UNIT -4 : PRODUCTION AND COST ANALYSIS

STRUCTURE
1. INTRODUCTION
2. OBJECTIVES
3. PRODUCTION FUNCTION
4. SHORT PRODUCTION FUNCTION – DIMINISHING MARGINAL RETURNS
5. LONG RUN PRODUCTION FUNCTION – RETURNS TO SCALE
6. OPTIMAL USE OF INPUTS
7. COST THEORY
8. SHORT RUN COST FUNCTIONS
9. LONG RUN COST CURVES
10. PLANT SIZE AND ECONOMIES OF SCALE
11. LEARNING CURVES
12. SUMMING UP
13. KEY WORDS
14. KNOW YOUR PROGRESS
15. FURTHER READINGS/REFERENCES
16. MODEL ANSWERS
1. INTRODUCTION

Production means transformation of inputs / resources into outputs of goods and

services. For example, IBM company hires workers to use machinery, parts, and raw materials
in factories to produce personal computers. An output of a firm can be a final commodity or
intermediate commodity (which are used in the production of other goods). The output can also
be a service rather than a good. “Production refers to all the activities involved in the production
of goods and services, from borrowing to set up or expand production facilities, to hiring
workers, purchasing raw materials, running quality control, cost accounting, and so on” rather
than referring merely to the physical transformation of inputs into outputs of goods and services.

Inputs are resources used in the production of goods and services. Inputs may be fixed
or variable. Fixed inputs are those that can not changed during the time under consideration
(examples : firm’s plant and specialized equipment). Variable inputs are those that can be varied
easily and on very short notice (examples are raw material and unskilled labour).

Short run is the period in which atleast one input is fixed and the long run is all the
inputs are variable. The firm operates in the short run and plans increases or reduction in the
scale of operations in the long run.

2. OBJECTIVES
After completing this Unit, you will able to :
1. Understand the meaning of production and production function
2. Distinguish between different types of production functions
3. Make out how the output of the firm changes with increase in inputs both in the short run
and long run
4. Classify various cost concepts and find out their usefulness in managerial decision
making
5. Understand the various components of cost of production both in the short and long run
3. PRODUCTION FUNCTION

Production Function shows the physical relationship between inputs and output in a given
period of time. Technology is assumed to be constant. Let there be only capital and labour
inputs then the production function becomes

Q = f (L, K)

where Q = number of units of commodity produced; K = amount of equipment used in

production ; L = number of workers employed. The above equation says that the quantity of
output is a function of or depends on the quantity of labour and quantity of capital. Quantity of
output refers to the number of units of the commodity produced, labour refers to the number of
workers employed and capital refers to the amount of the equipment used in the production.

K Q
6 10 24 31 36 40 39
5 12 28 36 40 42 40
4 12 28 36 40 40 36
3 10 23 33 36 36 33
2 7 18 28 30 30 28
1 3 8 12 14 14 12
1 2 3 4 5 6 L
Production Function with Two Variable Inputs

The Law of Diminishing Returns and Stages of Production

This law states :

“As additional units of variable input are combined with a fixed input, at some point the
additional output (the marginal product) starts to diminish”

Variable Total Product (TP) Marginal Product Average Product

Input (X) (MP) (AP)
0 0
1 8 8 8
2 18 10 9
3 29 11 9.7
4 39 10 9.8
5 47 8 9.4
6 52 5 8.7
7 56 4 8
8 52 -4 6.5

L Q MPL APL EL
0 0 - - -
1 3 3 3 1
2 8 5 4 1.25
3 12 4 4 1
4 14 2 3.5 0.57
5 14 0 2.8 0
6 12 -2 2 -1
Diminishing returns are illustrated in both the numerical example in the above Table and
depicted in the above fig. From the table it is clear that the marginal product of the first unit of
the input is 8. Marginal product reaches its maximum of 11 between the second and third units
of input. It is precisely 2.5 units of input, that we can say that the law of diminishing returns will
began to take effect. Thus the law states that when additional units of a variable input are
combined with a fixed input, at some point, the marginal product of the input will start to
diminish. Therefore, it is reasonable to assume that a manager will only discover the point of
diminishing returns by experience and trial and error.

Reasons for the occurrence of Diminishing returns

1. In the earlier numerical example, when no workers are employed total product is zero.
The first worker produces 8 units. Thus his marginal product is equal to 8 and also his
average product is also equal to 8. When two workers are used, their combined efforts
yield a total output of 18. This implies that 2 people working together can produce more
than the sum of their efforts working as separate individuals (AP of one worker =8 and
AP of two workers 9). MP of second worker is greater than that of the first.
2. Because it is assumed in economic theory that each worker is equally productive, this
means that the effect of team work and specialization enables additional workers to
contribute more than those added previously to the production process, a phenomenon
that we can refer to as “increasing returns”
3. But as still more workers are added, there are fewer and fewer opportunities for
increasing returns through specialization and teamwork and at some point additional
workers result in diminishing returns.
4. In this case, the additional workers lead to negative marginal returns, causing the total
product to decrease. “too many cooks spoil the dish” seems to have realized.

Three Stage of Production in the short run

In the above figure it is clear that Stage I runs from zero to 4 units of variable input (i.e to the
point where the AP reaches maximum). Stage II begins from this point and proceeds to seven
units of input X (i.e to the point at which total product is maximized). Stage III continuous on
from that point. According to Economic theory, the rational firms operate till Stage II. Stage III
is irrational because the firm would be using more of its variable input to produce less output.
Stopping production at Stage I is also irrational because if it stops producing at this stage, it
would be grossly underutilizing its fixed capacity. That is, it would have so much fixed capacity
relative to its usage of variable inputs that it could increase the output per unit of variable input.

The long run production function

In the long run, the firm has enough time to change scale of its operations by changing the all of
its inputs.

Returns to scale is the increase in the total output as the two inputs increase (say X and Y). If
an increase in a firm’s inputs by some proportion results in an increase in output by a greater
proportion, the firm experiences increasing returns to scale. If output increases by the same
proportion as the inputs increase, the firm experience constant returns to scale; A less than
proportional increase in output is called decreasing returns to scale.

Why increasing returns to scale operate?

1. A larger scale of production might enable a firm to divide up tasks into more specialized
activities, thereby increasing labour productivity
2. Also a large scale of production might enable a company to justify the purchase of more
sophisticated (hence more productive) machinery.
These factors help to explain why a firm can experience increasing returns to scale.
Why decreasing returns to scale?

Operating on a larger scale might create certain managerial inefficiencies (eg communications
problems, bureaucratic red tape) and hence cause decreasing returns to scale.

Coefficient of output elasticity measures the returns to scale. It is defined as the percentage
change in output divided by percentage change in all inputs. If this elasticity is greater than 1,
the firm is experiencing increasing returns to scale; if it is less than one the firm experiences
decreasing returns to scale and if it is equal to one it is experiencing constant returns to scale
(figure below).
The Production Function with two variable inputs

Isoquants

An isoquant shows the various combinations of two inputs (say labour and capital) that the firm
can use to produce a specific level of output. A higher isoquant refers to higher output and vice
versa (fig below).
The fig above shows that 12 unit of output can be produced with 1 unit of capital and 3 units of
labour or with 1k and 6L. This output can also be produced with 1L and 4 K and 1L and 5K. 28
Q can be produced with 2K and 3 L or 2 K and 6 L; 2L and 4 K and 2L and 5 K. For producing
higher quantity higher quantities of both the inputs are required.

Economic Region of Production

In the above fig isoquants have positively sloped portions also. However, these portions are
irrelevant. That means the firm will not operate on the positively sloped portion of an isoquant
because it could produce the same level of output with less capital and less labour. For eg., the
firm would not produce 36q at point u in the above fig with 6L and 4 K because it could produce
36 Q by using smaller quantities of L and K indicated by point V in the above figure. Similary
the firm will not produce at point W with 4 L and 6K because it could produce 36 Q at point Z
with less L and K. Ridge lines separate the relevant (negatively sloped) from the irrelevant
(positively sloped) portions of the isoquants. In the fig below the ridge line OVT joins points on
the various isoquants where the isoquants have zero slope. The isoquants are negatively sloped
towards the left of the ridgeline and positively sloped towards the right of the ridge line. The
ridge line OZI has infinite slope. The isoquants are negatively towards the right of the ridge line
and positively towards the left the ridge line. The MPL is negative to the right of the ridge line
of OVT. The MPK is negative to the left of the ridge line OZT. This corresponds to the stage III
of production of labour and capital (diminishing returns).
Marginal Rate of Technical Substitution

The rate at which one input is substitute for another is called marginal rate of technical
substitution (MRTS). In order to be on the same level of output (on a particular isoquant), the
firm should give up some amount of one input to gain some amount of another input. MRTS
gives the slope of the isoquant.

MRTSKL=∆ K / ∆ L = MPK/ MPL

MRTSLk=∆ L / ∆ K = MPL / MPK

The shape of an isoquant reflects the degree to which on input can be substituted for another in
production. The smaller the curvature, the greater is the degree of the substitutability of inputs in
production and vice versa.
If isoquants are straight lines as in below fig the labour and capital are perfect substitutes. That
means the rate at which labour is substituted for capital is constant. That means labour can be
substituted for capital (vice versa) at the constant rate given by the absolute slope of the isoquant.

In the above figure it is clear that 2L can be substitute for 1 K regardless of the point of
production on the isoquant. Infact, point A on the labour axis shows that the level of output
indicated by the middle isoquant can be produced with labour alone (without any capital).
Similarly point B on capital axis indicates that the same level of output can be produced with
capital alone (without any labour).
The above figure shows that the isoquants are rightangled. In this case, labour and capital are
perfect complements. That is, labour and capital should be used in the fixed proportion. In this
case there is zero substitutability between the two inputs.

While perfect substitutability and perfect complementarity of inputs are production, in

most cases isoquants exhibit some curvature (i.e inputs are imperfect substitutes). This means
that in the usual production situation labour can be substituted for capital to some degree.

Isocost Line:

Iso cost line shows the various combinations of inputs that a firm can purchase or hire at a given
cost. Let us assume that firm uses only two inputs such as labour and capital in production. The
total cost incurred by the firm then is:

C = wL + r K

Where C = total cost; w is the wage rate; L is the quantity of labour used; r is the rental price of
capital and K is the quantity of capital used. This equation is called isocost line. If prices of the
inputs change, then isocost line also changes. If C = Rs 100 w = Rs 10 and r = Rs 10. The firm
could either hire 10 L or rent 10 K or any combination of L and K as shown in the isocost line
AB in the figure below. If total cost changes given the input prices, the isocost line shift
parallel. If the total cost increases from Rs 100 to Rs 150 then the isocost line shifts towards
right. With this increased cost the firm will employ 15 L or rent 15 K or any combination of L
and K as shown in the isocost line A’B’ in the below figure. If the total cost decreases, given the
input prices, the isocost line shifts leftward to A”B”.

Optimum combination of inputs for minimizing costs or maximizing output

The firm maximizes output with the optimal combination of inputs at a point where the isoquant
line is tangent to the isocost line. In the below fig it is clear that the firm maximizes output at
point E where isoquant 10 Q is tangent to isocost line AB. At this point firm produces 10 units
with 5 L at a cost of Rs 50 and 5 K at a cost of Rs 50, for a total cost of Rs 100.

The firm could also produce 10 Q at point G (with 3L and 11 K) or at point H (with 12 L and 2
K) at a cost of Rs 140/-. But this would not represent the least cost input combination required to
produce 10 Q. In fact, with a cost of 140 the firm will be on a higher isocost and will be able to
produce more output (it will be on a higher isoquant. Thus the optimum input combination
needed to minimize the cost of producing a given level of output or the maximum output that the
firm can produce at a given cost outlay is given at the tangency of an isoquant and an isocost.
Joining points of tangency of isoquants and isocosts (joining points of optimal input
combinations) gives the expansion path of the firm. With optimal input combinations, the slope
of the isoquant or marginal rate of technical substitution of labour for capital to the slope of
isocost line or ratio of input prices. That is
 MRTS = w / r

Where MRTS = MPL / MPK

So MPL / MPK = w / r

Or MPL / w = MPK / r …………………..1

The meaning of the above equation is that to minimize the production cost (or maximize the
output for a given cost outlay), the marginal product per rupee spent on labour must be equal to
the marginal product per rupee spent on capital. If MP L = 5 and MPK = 4 and w = r, the firm
would not maximize the output or minimize the cost since it is getting more extra output for a
rupee spent on labour than on capital. To maximize output or minimize cost, the firm would
have to hire more labour and rent less capital. As the firm does this, the MPL decline and MPk
increases. The process would have to continue until condition 1 to hold.

Effect of change in Input Prices

Starting from the optimal input combination, if the price of an input declines, the firm will
substitute the cheaper input for other inputs in production in order to reach a new optimal input
combination. For eg., if r remains at Rs 10, but w falles to 5, the isocost line becomes AB* and
the firm can produce 14 Q iisoquant with C = Rs 100 (point N in the below fig). The firm can
reach isoquant 10 Q with C = Rs 70. This is given by isocost A*B’, which is parallel to AB* and
is tangent to isoquant 10Q at point R. Thus, with a reduction in w, a lower C is required to
produce a given level of output.

Q TFC TVC TC AFC AVC ATC MC

0 $60 $0 $60 - - - -
1 60 20 80 $60 $20 $80 $20
2 60 30 90 30 15 45 10
3 60 45 105 20 15 35 15
4 60 80 140 15 20 35 35
5 60 135 195 12 27 39 55