Production analysis

Production Production AnalysisAnalysis

BY: MILAN PADARIYAPharma MBA

Meaning of Meaning of ProductionProduction

• The basic function of a firm is to produce one or more goods and /or services and sell them in the market.

• Production requires employment of various factors of production, which are substitutes among themselves to certain extent.

• Thus, every firm has to decide what combination of various factors of production, also called inputs, to choose to produce a certain fixed or variable quantities of a particular good.

• The problem is referred to as “ how to produce?”


• Production has a broad meaning in economics.• Production means presenting an item for sale,

where the item could be a tangible good or an intangible good.

• Tangible goods could be presented for sale through either their manufacturing or through just trading in them.

• Production include activities such as transporting, storing, and packaging of goods.

• Thus, people who are engaged in transporting, say, wheat from Haryana to Kerala, are also considered as producers of wheat.


• Firms which procure wheat from the market, convert it into wheat flour and then pack it in bags under their brand name are also producers of wheat.

• In case of services, however, intermediaries do not exist and their production comes through manufacturing only.

Production FuctionProduction Fuction• A production function expresses the technological

or engineering relationship between output of a good and inputs used in the production, namely land, labour, capital and management(organization)

• Traditionally, production functions are defined in terms of quantities of output and inputs.

• The production function could be written as

Q = f (Ld, L, K, M, T)

= f1, f2, f3, f4, f5 > 0

Where

Q = output in physical units of good X

Ld = land units employed in the production of Q

L = Labour units employed in the production of Q

K = capital units employed in the production of Q

M = managerial units employed in the production of Q

T = technology employed in the production of Q

f = unspecified function

fi = partial derivation of Q with respect to i th input

• This function assumes that output is an increasing function of all inputs. This is generally true.

• This function gives the maximum possible output that can be produced from a given amount of various inputs, or, alternatively, the minimum quantity of inputs necessary to produce a given level of output.

• The relative importance of various inputs in production varies from product to product.

• For ex, production functions for agricultural products generally have inputs as land, fertilizer, rainfall, seeds, etc.

• In contrast, the production function for industrial products have inputs as labour, capital, management and technology.

• Land is an important factor of production in agriculture, while labour is an important factor of production for industry.

• If the two inputs considered are labour and capital, the production function reduces to

Q = f (L, K) = f1, f2 > 0Short run is the period during which atleast

one of the factors of production is available in a fixed quantity.

Thus , during such a period, production could be increased or decreased by changes in other inputs only.

• For ex, in a given season, a farmer might have a fixed quantity of land to grow wheat, but he could still produce more or less wheat by using more or less fertilizer.

• Similarly, Maruti Udyog has a fixed capacity to manufacture cars but it could still vary its production by scheduling work on one shift instead of two shifts or on all the three shifts instead of two shifts.

• How short is the short-run?• It depends! In the case of a farmer, the short-run

could be just about a year, while in the case of Maruti Udyog, it could well be around five years.

• This is beacause, land is not fixed for the cultivation of wheat beyond a perticular season, and the next season would come after one year only. In constrast, Maruti udyog would need aroung five years to add to its capacity, fund raising, assets purchasing and installation, etc.

• Thus, short-run is a time concept and not a time period.

• The short-run version of production function assuming capital as the fixed input (K) and labour as the variable input, could be written as

Q = f (L, K)On the other hand, Long run is the period during

which all the factors of production are variable.

Special Features of Production Special Features of Production

FunctionFunction

1. Labour and capital are both inevitable inputs to produce any quantity of a good

2. Labour and capital are substitutes to each other in production.

These features imply that one need some quantity of both the inputs to produce any quantity of a good but there are alternative combination of these two inputs to produce a given quantity of output.

ISOQUANTSISOQUANTS• Observations:• 1) For any level of K, output increases

with more L.• 2) For any level of L, output increases with

more K.• 3) Various combinations of inputs produce

the same output.

Isoquants are curves showing the combinations of inputs that yield the same output.

IsoquantsIsoquants

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Capital Input 1 2 3 4 5

Labor Input

IsoquantsIsoquants

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Capital Input 1 2 3 4 5

Labor Input

Production withProduction withTwo Variable InputsTwo Variable Inputs

Labor per year

1

2

3

4

1 2 3 4 5

5Capital per year


Labor per year

1

2

3

4

1 2 3 4 5

5

Q1 =55

The isoquants are derivedfrom the production

function for output levelsof 55, 75, and 90.

A

D

Capital per year


Labor per year

1

2

3

4

1 2 3 4 5

5

Q1 =55



A

D

B

Q1=2 =75

Capital per year


Labor per year

1

2

3

4

1 2 3 4 5

5

Q1 =55



A

D

B

Q2 =75

Q3 =90

C

ECapital per year

Properties of Properties of IsoquantsIsoquants

1. They are falling.2. The higher the isoquant, the higher is the output3. They do not intersect each other.4. They are convex from below.

IsoquantsIsoquants• The isoquants emphasize how different input

combinations can be used to produce the same output.

• This information allows the producer to respond efficiently to changes in the markets for inputs.

IsoquantsIsoquants• The Short Run Versus the Long Run

Short-run:• A time period when one or more factors of production cannot be

changed to change output. These inputs are called fixed inputs.

Long-run• A time period when all inputs are variable.

Short run Production Short run Production FunctionFunction

• The shape of a short-run production curve is such that it is first convex from below and then concave from below.

• This is because of the operation of the Law of Variable Returens.

• Under this law, as more and more units of the variable input are employed in the production, fixed inputs remaining in an original state, production first increases at an increasing rate and then at a diminishing rate, leading to a decline in total production eventually.

• The law generally holds good, for • (a) in the beginning as more labour is used, fixed

capital is utilized better and more efficiently than before, thereby output increases at an increasing rate, and this continues until optimal utilization of fixed capital is achieved;

• (b) after this point, new(additional) labour finds the fixed capital inadequate and hence increment in output is at a diminishing rate and

• (c) eventually labour input becomes so much that there is no work for new labour and so they disturb the earlier labour, thereby leading to a decrease in total output.

Short run Production Short run Production FunctionFunction

• There are three stages of production1.Increasing such that average product is

rising.2.Increasing but average product is falling3.Decreasing.

In practice, the first stage is short, the second stage is long and the third stage is never entertained by a prudent enterpreneur.

Long RunLong RunThe decision problem which a production

manager faces in the long-run could be 1.What are the optimum quantities of labour

and capital that he should hire and employ?• The answer to this question might depend on

his specific problem. For ex, he may have a fixed production target and wish to find out the least-cost input combination for that level of output. Alternatively, he could have a fixed rupee budget for production and wish to determine that

Input combination which maximizes his output for a given cost. Lastly, neither production target nor production budget may be fixed and the manager might seek that input combination which maximizes his profit.

• Three approaches to solve the problem.1. Least-Cost Input Combination2. Maximum-output Input Combination3. Maximum-Profit Input Combination

Least-Cost Input Least-Cost Input CombinationCombination

• The least-cost input combination for a given output could be explained through any of the three forms of the production function : table, graph and equation.

• However, since the table provides only a limited no of alternative input combinations for any given level of output. So consider graph only.

• For determining the least-cost technology, one needs besides the production function, factor prices.

• If PL and PK were the prices of labour and capital, respectively, then the total cost equation would be the following.

C = L* PL + K* PKWhere C = total cost, and L and K are units of

labour and capital. In function PL and PK are fixed and L, K and C are variable.

• As isoquant map was drawn from the production function, a map of isocost lines could be drawn from the equation, where a specific isocost would be for a given value of C. Thus, if factor prices were PL = 3 and PK = 3, an isocost line for C = 30 would have input combinations such as

L K

10 0

8 2

5 5

0 10

• Similarly, more isocost lines could be drawn, one for each value of C.

• Thus, an isocost line gives alternative combinations of labour and capital that a firm could hire with a given cost.

• Since factor prices are assumed constant, isocost lines are linear, and they are all parallel to each other.

• Further, the higher the cost line, the greater is the cost.

• Given the isoquant map and isocost lines, the least cost input combination could easily be derived.

• Super impose the isoquant specific to the target population level (Q=122) and the isocost lines map on a graph .

• Figure indicates that Q=122 could be produced by any one of the input combinations given by points A, B, and E.

• However, the production cost associated with

points A and B is higher than the one at point E, for the former points lie on a higher cost line (C=48) then does the latter point (C=45).

• Thus, in this case, point E is the least-cost point for Q = 122, and so it is called the equilibrium point.

• The input combination corresponding to this point (L=7, K=8) is then the least-cost input combination for Q =122.

• The special feature of the equilibrium point is that it

is the point where the specific isoquant is tangent to an isocost line. Tangency implies equal slope.

• Thus, it can be concluded that the least-cost input combination is that combination at which the slope of the isoquant equals the slope of isocost line.

• The equality of these two slopes is the necessary condition for least cost input combination.

• There is also a sufficient condition for the least-cost combination, which is met if the isoquant is convex from below.

• It should be clear that the least cost input mix depends both on the production function (isoquant) and factor prices (isocost lines).

• If any one of them undergoes a change, the equilibrium point would change.

• Let us analyse the effect of a fall in the price of labour(PL).

• As labour price falls, the isocost lines change.• Since PK has not changed, their coordinate at

vertical axis will remain unaltered but since PL has fallen, their coordinate at horizontal axis would increase.

• The original isocost line is AB and original equilibrium point is E. As PL falls, the cost line changes to AC.

• The original output is now producable at original cost by choosing the input combination of point F.

• However, this is not the least-cost technology. The least-cost input-mix for original output level is given by tangency point G, where the cost is lower than at point F for the same quantity of output.

• Thus, due to a fall in PL, equilibrium moves from point E to point G, showing a decrease in the employment of capital, whose price has remained constant, and an increase in the employment of labour, whose price has fallen.

• As, PL falls, cost of producing a given output declines, and this causes firms to expand its production, leading to an increase in the demand for both labour and capital. This is the output effect of a fall in PL.

• Under the substitution effect, as PL falls, labour becomes relatively cheaper to capital, which induces firms to substitutes labour and capital, thereby demand for labour expands while that for capital contracts.

• The total effect, which is the sum of the two, of a fall in PL is thus an increase in the employment of labour and uncertain change in the employment of capital. The movement from point E to point K indicates this total effect.

• But if output is held constant at the original level , a fall in PL would lead to an increase in labour input and a decrease in capital input, as indicated by a movement from point E to point G.

• The movement from point E to point G is the pure substitution effect.

Maximum–Output Input Maximum–Output Input

CombinationCombination

• When a firm has a fixed rupee budget for its production, its optimization problem is one of maximizing output for a given cost.

• Since the cost is fixed, the isocost line will be unique and output is a variable, there will be a family of isoquants.

• The equilibrium would be determined as in figure.

• In figure, the cost line (C=45) is fixed, and there are three isoquants, one for Q = 122, second for Q < 122 and third for Q >122.

• With a budget of Rs. 45, less than 122 units of output is producible (e.g at points a and b) but obviously that is not the best the firm could do.

• Point E would still mark the equilibrium point, where 122 units are produced by employing 7 units of labour and 8 units of capital.

Maximum-Profit Input Maximum-Profit Input

CombinationCombination

• Most firms today have neither a fixed output target nor a fixed rupee budget for their production.

• For the purpose, one needs, besides the production function and factor prices, the product price or the demand curve.

• For a constant product price case, the equilibrium is explained in figure.

• Quadrant I gives the equilibrium input-combinations for various output levels.

• The result of this quadrant in terms of outputs and the corresponding least-costs are transferred in terms of the total cost curve in quadrant III.

• The total revenue(TR) curve is drawn on the basis of a given product price (= slope of the TR curve).

• The horizontal gap between TR and TC curves represents profits for various output levels.

• The output at which profit is maximum is the profit-maximizing output and the input combination corresponding to this output is profit-maximizing technology.

• Thus, L3 units of labour and K3 units of capital is the profit-maximizing input combination, and the line AB in quadrant III gives the measure of maximum profit

Expansion Path & Returns to scaleExpansion Path & Returns to scale

• The curve OP is the expansion path. It is the set of lines of the least-cost input combinations for various output levels, which is the same as the set of lines of maximum-output input combinations for various cost constraints.

• Thus, if a firm desires to expand its output from Q1 to Q2 its total cost would increase from C1 to C2, and so on.

• This, together with the output-revenue relationship would help the firm to decide on its expansion strategy.

• Figure also includes the ridge lines OR1 and OR2.

• These lines separate the economic region from the non-economic region.

• All least cost input combinations are in the economic region and thus the expansion path necessarily falls between the two ridge lines.

• The ridge line OR1 passes through those points on various isoquants, where the isoquants are either vertical or upward sloping.

• This is because the economic choice can not fall on the vertical or rising part of any isoquant, for in that region the firm would need to employ more of capital with a same amount of labour or more of both inputs than on a point immediately preceding such a point for producing the same level of output.

• For ex, for producing Q1 output, input combination of point B is inferior to that of point A, as the former requires more of both labour and capital than the latter for producing the same output.

• Similarlyl, line OR2 passes through those points on various isoquants, where the isoquants are either horizontal or upward sloping.

• The economic region must fall on the falling and convex (from below) parts of isoquants.

Return to scaleReturn to scale• Returns to scale provides a measure of the

direction of change in total factor productivity when all factors of production change in the same direction and same proportion.

• Thus, increasing returns to scale, which means as all inputs increase in a given proportion(multiple), output increases by more than that proportion (multiple), implies increase in total factor productivity.

• If output increases by the same multiple as all inputs have increased, there are constant returns to scale and there is no change in total factor productivity

• Finally, if output increases by a smaller multiple than have all inputs, there are decreasing returns to scale and a decrease in total factor productivity.

• In general production function is given by Q = A * Lᵅ * Kᵝ

Elasticity ConceptElasticity Concept• There is an elasticity concept which is related to the

returns to scale concept.• This is called the all input elasticity of output and is

defined as follows:

e Q,I = % change in output % change in all inputs

Where Q = output, I = all inputs

If e Q,I >1, there are increasing returns to scale. Returns to scale are constant if e Q,I =1 and decreasing if e Q,I <1.

Production Analysis : Short-Production Analysis : Short-

runrun

• Factor productivities in the short-run consist of total, average and marginal physical products of each of the variable inputs.

• Since all but one inputs are taken as constant, these are referred to as partial factor productivities.

APPL = TPPL / L

MPPL = Δ(TPPL) / ΔL (if function is discrete)

Total Marginal and Average physical Total Marginal and Average physical

Product curvesProduct curves

1. As long as TPPL increases at an increasing rate, both APPL and MPPL increase. MPPL declines monotonically when TPPL increases at a decreasing rate.

2. MPPL is maximum at the point of inflexion (where the curvature of the TPPL curve changes from convex to concave or vice versa) on the TPPL curve (L=OL1)

3. MPPL = 0 when TPPL is maximum (L=OL3)4. APPL is increasing when MPPL > APPL

5. APPL is maximum when MPPL = APPL, or at the point where the slope of the straight line from origin to the TPPL curve is maximum (L=OL2)

6. APPL is decreasing when MPPL < APPL

7. MPPL reaches its maximum value before APPL and APPL before TPPL

• As seen in the short-run production function, the TPPL curve is first convex from below and then concave from below because of the operation of the law of variable (diminishing) returns.

• Since APPL and MPPL curves are simple mathematical derivations from TPPL curve, the shapes (close to inverted U) are also due to the working of the law of diminishing returns.

• Short-run factor productivities depend on the magnitudes of fixed inputs.

• If the quantity of fixed inputs employed by the firm increases, each of the three short-run productivities would increase.

• Thus, in the above example, if K increases from K =2 to K = 3, each of TPPL, APPL and MPPL would increase, thereby there would be an upward shift in each of the three curves in figure.

• The same thing would result in the face of an

improvement in the technology. • Thus, the introduction of computer into

business would result into an improvement in labour productivity.

Production Analysis:Production Analysis:

Long run versus Short run Long run versus Short run

• The long run expansion path is given by the curve OABCDE.

• If capital input was fixed at K = K bar, the short run expansion path will be given by the curve OXYCZ.

• Thus, point A denotes the least-cost input combination for output level of Q1 in the long-run, point X denotes the same in the short-run.

• This is because if the firm operates at point A in the short-run it would use OL2 units of labour and OK1 units of capital, but since it has fixed units of capital, it would

• have to pay for OL2 units of labour and OK bar units

of capital, leaving K1 K-, units of capital unemployed.• In contrast, if it operates at point X, it would pay for a

fewer units of labour (=OL1 < OL2) and the same units of capital as at point A.

• Thus, assuming the firm has no other use of extra units of capital, the short-run least cost input combination for Q = Q1 is given by point X and not by point A.

• By the same reasoning, the short-run least-cost technologies for output levels Q2,Q3,Q4 are given by points Y,C and Z respectively.

• Note that there is no way by which the firm could

produce Q5 units of output in the short-run, for Q5 isoquant lies above the capital constraint (K bar).

• In other words, Q5 is above the firm’s capacity output in the short-run.

• It is interesting to note that one and only one of the least-cost input combinations of the long-run is also the least –cost input combination of the short-run.

• Here it is represented by point C and it is for Q=Q3.• At this point alone, long run total cost equals short-

run total cost.

• For all other output levels, short-run total

cost exceeds long-run total cost.• This point can be seen easily by observing

that the cost line passing through point X would be above the one passing through point A (both cost lines would have the same slope, for factor prices are given), the one passing through point Y would be above the one passing through point B, and so on.

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Production analysis