
If the MC of the monopolist is positively sloped, he cannot again raise the
price level by the full amount of the tax. This case has been illustrated in fig.
9.10, where, ∆P< tax per unit ‘ab’.
Case III
The monopolist can even raise the price level by the full amount of the sales tax
or even raise the price level by more than the tax per unit.
Thus, imposition of sales tax obviously affects the equilibrium of the
firm which results generally in a rise in price level and a fall in the equilibrium
quantity.
119. What will be the effect of change in demand in monopoly
equilibrium?
Generally a rightward shift in the demand curve results in a rise in the price
level. In case of perfect competition, an outward shift in market demand means
a new equilibrium in the short run with a higher price and higher quantity.
Fig.9.9
O X
P
D
MR
PP
2
P1
X2
X1
MC1
MC2a
btax
Fig.9.10
O X
P
D
MR
PP
2
P1
X2
X1
MC1
MC2
a
tax
b
}
192
However, it may not hold true in case of monopoly market where the outward
shift in demand curve may raise, keep constant or reduce the price level. This
all depends on the elasticity of the demand curve and nature of shift in it. We
below discuss the three possibilities:
Possibility I
After the shift in the demand curve, both price and quantity may be
higher. This case has been illustrated in fig. 9.11 below. If the demand shifts
from D1 to D2, the new equilibrium is established at point e' at which price as
well as quantity supplied by the monopolist are greater than the original
equilibrium. That is why, in fig.9.11, P2>P1 and OX2>OX1.
Effect of Increase in Demand
Possibility II:
With the shift in the demand curve, the equilibrium price level may
remain constant but the quantity increases in this case too. This case has been
illustrated in fig.9.12 .As demand curve shifts to D2 from D1 with no change in
MC, the new equilibrium position is established at point e' with the same price
but a higher output OX2>OX1. The revenue as well as profit of the monopolist
will increase.
Fig.9.11
O X
P
D1
MR2
P2
P1
X2X
1
MC
D2
MR1
ee1
193
Effects of Increase in Demand
Possibility III:
The new market equilibrium may result in higher output and lower
price. This case has been illustrated fig.9.13. As demand curve shifts from D1
to D2, the new market equilibrium is established with a larger output OX 2>OX1
and a lower price OP2<OP1.
Effect of Increase in Demand
It is thus clear that the effect of shift in demand depends on the extent of shift
of demand and elasticity of demand.
120. Discuss the price and output determination under Multi plant
monopoly.
When the monopoly firm uses more than one plant to produce the same
output, it is called a multi plant monopoly. In this case the firm has to decide:
How much to produce and at what price to sell?
How much to produce from each plant?
Fig.9.12
O X
P
D1
MR2
P1
X2X
1
MC
D2
MR1
e e1
Fig.9.13
O X
P
D1
MR2
P1
X2
X1
MC
D2
MR1
P2
ee1
194
To illustrate how the firm makes these decisions, we take the case two plant
firm. However, the results from the discussion can be generalized.
Assumptions:
There are two plants: plant I and plant II, with a different cost
structure.
The monopolist knows his market demand and marginal revenue and
the cost structure of different plants.
The total MC can be derived by taking the horizontal summation of individual
plant MCs i.e.
MC = MC1+MC2
The above mentioned decisions are taken on the basis of MR=MC
rule. The total output is determined by the point where total MC equals the MR
and the output to be produced by each plant is decided on the basis of the rule
MC1=MC2=MR. In other words, the firm maximizes profit by utilizing each
plant up to the level at which MCs are equal to the common MR. This is
because if MC1 is less than MC2, the monopolist would produce more in plant
first as it would be more profitable until the condition MC1=MC2=MR is
fulfilled.
This argument has been graphically illustrated in fig. 9.14 The profit
maximizing output and price are determined by the intersection of MC and MR
curves at point e and accordingly the price level is P and the output level is OX.
From the point of intersection, we draw a parallel line until it intersects the
individual MCs at e1 and e2 and by drawing perpendiculars from e1 and e2, we
get the required output to be produced by each plant as OX1 by plant I and OX2
by plant II such that OX=OX1+OX2. The profit earned from I plant is abcp and
that of second plant is gfhp.
Equilibrium of Multiplant Monopolist
Mathematically,
Let the market demand be P= f(X) =f(X1+X2)
And the cost structures be C1=f1(X1) and f2(X2)
The monopolist aims at profit maximization and his profit is given by =R-
C1-C2
O X
P
X1
Fig.9.14
O X
P,C
X2
O X
P
MR
P
X
MC
D2
MC1AC1
AC2
MC2
a b
c
fg
hP
ee1 e2
(a) (b) (c)
195
The first order condition for maximum requires that
).(..............................0,
).(..............................0,
0,0
22
222
11
111
21
iiMCMRx
C
x
R
xor
iMCMRx
C
x
R
xor
xand
x
Fromm (i) and (ii) MR=MC1=MC2 (Since price is same MR1=MR2=MR)
The second order condition requires that,
0.
,,
2
2
2
2
2
1
2
2
2
2
2
2
2
2
1
2
2
1
2
yxxx
andx
C
x
R
x
C
x
R
This implies that MC in each plant must be increasing more rapidly than MR of
the output as a whole.
121. Analyze the price determination under bilateral monopoly.
Bilateral monopoly is a market where a single seller sells his product to a
single buyer. The single seller is called monopolist and the single buyer is
called monopsonist. For example if there is a single producer of copper and
single industry that buys and uses copper, it is a bilateral monopoly. Though it
is difficult to find in commodity market, it can be easily found in the factor
markets.
The equilibrium price and output levels in case of bilateral monopoly
cannot be determined by the traditional tools of demand and supply. In a way,
economic analysis can not determine the exact price and output levels but can
define the range within which price will be finally established. The price level
and output level will be determined by non economic factors like bargaining
power of firms, skill and other strategies. This is because both the seller and
buyer are both powerful to affect the price level in this case.
The price and output determination in this case can be illustrated with
the help of fig.9.15 where the monopolist will be in equilibrium at point e by
equating MR and MC and the price level will be P1 and output will be X1. But
this cannot happen because the buyer is also powerful to affect price and the
buyer wants to put his own terms. The buyer monopsonist's equilibrium is
defined by the point of intersection of his marginal expenditure curve and
demand curve. It is point e2 and the corresponding price is OP2 and quantity
196
OX2. So, the buyer wants to pay only P2 price whereas the seller wants to sell at
P1.
Equilibrium Under Bilateral Monopoly
Thus, it leads to a situation of indeterminacy where no output will be sold.
They now start bargaining and the price will finally be settled in the range P1 to
P2 i.e. P1>P>P2 depending on the bargaining skill and power of the firms. If the
seller is strong enough as compared to the buyer, price may be quite high
nearer to P1but less than P1 and if the buyer is quite strong in bargaining, price
may be quite low nearer to P2 but more than P2.
Thus, in case of bilateral monopoly, the price and output level depends
on the non-economic factors also.
122. What is price discrimination? What are the conditions for applying
price discrimination?
Price discrimination refers to the phenomenon when the same product is
sold at different prices to different customers. The product may be same or may
have slight differences. But for our simplicity purpose, we take the case of
identical product produced at same cost but sold at different prices according to
the preferences of the buyers, their income, their location, ease of availability
of substitutes, etc.
The necessary conditions for applying price discrimination are:
The market must be divided into submarkets with different price
elasticities.
There must be effective insulation or separation between the two
submarkets so that reselling ( buying in one market and selling in the
other) is not possible.
Fig.9.15
O X
P,C
D
MR
P1
X2 X
1
MC
ME
P2
X*
e1
e2
197
123. What do you mean by first degree price discrimination?
First degree price discrimination is said to exist when the seller monopolist
is able to negotiate with each buyer so that he can sell each unit of commodity
at different price. So, it is called a take it or level it bargain. If the commodity
is sold, the monopolist will snatch (get) all consumers surplus and nothing is
left to the consumers. So, here the monopolist charge the reservation price of
each consumer i.e. he takes the maximum price that one is willing to pay. That
is why here the demand curve become the marginal revenue curve of the
monopolist.Consider fig.9.16.
First Degree Price Discrimination
If the monopolist were not to discriminate and sell at a single price OP, his
revenue will be OPAX and the PAD part is enjoyed by the consumers as
consumers' surplus. But due to perfect price discrimination, his revenue is
OXAD and no surplus is left with the consumer.
Here, the outcome will be efficient in the sense that there is no way to
make both consumer and seller better off. So, it is an idealized concept and
rarely exist in the world. The closest example will be something like a small
town doctor who charges his patients different prices based on their ability to
pay.
124. Define the second degree price discrimination.
In this case, the monopolist divides his buyers into groups or blocks and
charges a different price from each group. Thus, it is also called ‘block pricing
system’. For example: in terms of fig. 9.17, if the seller monopolist sells OX1 at
price P1, X1X2 at price P2 and X2X3 at P3, etc, he will receive a larger part of
consumers' surplus than the case of third degree price discrimination and this is
called the second degree price discrimination.
Fig.9.16O X
P,C
P
X
A
D1
D
198
Second Degree Price Discrimination
This form of price discrimination is often used by public utility companies e.g.
electricity, gas etc. where buyers are divided into different groups and from
each group a different price is charged which is the lowest demand price of that
group. Thus, in this case, some consumer surplus is left as shown by the shaded
area in fig.9.17
125. Define third degree price discrimination.
In this case, the monopolist divides his market into submarkets and charges
different prices depending on the elasticity of demand. Let us suppose that the
monopolist sells into two markets with respective demands D1 and D2, marginal
revenues MR1 and MR2 and marginal cost MC as shown in fig.9.18. He has to
decide how much output to produce and how much to sell in each market to
maximize profits.
The total quantity is defined by the intersection of MC and total MR
curve. In fig.9.18, the equilibrium point is established at point e with output X.
If he were to sell at a uniform price OP, his revenue would be OXAP.
Fig.9.17
O X
P,CD
P1
P2
P2
P4
X1
D1
X2
X3
X4
199
Third Degree Price Discrimination
If the monopolist exercises price discrimination, he will fix the price in both the
markets according to price elasticity of demand in both markets so as to
maximize his total profit. His profit are maximized when MR1=MR2=MC.
Thus, he would sell OX1 with price P1 in market I and OX2 with price P2 in
market II. Clearly, OX1+OX2=OX.
Here, the revenue with price discrimination will be higher. Revenue
with price discrimination
R1=OP1FX1+OP2EX2.
Or, R1=OP1FX1+OX2DP+PDEP2
Revenue without price discrimination (R2) = OPAX
Or, OX2DP+X2XBC+ABCB
But area OP1FX1 = area X 2XBC
Thus R2 = OX2DP+OP1FX1+ABCD
Subtracting R2 from R1
R1-R2 = PDEP2-ABCD>0
Because PDEP2>ABCD
Here total revenue increases by taking a part of the consumer's
surplus.
Mathematically:
Let, the demand function of the monopolist be, P=f(X) and the demand of the
two markets be P1=f1(X1) and P2=f2(X2) and the cost of the firm be C=f(X)
=f(X1+X2)
The firm aims at maximization of profit
i.e. max =R1+R2-C
Fig.9.18
O X
P,C
D=D1+D2
MR2
P1
P
X2
X1
P2
EA
B
e1e2
e
CF
D2D1
X
MR1
MR
D
200
The first order conditions are:
0,021
xand
x
2211
2211
,
0,0
x
C
x
Rand
x
C
x
R
x
C
x
Rand
x
C
x
R
But MC1=MC2=MC=x
C
Therefore, the equilibrium condition is MR1=MR2=MC
The second order condition requires,
2
2
2
2
2
2
2
1
2
2
1
2
x
C
x
Rand
x
C
x
R
We know that
e
11PMR Thus,
1
11
11
ePMR , and
2
22
11
ePMR
Where e1= elasticity in market I and e2= elasticity in market II
From equilibrium condition MR1=MR2
Or,
2
2
2
1
11
11
eP
eP
Or,
2
2
2
1
11
11
e
e
P
P
Thus, if P1>P2, 1 2
2 1 2 1
1 1 1 11 1 , e e
e e e e
This implies that the market with a lower elasticity of demand will have a
higher price level.
This type of price discrimination is most often found in the real world. The
monopolists most often charge a higher price for those markets where the
increase in price level does not reduce sales by a large or significant amount or
where the elasticity of demand is low and charge a lower price in those markets
where the increase in price level causes a significant fall in the market sales or
where the elasticity of the demand is high.
201
126. What are the similarities and differences between monopoly and
perfect competition?
Give a short introduction of both markets
The main similarities between them are:
In both market models, firms have single goal of profit maximization.
In the both markets, short and long run cost curves are U-shaped.
Full information is assumed in both markets.
In both markets, firm acts atomistically, i.e. it takes the decisions
which maximize its profits ignoring the reactions of the other firms.
Both models are basically static.
Effects of taxation are same to some extent.
Both apply MR=MC rule.
The main differences between them are:
Perfect Competition Monopoly
Product is homogeneous. Product may/may not be homogeneous.
There is large number of
sellers.
There is a single seller.
Entry and exit is free in the
long run.
Entry is blocked by definition.
The demand curve is perfectly
elastic or horizontal.
The demand curve is negatively sloped.
The policy variable is output
only since price is given.
The two policy variables are price and
output.
Earns only normal profit in
the long run.
Earns supernormal profit even in the long
run.
Produces at minimum LAC in
the long run.
May produce any where: falling, minimum
or rising LAC depending on market demand.
Elasticity of demand may
assume any value.
Elasticity of demand is greater than unity.
Supply curve is uniquely
determined given MC curve.
Supply curve is not uniquely determined.
202
CHAPTER 10: MONOPOLSTIC COMPETITION
127. What do you mean by a monopolistic market structure? What are
the main assumptions underlying the Chamberlin model?
Monopolistic market is a market structure where the elements of both
perfect competition and monopoly are combined. It is a market structure in
which is a large number of sellers sell differentiated products which are close
substitutes of each other. The main features of monopolistic competition are:
Product Differentiation: Firms sell the products that are different in
physical qualities, taste, selling services, etc.
Large Number of Sellers: The number of sellers is large but not as
large as in perfect competition. That is why monopolistic firms have
some control over the price.
Free Entry and Exit: The firms are free to enter the group if there is
scope of earning excess profits and they are also free to leave the
group if they incur losses in the long run.
Selling Costs: Chamberlin has introduced selling costs as one of the
strategic variables in the monopolistic competition.
Downward Sloping Demand Curve: Since the monopolistic firms
have some control in price level, the firm’s demand curve is
downward sloping but it is highly elastic.
The following assumptions underlie the large group model by Chamberlin:
i) There is a large number of buyers and seller in the group.
ii) The products of the seller are differentiated yet they are close
substitutes of one another. This implies that the sellers sell products that vary in
slight ingredients, outlook, taste, selling services etc, but the goods satisfy same
wants i.e. they are close substitutes of one another.
iii) There is free entry and exit of firms in the group. However, entry
or exit occurs in the long run only.
iv) The goal of the firm is profit maximization both in the short run
and long run. No other goals are attempted to achieve.
v) Price of factors and technology are given.
vi) The firm is assumed to behave as if it knows its demand and cost
with certainty.
v) The long run consists of a number of identical short run periods
which are assumed to be independent of one another. This implies that the
action taken in one period does not have any effect on another period and that
action is also not affected by the actions undertaken in the past period. This
also implies that the best decision for one period is the best one for another
203
period and maximization of short run profits implies the maximization of long
run profits.
vii) Demand and cost curve for all products are uniform (identical)
through out the group. This implies that the demand curve for the product of all
firms is same and the cost curve is also the same. These Heroic assumptions
are taken to simplify the analysis by showing the equilibrium of the firm and
the group in the same diagram.
128. Explain the nature of cost and demand curves under Chamberlin's
large group model.
Chamberlin’s large group model of monopolistic competition has
incorporated selling costs as a strategic variable. He uses the traditional U-
shaped cost curves in his model. However, his total cost is made up of
production cost and selling cost. The average production cost as well as
average selling costs is U-shaped. When U shaped production cost is added to
U shaped selling cost curve, it gives us a U-shaped average total cost. But
whatever is the shape of average total cost, it does not bear a large significance
so long as the slope of MC is greater than slope of MR which is the required
condition for equilibrium.
On the other hand, product differentiation gives the firms some power
to control the price level. That is why the demand curve for the product of a
monopolistic firm is downward sloping. But in this case, the demand curve is
rather flatter or it has a relatively higher elasticity. This implies that if the firm
increases its price, it will lose a lot of its customers and if it reduces its price, it
will attract a lot of customers from other firms. So, the demand curve is highly
elastic as shown in fig. 10.1.
Demand Curve
Fig.10.1
O X
P
D
X2X
1
demand curveP
1
P
204
129. Discuss the short run equilibrium of monopolistic firm.
In the short run, the monopolistic firm acts like a monopolist i.e. price and
output are determined by the marginalistic principle MR=MC. So, in the short
run monopolistic firm enjoys abnormal profit. The equilibrium of the firms is
shown in fig 10.2.
Short-run Equilibrium of Monopolistic Firm
In the fig 10.2, equilibrium of the monopolistic firm is defined at the point e,
which determines the equilibrium price as OPm and equilibrium quantity as
OXm. The excess profit enjoyed by the firm is the shaded area ABCPm.
However, Chamberlin does not deny the fact that a monopolistic firm
may incur losses in the short run.
130. Discuss the long run equilibrium under Chamberlin’s large group
model.
In the monopolistic market structure, only normal profits are possible in the
long run equilibrium. Thus, the long run equilibrium is established after the
adjustment process which leads to such a situation that the LAC becomes
tangent to the demand curve and only normal profits exist. Chamberlin has
developed three models for analyzing the long run equilibrium.
Mode I: Equilibrium with New Firms Entering the Group
In this first model, the long run equilibrium is reached by the
adjustment due to the entry of the new firms in the group being attracted from
the excess profit in the short run. All the firms in the group are assumed to be
making excess profits initially. Since the profit is maximum no firm will be
willing to change its price but the excessive profit will attract new firms to the
group in the long run. This entry initiates the adjustment process as shown in
fig. 10.3 below.
Fig.10.2
O X
D
Xm
SMC SAC
MR
e
Pm
AB
C
P,C
205
Equilibrium with New Firm Entering the Group
In fig. 10.3, suppose the firm is in the short run equilibrium at point A and
enjoying abnormal profits equal to the area PABC. This abnormal profit attracts
new entry in the long run. As new firms start production, the market share of
each firm reduces as such the individual demand curve dd shifts downwards. If
we assume that there is no change in costs by the entry, the downward shift in
the dd curve means a reduction in price level too. The new entry and
accordingly the price adjustment will continue until the demand curve is
tangent to LAC where excess profit disappears. In the final long run
equilibrium, price will be Pe and there will no entry further because profits are
normal. The equilibrium is stable because no firm will want either to raise the
price level or reduce the price level and there will be neither entry nor exit.
Model II: Equilibrium with Price Competition:
In the second log run equilibrium model, Chamberlin has presented a
possible scenario in which there is no entry in the long run and the equilibrium
in the long run is reached through price competition only.
He analyzes this case with the help of share of the market curve
labeled DD' in fig. 10.4 which includes the effects of actions of competitors too
to the price changes made by the firm. The market share curve or DD' curve is
the locus of shifting points of dd' as competitors change their price. However,
the change in price level does not occur due to the reaction to other firm’s price
change but as an independent action by each firm aiming at profit
maximization. This means each firm will reduce the price level thinking that if
it reduces its price level, its sales would increase and thus profits will rise
accordingly. Clearly, the share of the market curve DD' is steeper than the
individual demand curve dd' (Fig. 10.4) because actual sales from a reduction
in price are smaller than expected on the basis of individual demand curve dd'.
Fig.10.3
O XXe
LMC
LAC
MRe
P A
BC
P,C
Pe
d
de
XMR
d
e
206
Equilibrium with Price Competition
Consider a situation in fig. 10.4 where the firm is in initial short run
equilibrium at price P0 and quantity X0. At this price level, the firm is earning
profits. But to maximize profit, the firm will reduce price level to P1 thinking
that it can sell OX1 on the basis of dd'. This level of sales is not realized
because all other firms act simultaneously but independently and reduce the
price level. As a result, the firm is not able to attract the customers from others
firms as much as it expected. This results in the shift of the dd' curve
downwards to d1d1' and the firm is able to sell only OX1. The firm suffers from
myopia and thus does not learn from past experiences. So, it goes on reducing
price levels and the adjustment process continues until the dd' curve becomes
tangent to LAC and the excess profits disappear. At the long run equilibrium
point, LAC curve will be tangent to the individual demand curve ded'e and the
market share curve intersects the individual demand curve as well as LAC
curve. Thus, this independent price reduction will lead to the long run
equilibrium price Pe and equilibrium quantity Xe and the equilibrium thus
established is stable.
Model III: Equilibrium with Free Entry and Price Competition
This third model is the combination of first and second models and is
nearest to the real life situation in its analysis results. Chamberlin argues that in
actual life equilibrium in the long run of a monopolistic firm as well as group is
reached by price competition and free entry. Entry or exit causes a shift in the
market share curve or DD' curve whereas price competition shifts the
individual demand curve or dd' curve. The final long run equilibrium is
established at a point where dd' curve is tangent to LAC and actual sales are
equal to planned sales. In such a equilibrium condition, there will be normal
profits only and thus no firm is willing a change in price and there will be no
entry nor any exit. Thus, the long run equilibrium is a stable one. The
O
P,C
P1
Pe
P0
Fig.10.4X
LMC
LAC
e
XeX
1X
0
MRe
MR2
MR1
d11
D
D1
de
d1
d1
d
d1e
X1
1
207
adjustment process in the third case has been explained with the help of fig
10.5. is explained below.
Assume that the short run equilibrium of the firm is at the point e1 in
fig. 10.5 where it is enjoying abnormal profits. Due to these abnormal profits,
new firms are attracted to the group. The entry of new firms reduces the market
share of each firm resulting into a leftward shift of the market share curve. The
entry continues until the DD curve shifts to D1D1' and the abnormal profits
disappear. For the time being, we may think that point e2 is the long run
equilibrium point because the excess profits have been eliminated. However, it
is not so because entrepreneur thinks that if he reduced price, his sales would
expand along the dd' curve and increase his profits. This feeling makes all firms
in the group reduce the price simultaneously though independently. As a result
of price competition, the dd' curve shifts downwards. Since the firms are
assumed to be suffering from myopia and they do not learn from past
experiences, the firms continue the reduction in price expecting an increase in
sales and accordingly profits. The act of reducing the price level does not stop
even after the shifting dd' becomes tangent to LAC. So, they further reduce
price leading to ever increase losses.
Equilibrium with Free Entry and Price Competition
Due to the ever-increasing losses, the financially weakest firms ultimately leave
the group. The exit of the firms will continue until dd' curve shifts upwards to
d*d* and becomes tangent to LAC curve and the market share curve D1D1' shift
rightwards to D*D* and intersects the point of tangency of LAC and d*d*. This
is the point e in fig 10.5 which is the long run equilibrium of the firm. P* is the
unique price and each firm has a share equal to OX*.
Fig.10.5O X
P,C
d1
d1
1
d*
D*D1
D
D1
1
D* D
e
LMC
LACP
1
P*
P0
A B
C
X1 X2 X3
e1
e2
X*
d*
d1
d
MR*
208
131. What is the main contribution of Chamberlin? Give a critique of
Chamberlin model.
The Chamberlin’s large group model is the most realistic form of market
structure that mixes the two extremes: monopoly and perfect competition. The
main contributions of Chamberlin Model are:
Introduction of product differentiation and selling strategy as two
additional policy variables in decision making.
Solution to the dilemma of falling cost.
Discussion of the selling activity into price theory is an important step
to the explanation of the phenomena of business world.
Introduced the share of the market demand curve as a tool of analysis.
Attempt to preserve the concept of industry is important.
Chamberlin's model has been criticized on the following grounds:
The assumption of product differentiation and independent action by
the firm are inconsistent.
It is hard to accept the myopic behavior of the businessman as implied
by the model.
Assumption of product differentiation is incompatible with the
assumption of free entry.
The concept of industry is destroyed by the recognition of product
differentiation.
It does not tell how large the number of sellers should be so as to
justify myopic disregard.
It does not tell the expected value of elasticties between substitutes
sold in monopolistic markets. It only tells that they must be high.
The assumption from which he derived the negatively sloped demand
curve has been attacked by Andrews.
132. What are the similarities and differences between perfect competition
and monopolistic competition?
(First define the perfectly competitive market and monopolistic market)
The main similarities are:
There are large numbers of buyers and sellers.
There is freedom of entry and exit in the long run.
MR=MC principle for equilibrium.
Normal profit in the long run in both markets.
Firms compete with each other in both markets.
209
The main differences are:
Perfect Competition Monopolistic Competition
Product is homogeneous. Products are differentiated yet they
are close substitutes of each other.
Demand curve is perfectly elastic and
thus firm is a price taker only.
Demand curve is negatively sloped
and thus firms have some power over
price.
P=AR=MR P=AR>MR
Selling activities has no place in its
analysis.
It is an important policy variable.
There is no excess capacity because
long run equilibrium is always at
minimum LAC.
There is excess capacity as long run
equilibrium is always at the falling
part of LAC.
Price lower and output larger than in
monopolistic competition.
Price higher and output lower than in
perfect competition.
Optimum allocation of resources and
thus welfare is maximized
No optimum allocation of resources
and thus welfare is not maximized
133. What are the similarities and differences between monopoly and
monopolistic competition?
(First define the monopoly market and monopolistic market.)
The main similarities are:
MR=MC principle and slope of MC> Slope of MR for equilibrium.
Demand curve slopes downwards in both.
In both markets, P>MR.
Producer is price maker in both markets.
Excess capacity may remain in both models
The main differences are:
Monopoly Monopolistic competition
Single seller. Large number of sellers.
No product differentiation. Product differentiation.
No selling cost. It is important variable.
Price discrimination possible. Price discrimination is not possible
due to presence of competitive
elements.
The demand is less elastic due to The demand curve is more elastic due
210
absence of close substitutes. to presence of close substitutes.
Monopoly price is greater than
monopolistic firm's price.
Monopolistic firm's price is less than
Monopoly price.
No freedom of entry. Free entry and exit.
Supernormal profit even in the long
run.
Normal profit in the long run.
134. Differentiate between monopolistic competition and imperfect
competition.
E. H Chamberlin and Joan Robinson are the two prominent figures who
challenged the prevailing concept of perfect competition and monopoly. They
both published their work: Monopolistic Competition Theory by Chamberlin
and The Economics of Imperfect Competition by Joan Robinson in the same
year 1933 though independently. These two works are considered as single one
and many economists are of the view that Monopolistic Competition of
Chamberlin and Imperfect Competition of Robinson are the two different
names for the same thing. But, Chamberlin, from the very beginning, has been
asserting that there is not only the difference in terminology between the two
concepts but there exists the fundamental difference between them.
The main differences are:
i) Chamberlin's monopolistic competition is a challenge to the traditional
view point of economics. He made a revolutionary break from the past by
presenting the gradations with varying degrees between the two extremes:
perfect competition and monopoly economic situation by blending both.
However, Joan Robinson could not see the real world as the blend (mixture) of
two extreme situations.
ii) Product Differentiation: Product differentiation is the cornerstone of
Chamberlin's theory but it has not a significant role in Robinson’s theory.
Instead, she assumes homogeneity. She lists the reasons why the consumers
prefer different producers. Cost of transport, difference in quality, difference in
facility, price, advertisement, etc are causes of imperfect competition.
iii) Chamberlin's Analysis of Non-price Competition: Product variation and
selling cost play an eminent role in Chamberlin's analysis. But Robinson
defines imperfect competition in terms of demand curve which is negatively
sloped. She takes only price competition into account but Chamberlin discusses
equilibrium in regard to three variables: price, product and selling cost. The
greater emphasis on product variation and selling cost is a significant
contribution of Chamberlin.
iv) Analysis of Oligopoly Neglected in Robinson's Model: Chamberlin
discusses the oligopoly problem in detail and provides his solution of it. But
211
this issue is neglected by Robinson which is a serious lacuna (weakness) in
Robinson's model as it is the predominant form of market in the real world.
v) Perfect Competition cannot be Called Welfare Ideal-Chamberlin: To
Chamberlin, perfect competition may no longer be regarded as welfare ideal in
any sense for the purpose of welfare economics. It can represent welfare under
two assumptions which Robinson has made:
Product homogeneity.
All people wanted no varieties.
But people's liking and demand for variety is important and must be
paid attention for promoting welfare.
vi) Difference in Concept of Exploitation of Labor: According to Robinson,
labors get wage rate equal to marginal revenue productivity of labor (MRPL)
which is less than the value of marginal product of labor (VMPL). It’s only the
entrepreneur who gets income over the value of marginal product which is the
exploitation of labors. But according to Chamberlin, the theory of monopolistic
competition indicates neither the exploiter nor the exploited. If all factors are
paid according to VMPL, the total income of all factors will add up to more
than the revenue of the firm. So, all factors get rewards according to
MRP<VMP and no exploitation is indicated.
212
CHAPTER 11: OLIGOPOLY
135. Define Oligopoly.
Oligopoly is a form of market structure in which there are a few sellers
selling homogeneous or differentiated products. Economists do not specify how
few can be the number of sellers in such a market but two firms is the limit. In
case of two firms, oligopoly market is called a duopoly market. Further, it can
be a homogeneous or pure oligopoly selling homogeneous product or
heterogeneous one selling differentiated products.
Factors causing Oligopoly:
High capital investment.
Economies of scale.
Patent rights.
Control over certain raw materials.
Merger and take over.
Features of Oligopoly:
i) There is small number of sellers so that each firm can affect the price and
business strategy of the rival firms.
ii) The fewness of the firms makes competition keener and as such one firm’s
decisions clearly affect other firms’ decisions. Thus, firms in the oligopoly
market cannot decide independently.
iii) Due to the huge initial investment, loyalty of the consumers’ to the product
of a firm, and other strategies, there exits barriers to entry.
iv) Due to the interdependence in decision making, pricing and output decisions
are said to be indeterminate in oligopoly. However, in case of collusive
oligopoly, they are determinate.
Non-Collusive Oligopoly
136. Discuss the Cournot model.
Cournot model is the simplest exposition of the action reaction pattern and
interdependence in decision making in the oligopoly market. It is a duopoly
model which was formulated by Cournot in 1838. His original version of the
duopoly model can be presented with the following assumptions:
i) There are two firms A and B.
ii) The production is costless.
iii) The firms have identical products and identical costs.
iv) Both sell their output with a straight line demand curve.
v) Each firm assumes that the output of the rival firm will remain constant.
vi) Firm A starts the production first.
213
Cournot has taken the example of mineral after selling to illustrate his
model. Each firm owns a spring of mineral water produced at zero cost.
Suppose that the market demand curve is as presented fig. 11.1 .When firm A
starts to produce first, he sells his output being at point A which is defined by
the famous profit maximizing marginalistic rule MR=MC. The price level
charged by the firm is OP1 price and at this price level, A sells half of the
market.
Now B comes to the scene and starts production assuming that output of firm A
will be constant and B considers CD' as its demand curve. B sells AB output at
OP' price defined by the MR=MC rule and thus supplies the 1/4 of the market.
Next time, firm A assumes that B will keep its output constant and supplies half
of the market that is not supplied by B. Thus A's output in next period is 1/2(1-
1/4) = 3/8 of the total market. Further, firm B assumes the same and produces
half the market that is not supplied by A i.e. 1/2(1-3/8) = 5/16 of the market.
This action reaction pattern goes on due to the naive behavior of firms
because the firms never learn from their past experiences. But finally, the firms
reach an equilibrium situation where both produce 1/3 of the market each
maximizing their profit. However industry profits are not maximized. Their
equilibrium can be derived as follows.
i) The production of firm A in successive period:
Period 1: 2
1
Period 2: 8
1
2
1
8
3
4
11
2
1
Period 3: 32
1
8
1
2
1
32
11
6
51
2
1
Fig.11.1
O
P,C
D1
P1
P2
MRA MRB
A B
D
Q
C
214
Period 4: 128
1
32
1
8
1
2
1
128
42
128
421
2
1
…………………………………………………
We see that A's output is decreasing slowly. The sales of firm A in equilibrium
can be calculated as = ...................128
1
32
1
8
1
2
1
......................
16
1
4
11
8
1
2
1
The expression in bracket is an infinite and declining geometric series. We can
use the following formula to find the sum of items in such a case.
r
aS
1 ; Where S= sum, a= first term, r = common ratio,
Thus, we have,
1 1 1 1 1 4 1 1 1
' Output .12 8 2 8 3 2 6 3
14
A s
i) The production of B in successive periods:
Period 1: 4
1
Period 2: 16
1
4
1
16
5
8
31
2
1
Period 3: 64
1
16
1
4
1
64
21
32
111
2
1
Period 4: 128
1
64
1
16
1
4
1
256
85
128
431
2
1
………………………………………………….
We see from the above calculation that firm B's output is increasing slowly.
Thus product of B in equilibrium= ...................128
1
64
1
16
1
4
1
Again applying the formula of summation for an infinite and declining
geometric series, we have:
114' Output
1 314
B s
215
Thus, in final stage both the firms reach a stable solution each producing 1/3 of
the market and together they will supply 2/3 of the market. We can generalize
this result to a larger number of firms as such if there are n firms, each of them
will produce 1/(n+1) number of the market and together they will produce
n/(n+1) part of the market. The price level will be a common price which is
lower than the monopoly price but greater than the competitive price.
Cournot model has the following weaknesses:
The model is closed. Entry is not allowed.
The assumption of costless production is unrealistic.
Firm's behavioral pattern is naive, they do not learn from the past
experiences.
The assumption that each firm assumes others’ output constant is not
realistic.
137. Discuss the Cournot model with the help of reaction functions.
Cournot model can also be discussed and analyzed with the help of reaction
functions. The major advantage of this approach is that we need not assume
identical cost and demand curve for all the firms. So, this analysis is more
realistic.
The equilibrium of the duopoly firms is derived from the point of intersection
of the firms’ reaction functions and the reaction curve for each firm is derived
from the iso-profit map of the respective firm.
Reaction curve of Firm A:
Reaction curve for firm A is derived from A's iso-profit map. An iso-
profit curve for the firm A is the locus of points of different level of output of A
and his rival firm B which yield to A the same level of profit. It has the
following properties:
i) Iso-profit curve of firm A is concave to the output axis on which A’s output
is measured.
ii) The farther the iso-profit curve, the lower is the level of profit.
iii) The successive maximum points of the iso-profit curves lie left to each
other.
A's iso-profit map is shown in fig.11.2. If we join the highest points
of the iso-profit curves, we obtain firms A's reaction curve. Thus, A's reaction
function is the locus of highest profit that firm A can attain given the level of
output of rival B. Firm A's reaction function is derived in fig.11.2
216
Firms A's Reaction Function
Reaction curve of Firm B:
Similarly B's reaction function can be derived from the iso-profit map of firm
B, whose iso-profit curves has properties as below:
i) They are concave to QB axis.
ii) The farther the iso-profit curve, the lower is B's profit.
iii) The maximum points of successive iso-profit curve lie right to each other.
In fig.11.3, we have derived B's reaction curve by joining the
maximum points of iso profit curve of firm B.
Firms B' Reaction Function
Cournot equilibrium is determined by the intersection of the reaction curves. It
is stable provided A's reaction curve is steeper than B's reaction curve. In
fig.11.4, equilibrium is established at point e which is called the Cournot
equilibrium.
Fig.11.2O QA
QB
A5
A4
A3
A2
A1
Firm A’s reaction curve
B5B4B3
B2
B1
Fig.11.3O QA
QB
B5
B4
B3
B2
B1
Firm B’s reaction curve
A5A4A3A2A1
217
Equilibrium in Cournot Model
The equilibrium thus established is stable one. To show that suppose that the
firms are at disequilibrium situation in fig.11.4 where A is producing output A1
which is lower than the equilibrium quantity. In this situation, firm B will react
by producing B1 following the Cournot assumption. Reacting to this, A
produces a higher quantity A2, assuming that B will keep its quantity constant
at B1. This action reaction process will continue until the equilibrium point is
reached.
One point to be noted is that in the Cournot model, though individual profits
arte maximized, joint profit are not maximum. It can be seen from fig. 11.5
where at the equilibrium point e, A's profit level is A3 and B's B4.
However if the firms produce at some point on the contract curve at least one of
them will be better off by enjoying a higher profit than before while other
firm’s profit will not be reduced. For example, if they move to point ‘a’, B's
profit is B3 and A's profit is A3. Clearly, B is better off as B3>B4. Similarly if
they move to point ‘b’, B's profit is same but A's profit level is A2 (A2>A3)
Fig.11.4O QA
QB
Firm B’s reaction curve
AeA2A1
Firm A’s reaction curve
eB1
Be
Fig.11.5O QA
QB
A5
A3
A2
A1
Firm A’s reaction curve
B5
B4B3
B2
B1
Firm B’s reaction curvea
e
b
A4
Contract Curve
218
and thus A is better off. If they move to a point between a and b, both of them
will be better off and enjoy higher level of profit.
Thus, point e is suboptimal point for the firms because by moving to
the disequilibrium point on the contract curve the profit levels enjoyed by both
of them will increase. The reason behind this is the firms’ behavior of never
learning from the past experiences in this model.
138. Discuss the Bertrand model.
Bertrand model also is a duopoly model in which the action reaction pattern
is assumed to occur in terms of price. Thus, in this model equilibrium is
reached by the action reaction in terms of price by the both firms. Here, each
firm revises his price level on the assumption that the price of thee rival firm
will remain constant. This model also can be analyzed with the help of reaction
curves.
Here, also reaction functions are derived from the iso-profit map of
each firm. Suppose that there are two firms A and B.
Reaction curves for firms A and B
Reaction curve for firm A is derived from A's iso-profit map. A's iso-
profit curve shows the same level of profit which would be available to A from
various level of prices charged by firm A and its rival firm B. It has following
properties:
An iso-profit curve for A is convex to the axis on which PA is measured.
The farther the iso-profit curve, the higher the profit level.
The minimum points of iso-profit curve lie right to each other in this case.
Firm A's Reaction Curve
By joining the minimum points of the iso-profit curves, we get the
reaction function of firm A as shown in fig.11.6
A4
A3
A2
A5
Fig.11.6O PA
QBFirm A’s reaction curve
A1
219
Similarly, B's reaction curve can be derived from the iso-profit map of B. Firm
B’s iso-profit curve has the flowing properties:
Each iso-profit curve is convex to PB axis.
The farther the iso-profit curve, the higher the profit level.
The successive minimum points lie right to each other.
B’s reaction function can be derived by joining the minimum points of the B’s
iso-profit curves as derived in fig.11.7
Firm B's Reaction Curve
By bringing both the reaction functions together, we can find thee Bertrand
equilibrium as shown by the point of intersection of the reaction functions as
point e in fig.11.8. The equilibrium thus established is also stable as in Cournot
equilibrium as such any departure from it sets in forces which will finally bring
the system back to the point e.
Bertrand Equilibrium
This model also does not lead to the maximization of joint profit due
to the assumption of naive behavior of the firms which never learn from past
experiences. To show this, consider fig.11.9
Fig.11.7O PA
PB
B1
B2
B3B4
B5
Firm B’s reaction curve
Fig.11.8O PA
PBFirm A’s reaction curve
Firm B’s reaction curve
PA1 PAe
PB1
PBee
220
At equilibrium, A's profit level is A2 and B's profit is B4. If they move to a
point on contract curve, profit of at least one firm will increase without any
decrease of others profit. For e.g. if they move to point a, firm B's profit is
same (B4) but A's profit will increase to A5. Similarly, if they move to b, A's
profit is same but B's profit will increase to B7. If they move to a point
between a and b, both firms’ profit will increase. Thus, points on the contract
curve are optimal and Bertrand equilibrium is not an optimal point where
through individual profit are maximized, joint profits are not maximized.
The weaknesses of the model are:
The assumption that firm never learns from past experiences is
unrealistic.
Each firm maximizes its own profit, but the industry profits are not
maximized.
iii)It does not allow entry.
139. Analyze Chamberlin's small group model.
Chamberlin's small group model is a more realistic model than other models
in the sense that the firms are assumed to recognize their interdependence.
Chamberlin ages that if firms can recognize that they cannot act independently,
a stable equilibrium can be reached with the monopoly price being charged by
all firms so as to maximize the industry profit. To him, firms are not as naïve as
Cournot and Bertrand assume. They recognize the direct and indirect effects of
their decisions. Direct effects are those which would occur if competitors were
assumed to remain passive and the indirect effects are those that would occur if
rivals react to the decision of the firm which changes price and output. Thus, if
the firms are clever enough to learn from their past experiences, a monopoly
stable solution can be reached in oligopoly market.
Assume the situation of Cournot solution in duopoly market, i.e.
production is costless and demand is a straight line with negative slope ( fig.
.11.10) If firm A is the first to start production, it maximizes profit by selling
Fig.11.9O PA
P B
B1
B2B3B4B5
Firm B’s reaction curve
B6B7
ab
e
A1
A2
A3
A4
A5
Firm A’s reaction curve
221
OXm at price Pm and then B comes and produces XmXB assuming that his
demand curve is CD and charges price OPB. Now, firm A understands that its
rival will react to its action and reduces his quantity to OA which is half of the
OXm quantity and equal to B's output. Firm B understands that this is the best
for both of them. So, B keeps his output the same AXm=XMXB . Thus, by
recognizing their interdependences, the firms reach the monopoly solution
where the market is shared equally between the two firms.
Chamberline's Small Group model
This model is advancement over other models because of its more
realistic assumptions. But it is a closed model and ignores entry.
140. Discuss Stackelberg Duopoly Model.
This model was developed by German economist Stackelberg and is an
extension of Cournot model. Here, in this model, one of the duopoly firm is
assumed to be sophisticated to recognize the interdependence and competitor’s
reactions. Thus, the sophisticated firm will first determine the rival’s reaction
function and includes it in his profit function while maximizing profits.
To illustrate this model, consider that the iso-profit curves and
reaction functions of the duopolists are those in fig. 11.11. If firm A is the
sophisticated duopolist, he chooses to maximize his profit being on B's reaction
curve. In fig 11.11, A's equilibrium is at point ‘a’ where he reaches his lowest
iso-profit curve and produces OXA quantity and B produces only OXB. Clearly,
A is better off and B is worse off than the Cournot equilibrium.
On the other hand, if B is the sophisticated firm, his equilibrium is the
point ‘b’, where it can reach the lowest iso-profit curve being on A's reaction
curve. He produces X'B and A produces X'A only.
In summary if only one firm is sophisticated, it will be the leader and a stable
equilibrium will emerge since the naïve firm will act as a follower.
Fig.11.10
O QA
P,R
A Xm XB
MRA
D
MRB
CPm
PB
222
However, if both firms are sophisticated, then both won't to be leader
and there arises instability which is known as Stackelberg disequilibrium. It
will result either in price war or in collusion. Finally if both want to be
followers, it results in a Cournot solution.
Stackelberg model
In summary the four scenarios are:
When A is sophisticated and B is a follower there is a stable solution,
where A is better off and B is worse off than Cournot model.
When B is sophisticated and A is a follower, there is a stable
solution, where B is better off and A is worse off than the Cournot
model.
If both try to be leader, it results in a price war or collusion.
If both are followers, it results in Cournot equilibrium.
Implications:
Firms should recognize their interdependence.
By recognizing the follower reaction function, a duopolist maximizes
profit.
If both recognize interdependence but each ignores the other, a price
war will be inevitable where both are worse off.
Collusive agreements between them may lead to a situation where
both are better off.
141. Analysis Kinked demand curve model.
The kinked demand curve model was formulated in 1939 by Prof. Sweezy
to analyze the price and output determination in the oligopoly market. His
model may be presented as below.
The demand curve of the oligopolist has a kink reflecting the following
behavioral pattern of the firms:
Fig.11.11
O XA
XB
A3
A2A1
Firm A’s reaction curve
B3B2
B1
Firm B’s reaction curve
Cournot equilibrium
e
b
a
X1B
XB
X1A XA
223
If the entrepreneur reduces his price, he expects that his competitors
will follow him with price reduction so that the shares of competitors
remain more or less unchanged. So for price reduction below P
(fig.11.12), the share of the market demand curve is relevant for
decision making.
If he increases his price he expects that his competitor will not follow
him and he loses a considerable part of his customers. Thus for price
increase above P, the relevant demand curve is de section of the
individual demand curve dd'. Clearly, the upper section of the demand
curve has the higher elasticity than the lower part.
Due to the kink in the demand curve, the MR curve is discontinuous. It is
made up of two segments: segment dA corresponds to the upper part of the
demand curve while segment BMR corresponds to the lower part of the
demand curve. (Fig. 11.12).
Equilibrium of the Firm:
The equilibrium of the firm is defined by the point of the kink because
to the left of the kink MR is greater than MC and to the right of the kink
MR<MC (fig.11.12). Total profits are thus maximum at the point of the kink.
However, this equilibrium is not defend by the rule MR=MC because in
general the MC curve passes through the discontinued section of MR. Thus,
this model does not use the MR=MC rule for the determination of equilibrium
price and output. The intersection of MR and MC need a very high or very low
MC which are not commonly found in practice.
Rigidity of Price:
i) Change in MC:
Price and output remain constant even if MC changes so long MC is within the
discontinuous section of MR. However, when the rise in cost is general and
Fig.11.12
O X
P,C
X MR
D
Pe
d1
D1d
MC1
MC2
A
B
224
affects each firm similarly e.g. imposition of a specific tax, if one firm
increases the price, others will for him and kink shifts to the left. Consequently
price will be higher and quantity falls. It is shown in fig. 11.13 below.
Change in Demand:
Further, price may remain sticky with the shift in demand also. If the demand
curve is kinked, a shift in market demand will affect the volume of the output
but not the level of price so long as marginal cost passes through the
discontinuity of new MR. It is shown in fig. 11.14.
Critical Appraisal:
Through, the kinked demand hypothesis appears attractive and seems quite
realistic in the highly competitive business world dominated by oligopolistic
competency, it has the following weaknesses:
It does not explain the price and output decision of the firm that
maximizes the firm's profit. It only explains why price once
determined tends to remain sticky.
Fig.11.13
O X
P,C
XMR
D
P
B1
X1
MC1
MC2
A
B
P1
A1
SAC1
S A C 2
Fig.11.14
O X
P,C
MR1
e
D1d
X1MR2
D2D1
d1
2
d1
1
X2
A A1
ACMC
225
It does not explain the height of the kink.
It is not supported by empirical facts. Most empirical studies show
that there is a lack of stability of price in oligopolistic market.
If conflicts with marginal proclivity theory. It concludes that MC may
change; MR remaining the same and thus conflicts with the marginal
productivity theory that factor price are equal to the marginal revenue
product.
Hence, this model is too less a theory of pricing and more a tool for
explaining why the price once determined, in one way or another will tend to
remain sticky.
COLLUSIVE OLIGOPOLY
142. Define cartels.
Cartel is a formal organization of the oligopoly firms in an industry. The
general purpose of cartels is to centralize certain managerial decisions with a
view to promoting common benefits. Cartels may be in the form of open or
secret collusion. Whether open or secret, cartel agreements are explicit and
formal in the sense that agreements are enforceable on member firms not
observing the cartel rules. Cartel and cartel type agreements between the firm
in manufacturing and trade are illegal in most countries. Yet, cartels in the
broader sense of the term exist in the form of trade associations, professional
organization and the like, cartel are of two types:
Cartel aiming at joint profit maximization.
Market sharing cartels:
143. Write a note on cartel aiming at joint profit maximization.
In the cartels aimed at the joint profit maximization, all the firms agree to give
authority to a central agency which decides how much to sell and what price in
order to maximize joint profits. The agency also allocates the quota of output to
be produced by each firm. The agency is assumed to know the MCs of all firms
so it can sum them to get aggregate MC. Also, it is assumed to know the market
demand and MR curve.
The agency acts like a multi plant monopolist while determining the
price and output on the basis of MR=MC rule. This condition is fulfilled at
point e in fig. 11.15(c) which determines price OP and the total output OX.
Now, the agency allocates output among the firms so as to equate the MR with
individual MCs. Thus, firm I produces OX1 and firm II produces OX2 and
clearly OX=OX1+OX2.
226
The total industry profit is the sum of the profit earned by the two firms,
denoted by the shaded area PABC and area MNQP in fig 11.15(A) and (B), the
distribution of the profit is decided by the central agency of the cartel. This
analysis of two firms case can be generalized to a number of firms.
Difficulties in Maximization of Joint Industry Profit
Mistakes in the estimation of market demand
Mistakes n the estimation of MC
Slow process of cartel negotiation
Stickiness of the negotiated price
Bluffing attitude of firms
The existence of high cost firms
Fear of government intervention
Wish to have a good public image:
Fear of entry:
Freedom regarding design and selling activities
144. Explain the price determination under market sharing cartels.
In this type of cartels, the oligopoly firms agree to divide the share of the
market, but keep a considerable degree of freedom concerning the style of the
product, their selling activities and their decisions. There are two basic method
of sharing the market:
i) Non-price competition:
Here, the firms agree on a common price at which each of them can
sell any quantity demanded. The price is set by bargaining process, with the
low cost firm pressing for a lower price and high cost firm for a high price. But
the agreed price must be such that it gives some profit to all members. The
firms are free about the style of their product. Thus, in this type of cartel, the
firms compete on a non-price basis.
Fig.11.15
O X
P
X1 O X
P,C
X2
O X
P
MR
P
X
MC=MC1+MC2
D
MC1AC1
AC2
MC2
A B NM
QP
e
C
(A) (B) (C)
227
This type of cartel is often short lived whether the firms have same
cost or different costs conditions. In case of different cost, the low cost firms
will always have incentive to break away from the cartel because by doing so,
it will attract a lot of customers. Soon, it is discovered by others and it either
ends in a price war and instability develops. Another possibility is that the
member of the cartel may decide to reduce price and start a price war until the
cheater firm is driven out of business.
The price determination under such type of cartel has been shown in fig. 11.16
below, where firm B has lower cost than firm A and B will have incentive to
cut the price below the monopoly level to drive out the high cost competitor A
out of the business. Thus this type of cartel is highly unstable.
ii) Agreement on Quotas:
In this type of cartel, the firms share the market at the agreed price and
sell accordingly. If all firms have identical cost, the monopoly solution will
take place where all firms get equal share of the market. For example: if there
are two firms, each firm will sell half of the market at the monopoly price. In
fig. 11.17 a, b and c monopoly price is Pm and the equal quotas are
OX1=OX2_and OX1+OX2=OXm.
However if cost structures are different, the quotas and shares of the
market will differ. Share in case of cost differentials are decided by bargaining.
The final quota of each firm depends on the level of its cost as well as
bargaining power. During the bargaining process, two main statistical criteria
are most significantly adopted: past level of sales and productive capacity.
Fig.11.16
O XX
A O X
P,C
XB
O XMR
D
MCAACA
ACB
MCB
(A)(B) (C)
Xm
Pm
Pm
Pm
PB
P,C P,C
MRAMRB
DD
Fig.11.17
O XX
A O X
P,C
XB
O XMR
D
MCA
MCB
(A)(B)
(C)X
m
Pm
Pm
Pm
P,C P,C
MC=MCA+MCB
MRA
MRA
DD X
AX
B
228
Another popular method of market sharing is geographical sharing. In such
case, the price as well as the style of the production will differ. Whatever is the
way of sharing, the cartel type of market is highly unstable.
145. Write a note on low-cost price leadership.
In this model, the firms with the lowest cost act as the leader firm and
determines price in his own way so as to maximize its own profits and all other
firms follow the price determined by it.
The following assumptions underlie our analysis:
There are two firms A and B.
The product is homogeneous.
Their cost structures are different and A is the low cost firm.
Under these assumptions, there may appear two cases:
i) The two firms may share the market equally when the demand curve is same
for both firms as shown in fig. 11.18 or they may have unequal market shares
when the demand curves are different as shown in fig. 11.19.
The lowest cost firm sets price so as to maximize his profit at which
the profit of B is not maximized. The follower would maximize profit by
selling XBe output at PBe Price. However, it likes to follow the leader
sacrificing some profit to avoid a price war.
However for the profit of A to be maximum, firm B must product the quantity
XAX in fig 11.18 and fig 11.19. Thus, in price leadership also, the firms must
agree on the quota to be produced. If the follower does not produce the required
quota, the leader may be pushed to a position where its profit is not maximized.
O XX
B
P,C
MCAPBe
MRA
D
MCB
d
PA
XA
X O XX
B
P,C
MCAPBe
MCB
PA
XA MRA
MRB
dB
dA
ACB
ACA
ACB
ACA
XBe
Fig.11.18 Fig.11.19
229
146. Write a note on dominant firm price leadership model.
In this model, it is assumed that there is a large or dominant firm
selling a large share of the market. It is assumed to have the knowledge of
market demand and marginal costs of small firms. So, it can find the supply of
the small firms and supply left to him and accordingly can find his demand and
sets price and quantity so as to maximize his profit.
Assume that the market demand is as given in fig. 11.20 below. The
dominant firm finds the supply by small firms as S1S1 by adding the MCs of
small firms. By subtracting the supply of small firms from the total market
demand, the dominant firm finds the demand left for him. His demand at some
piece is the part of the market unsupplied by the small firms.
At the price P1, all the market demand is supplied by the small firms and
leader’s demand is zero. At price P2, P2A has been supplied by small firms the
remaining AB part is the demand for the leader. At price P3, all the market is to
be supplied by the leader. Thus the leader's demand curve is ddL as shown in
fig 11.20(B).
Having derived the demand curve and given his MC, the dominant leader firm
determines the price by the MR=MC rule as OP at which it supplies OX (=KL)
and the small firms supply PK part of the market demand.
Here also, the leader maximizes his profit and the followers may or
may not maximize profits. Further, in order that the profits of the leaders be
maximum, the followers must produce the right quantity.
147. Write a note on Barometric price leadership.
In this type of leadership model, the firms agree to follow the price
changes made by a firm which is considered to have a good knowledge of the
prevailing conditions in the market and can forecast the future developments in
O X
P
MRO X
P,C
Fig.11.20
P1
P2
P3
PA B
C
LKP Q
MN
DS
MC
AC
(A) (B)X
dL
230
the market better than other. In short, the leader firm is considered as a
barometer reflecting the changes in economic environment. The barometric
firm may neither be a low cost firm nor a large firm. Rather, it is a good
forecaster. Further, a firm from another industry may also be chosen as the
barometric leader. For example: a firm in the steel industry may be agreed as
the leader for the price changes in motorcar industry. Barometric price
leadership may be established for several reasons. Some are:
Rivalry between several large firms in an industry may make it
impossible to accept one among them as the leader.
Followers avoid the continuous calculations of costs as economic
conditions change.
The barometric firm has proved itself as a reasonably good forecaster
for change in cost and demand conditions in the particular industry
and the economy as a whole and by following it, the other firms can
be reasonably sure that they chose the correct price policy.
231
CHAPTER 12: OTHER MARKET MODELS
148. Give a critique of neo-classical controversy.
The traditional theory of the firm which is based on the single goal of profit
maximization, with the assumption of single owner entrepreneur, with the
marginalistic rule of price and output determination and with the assumption of
perfect information has been heavily criticized in the recent years due to its
unrealistic assumptions. The critics have argued, on the basis of empirical
studies, that the firm cannot move ahead with the single goal of profit
maximization and it does not determine price and output on the basis of
marginalistic rule(MR=MC). Some points of criticisms have been discussed
below:
1. The Single Owner Entrepreneur:
The traditional theory assumes that the owner is the manager of the firm
and owner entrepreneur acts with global rationality; he has all the information
and abilities to follow the goal of profit maximization. There are no time,
information and other constraints.
But these assumptions are clearly unrealistic. Today, owner share
holders and manager are different persons. The manager has time, information
and other constraints in the present complex environment.
2. The Goal of Profit Maximization:
The traditional theory assumes that the firm has the single goal of
profit maximization. This assumption is also criticized by the critics. Since
the owners and managers are two different things, the firm follows other
goals rather than profit maximization. Some of the most often followed
goals are:
a) Maximization of managerial utility function
Managerial utility = f (Salaries, prestige, market share,……)
b) Satisfying behavior
c) Long run survival and market sharing
d) Entry prevention and risk avoidance.
In following these goals also, the firm must earn a minimum level of
profit.
3. The Treatment of Uncertainty in Traditional Theory:
In traditional theory, the firms are assumed to have perfect knowledge
of demand and cost. Thus, uncertainty did not affect any decisions of the
firm. However, later it was argued that firms do not have perfect
232
information on cost, revenue and environment. Thus, economists used a
probabilistic approach which was a little bit better approach. But
probability approach is also subjective.
4. The Static Nature of Traditional Theory:
The traditional theory is static in the sense that the time horizon of the
firm is made up of identical and independent short run time periods. Since
the time periods are independent, decisions are not assumed to be affected
by the decision in the past periods and influence the future decision of the
firm. This is one great shortcoming of the traditional theory.
5. Entry Consideration:
In the traditional theory deals with only the actual entry but potential
entry and its effects on decision making are neglected.
6. The Marginalistic Principle:
The behavioral rule for decision making in the traditional theory is the
marginalistic principle MR=MC. But critics argue that firms do not make
pricing decisions on the basis of this rule. Rather they follow average cost
pricing.
Thus, critics of the neo-classical theory or traditional theory of the firm
basically attack on the unrealistic assumptions of perfect information and
certainty, single goal of profit maximization, single owner entrepreneur of the
firm, etc.
149. Highlight the Hall and Hitch report.
The Hall and Hitch report is the report of a research by ‘The Oxford
Economists Research Group’ about the decision making process of the firms.
Two economists Hall and Hitch published their report in 1939. Their study
covers 38 firms out of which 33 were manufacturing firms, 3 retail trading and
2 building firms. The main findings of the study are:
Firms do not act automatically but they are continuously conscious of
the reaction of their competitors.
Firms do not attempt to maximize short run profit by MR=MC rule but
aim at long run profit maximization.
Firms set their price on the basis of average cost principle
P=AVC+AFC+ profit margin.
Firms’ main concentration is price not the output. They would set their
price according to AC and sell whatever the market would take at this
price.
Oligopoly was the main market structure.
233
Price of manufactures was fairly sticky despite changes in demand and
costs.
150. Critically present the representative model of average cost pricing
principle.
The basis argument of the average cost pricing models is that price is
determined according to average cost i.e.
P =AVC+GPM=AC
Where, AVC= average variable cost
GPM= gross profit margin
Where, GPM includes Average Fixed cost and a certain profit margin. Thus,
the average cost pricing models reject the famous marginalistic MR=MC
principle of price and output determination and assert that price is determined
according to the average cost (AC).
There are many models on average cost pricing principle. Their views
can be summarized under the following representative model.
The Model
Goal of the Firm:
The goal of the firm is maximization of long run profit which
is realized by equating price to average cost and not by maximizing
short run profit in each period within the time horizon of the firm by
using MR=MC rule as in traditional theory.
Demand and Cost Schedules:
These theories reject demand curve as a tool analysis as the traditional
theory of the firm because there is uncertainty in estimating demand
due to change in tastes, competitions reactions etc. Further, the long-
run cost curves are also not used as they cannot be estimated correctly
due to rapid technological change and change in factor prices. So,
these theories use the short run cost curve and the cost curve are based
on modern cost theory i.e. there is a flat stretch over which AVC=MC
implying reserve capacity. The curves are shown in fig. 12.1.
234
Price Determination:
The determination of price would involve two steps: first, the firm
determines the price that it would like to charge to cover its total cost. The price
will be such that the plant of the firm is operated within its optimal range of
capacity and it earns reasonable profit and secondly, the firm compares its
estimated price with the level of price at which entry would occur and finally
sets the price at the level P* which would effectively prevent entry in the
market. We will discuss these two steps in some detail.
Step 1: Subjective Estimate of the Desired Price
The firm uses the rule P=AVC+GPM to determine the subjective price.
The AVC is assumed to be known to the firm with certainty and short run
AC is assumed to be a good approximation of the long run AC.
The GPM includes AFC and net profit margin. The net profit marginal
is assumed to be known to the firm from past experiences. The net profit
margin should be enough to provide return on capital and cover all risks
related to the product. The AFC is given by:
AFC=TFC/X*; where X* = planned output.
Step 2: Actual Price Setting:
The estimated price will not be charged in the market but only taken
as a basis for the actual price determination. Actual price depends mainly
on the threat of potential entry. Competition among the existing firms is
solved either by tacit collusion or price leadership. The tacit collusion is
typically done within trade associations. In case of price leadership, the
leader makes his calculation according to average cost principle but
charges actual price which depends on:
Potential competition
OX
C
xA xB
Fig.12.1
MC
SAVC
SATC
235
General economic condition.
If there are barriers to entry, the actual price P* will be higher than
the normal price p and the leader will be making abnormal profit (fig. 12.2)
and other firms also possibly earn excess profits. But if the threat of
potential entry is strong, the actual price P* will be just normal price or
even below the normal or desired price as shown in the figure. In fig. 12.2,
the horizontal lines are not demand curves but they show price levels. The
leader’s normal price is P which covers his SAVC and gross profit margin
ab.
If the barriers to entry exits or the economy is in booming stage, the
leader would charge the price P* and earn abnormal profit. In this case, clearly,
the effective GPM is more than the desired one ac > ab.
If potential threat of entry is strong or in case of depressed business
conditions, the leader would actually charge the price, say P** lower than the
desired one i.e. ad<ab.
Comparison:
Price will be higher and output lower than in perfect competition.
However, if threat of potential entry is strong they may converge to perfect
competitive price. There will be some underutilization of plant as firm
operates at less than full capacity.
Change in cost
If there is small change in cost, firms would react this by changing the
quantity and quality of their product, not by changing the price level. However,
if the change in cost is substantial, price will be accordingly changed.
Change in demand:
If demand increases, the firms will not increase price because they do
not know whether the pressure of demand will last long. If the pressure of
demand seems to exist for a long time period, they will install new plant and
OX
P,C
Fig.12.2
MC
SAVC
SATC
P*
P
P**
X*
c
a
b
d
236
increasing their capacity moving to a new point on their LRAC where cost is
not higher but may be lower. So, price tend to be sticky.
Imposition of tax:
In case of imposition of lump sum tax, all firms raise their prices and
shift the tax to the customers and in case of sales tax, AVC would shift upwards
and even with the same GPM, price would increase by the full amount of the
tax.
Critical Appraisal:
The critics argue that average cost pricing principle is not a new
theory but reduces to marginalistic principle. To them, if the only goal of long
run profit maximization is taken, it can be proved that the same long run
equilibrium solution would be reached if the firms follow marginalistic rule in
the long run. The major argument of this theory is that firms do not know their
demand elasticity with certainty is wrong because the concept of demand
elasticity is hidden up in setting the GPM. A firm would put low mark-up of the
commodities with close substitutes and vice versa.
However, there are some points to justify this principle:
The information on AVC is easier than MC. It is thus easy to estimate
the average cost (AC).
Many empirical researches have supported the view that firms do not
use MR=MC rule for the price determination but they determine the
price level on the basis of average cost.
It facilitates price setting in multi product firms.
It is easier to be applied by businessman and accountants.
It is based on more realistic assumptions.
Thus, it is useful for avoiding uncertainty and to coordinate the market.
151. Discuss Bain’s Limit Pricing Theory.
The central idea of this theory is the notion of limiting price.
According to J.S. Bain, the firms in the collusive oligopoly do not set price
according to the MR=MC principle but set a price level that effectively
prevents the entry of new firms. In other words, firms charge the limit price.
Assumptions:
There is effective collusion among the firms.
The goal of the firms is the maximization of the long run profits.
The product of the established firms and potential firms are
homogeneous.
The demand of the industry is given and stable.
237
Under these conditions, the firms in the collusive oligopoly set price at the
level that prevents the entry of new firms. According to Bain, this price level
depends on:
a. The cost of the potential entrants.
b. Price elasticity of the demand for the product.
c. The size of the market.
d. The number of established firms in the industry, and
e. The level and shape of LAC.
The price determination under Bain’s theory can be illustrated in fig. 12.3
below.
Bain’s Limit Pricing Model
In fig. 12.3, DD is the market demand curve and MR is the
corresponding MR curve facing oligopoly. LACEF is the long run average cost
curve of the established firms. As LACEF is constant, LMC will be equal to it.
If collusive oligopoly wishes to maximize its short run profits, it will set price
at Pm which is determined by the intersection of MR and LMC curves. LACPE
is the cost curve of the new potential entrants. We see that if Pm price level is
charged, the new potential firms will also earn profits and are thus attracted to
the industry. As a result, the established firms would lose a part of the market
demand.
If price is set at PL level which is equal to the long run average cost of
the potential entrants, the established firms sell Q2 amount of output. At this
price level the established firms will earn a profit equal to C1C2 per unit and the
Fig.12.3
O QA
Price
A
D
MR
G
Pm
PL=C2
Y
D
H
e=1
e<1
Output
LACEF
LACPE
J
C1 BE
Q1 Q2
238
total profits will be C1C2AB. While at this price level, it is not beneficial for the
entrants to enter the industry .If they enter, industry supply will increase and
given the demand, the price level falls below the average cost of production and
the potential firms will incur losses. So PL is the limit price of entry preventing
price.
In this case, the short run profits of the oligopoly firms is the area
C1EHPm which is larger than the profits that is gained by charging the limit
price PL. Firms are sacrificing some short run profits hoping that the profits in
the long run by preventing the entry would be higher.
If the demand and cost curves are such that the monopoly price is less
than the limit price, the oligopolists will charge the monopoly price to
maximize their profits because such a price would maximize short run profits
and effectively prevent entry.
Thus, according to Bain’s Limit pricing theory, the firms in the
collusive oligopoly charge price level in such a way that it prevents the entry of
new firms effectively. Such a price is called limit price. With the help of this
theory, Bain was able to explain why some oligopoly firms set the price level at
the level of the demand curve at which the elasticity of the demand is less than
unity.
152. Discuss Baumol's Sales revenue maximizing model.
William J. Baumol has proposed sales revenue maximization model as an
alternative model to the theory of the firm. According to him, due to the
separation of the ownership and management in modern firms, firms aim is to
maximize the sales revenue rather than to maximize profits. The justifications
given by him for this goal are as follows:
Salaries and other earnings of the managers are related with sales not
profits.
The banks and other financial institutions consider the sales of a firm
and provide more credit to the firms whose sales are growing rapidly.
Personnel problems are more easily solved with growing sales.
Growing sales give prestige to managers while profits give prestige to
shareholders.
Growing sales increases competitive power.
We below discuss Baumol’s static model to explain Baumol’s arguments.
Assumptions
Time horizon of the firm is single period.
The firm attempts to maximize sales subject to a profit constraint.
Conventional cost and revenue curves are assumed.
The profit constraint is determined exogenously.
239
No advertising cost.
Baumol’s static model with no advertising can be illustrated with the help of
fig. 12.4where the profits are maximized at output level XM, Where slope of
TR and PCR equal. However, According to Baumol, The firm aims at the point
where sales revenue rather than profits are maximum. Such a point is point a in
fig.12.4, where the TR curve has reached the maximum point. The firms in this
case produces XA level of output. Thus, in Baumol's model, the firm is a sales
maximizer. It does not mean that the firm does not earn profit. There is a
certain level of profit constraint as shown by SM in the figure.
Sometimes the profit constraint does not allow the firm to reach the
goal of sales maximization. For example; if the profit constraint is 1as shown
in figure, the firm can achieve the goal of profit maximization where as if profit
constraint is 2, the firm can not maximizes its' goal of sales revenue
maximization. It is because the firm can not earn the minimum required profit
2 by maximizing the sales revenue producing XA level of output. In the latter
case, the profit constraint stands as a barrier to the goal of the firm where the
firm produces only Xs level of output at which the sales revenue is less than
maximum. In this case also, the sales revenue maximizing firm will produce
greater output than the profit maximizing firm.
Thus, we see in the Baumol model that the firm is in equilibrium at the
output level that maximizes the sales revenue of the firm rather than the output
level which maximizes profits. If the profit constraint creates barrier in
Fig.12.4
O
TR
TC
TR, TC,
SM
2
XM XA XB
X
a
Xs
240
achieving the goal, the firm will produce the output at which sales revenue is
growing. This output will be larger than the output of a profit maximizing firm.
241
CHAPTER 13: FACTOR PRICING
153. Differentiate between Rent and Quasi rent.
Economic rent is the payment to a factor of production above and over what
is required to keep the factor in its current employment. In other words,
economic rent is a payment to a factor in excess of its opportunity cost or
transfer earning. For example, a land is being used to produce wheat worth Rs.
7000 and it can be used to produce potato worth Rs. 5000. Here, the
opportunity cost is Rs. 5000 and thus
Economic rent = Actual earning - Transfer earning.
= Rs 7000-5000= Rs 2000
The amount of economic rent depends on the elasticity of factor supply.
i) If the supply curve for the factor is perfectly elastic i.e. the factor can be
easily transferred to other uses, all the payment is transfer earning and
economic rent is zero. It has been shown in fig. 13.1
Zero Rent
In the figure, Actual earning= Transfer Earning = area OXMS. Thus, rent is
zero.
ii) If supply curve of the factor is perfectly inelastic i.e. the factor has no
alternative uses. All the payment is rent.
In fig 13.2, the factor has no alternative uses as shown by perfectly
inelastic supply curve further implying that opportunity cost or transfer
earning is zero. Thus, actual earning = economic rent.
MS
D
Y
X
Price
Quantity
S
D
X
Fig.13.1
O
TranforEarning
242
All Rent
iii) If supply curve is elastic, part of its price is rent and a part transfer earning.
For example consider fig 13.3
In the fig. 13.3, the total payment is OLew, opportunity cost is OLeA. Thus,
economic rent is Aew. Marshall called this producer's surplus.
Thus, in summary if the factor supply is less then perfectly elastic, it
earns economic rent. Thus, steeper the supply curve, the more is the economic
rent. If supply curve is perfectly elastic, the payment contains zero rent and if
supply curve is perfectly inelastic, all the payment is rent.
In the short run, fixed factor cannot be taken back from their present
use and transferred to another use where payments are higher. While the
variable factors are free to move to alternative uses, the firms pay them their
opportunity cost while the fixed inputs receive what is left over and that
residual payment obtained by the fixed factors of production in the short run is
called quasi-rent. Quasi-rents are thus residual payments.
To illustrate the concept of quasi rent, take the case of short run
equilibrium situation of perfectly competitive firm, the price OP and quantity
M
S
D
YPrice
Quantity
S
D
X
Fig.13.2
O
economicrent
e
AD
wS
D
L
Fig13.3
O
w
L
Rent
opertunitycost
243
OX, the firm maximizes its profit producing OX unit of output from which it
receives total revenue equal to the area OXeP. (fig.13.4)
Quasi Rent
Out of the total revenue, the firm pays OXBA= TVC to variable factors and the
remained part ABeP goes to fixed factor as quasi- rent.
Thus, Quasi rent = Total revenue - total variable cost
Quasi rent can be divided into two parts: TFC and Excess profit. From fig.13.4
,
Quasi rent = ABCD + DCeP
In the long run, the quasi rent becomes zero because in the long run both fixed
cost and excess profit disappear.
In summary the price of a factor whose supply is fixed in the long run
is called rent. The price of factor which is in fixed supply only in the short run
is called quasi rent. Rent continues in the long run whereas quasi-rent
disappears.
154. What are the main causes of wage differentials?
Wage differentials arise due to non-homogeneity of labor. Non homogeneity
of labor means the differences in skill, type of work, place of work, market
imperfections, etc. Some of the causes of wage differentials are:
Differences between the natures of various occupations.
Differences between the biological and acquired abilities of different
individuals.
Differences in the price of the output which labor produces.
Market imperfections.
ATC
D
X
P,C
Quantity
P
X
Fig.13.4
O
A
e
SAVC
MC
C
B
244
a) Differences arising from nature of occupations are called compensating
differentials. These types of differences arise from the following sources:
Differences in the cost of training.
Difference in the cost of performing jobs.
Differences in the degree of difficulty and unpleasantness of job.
Differences in the risk of the occupation.
Differences in the number of hours required for an adequate
Practice.
Differences in the stability of employment.
Differences in the length of employment.
Differences in the prestige of job.
Differences in the environment.
Differences in the cost of living in various areas.
b) Differentials due to biological and acquired ability are called non-
compensating differentials. These differences arise either due to the inherent
qualities or due to the differences in acquired skills.
c) A major cause of wage differential is the price of the commodity which labor
produces e.g. there are two workers: one produces computer parts which are
sold at Rs. 5000 and another makes furniture sold at RS. 1000. Clearly, the first
worker gets higher wages.
d. Wage differentials also arise from market imperfections. The main reasons
are:
Imperfect knowledge.
Minimum wage requirements.
Immobility of labor.
Discrimination against minorities.
Labor unions.
Over time, the degree of wage differential may either widen or it may also
become lower.
155. Derive the demand curve of labor for a market situation where the
factor market is perfectly competitive and the product market is
monopolistic.
In case of product market and factor market being perfectly competitive, the
value of marginal product of labor (VMPL=MPPL×P) is itself the demand
curve of labor. But if the product market is imperfect, the VMPL curve does
not work as the demand curve of labor because in this case equalizing the
VMPL with the price level will not maximize the firm’s profits. If we suppose
that there is monopolistic competition in commodity market and perfect
245
competition in factor market, we will get from the analysis that the marginal
revenue product of labor (MRPL) defined by MRx×MPPL works as the demand
curve for labor. In such a product market, price of a commodity; say X, is
greater than the marginal revenue i.e. Px > MRx. Since MRx < Px, MRPL lies
below VMPL. Both MRPL and VMPL curve are negatively sloped because
MPL declines as output expands. The derivation of the curves are shown in
fig.13.5(b)
Imperfect market Perfect market
Since the market for labour is perfectly competitive in the present situation,
labor supply is perfectly elastic at given wage rate. The equilibrium of the firm
is defined by the point of intersection of MRPL and wage supply curve as
shown in fig. 13.6
The equilibrium point is e where MRPL= MCL= w and the firm
maximizes profits by operating at such a point. To the left of it, MRPL is
greater than the wage rate which induces the firm to incease the level of labor
use and on the opposite case beyond e, MRPL is less than the wage rate which
compels the firm to reduce the use of labor. Thus, a profit maximizing firm will
demand labour at which MRPL=w= MCL
Mathematically,
The firm’s aim is to maximize profits and
Profit () = R-C
Or, = Px.Qx-wL-F
Where Px=f(Qx) and Qx=f(L)
The first order condition for profit maximization is
x x
x x
x
dQ dPP Q . w 0
dL dQ
Dx
X
P
MRXO
Fig.13.5(a)
L
w
O
Fig.13.5(b)
MRPL=MPPL×MRX
VMPL=MPPL×PX
246
Or,MPPL.MRx-w=0 x x x x
x x x
d(TR ) d(P .Q ) dPMR P Q
dX dX dX
Or, MRPL= w
If we repeat the above analysis for every wage rate, we get the demand curve
for a single variable factor the firm as shown in fig .13.6(b)
The MRPL curve in fig. 13.6(b). shows the demand for labor by the firm at
different wage rates and it serves as the short run demand curve for labor. That
is why it is called the demand curve for labor when only one factor labor is
variable in the short run.
However, if several factors are variable in the long run , the demand for labour
is not the MRPL curve but such a long run demand curve for labor is formed
from the points on shifting MRPL curves. For clarifying why that happens so,
suppose that market wage is w1 and the firm's MRPL is MRP1 as shown in
fig.13.7. The equilibrium point in such a case is point A. When wage rate falls
to w2, other things remaining the same, equilibrium would be in the same
MRPL at point B'. But other things do not remain the same. A fall in the wage
rate has three effects: substitution effect, output effect and profit maximizing
effect. Generally the net results of these effects in case of a fall in wage rate is
the shift of MRPL to the right and equilibrium point is B at which MRPL2= w2.
Generating the points like A and B, we get the long run demand curve for labor
of a firm when several factors are variable.
ew
OL
Le
w
MRPL
SLw
Fig.13.6
OLLe
w
MRPL=DL1
SL2
SL
SL1
Le1Le2
w2
w1
e
e2
e1
(a) (b)
247
Derivation of Long run Demand Curve for Labor
The Market Demand for Labor:
The market demand for a factor is the summation of demand curves of
the individual monopolistic firms. But while adding the individual demands, a
note should be taken about the shift in MRPL to the left through decline in
commodity MRx as a result of reduction in wage rate. When wage rate is
reduced, all firms employ more labor and more amount is produced. The
consequence of this is an increase in supply of the commodity and a resultant
fall in the price of commodity. As the commodity price falls, the MRx also falls
which shifts the MRPL curve leftwards.
156. Derive supply curve of labor.
The most important variable factors are raw materials, intermediate goods
and labor. Among them, the demand for the first two can be derived in the
same way as the demand for commodities. The supply of labor, however,
requires a different approach.
The main determinants of supply of labor are:
The price of labor.
The testes of consumers that define the tradeoff between leisure and
work.
The size of the population
The labor force participation rate.
The occupational educational and geographic distribution of labor.
Supply curve is the relationship between supply of labor and wage
rate, the other determinants can be considered as shift factors. So, we assume
that other determinants are given to derive the supply curve of labor. We also
assume that labor units are identical.
We use the indifference curve analysis to derive the supply curve. For
this, we need a utility function and budget constraint of the worker. A worker's
satisfaction depends on the income that he gets from his work and leisure time
Fig.13.7O
L
w
MRPL1
SL1
MRPL2
SL2
dL
w1
w2
A
B
Long run demandcurve for labor
B1
248
available to enjoy. However, the more time he devotes to work, the less he has
for leisure. Thus, for a given wage rate, there is a trade-off between work hours
and leisure time which we can represent through indifference curve.
In fig 13.8, on X-axis, we have measured time for leisure and on Y-
axis, we have measured money income. The slope of each line from Z to any
point on Y-axis represents wage per hour. For example, if he were to work OZ
hours and earn total income OY0, the per hour wage would be.
OZ
OYw 0 =slope of the line ZY0
The indifference curve here represents the points of combinations of income
and leisure among which period the same level of satisfaction to the labor.
If the wage rate is w1, the individual is in equilibrium by working AZ hour and
earning AA' income and spending OA hours for leisure. If the wage rate
increase to w2, he will work more hours (BZ>AZ) and earn a higher income
BB' and will choose less hours for leisure. It can be summarized in table below.
Wage rate Work hour Leisure hour
w1 AZ OA
w2(w2>w1) BZ(BZ>AZ) OB(OB<OA)
w3(w3>w2) CZ(CZ>BZ) OC(OC<OB)
From the relationship in the table, we can obtain points on the supply curve like
A'', B'', C'', in terms of fig 13.9 etc. The supply curve becomes upward
slopping as derived in figure.
O Leisure
Income
IC3
IC2
IC1
B1
A1
C1
Y2
Y1
Y0
ABC
Work
Z
Fig.13.8
W1
W3
W2
Leisure
249
At lower wage rates, there is positive relationship between increase in wage
rate labor supply. However, at a very high wage rate, there may be a decline in
the hours offered for work. In other words, after a sufficiently high wage rate,
supply of labor hours may fall with the further rise in wage rate. This
phenomenon gives rise to a backward bending supply curve of labor.
157. Write a note on backward bending supply curve of labour?
At lower wage rates, there is a positive relationship between increase
in wage and labor supply. However, at some higher wage rate, hours offered for
work may decline. In other words, there may be a wage rate so high that
quantity of labor supplied reaches a maximum level and after that it might
decline with further increase in wage rate this would give us a backward
bending supply curve of labor.
As wage increases, the consumer can earn income for his Subsistence
living substances by working less hours. Thus, he desires for comfort. As the
standard of living increases; people think that it is not worth while for them to
work for more income unless they get more leisure. Thus as income reach a
level required for a comfortable standard of living, workers put forward greater
demand for more holidays, longer vacation, fewer working hours rather than
demanding ever higher wages associated with longer working hour.
This is called the income effect which effect outweighs the
substitution effects which tends it increase the work effort which gives thee
backward bending supply curve of labour.
In the fig. 13.10 if the wage rate is w, the individual will work AZ
hours, if w2, BZ (BZ>AZ), if w3 CZ, (CZ>BZ), if wage rate increase tow4, he
will reduce his work to BZ hours. and if wage rate increase to w5 he will work
only AZ hours
L
w
O
w3
w2
w1
A* B* C*
SL
B11
A11
C11
Fig.13.9
250
Form fig.13.10 backward bending supply curve can be derived. Up to w3,
increase in wage rate increases the supply of labor. However, higher wage rate
creates a disincentive for longer hours of work. This is because beyond a
certain level of wage rate, the supply of labor decreases as wage rate increases
and gives a backward bending supply curve of labor as shown in fig. 13.11
Backward Bending Supply curve
158. Write a note on monopolistic exploitation.
If firms have monopolistic power in the product market but factor market is
perfectly competitive, the demand curve for labour is the MRPL curve not the
VMPL curve. It means that the factors are paid according to their MRP which is
smaller than VMP. This effect has been called monopolistic exploitation by
Joan Robinson. According to her, a productive factor is exploited if it is paid a
price less than the value of its marginal product (VMP).
O Leisure
Income
IC3
IC2
IC1
ABC
WorkLeisure
Z
Fig.13.10
IC4
IC5
Y2
Y2
Y1
Y0
B1
A1
C1
D1
E1
Y3
Y4
W1
W5
W4
W3
W2
L
w
O
w3
w2
w1
A* B* C*
SL
Fig.13.11
w4
w5
251
There is no monopolistic exploitation when both the factor and
product market are perfectly competitive because we see that in a perfectly
competitive market, VMPL= MRPL because MRx=Px.
But if firm have monopolistic power in the product market, MRPL<VMPL
because MRx<Px. So, in case of monopolistic firms, there is exploitation of the
factors of production. The concept of monopolistic exploitation has been made
clear with the help of a factor labor in fig. 13.12.
Firm Labor market
However, her concept of exploitation has been criticized by many economists.
In imperfect competition, the demand for variety creates such a situation where
the demand curve becomes downward sloping and which leads to the case of
MRx<px and accordingly VMPL >MRPL.
159. Analyze the price determination of factor in a scenario in which
there is monopolistic power in product market and monopsonistic power
in factor market.
Here, we assume that the firms in the product market have monopolistic
power (not monopoly power) in the product market while in the factor market
there is monopsonistic power. We analyze the price determination in such a
situation in two different cases:
a) Equilibrium of a monopsonist who uses a single variable factor labor:
In this case, the demand curve for the monopolistic firm is the MRPL curve but
the supply curve is not perfectly elastic. It is positively sloped. It is because as
the single buyer firm (monpsonist) increases his use of labour, he must pay
higher wage rate. However, the relevant magnitude of the equilibrium is the
marginal expense curve (ME). The marginal expense is the difference between
successive total expenditures at successively higher levels of employment.
Obviously, ME curve lies above the average expenditure (supply) curve
w
OL
w
MRPL1
MRPL2
SL
Le
}
Monopolistic exploitation
OL
w
MRPL
VMPL
Lm
Monopolistic exploitation
LL
wL
wm
SL
Fig.13.12(a) (b)
252
because in hiring an additional unit, all previous unit employed are paid higher
price.
The equilibrium of the firm is shown on fig 13.13 where it equates ME
to MRPL at point e. To the left of e, a unit of labour adds more to revenue than
to total cost, hence it pays the firm to expands the use of labor and to the right
of the point e, an additional unit of that factor adds more to cost than to revenue
and so profit is reduced.
The wage that the firm will pay for Le unit of labour is Wf defined by the point
on supply curve corresponding to the equilibrium.
b) Equilibrium of a monopsonist who use several variable factors:
In a perfectly competitive market, the firm using two variable factor L and K
will be in equilibrium when MPL/w= MPK/r. But in monopsonistic market,
prices are not given. It can be shown that the firm will be if equilibrium when
the ratio of MPP to ME is equal for all variable inputs. For the two inputs case,
the condition is K
L
K
LLK
ME
ME
MPP
MPPMRTS
Mathematically
Let the demand function be Px= f1(Qx)
The production function be Qx= f2(L,K)
Supply function of labour be w= f3(L)
Supply function of capital be r = f4(K)
Then profit () = Px.Qx-wL-rK
The first order condition is,
0.,0
L
wL
L
Lw
L
PxQx
L
QxPx
L
0..,
L
wL
L
Lw
L
QX
Qx
PxQx
L
QxPxor
Le
OL
w
eSL
MEL
MRPL
wf
Fig.13.13
253
Qx Px wor, Px Qx w L 0
L Qx L
Or, MPPL×MRx-MEL=0……….(i)
Because Qx
PxQxPx
dx
dTRxMRXMPP
L
QxL
And dL
dwLw
dL
TEdME L
L )(
0
K0...,
K
rKr
K
Qx
Qx
PxQx
K
QxPxor
Qx Px ror, Px Qx r K 0
L Qx K
Or, MPPK×MRx-MEK=0……….(ii)
Dividing (i) by (ii)
K
L
K
L
ME
ME
MPP
MPP
Thus, the prices of the factors will be determined in accordance with the above
equilibrium formula when there are several factors variable and there is
monopolistic power of firms in the product market and monopsonistic power in
the factor market.
254
CHAPTER 14: GENARL EQUILIBRIUM
160. Write note on interdependence of economy.
The basic feature of an economic system is that the economic units in the
economy are interrelated among themselves. In such an economy, all the
markets: market of commodities and markets of factors of production are
interrelated in such a way that price determination in one market is affected by
another markets. In such a scenario, the prices of commodities and the prices of
factors of production are determined together or they are determined by the
simultaneous reaction behavior of all markets. To make the concept of
interdependence crystal clear, lets take an example: consumer's demand for
various goods and services is affected by their tastes and incomes . In turn
consumers’ income is affected by the amount of resources they own and factor
prices, factor prices depend on the demand and supply of various inputs. The
demand for factors by firms depends on the state of technology and on the
demand for the final goods which they produce, the demand for the goods
depend on consumers' income which in turn depend on the demand for the
factors of production. This circular interdependence in a simple economy
consisting of two sectors: consumer sector and business sector is given below
in fig. 14.1.
The following assumptions underlie our analysis:
All production takes place in business sector.
All factors of production are owned by the households.
All factors are fully employed.
All incomes are spent.
As shown in the fig.14.1 there are two types of movements or flows: real flows
and monetary flows. Real flow means movement in physical terms i.e. goods
move from business sector to household sector and the labor services move
from household sector to business sector. And monetary flow is the flow of
monetary value of the real flow i.e. labor payments move from business sector
to house hold sector and payments for goods move from household sector to
business sector.
We see clearly in the fig. 14.1 that the two flows move in opposite
direction. They are related to each other in terms of factor prices and the prices
255
of goods. The economic system as a whole will be in equilibrium when a set of
prices is attained at which the income flow from firms to households is equal to
the money expenditure flow from households to firm
Interdependence in the simple Two sector Economy
. This interdependence between the various markets market is not
covered in partial equilibrium approach. An economic system consists of
millions of economic decision making units who are motivated by self-interest
and follow their own goals and want to achieve their own equilibrium
independent of other. But all the economic units whether they are consumers,
producers or suppliers of factors are interdependent. The analysis of market
considering such interdependence is included in the general equilibrium theory.
A general equilibrium is defined as a situation in which all markets and all
decision making units are in equilibrium simultaneously (together). A general
equilibrium exists if each market is cleared at a positive price with each
consumer being in equilibrium maximizing satisfaction and each firm being in
equilibrium maximizing profit.
This analysis implies that the actions and behaviors of economic units
in the economy are affected by the behaviors of other economic units and such
interdependence is analyzed in the general equilibrium analysis.
161. Distinguish between partial equilibrium and general
equilibrium.
Partial equilibrium is the study of equilibrium of a certain individual firm or
industry viewed in isolation. It is a market process for the determination of
product prices and factor prices in which one or two variables only are
discussed, other things remaining constant. Stigler says "A partial equilibrium
Factor services
Money income
Commodities
Expenditure on commodities
FirmsHouse hold
Fig.14.1
256
is one which is based on only a restricted range of data, a standard example is
price of a single product, the price of all other products being held fixed during
the analysis."
However, a general equilibrium is an extensive study of a number of
economic variables, their interrelationships and interdependence for
understanding the working of the economic system as a whole. It brings
together cause and effect series of changes in prices and quantities of
commodities and services in relation to the entire economy. An economy can
be in general equilibrium only if all consumers, all firms, all industries and all
factors services are in equilibrium simultaneously.
We can list out the main differences between them as follows:
Partial Equilibrium General Equilibrium
It is the equilibrium
analysis of single market,
viewed in isolation.
It is the study of simultaneous equilibrium in all
markets.
Each economic agent’s
equilibrium is determined
under the ceteris paribus
assumption.
There is no place of ceteris paribus assumption in
general equilibrium.
Here, each market is
independent of the effect
of other markets.
Here, all the markets are interdependent.
One price is determined at
a time.
All prices are simultaneously determined.
For example, the mango
market is in equilibrium
when Dm=Sm
Where,
Dm=f(Pm);ceteris paribus
Sm=f(Pm); ceteris paribus
Pm= price of mango.
The economy is in general equilibrium when all
the markets and all economic agents (producers
and consumers) are in equilibrium. For this
situation, the conditions are:
Consumers' utility be maximum.
Producers' profit be maximum.
Excess demand in all markets is zero
(QD=QS).
162. What do you mean by existence, stability and uniqueness of
equilibrium?
General equilibrium is said to exist in an economy when all the markets
and all the economic agents (consumers and producers) are simultaneously in
equilibrium. In other words, general equilibrium exists when there is zero
excess demand in all markets and all the economic agents are in simultaneous
equilibrium i.e. consumers have maximized their satisfaction and all the
257
producers have maximized profits. Generally, three issues are related with
general equilibrium. They are:
Existence
Stability
Uniqueness.
Existence: An equilibrium is said to exist when all the market are cleared at
positive price. In other words, equilibrium is said to exist when excess demand
is zero in all the markets. Formally, if Ej= 0 for Pj>0, equilibrium exists, where
j =1, 2, 3,……m are m commodities.
We illustrate this issue with a simple example of particular
equilibrium. Suppose that a commodity is produced and sold in perfectly
competitive market where the price of the product is determined by the demand
and supply functions for the product.
Existence Issue of Equilibrium
Equilibrium in fig.14.2(a) exists because at positive price demand and
suppy curves have intersected where as equilibrium in fig. 14.2(b) does not
exist. In terms of excess demand function, where excess demand is Qd-Qs,
equilibrium exists if the excess demand function meets the price axis in terms
of fig.14.3(a) and does not exist if it does not fig 14.3(b)
P
O Qty
e
D
SD
S
P
Fig.14.2
Q
(a)
P
O QtyD
SD
S
(b)
258
Existence Issues of equilibrium
This result can be generalized to general equilibrium analysis.
Stability: The stability issue is related to whether the disturbed prices return to
the equilibrium or not. If the answer is ‘yes’, the system is said to be stable and
if ‘no’, the system is said to be unstable. In other words if there is tendency of
the disturbed prices to return to equilibrium, the system is stable and otherwise
not.
In the above example of particular equilibrium, equilibrium is stable if
demand curve is negatively sloped and supply curve is positively sloped and on
the opposite case, it would be unstable.
Stability Issue of Equilibrium
In the fig. 14.4(a), at disturbed price P1, there is excess supply which drives
price down and at price P2, there is excess demand which drives price up. So
equilibrium is stable. Similarly in fig. 14.4 (b), equilibrium is unstable.
In terms of excess demand function, we can say that equilibrium is
stable if excess demand curve is negatively sloped and it is unstable if the
excess demand curve is positively sloped ( Fig. 14.5(a) and. 14.5(b)).
P
O
Fig.14.3(a)
P
O
(b)
ED
ED=Qd-Qs
ED
ED=Qd-Qs
P
OQty
e
D
SD
S
P
Fig.14.4(a)
(b)
P1
P2
excess demand
excess supplyP
OQty
e
D
SD
S
P
P1
P2
excess demand
excess supply
259
Stability Issue of Equilibrium
Uniqueness: Equilibrium is unique if there is a single equilibrium i.e. demand
curve meets the supply curve only once and if the demand curve meets the
supply curve more than once, there are multiple equilibria (Fig14.6(a)
and14.6(b)).
Uniqueness Issue of Equilibrium
In term of excess demand function, if excess demand function meets the price
axis only once, equilibrium is unique. If it meets more than once, there are
multiple equilibrium (Fig 14.7(a) and 14.7(b)).
P
O
Fig.14.5(a)
P
O
(b)
ED
ED=Qd - Qs
ED=Qd - Qs
ED
ee
P
O Qty
e
D
SD
S
Fig.14.6(a)
P
O QtyD
DS
(b)
S
D e2
e1
260
Uniqueness Issue of Equilibrium
Thus, we see that existence issue is related with the equality of demand and
supply, stability issue is related with the slopes of demand and supply function
and uniqueness issue is related with the slope of excess demand function.
The examples of the three issues with an example of partial
equilibrium can be easily generalized to the general equilibrium.
163. Differentiate between Marshallian and Walrasian conditions for
stability.
Leon Walras analyzes the equilibrium process through totonnement
process i.e. his analysis is in terms of excess demand and excess supply. If
equilibrium price is disturbed, excess demand drives price upwards and excess
supply drives price downwards and accordingly equilibrium may be stable or
unstable. However, Marshall does such an analysis through the auction
mechanism i.e. if there is positive excess demand price, quantity to be sold is
increased and if there is negative excess demand price, quantity to be sold is
decreased and accordingly equilibrium may be stable or unstable.
Both approaches may not lead to the same conclusions for stability. If
equilibrium is stable in Marshall's sense, it may be unstable in Walras’s sense
and if equilibrium is stable in Walras’s sense, it may be unstable in Marshall’s
sense. We present below the three possibilities:
Case I: When demand Curve is negatively sloped and supply curve is
positively sloped.
In this standard case, equilibrium is stable from the view of both approaches. It
is shown in fig.14.8 (a)and fig.143.8(b).
P
O
Fig.14.7(a)
P
O
(b)
ED
ED=Qd - Qs
ED=Qd - Qs
ED
e
e2
e1
261
Walrashian Stable Equilibrium Marshallian Stable Equilibrium
In fig.14.8 (a), the demand and supply curves are sloped in such a way that the
excess demand price drives price up and the excess supply drives price down
and the equilibrium is stable. In fig. 14.8(b), in case positive excess demand
price, producers increase the quantity brought to market and in case of negative
excess demand price, producers reduce the quantity brought to market and the
equilibrium is accordingly stable.
Case II: When both demand and supply curve are negatively sloped
In this case, equilibrium cannot be stable according to both approaches. If it is
stable according to Walrasian approach and it is unstable according to
Marshallian approach, vice versa.
If demand curve is steeper than the supply curve, equilibrium is stable
in Marshallian sense and unstable in Walrasian since. It is shown in fig.
14.9(a). and fig.14.9(b)
P
OQty
e
D
SD
S
P
Fig.14.8(a)
P1
P2
excess demand
excess supplyP
OQty
e
D
SD
S
Pnegative excess demand price
positive excessdemand price{
Q1 Q2Q
Fig.14.8(b)
262
Walrashian Unstable Equilibrium Marshallian stable Equilibrium
If supply curve is steeper than the demand curve, equilibrium is stable
in Walrasian sense but unstable in Marshallian sense. It is shown in fig.
14.10(a) and fig.14.10(b)
Walrashian Stable Equilibrium Marshallian Unstable Equilibrium
164. Differentiate between Marshallian and Walrasian equilibrium
approaches.
See the introduction part from the above question.
The main differences between them are:
Walrasian Approach Marshallian Approach
It is a hypothetical model and does not Here, the market works through the
P
OQty
e
D
S
D
S
P
Fig.14.9(a)
P1
P2
excess demand
excess supply
P
OQty
e
D
S
D
S
P negative excess demand price
{
Q1 Q2Q
positive excessdemand price
Fig.14.9(b)
P
O Qty
e
D
S
D
S
P
Fig.14.10(a)
P1
P2
excess demand
excess supply P
O Qty
e
D
S
D
S
P
negative excess demand price{
Q1 Q2Q
positive excessdemand price
Fig.14.10(b)
263
analyze how market works. There is a
central individual working as a market
coordinator. He announces to all
decision makers a single market price
which they take as a parameter in
choosing their planned supplies and
demands. Then, he revises the price
according to the nature of excess
demand until excess demand is zero
and the market is in equilibrium.
auction mechanism. When a
commodity is produced, it is brought
to market. The sellers sell to one who
pay the highest price.
In the standard case of negatively
sloped demand curve and positively
sloped supply curve, it results in stable
equilibrium but here it happens
directly through tatonnement
process.
Here, the same conclusion is reached
in the standard case of negatively
sloped demand curve and positively
sloped supply curve but it happen
through the auction mechanism
which establishes the demand price.
Here, information is passed through
the umpire.
Here, information is passed through
the auction mechanism which rations
off available output and the demand
and price are immediately made
known. Buyers never need to know
the supply price.
Here, trade takes place only at
equilibrium.
Here, trade takes place at every point/
instant as available supply is
auctioned off.
165. Analyze the 2×2×2 general equilibrium model.
General equilibrium solution in an economy is said to exist when all the
market are cleared at positive prices and each economic agent is simultaneously
in equilibrium. In the case of a simple economy with two factors, two
consumers and two commodities, general equilibrium solution, thus, exists
when the two product market, two factor markets are cleared at positive price
and the two consumers are in equilibrium by maximizing their utilities and two
producers are in equilibrium by maximizing profits simultaneously.
We concentrate our analysis with only the static conditions to be
fulfilled for the general equilibrium exists to exist in 2×2×2 economy.
The following assumptions underlie our analysis.
Assumptions of the 2×2×2 model:
i) There are two factors of production labour (L) and capital (K), which are
perfectly divisible homogeneous and exogenously given.
264
ii) There are two commodities X and Y. Technology is given, the production
function of X and Y are represented by the iso-quants with usual properties.
Further, production functions are independent.
iii) There are two consumers A and B whose preferences are given by the
indifference curve with usual properties. The utility functions are also
independent. Bandwagon, snob, Veblenesque and other external effect are ruled
out. The consumers are the king of themselves in consuming the commodities.
iv)The goal of each consumer is maximization of his own satisfaction subject
to the income constraint.
v) The goal of each producer is maximization of profit subject to technological
constraint of the production function.
vi) The factors of production are owned by the consumers.
vii) There is full employment of factors of production and all incomes received
by their owners A and B are spent.
viii) There is perfect competition in commodity and factor market.
The solution of the system requires determination of the following
variables.
i) Total quantity of X and Y to be produced.
ii) The allocation of given inputs K and L to the production of each commodity
( Lx, Ly, Kx, Ky)
iii) The quantities of X and Y to be bought by A and B (XA, XB, YA, YB)
iv) Price of factors ( w, r).
v) Price of commodities (Px, Py).
vi) The determination of resource ownership (LA, LB, KA, KB)
In the perfectly competitive economy, when it reaches a general equilibrium,
three static properties are to be observed.
Efficient allocation of resources among firms (Efficiency in
Production)
Efficient distribution of commodities among consumers
(Efficiency in Distribution)
Efficient Combination of Products.
These three properties are also called marginal conditions of Pareto
Optimality.
i) Equilibrium in Production:
Equilibrium in production requires the determination of efficient
distribution of the available productive factors among the existing products or
firms.
A firm is in equilibrium when it chooses the factor combination which
minimizes the cost of production. In such a situation, the following condition is
fulfilled.
265
Slope of iso-quant = slope of iso-cost
Or, MRTSLK= w/r
Where, MRTSLK is marginal rate of technical substitution of labor for
capital and represents the slope of iso-quant.
The joint equilibrium of production of two firms in our 2×2×2 model
can be shown by the use of Edge worth box of production. In fig. 14.11 below,
the iso-quant of X are plotted taking Ox as origin and that for Y are plotted
taking OY as origin. The locus of points of tangency between X and Y iso-quant
is called Edgeworth contract curve (ECC) of production.
Edge worth Box Diagram of Production
Any point on this box diagram refers to six variables: the amount of X and Y,
and the allocation of K and L in the production of X and Y, e.g. point Z in fig.
14.12. represents X3,Y3,Lx, Ly,Kx, Ky. However all the points on the box
diagram are not efficient. A point is efficient if it is impossible to increase the
production of one commodity without decreasing the production of other by
moving from one point to another. In this sense, only the points on the contract
curve are efficient that by moving from a point off the contract curve to a point
on it, production of at least one commodity is increased without reducing the
other.
Along the Edge worth contract curve,
Slope of X iso-quant = Slope of Y iso-quant.
i.e. MRTSx
LK= MRTSy
LK
In our model due to perfect competition
MRTSxLK= w/r and MRTS
yLK = w/r implies MRTS
xLK= w/r
The general equilibrium occurs at a point where MRTSx
LK= MRTSyLK.
So, the equilibrium is not unique in the sense that the condition for equilibrium
OY
OX
y6
y5
y4
y3
y2
y1
x1
x2
x3
x4
x5
x6
K
L
a
b
c
d
z
LX
Fig.14.11LY
KX
KY
edge worth contract curve of production
266
is satisfied at every point of the contract curve. So there will be an infinite
number of Pareto optimal equilibrium points. However with perfect
competition, only one of the equilibrium will be realized where the following
condition is satisfied.
MRTSxLK= MRTS
yLK =w/r
Given the Edge worth contract box of production, we can determine the amount
of X and Y that maximizes the firms' profits but these quantities must be equal
to those that consumers are willing to buy to maximize their profits. Thus, to
bring both production side and demand side together, we derive the production
possibility curve from the Edge worth contract curve of production by plotting
the points in output space. For example, point a, b and c corresponds to point a',
b' and c' fig. 14.12.
Production Possibility Frontier
All the points on the PPC are Pareto efficient. The negative of the slope of the
PPC is called marginal rate of product transformation (MRPTxy) and is given
by,
y
xxy
MC
MC
dx
dyMRPT
Since in perfect competition, firms equate MCx and Px, and MCy and Py for
profit maximization, we have,
y
x
y
xxy
P
P
MC
MCMRPT
Given the commodity price Px and Py, general equilibrium is reached at the
point on the PPC that has a slope equal to the ratio of these prices. Such a
Fig.14.12
a1
b1
c1
production possibility frontier
x2
x3
x4
y2
y3
y4
x1
y1
y5
x5 X
Y
P
P1
267
solution is shown by point T in fig.14.13 where y
x
y
x
P
P
MC
MC
OB
OA . The two
firms will be in equilibrium in equilibrium producing the levels of output Xe
and Ye.
Equilibrium of production
Equilibrium of Consumption:
Equilibrium of consumption requires the maximization of utility by all
consumers together. A consumer maximizes his satisfaction, faced
with market prices Px and Py when the marginal rate of substitution of
X and Y equals to be the ratio of Px and Py. The condition for
equilibrium is y
xxy
P
PMRs . Since both consumers face the same
price, the condition for joint equilibrium is, y
xxy
Bxy
A
P
PMRSMRS
The general equilibrium of consumption is shown in fig. 14.15, where
we have constructed an Edge worth box diagram of consumption with the
equilibrium quantities of X and Y as Xe and Ye by dropping from point T
parallel to the axes. A's indifference curves are plotted taking O as origin and
B's indifference curves are plotted taking T as origin.
xe
ye
X
Y
P
P1
Fig.14.13
T
A
B
O
268
Equilibrium of Consumption
Here also, all the points on the box are not efficient. Just like before only the
points lying along the Edgeworth contract curve of consumption are efficient
and all the points lying out of the contract curve are inefficient in Pareto sense.
The Edgeworth contract curve is the locus of points of tangency between the
indifference curves of the two individuals and along the contract curve, the
following condition is fulfilled MRSA
xy= MRSB
xy.
Here also, the condition for equilibrium is fulfilled at each point of the
contract curve and as such there are an infinite number of possible Pareto
optimal equilibrium of distribution. But with the presense of perfect
competition, only one of these points is consistent with the general equilibrium
of the system. This is the point T' where the following condition is fulfilled:
y
xxy
Bxy
A
P
PMRSMRS
The equilibrium in consumption is represented by the point T' in fig. 14.15,
where consumer A enjoys utility level A2 by consuming OM of X and ON of Y
and consumer B enjoys utility level B4 by consuming MXe of X and NYe of Y
commodity.
Simultaneous Equilibrium in Production and Consumption:
The third condition for the existence of a general equilibrium solution
in the 2×2×2 model is that the marginal rate of product transformation be equal
to marginal rate of substitution of the two commodities between the consumers
i.e.
xe
ye
X
Y
P
P1
Fig.14.15
T
A
B
O
edge worth contract curve of consumption
A1
A2
A3
A4
A5
B1
B2
B3
B4
B5
N
M
T1
yB
yA
XBX
A
269
xyB
xyA
XY MRSMRSMRPT
In perfect competitive market, this condition is satisfied since MCx= Px and
MCy= Py
y
xxy
Bxy
A
XYP
PMRSMRSMRPT
This is called the third condition for Pareto optimality. This condition
implies that the behavior of producers as shown by the MRPT matches with the
behavior of consumers as shown by the MRS. MRPTXY shows the rate at which
one product can be transformed to another product and MRS shows the rate at
which the consumers are willing to exchange one good for another. Their
equality shows that the production sector plans are consistent with household
sectors plans. For example if x
yMRPTXY
1
3 and
x
yMRSXY ; it implies that
the economy can produce one unit of X by sacrificing 3 unit of Y while the
consumers are ready to exchange X and Y on a one-to-one basis. As a result of
this inequality, firms under produce Y and overproduce X commodity. So, the
inefficiency in product mix results in an inefficient production of commodities
in comparison to the desire of the consumers. The above discussed inequality
and its consequences is illustrated in fig. 14.16
So, for attaining the general equilibrium, the third condition says that the
combination of output must be optimal (best) both from consumers’ and
producers’ point of view.
To summarize the above three conditions, we can say that in perfect
competition with no discontinuities and constant returns to scale, the simple
X
Y
P
P1
Fig.14.16O
MRSXY=
MRPTXY=
MRPTXY=
YX
YX
3Y X
X
Y
3Y
X
270
2×2×2 economy can reach the general equilibrium solution when the Pareto
optimality conditions are fulfilled.
The MRSxy is equal for both consumers.
The MRTS between two factors is equal for both firms.
The MRPT and MRS are equal for both goods.
Allocation of Resources:
Allocation of L and K to the production of X and Y can be found by
just going one step back to Edge worth box diagram of production from the
PPC. Suppose point T in fig.14.15 which is the equilibrium point of production
corresponds to T'' point oh the Edge box diagram in fig.14.17 below which has
determined the allocation of factors as Lx and Kx for producing X and Ly and
Ky for producing Y.
Price of Commodities and Factors:
For the determination of factor price Px, Py, w and r we have the
following equations in our above model:
i) From profit maximizing tendency of firms
r
wMTSMTS LK
yLK
x …………………..(i)
ii) from utility maximizing behavior of individuals
OY
OX
y6
y5
y4
y3
y2
y1
x1
x2
x3
x4
x5
x6
K
L
LX
F i g . 1 4 . 1 7LY
KX
KY
..............................( )A B xxy xy
y
PMRS MRS ii
P
271
iii) In perfect competition, the producer will employ each factor up to the point
where its marginal physical product times the price of the output it produces
just equals the price of the factor i.e.
w=MPPL,x×Px= MPPL,y×Py……………………………..…(iii)
r= MPPK,x×Px= MPPK,y×Py…………………………………(iv)
Even if there seem to be four equations for finding the values of four variables
or four prices, they are not independent because by dividing (iii) by (iv), we
have,
LK
yK
yL
XK
XLMRPT
MPP
MPP
MPP
MPP
r
w
,
,
,
, which is same as equation (i)
So the value of Px, Py, w, r, are not uniquely determined in Walrasian
system. However by taking one price as numerarie, all other price can be found
to ratio of prices.
Allocation of Factor Ownership:
To determine the equilibrium values for the unknowns LA, LB, KA, KB,
we have the following four equations:
i) From the assumption of constant returns to scale, Euler's theorem suggests us
that total factor payment is equal to the total value of the product i.e.
Px.X+Py.Y= w.L+r.K………………………………..………..(i)
ii) The income of the consumer is totally spent so that we have,
wLA+rKA= Px.XA+Py.YA………………………………..……….(ii)
wLB+rKB= Px.XB+Py.YB………………………………………...(iii)
iii) Finally from the assumption of full employment
LA+LB=L………………………………...………..…………….(iv)
KA+KB=K………………………………………..………..…….(v)
The above five equation gives only three independent equations because (ii)
and (iii) equals (i).
So, again, the values of KA, KB, LA, and LB cannot be determined
uniquely. Here, also we can take the help of a numeraire to get rid of this
indeterminacy problem.
272
CHAPTER 15 : WELFARE ECONOMICS
166. What do you mean by welfare economics?
Welfare economics is concerned with the effects of economic activities on
economic welfare of the people. It weighs all alternative economic situations
from the point of view of society's well being or social welfare. Let the total
welfare in a country be W but given the factor availability endowment and state
of technology, suppose this welfare could be larger e.g. W*. The aim or task of
welfare economics is:
To show that in the present state W<W* and
To suggest way of raising W to W*.
Thus, welfare economics is mainly concerned with the evaluation of the effects
of activities of the different economic units on social welfare of the people.
167. Write a note on growth of GNP criterion of welfare.
According to Adam Smith, the growth of the wealth of a society or the
growth of GNP means an improvement in the social welfare of the people.
Thus, his criterion is the GNP criterion. His logic behind this assertion is that
increase in GNP indirectly means increase in employment and increase in the
production of goods and services available to the society.
Importance: This criterion emphasizes the importance of efficiency in social
welfare. The more efficient is the production, the more will be the level of
social welfare. However, production efficiency only does not guarantee the
maximization of social welfare. If the production is not distributed efficiently,
welfare may not increase with the rise in GNP rather it may fall.
Weakness: This criterion assumes the state of income distribution as ideal or
just and does not take care on the distribution part of the GNP. That is why, if
there in highly unequal distribution, increase in GNP will not raise the level of
social welfare.
168. Write a note on Bentham's Criterion.
According to Bentham's criterion, there is an increase in welfare when the
greatest good is secured by the greatest numbers. It indirectly assumes that total
welfare is the sum of the utility of the individuals i.e. W=Ui
Where Ui = utility of ith
individual.
Weaknesses:
i) Interpersonal comparison is hidden in his criterion.
273
Let there be only three individuals in a society A, B and C. so that
total welfare W=UA+UB+UC.
Suppose, individuals A and B are better off and C is worse off and
W>0 because (UA+UB)>UC. Here, A and B have a greater worthiness
than C which is clearly inter personal comparison.
ii) It cannot be applied when both greatest good and greatest number do not
exist simultaneously. For example let UA=100, UB=80, and UC=20 so that W=
200. In other situation, let, UA=50, UB=60 and UC=50 so that W=160. Here, in
the first situation there is only greatest good but in the latter, there is amount
even distribution among the greatest number. So, there is sometimes difficulty
of both greatest good and greatest number being together.
169. Write a note on cardinalist criterion.
According to cardinal welfare economists, social welfare will increase when
income is more evenly distributed among the individuals in the society. To
them, if the distribution of income is perfectly equal, the social welfare is
maximum. They have used the law of diminishing marginal utility of money as
a criterion of welfare and suppose that the MU of Rs. 1 for rich is less than the
MU of Rs. 1 for the poor. That is why, a transfer of income from the rich to the
poor increases social welfare. For example, there are only three individuals A,
B and C. A's a millionaire while B and C earn only Rs 50000. In this case, the
value of Rs. 1 for A is very small in comparison to B and C. Thus, welfare can
be increased by redistributing the income equally among all member of the
society.
Weaknesses:
These assumptions will works only when all individuals have same
utility functions. If the rich get more utility from Rs.1 than the poor, the
redistribution will reduce the welfare instead. Another problem with it is that
sometimes redistribution may inspire some people to work less, thus leading a
reduction in total GNP. In this case, Pareto inefficiency in the resource
allocation will lead the reduction in social welfare.
170. Explain the Kaldor-Hicks compensation criterion.
According to the compensation criterion by Hicks and Kaldor, a change
leads to an increase in social welfare if the monetary value assigned by the
gainers is greater than the monetary value assigned by the losers. Suppose, a
change is being brought which will benefit some (gainers) and harm others
(losers). We can ask the gainers "How much are they ready to pay in order to
bring the change?" We can also ask the losers, "How much are they ready to
pay in order to stop the change?” If the amount of money told by gainers is
274
greater than the amount of money told by the losers, the change results in
increase in social welfare because the gainers have gained such an amount that
is enough to compensate the losers and still they will have some net gain. This
criterion, thus, evaluates the increase in social welfare on the basis of monetary
valuation of the gainers and losers.
Weaknesses:
It addressees only potential compensation rather than real
compensation.
It would be a correct criterion if marginal utility of money is equal for
all the individuals. But it is not realistic to assume so. That is why it
may become meaningless. For example, a change benefits a billionaire
and he is ready to pay Rs. 100,000 but it harms a labor and the labor is
ready to pay Rs. 1000 (90% of his income). To this criterion, it results
in the increase in welfare but indeed the value of Rs. 1000 for a poor is
far greater than the value of Rs. 100,000 for a billionaire.
It is also not free from interpersonal comparisons.
Scitovsky has found it contradictory.
171. Clarify the Bergson's criterion.
Bergson has used the social welfare function to evaluate the different
economic situations. A social welfare function is just like an individual
consumer’s utility function or indifference curve in the sense that it gives us the
same level of social welfare from different utility levels of the individuals. In
case of only two individuals, it can be represented by a social Indifference
Curve with the usual properties. With the help of such indifference contours,
we can tell about the welfare conditions of different economic situations.
275
For example, in fig. 15.1 , a change that takes the society from point ‘b’ to
point ‘c’ or ‘d’ increases the social welfare. However, a change that takes the
society from point ‘a’ to point ‘b’ will bring no change in social welfare.
Weaknesses:
The first problem with this criterion is that it is not easy to construct
the social welfare function.
The social welfare function cannot be used to derive social
indifference curve in output space as similarly to the indifference
curve of an individual without taking into account the distribution of
income among the various individuals in the economy.
172. State the Pareto Optimality criterion.
This is the most objective criterion of measuring the change in social
welfare. According to this criterion, any change that makes at least one
individual better off and no one worse off is an improvement in social welfare.
Speaking in a just opposite way, a change that makes no one better off and at
least one worse off is a decrease in social welfare. In other words, a situation in
which it is impossible to make some one better off without making someone
worse off is said to be Pareto optimal or Pareto efficient situation.
For achieving the Pareto optimal situation in an economy, there
marginal conditions should be satisfied.
i) Efficiency of distribution of commodities among consumers.
ii) Efficiency of the allocation of factors among firms.
iii) Efficiency of allocation of factors among commodities.
Fig.15.1
O
UB
UA
W1
W2
W3
W4
a
b
c d
276
We analyze below the three conditions in a two consumers, two
commodities and two factors of production economy (2×2×2 model) with the
following assumptions:
i) There are two factors of production: labor (L) and capital(K), which are
perfectly divisible homogeneous and exogenously given.
ii) There are two commodities X and Y. Technology is given, the production
function of X and Y are represented by the iso-quants with usual properties.
iii) There are two consumers A and B whose preferences are given by the usual
indifference curve with usual properties.
iv) The goal of each consumer is maximization of his own satisfaction and the
goal of each producer is maximization of profit subject to the given constraints.
vi) The factors of production are owned by the consumers.
vii) There is full employment of factors of production and all incomes received
by their owners A and B are spent.
viii) There is perfect competition in commodity and factor markets.
i) Efficiency in Distribution:
The distribution of commodity X and Y between the consumers A and B is
efficient if it is impossible by a redistribution of goods to increase the utility of
one individual without decreasing the utility of the other. Taking the help of
Edgeworth box diagram, we get that only the points on the Edge worth contract
curve satisfy the Pareto optimal condition. It is shown in fig. 15.2.
Efficiency in distribution
OB
OA
B5
B4
B3
B2
B1
A1
A2
A3
A4
A5
Y
X
a
b
c
z
XA
F i g 1 5 . 2XB
YA
YB
edge worth contract curve
277
Any distribution that lie off the contract curve is inefficient e.g. z because by
moving to any point between a and b on the contract curve from the point z,
there is increase in the utility of both individuals. If we move to pint ‘a’, utility
of A remains same but B's utility increases to B3 (B3>B2). Similarly, if we
move to point ‘b’, utility of B remains same but utility of A increases to A4
(A4>A3). So, all the points from a to b represent improvement in social welfare
compared with the distribution at z. Conversely, we can say that if we move off
the curve, we result in a decrease in social welfare.
So, the contract curve shows the locus of Pareto optimal or efficient
distribution of goods between consumers. The curve is made up of the points of
tangency of the two consumers' indifferent curves i.e. points where the slopes
of ICs are equal. In other words, at each point on the Edge worth contract
curve, the following condition is satisfied.
MRSA
XY=MRSB
XY
Therefore, the first marginal condition for Pareto efficiency is that MRS
between two goods be equal for all consumers.
ii) Efficiency in Allocation of Factors:
Reasoning in the same way as (i), we can say that the Edge worth contract
curve of production is the locus of points that are efficient and all points off the
curve of (e.g. H) are inefficient (fig 15.3). Also along the Edge worth contract
curve of production (ECC), the slopes of the iso-quants for the production of X
and Y commodities are equal i.e. at each point on the ECC, the following
condition is satisfied.
OY
OX
y5
y4
y3
y2
y1
x1
x2
x3
x4
x5
K
L
H
LX
F i g . 1 5 . 3LY
KX
KY
Edge worth contract curve of productionMRTSX
LK=MRTSX
LK
278
Efficiency in Production
Thus, the second marginal condition for Pareto efficiency is that MRTS
between capital and labor be equal for all commodities produced by different
firms.
iii) Efficiency in Product Mix:
The third condition for Pareto optimality or efficient composition of output
requires that the MRPT between any two commodities be equal to the MRS
between the same two goods i.e.
MRPTXY = MRSA
XY=MRSB
XY
Since MRPT shows the rate at which a good can be transformed into another
and MRS shows that rate at which consumers are willing to exchange a good
for another, the rate must be equal for Pareto optimality. Suppose, if
x
yMRPTXY
1
3 and
x
yMRSXY i.e. MRPTXY>MRSXY, it shows that the
economy can produce one unit of X by sacrificing 3 unit of Y while the
consumers are ready to exchange X and Y on a one to one basis. Clearly, the
economy produces too much of X and too little of Y relative to the tastes of the
consumers. Therefore, welfare can be increased by increasing the production of
Y and decreasing the production of X.
In summary the conditions for Pareto Optimality are:
i) The MRS between any two goods must be equal for all consumers.
ii) The MRTS between any two inputs be equal in the production of all
commodities.
iii) The MRS of any two goods must be equal to the MRPT between those
two goods.
Weaknesses:
The first weakness of it is that it cannot evaluate a change that makes
some individual better off and other worse off.
The second one is that fulfillment of Pareto optimal situation does not
guarantee the maximization of social welfare. It is only a necessary
but not a sufficient condition.
173. Write a note on Scitovsky Paradox.
According to Scitovsky, the Kaldor Hicks Compensation criterion gives
paradoxical results about the social welfare. He proved that in the Kaldor Hicks
compensation criterion it can be shown that if situation A is better than
situation B in terms of social welfare then situation B also can be shown to be
superior to situation A. Thus, according to Scitovsky, the Kaldor Hicks
criterion gives contradictory and paradoxical results which is called Scitovsky
paradox. Such a case arises when the new utility possibility frontier intersects
279
the old utility possibility frontier due to some policy changes. This fact has
been illustrated in fig.15.4.
In fig.15.4, GH and JK are two utility possibility frontiers. Suppose the initial
situation is ‘C’ which lies on the JK utility possibility frontier. Further suppose
that a policy change shifts the JK frontier to GH. And the two individuals find
themselves at situation D. Here, situation D is better than situation C because
from situation D, we can reach situation F by redistributing the goods between
them where the utility of A increases by CF though the utility of B remains
constant. Thus, a movement from C to D is the improvement in social welfare
according to Kaldor Hicks criterion. But according to Scitovsky, a movement
from situation D to situation C also can be shown to be an improvement in
social welfare according to Kaldor Hicks criterion because by redistributing the
goods from point C, we can reach situation E where utility of B increases as
compared to situation D while the utility of a remains constant. Thus, according
to the Kaldor Hicks compensation criterion, situation D is better than situation
C and situation C is also better situation D.
174. Write a note on Scitovsky Double Criterion of social welfare.
To correct the difficulties of the contradictory results in the Kaldor Hicks
Criterion, Scitovsky proposed his Double Criterion according to which a
change is an improvement if the gainers in the changed situation are able to
persuade the losers to accept the change and simultaneously the losers are not
able to persuade the gainers to remain in the original situation.
This fact can be illustrated with the help of fig.15.5.
B's Utility
Fig.15.4O A's Utility
E
D
G
J
H K
C
F
280
In fig. 15.5, CD and EF are the two utility possibility frontiers which have not
been intersected. Suppose that the original situation is represented by point Q.
A change brought the individuals to the situation G. Point G shows an
improvement in social welfare because with the redistribution of resources
situation R can be reached where both individuals utility is higher as compared
to the situation Q. In this case, a movement from Q to G fulfils the Kaldor
Hicks compensation criteria. But a movement from G to Q does not fulfill the
criteria because by redistributing from the point Q, we cannot reach a situation
in the CD curve where utility increases. That is why situation G is better than
situation Q and situation Q is not better than situation G. Thus, to fulfill the
Scirtovsky double criteria, two criteria are to be fulfilled:
The change from point Q to point G should fulfill the Kaldor Hicks
criterion. It is called Kaldor–Hicks Test.
The change or movement from point G to point Q should not fulfill
the Kaldor Hicks criteria. This is called Reversal Test.
In this way, the Scitovsky’s Double Criteria demands the fulfillment of two
separate conditions. That is why it is called double criteria.
Therefore, when the utility possibility frontiers do not intersect each other, a
movement from the lower utility possibility frontier to a higher one increases
social welfare according to the Scitovsky criterion. This is possible only when
the change increases aggregate output or real income.
B's Utility
Fig.15.5O A's UtilityD
G
C
R
Q
F
281
175. Write a note on ‘Pigovian Welfare Economics’.
According to the welfare economist A. C. Pigou, welfare is the utility
obtained by people. If we add the utilities of all individuals in the society, we
get social welfare. Since the meaning of the term ‘welfare’ is very broad, Pigou
has limited his analysis to economic welfare. That is why economic welfare is
not the indicator of social welfare because it cannot include the aspects like
quality of work, social security, working environment, etc that are included in
social welfare. Thus, economic Welfare is that part of social welfare that can be
brought directly or indirectly into relation with the measuring rod of money.
According to Pigou, the utility obtained from the goods and serviced
that can be exchanged in the market only is included in economic welfare.
Pigovian Welfare Conditions
Pigou has listed two conditions for the improvement in social welfare.
According to the first criterion, increase in national income increases social
welfare. In the state of equal distribution of desires, tastes and income, the
increase in national income increases social welfare. And according to the
second criterion, the redistribution of income also helps to increase the level of
social welfare. To him, such redistribution increases the satisfaction of the poor
by larger amount than the disutility of the rich thereby created from such
redistribution.
This concept of social welfare is rest on the following two assumptions:
Equal capacity for satisfaction
Diminishing marginal utility of income
According to Pigou, different people get different levels of satisfaction from the
same level of real income. Similarly, same amount gives less utility to the rich
than the poor because the poor uses that amount in the necessary purposes
whereas the rich use that amount to such needs whose intensity is rather low.
That is why a redistribution of income from the rich to the poor reduces the
inequality and increases the social welfare.
Dual Criterion
Pigou has used the double criterion to find out the improvement or increase in
social welfare. The first one is that the increase in income from the transfer of
resources to the activities with higher social value and increase in production
without reducing the production of other commodities and without reducing the
share of the poor can be taken as the increase in welfare. Secondly, the
reorganization of the economy without reducing the national income and the
share of the poor increases the social welfare.
Assumptions of Pigou Double Criterion
Each consumer aims at the maximization of utility with his income
constraint.
282
Interpersonal comparison of utility is possible.
Law of diminishing marginal utility of income.
Equal capacity for satisfaction.
Criticisms
The Pigovian welfare economics is the first analytical study on welfare
economics. But it has certain shortcomings which are listed below:
Welfare cannot be measured in cardinal numbers: According to
Pigou, welfare is the sum total of utilities of all individuals. But utility
is a subjective concept and cannot be measured cardinally.
National Income is not the appropriate measure of welfare:
According to the modern economists, national income cannot be an
appropriate indicator of social welfare because national income can
also increase due to inflation which makes the condition of the poor
rather worse. On the other hand, the measurement of national income
is not so much easy. Thus, ‘choice’ not the ‘national income should be
the basis of welfare.
The concept of equal capacity for satisfaction does not make
Pigovian economics a positive study. That is why it is not based on
scientific presentation.
Despite these weaknesses, Pigovian economics has contributed a lot to give
birth to the modern welfare economics. Based on the Pigovian analysis, the
modern economists have analyzed the social welfare function and
compensation principle.
176. Write a note on 'point of bliss'.
The point of bliss is the point where the society’s welfare becomes
maximum. Thus, the society is said to be reached the point of bliss when it
reaches the point of maximum social welfare. Further, social welfare is
maximum when the society reaches the highest possible social indifference
counter. We analyze this in a 2×2×2 model with the following assumptions:
i) There are two factors of production labor (L) and capital (K), which are
perfectly divisible, homogeneous and exogenously given.
ii) There are two commodities X and Y. Technology is given, the production
function of X and Y are represented by the iso-quants with usual
properties.
iii) There are two consumers A and B whose preferences are given by the
usual indifference curve with usual properties.
iv) The goal of each consumer is maximization of utility and the goal of each
producer is profit maximization.
v) The production functions as well as utility functions are independent.
283
vi) The social welfare function is exogenously given.
vii) A social welfare function W = (UA, UB) exists.
Now, to determine the point of maximum social welfare, we have to determine
the social welfare maximizing values of the following variables.
Welfare maximizing quantity of X and Y.
Welfare maximizing quantities of given K and L to the production
of each commodity i.e. Lx, Ly, Kx, Ky.
Welfare maximizing distribution of commodities between A and B
i.e. XA, XB, YA, YB.
For the determination of such a situation of maximum social welfare, we use
two tools:
Social welfare function
Grand utility possibility frontier (GUPF).
Derivation of Grand Utility Possibility Frontier:
The grand utility possibility frontier is derived from production
possibility curve (PPC). Each point on the PPC can be distributed between the
two consumers in an infinite number of ways represented by the points in Edge
worth contract curve of exchange corresponding to the particular output
combination. For example point 'a' on PPC in fig 15.6 can be distributed
between the two consumers A and B in an infinite number of ways as shown by
the points on the contract curve e.g. point 'c' denotes the utility of A as A2 and
that of individual B as B8. We can plot these combinations in a utility space in
fig 15.6 on whose axes we measure UA and UB in ordinal utility indexes.
Points c on fig 15.6 defines the point c' in fig. 15.7. Plotting the utilities
combinations represented by the points on Edgeworth Contract Curve (ECC),
we get a utility possibility frontier for the product mix 'a' as SS’ in fig. 15.7
x0
y0
X
Y
P
P1
Fig.15.6
A
B
O
a
b
x1
y1
A6B
3
B8
A2
284
Similarly, we can repeat this process for another point on PPC say point ‘b’ and
get another utility possibility frontier RR' in the utility space. The envelope of
all the utility possibility frontiers is called the grand utility possibility frontier.
Thus, the GUPF becomes tangent to one and the only point of each utility
possibility frontier. It has been derived in fig. 15.7 as shown by the curve UU’.
It is worth nothing that all the points on the GUPF e.g. c', b', etc are the points
satisfying the third condition of Pareto optimality i.e.
MRPTXY=MRSA
XY=MRSB
XY. Thus, point c' shows the grand utility that is
attainable to the society from the output combination X0Y0.
Determination of Point of Bliss:
Combining the GUPF with the social welfare function as shown by the
set of social indifference counters, we can determine the point of maximum
social welfare. The welfare is maximized at the point of tangency of the GUPF
with the highest possible social indifference contour. The point W*in the fig.
15.8 is called the point of bliss. In our example, the maximum social welfare is
W3 and the utility obtained by individual A is UA* and that of individual B is
UB*.
Fig.15.7
O
UB
UA
S
R
c1
b1
S1R1
A2
A6
B8
B3
Grand utility possibilityfrontier
U
U1
285
It is clear from the above discussion that Pareto optimality is a necessary but
not a sufficient condition. All the points on the GUPF are Pareto efficient.
However point N, though it is Pareto efficient, shows lower level of social
welfare.
Further, we can also determine the output levels of the two commodities,
distribution of the commodities between the individuals A and B and the
resource allocation in producing the two commodities that are compatible with
the point of bliss.
177. Prove that perfect competition leads to maximization of social
welfare.
The point of bliss is obtained at the point where the grand utility
possibility frontier is tangent to the social indifference contour. In other words,
the fulfillment of the Pareto optimality conditions is a prerequisite or necessary
condition for the maximization of social welfare. In other words, the bliss point
is attained by the fulfillment of the following Pareto optimality conditions.
MRSA
XY=MRSB
XY
MRTSX
LK=MRTSY
LK and
MRPTXY= MRSA
XY=MRSB
XY.
So, the welfare maximization solution does not depend on prices of
commodities and factors of production. However, as we see in the 2×2×2
general equilibrium model, perfect competition can lead to general
equilibrium in which all the Pareto optimal conditions are satisfied. It can,
thus, be shown that the general equilibrium with perfect competition in 2×2×2
economy leads to the point of bliss.
Fig.15.8
O
UB
UA
W1
W2
W3
W4
point of blissW*UB*
UA*
N
286
i) Utility maximization of each individual requires that MRSXY= PX/PY
Since in perfect competition all consumers face the same commodity prices, we
have.
Py
PxMRSMRS B
XY
A
XY ………………………………..…………...(i)
What we get from equation (i) is MRSA
XY= MRSB
XY which is the first marginal
conditions of Pareto optimality. Thus, existence of perfect competition leads to
the achievement of Pareto optimality in distribution.
ii) Profit maximization occurs at the point where MRTSLK= w/r. Since in
perfect competition all firms face the same prices, we have MRTSX
LK=
MRTSY
LK= w/r…………………………………..….(ii)
What we get from equation (ii) is MRTSX
LK= MRTSY
LK which is the
second condition of Pareto optimality.
iii) Finally, the simultaneous equilibrium in production and exchange requires
that MRPTXY= MRSA
XY= MRSB
XY
In competitive market Py
Px
MCy
MCxMRPTXY and
from (i) Py
PxMRSMRS B
XY
A
XY
Thus, it is follows that MRPTXY= MRSA
XY= MRSB
XY which is the third marginal
condition of Pareto optimality.
Therefore, a perfect competitive system guarantees the fulfillment of
all the three conditions of Pareto Optimality and accordingly the attainment of
maximum social welfare. This is the result of profit maximizing behavior of
firms and utility maximizing behavior of consumers under perfect competition.
In perfectly competitive system, each individual, pursuing his own self interest,
is led by an invisible hand to a course of action that increases the general
welfare of all.
So, despite the problem of welfare maximization does not depend on the prices,
the general equilibrium reached on the economy having perfectly competitive
market fulfills all the conditions of Pareto optimality and leads to the point of
bliss or to the point of maximum social welfare.
178. What is market failure? How does it occur?
Market failure does not mean that a given market has ceased (stopped)
functioning. Instead, it is a situation in which a given market does not
efficiently organize production or allocate goods and services to the consumers.
It can be viewed as a scenario in which the individual pursuit of self interest
leads to a worse result for the society as a whole.
287
Market failure generally happens due to imperfectness of the market
system. The existence of perfect competition fulfills all the conditions of Pareto
optimality. But perfect competition is a rare phenomenon in the real world. So,
markets fail resulting into the over production of some goods and under
production of other leading to the failure economic efficiency. In such case,
there is a clear economic case for government intervention.
Causes of Market Failure
The following are the prominent causes of market failure.
i) Imperfect Competition:
Imperfect competitive market violates the conditions of Pareto
optimality. Let, there be monopoly market. Then, P>MC. In a 2×2×2 economy,
equilibrium condition in a perfect competitive market are x
y
P MCx
P MCy
However, in monopoly, x
y
MC Px
MC Py . Thus, we have,
MRPTXY<MRSXY
For the fulfillment of third condition of Pareto optimality MRPTXY= MRSA
XY=
MRSB
XY, but due to presence of monopoly market, MRPTXY<MRSXY, i.e.
consumers desire more commodities to be produced but the monopolist does
not produce such quantity. So, there is reduced welfare and misallocation of
resources.
In fig.15.9, the point of maximum social welfare is the point E where
MRPTXY= MRSA
XY. But when X is produced under monopoly
. So, the consumer is having lower level of social welfare
W1. Therefore, imperfect competition comes as a hindrance to the
maximization of social welfare.
MCx MRx Px
MCy MRy Py
X
Y
P
P1
Fig.15.9
O
MRPTXY=MRSXY=PX
PY
E
H
MRPTXY=MRX
MRY
Q
w2
w1
288
ii) Externalities:
Externalities refer to the beneficial and detrimental effects of an
economic unit like a firm, a consumer or an industry, etc upon other units for
which there is neither corresponding receipt nor corresponding payment. The
beneficial externalities or external economies or positive externalities create
benefits for others for which one does not receive any payment e.g. making a
garden. Similarly, the detrimental effects or external diseconomies or negative
externalities occur when the economic unit inflicts costs on others for which it
is not required to pay e.g. pollution made by a factory. In case of positive
externalities, the private MC is greater than the social MC and the price fixed
on the basis of private MC will be higher than determined on the basis of social
marginal cost and there will be underproduction. In case of negative
externalities, the private MC will be lower than social MC and the society will
face overproduction. these case have been illustrated in fig 15.10(a) and
15.10(b).
Positive Exlernalities in production Negative Externalities in production
It is clear that production in case of externalities is not optimal in either case.
So, market loses efficiency and fails.
iii) Existence of public goods:
According to Samuelson, the good which can be consumed some
quantity by each consumer and each consumer consumes the quantity of total
production is called pubic good i.e. for public goods, q1=
q2=………………..=qn=Q
Where qi= quantity of goods consumed by ith
individual.
Q = Total quantity of produced good.
Characteristics of public gods:
Non-rivalry in consumption.
Non-excludability.
Indivisibility.
X
Y
S1(SMC)
Fig.16.10(a)
O
DS1
S(PMC)
S
Under production
SMC=PMC-positiveexternalities
X
Y
S1(SMC)
Fig.15.10(b)O
DS1
S(PMC)
S Over production
SMC=PMC+ negative externalities
289
Here, in case of public goods, marginal cost is zero if any consumer increases
the consumption of the good and no one can be excluded if he does not pay. So,
no one pays for the good (MR=0). Hence for public good, MR=MC=0. It
indeed implies that profit is zero. In such a situation, market system cannot
work because profit is the main target of the market and it fails. So, in case of
pure pubic gods, the free riders’ problem creates market failures.
iv) Asymmetric Information:
When there is uncertainty of information (e.g. a car may have been
used as a vehicle for carrying goods but it may not be known to the new buyer),
the market loses efficiency.
v) Inequality:
Wide differences in income, wealth, etc lead to a wide gap in living
standards between affluent households and those experiencing poverty which is
undesirable for efficient working of the market system.
vi) Merit Goods:
Merit goods are those goods which the government feels that if left to
the consumers themselves, they will under consume and thus they ought to be
subsidized or provided free at the point of use e.g. health services, education,
training, public library etc. In case of these goods, the market principle does not
work.
179. Write a note on the theory of second best.
The theory of second best is concerned with what happens when one or
more optimality conditions are not satisfied in an economic model. The
Canadian economist Richard Lipsey and Australian economist Kelvin
Lancaster showed that if one of the optimality conditions in not satisfied, it is
possible that the next best solution is involved in changing the other variables
away from the ones that are usually assumed to be optimal. This means that in
an economy with inevitable market failure in one sector, there can be a
decrease in efficiency due to a move toward greater perfection in another sector
because the disequilibrium in a single sector is enough to destroy the
equilibrium of the whole economy.
Thus the general theorem states that "If there is into the general
equilibrium system a constraint which prevents the attainment of one of the
Paretian conditions, the other paretian conditions, though still attainable, are
no longer desirable. If one of the Paretian condition cannot be fulfilled, then an
optimum situation can be achieved only by departing from all other conditions
and a second best optimum in the face of actual circumstance may be tried."
Richard Lipsey and Kelvin Lancaster.
290
This can be made clear with fig 15.11 where U1, U2, etc are the
community indifference curves. E is the point where all the Pareto optimal
conditions are fulfilled. But due to some imperfections in the economy, let
there exists a constrain MN. Hence, the first best point E is unattainable.
Now, we are forced to move inside PPC and produce along MN and
inside MN only. Point like R, A, S, etc can be produced. We need not produce
at point R or S as they are Pareto efficient because they provide lower level of
social welfare. Point A is the second best point because it provides the
maximum possible welfare in the changed situation though it is not a Pareto
Optimal point.
Formally, they argue that when an objective function F(x1,x2,………xn) is to be
maximized/ minimized subject to some constraint (x1,x2,………xn) = 0, it is
Pareto optimal solution. Here, x1,x2,………xn are the element of consumption
vector of all individuals in the economy in some given order Optimizing F(…)
such that (…) = 0, where can be seen as the transformation function
specifying the constraint given by the available technology and initial
resources, we get the following necessary conditions.
n
i
Fn
Fi
{ i= 1,2,3,……..n-1} ……………..………….(i)
The Pareto conditions can be interpreted as MRSi = MRSn= MRPT. They tried
to formulate another constraint that would cover the obstacles to achieving a
The readers who do not have knowledge of calculus may omit this part while reading.
X
Y
P
P1
Fig.15.11O
E
R
A
U1
U2
U3
S
M
N
291
first best Pareto optimum. The function is taken to be the production
constraint in the economy. If for some reason e.g. monopoly, externalities, etc,
one of the condition cannot be fulfilled due to the constraint, i.e.
n
iK
Fn
Fi
; where K1 is a constant.
The resulting problem amounts to optimize the Lagrangian function,
i
n
F iF- K
F n
; where and are Lagrange multipliers.
The necessary optimum conditions are:
i i i
n n n
( / Q KRFi.
Fn / Q KR
i=2,3,………………n-1
Where n 1i 1 ni
2
n
F F F FQi
F
and n 1i i ni
2
n
RRi
These second best conditions are quite complicated and thus extremely difficult
to apply. So, it remains only a theoretical excitement as it is difficult to
determine the sign of Fni and ni.
According to them, the constraints are of two types:
Technological constraint and
Behavioral constraint.
If one condition is violated, it may be technically impossible for the
government to fulfill other conditions, to correct externalities or instances of
imperfect market conditions, when government needs subsidy for public goods
production, there may not be any non-distortive taxation system available. The
second type of constraints are behavioral constraints on policy reflecting the
fact that certain measures though technically feasible are not at the
governments’ disposal or believed to be so e.g. the law may prohibit a specific
policy instrument, the government may simply dislike the nationalization of
some industries or it may believe that it may lose next election if the policy is
used.
Implications /Importance:
i) It has been used to question the desirability of advocating competitive pricing
in some particular market when it is known that Pareto conditions do not hold
in other markets.
ii) It has helped to establish the fact that universal trade is not leading to Pareto
optimum unless all countries achieve optimum conditions.
i 2Q n i i ni
n
F FR F F
F
292
iv) It is not true that nationalized industries should fix a price equal to MC
while other industries do not.
v) It helps to understand the fact that government should remove imperfections
by levying tax or giving subsidy in case of externalities.
