Utility theory

Utility is defined as want satisfying power of the commodity.

• Marginal Utility- Increase in the total utility as a result of consumption of additional unit of commodity.

MUn = TUn – TUn-1 MU = TU/Q• Total Utility – Sum of the utilities an individual

derives from the total consumption of his commodity

TU n = U1 + U2 + U3 +………… Un

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Approaches to measurement of utility-

• Cardinal Utility approach

• Ordinal Utility approach Indifference Curve Approach Revealed Preference Hypothesis

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CARDINAL UTILITY APPROACH

• Utility can be measured in monetary units by the amount of money consumer is ready to sacrifice for another unit of commodity.

• Measurement of utility can be done in subjective unit called utils

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ORDINAL UTILITY APPROACH

• The utility is not measurable.

• Consumer should be able to determine the order of preferences among different bundle of goods.

• Consumer need not know in specific units the utility of various commodity to know his preferences.

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CARDINAL - Assumptions

Rationality Cardinal Utility Diminishing Marginal Utility Constant Utility of Money Utility is additive

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Consumer Equilibrium

• When a consumer pays price for the commodity he is consuming, he compares the utility he derives from the additional unit of commodity with the utility he sacrifices in terms of price paid for the unit of commodity

MU = P In case there are more than two commodities the

equilibrium condition may be expresses as

n

n

C

C

B

B

A

A

P

MU

P

MU

P

MU

P

MU...........

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Ma r

gina

l U

t il i

t yM2

M1

Q3 Q2 Q3

MUx

Dx

P3

P3

P3

Q3 Q2 Q3

Pri

c e

Figure 4.3 : Derivation of Demand Curve

M3

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Criticism of Cardinal Approach

Satisfaction derived from various commodities cannot be measured objectively

Money used for measurement is not correct as it is not constant and the value of money keeps fluctuating.

It is psychological concept, therefore the very law is questionable.

The cardinal approach considers the effect of price changes on the demand curve ( price effect). This assumption is unrealistic as the price effect may include income and substitution effect

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Ordinal Utility Approach- assumptions

Rationality Utility is Ordinal Diminishing Marginal Rate of Substitution The total utility of the consumer depends on

the quantity of the commodity consumed i.e.

U=f (q1 q2 ….qn)

Consistency and transitivity of choice Non satiety

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Indifference Curve

An indifference curve may be defined as the locus of points giving particular combination or bundle of goods which yield the same utility or level of satisfaction to the consumer so that he is indifferent as to the particular combination he consumes.

89

25

20

15

10

5

05 10 15 2520

a

b

c

d

Commodity X

Com

mod

i ty

YFigure : Indifference Curve

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Indifference Curve Map

• A number of indifference curves representing various levels if satisfaction form an indifference map

Figure : Indifference Map

Quantity of X

Quanti

ty o

f Y

Y

O X

IC4

IC3

IC2

IC1

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Properties of Indifference Curve

Indifference curve have negative slope Indifference Curve are Convex to Origin Indifference cannot touch or Intersect each

other Higher Level of Indifference Curve

Represents Higher Level of Satisfaction

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DIFFERENT SHAPE OF INDIFFERENCE CURVE

Perfect Substitutes Perfect Complimentary

X1 X2 X3 X4

0

Y1

Y1

Y1

Y1

Commodity X

Figure : Perfect Substitutes

B

A

IC2

IC1

Commodity X

Com

mod

ity Y

Figure ) Perfect Complimentary Commodity

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Consumer Equilibrium

• Budget Constraint-Income acts as a constraint in the attempt for maximizing utility and is known as budget constraint.

Y = px qx+ py q y

y

xxy p

qp

py

yq

1

x

yyx p

qp

xp

yq

1

94

Y/Py

Y/Px

Com

mod

ity

Y

Commodity X

Figure : Budget Line

95

Commodity X

0 M

N C IC3

IC2

IC1

A

B

Com

mod

ity

YFigure : Consumer Equilibrium

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Two conditions must be fulfilled for the consumer to be in equilibrium

Scope of Indifference Curve (MRS) should be equal to the slope of budget line

At the point of consumer equilibrium, indifference curve is convex to the origin, i.e. MRS is diminishing

y

x

y

x

y

x

y

xxy

p

P

MU

MU

MU

MU

P

PMRS

xyMRS

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Derivation of Demand Curve Using IC Approach

P

Budget line shifts

New Equilibrium(E2)

Point of Tangency ofBLS & Higher IC

(Price Consumption Curve)

Join successive pointsOn QY axis to get DD

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Derivation of Demand Curve Using IC Approach

Change in the consumption basket as a result of Changes in price is called price effect.

The total price effect comprises of two components

(a) substitution effect

(b) income Effect

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• When the price of a commodity changes, the price of the substitute remaining the same, the price ratio changes (given constant money income). The change in the relative price induces substitution of cheaper good for the expensive one. This change is referred to a substitution effect.

• If the price of a commodity decreases, the consumer’s real income increases. The change in the consumption basket due to change in the real income in called income effect

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There are two methods followed for splitting the total price effect into income effect and substitution effect.

• Hicksian approach• Slutsky approach

Hicks assumes constancy of real purchasing power of the consumer by keeping the consumer on the same satisfaction level.

Slutsky keeps real purchasing power constant in the sense that the consumer could purchase the original combination of commodities.

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HICKSIAN APPROACH – Normal Commodity (Price Fall)

Figure : Income & Substitution Effect: Hicksian Approach (Price Fall)

N

IC2

LM

IC1

Co

mm

odit

y Y

Commodity XX1 X2 X3

B1B B3

A

A1

0

Income Effect

SubEffect

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HICKSIAN APPROACH – Normal Commodity (Price Rise)

IC1

IC2

L

N

M

A

0 X2 X3 B”X1 B

Income

Effect

Substitution

Effect

Commodity Y

Com

modit

y X

Income & Substitution Effect :

Hicksian Approach (Prise Rise)

Price Effect

B’

A’

103

Slutsky Approach – Income & Substitution Effect (Price Fall)

IC3IC2

IC1 MNL

0 X1 X2B X3

B1 B2

A

A1

Commodity X

Com

mod

ity Y

Income and Substitution effects SlutskyApproach

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TECHNIQUES OF DEMAND

FORECASTING

SURVEY METHODS

STATISTICAL METHODS

SURVEY METHODS

CONSUMER SURVEYDIRECT

INTERVIEW

OPINION POLL METHODS

COMPLETE ENUMERATI

ON

SAMPLE SURVEY

END-USE METHOD

EXPERT OPINION

MARKET STUDIES &

EXPERIMENTS

SIMPLE METHOD

DELPHIMETHOD

MARKET TEST

LABORATORY TESTS

STATISTICAL METHOD

TREND PROJECTION BAROMETRIC METHODECONOMETRIC

METHODS

GRAPHICAL METHOD

TREND FITTING / LEAST SQUARE METHODS

BOX-JENKINS METHOD

LEAD INDICATORS

COINCIDENTALINDICATORS

LAGINDICATORS

REGRESSION METHODS

SIMULTANEOUS EQUATIONS

FITTING TREND EQUATION

1. Linear Trend

S=a+bT

2. Exponential Trend

Y = a ebT

Log Y = Log a + bT

YEAR SALES T T2 ST

1992 10 1 1 10

1993 12 2 4 24

1994 11 3 9 33

1995 15 4 16 60

1996 18 5 25 90

1997 14 6 36 84

1998 20 7 49 140

1999 18 8 64 144

2000 21 9 81 189

2001 25 10 100 250

n=10 ∑=164 ∑T=55 ∑T2=385 ∑ST=1024

TABLE 1

S=a+bT

∑S=na +b∑T∑ST=a∑T + b∑T2

See table 1,

164=10a+55b

1024=55a+385b , by solving these two equations we get the trend

equation as

S=8.26+1.48T

For 11th year

S = 8.26 + 1.48 (11) = 24,540 tonnes

BOX JENKINS METHOD

• Used for short term projection• Uses stationary time series data Steps in Box Jenkins Method1.Eliminate trend from time series data2.Make sure there is seasonality in

stationary time series data (if value of one or more coefficients are different from zero, it reveals seasonality in time series data)

3. Apply models to it.

(1)Auto-regressive model

Yt = a1Yt-1 + a2Yt-2 +…..+anYt-n + et

et is random portion of Y which is not explained by the model

(2) Moving Average model

Yt = m + b1et-1 + b2et-2 +….+bpet-p + et

(3) Auto regressive moving average model

Yt = a1Yt-1 + a2Yt-2+..+anYt-n+b1et-1+b2et-2+…+ bpet-p + et

YEARPopulation(X)

SugarConsumed (Y) X2 XY

1992 10 40 100 400

1993 12 50 144 600

1994 15 60 225 900

1995 20 70 400 1400

1996 25 80 625 2000

1997 30 90 900 2700

1998 40 100 1600 4000

∑n=7 ∑X=152 ∑Y=490 ∑X2=3994 ∑XY=12000

Simple Regression Method

Y = a + bX∑Y = na + b∑X∑XY = ∑Xa + b∑X2

See table

490 = 7a +152 b

12,000= 152a + 3994b

By solving these equation we get

Y = 27.44 + 1.96 X

Multi- variate method

QX = a - bPx +cY +dPy+jA

Simultaneous Equation Model

Yt = Ct + It +Gt + Xt

Ct = a + bYt