NCERT Textbook - Productions and Costs Commerce Notes | EduRev

NCERT Textbooks (Class 6 to Class 12)

Commerce : NCERT Textbook - Productions and Costs Commerce Notes | EduRev

 Page 1


Chapter 3
P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs
A Firm Effort
In the previous chapter, we have discussed the behaviour of the
consumers. In this chapter as well as in the next, we shall examine
the behaviour of a producer. Production is the process by which
inputs are transformed into ‘output’. Production is carried out by
producers or firms. A firm acquires different inputs like labour,
machines, land, raw materials etc. It uses these inputs to produce
output. This output can be consumed by consumers, or used by
other firms for further production. For example, a tailor uses a
sewing machine, cloth, thread and his own labour to ‘produce’
shirts. A farmer uses his land, labour, a tractor, seed, fertilizer,
water etc to produce wheat. A car manufacturer uses land for a
factory, machinery, labour, and various other inputs (steel,
aluminium, rubber etc) to produce cars. A rickshaw puller uses a
rickshaw and his own labour to ‘produce’ rickshaw rides. A
domestic helper uses her labour to produce ‘cleaning services’.
We make certain simplifying assumptions to start with. Production
is instantaneous: in our very simple model of production no
time elapses between the combination of the inputs and
the production of the output. We also tend to use the
terms production and supply synonymously and often
interchangeably.
In order to acquire inputs a firm has to pay for them.
This is called the cost of production. Once output
has been produced, the firm sell it in the market and
earns revenue. The difference between the revenue
and cost is called the firm’s profit. We assume that
the objective of a firm is to earn the maximum profit
that it can.
In this chapter, we discuss the relationship between
inputs and output. Then we look at the cost structure of
the firm. We do this to be able to identifiy the output at which
firms profits are maximum.
3.1  PRODUCTION FUNCTION
The production function of a firm is a relationship between inputs
used and output produced by the firm. For various quantities of
inputs used, it gives the maximum quantity of output that can be
produced.
2020-21
Page 2


Chapter 3
P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs
A Firm Effort
In the previous chapter, we have discussed the behaviour of the
consumers. In this chapter as well as in the next, we shall examine
the behaviour of a producer. Production is the process by which
inputs are transformed into ‘output’. Production is carried out by
producers or firms. A firm acquires different inputs like labour,
machines, land, raw materials etc. It uses these inputs to produce
output. This output can be consumed by consumers, or used by
other firms for further production. For example, a tailor uses a
sewing machine, cloth, thread and his own labour to ‘produce’
shirts. A farmer uses his land, labour, a tractor, seed, fertilizer,
water etc to produce wheat. A car manufacturer uses land for a
factory, machinery, labour, and various other inputs (steel,
aluminium, rubber etc) to produce cars. A rickshaw puller uses a
rickshaw and his own labour to ‘produce’ rickshaw rides. A
domestic helper uses her labour to produce ‘cleaning services’.
We make certain simplifying assumptions to start with. Production
is instantaneous: in our very simple model of production no
time elapses between the combination of the inputs and
the production of the output. We also tend to use the
terms production and supply synonymously and often
interchangeably.
In order to acquire inputs a firm has to pay for them.
This is called the cost of production. Once output
has been produced, the firm sell it in the market and
earns revenue. The difference between the revenue
and cost is called the firm’s profit. We assume that
the objective of a firm is to earn the maximum profit
that it can.
In this chapter, we discuss the relationship between
inputs and output. Then we look at the cost structure of
the firm. We do this to be able to identifiy the output at which
firms profits are maximum.
3.1  PRODUCTION FUNCTION
The production function of a firm is a relationship between inputs
used and output produced by the firm. For various quantities of
inputs used, it gives the maximum quantity of output that can be
produced.
2020-21
Consider the farmer we mentioned above. For simplicity, we assume that the
farmer uses only two inputs to produce wheat: land and labour. A production
function tells us the maximum amount of wheat he can produce for a given
amount of land that he uses, and a given number of hours of labour that he
performs. Suppose that he uses 2 hours of labour/ day and 1 hectare of land to
produce a maximum of 2 tonnes of wheat. Then, a function that describes this
relation is called a production function.
One possible example of the form this could take is:
q = K × L,
Where, q is the amount of wheat produced, K is the area of land in hectares,
L is the number of hours of work done in a day.
Describing a production function in this manner tells us the exact relation
between inputs and output. If either K or L increase, q will also increase. For
any L and any K, there will be only one q. Since by definition we are taking the
maximum output for any level of inputs, a production function deals only with
the efficient use of inputs. Efficiency implies that it is not possible to get any
more output from the same level of inputs.
A production function is defined for a given technology. It is the technological
knowledge that determines the maximum levels of output that can be produced
using different combinations of inputs. If the technology improves, the maximum
levels of output obtainable for different input combinations increase. We then
have a new production function.
The inputs that a firm uses in the production process are called factors of
production. In order to produce output, a firm may require any number of
different inputs. However, for the time being, here we consider a firm that produces
output using only two factors of production – labour and capital. Our production
function, therefore, tells us the maximum quantity of output (q) that can be
produced by using different combinations of these two factors of productions-
Labour (L) and Capital (K).
We may write the production function as
q = f(L,K)    (3.1)
where, L is labour and K is capital and q is the maximum output that can be
produced.
A numerical example of production function is given in Table 3.1. The left
column shows the amount of labour and the top row shows the amount of
capital. As we move to the right along any row, capital increases and as we move
down along any column, labour increases. For different values of the two factors,
37
Production and Costs
Table 3.1: Production Function
Factor Capital
0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 3 7 10 12 13
2 0 3 10 18 24 29 33
    Labour 3 0 7 18 30 40 46 50
4 0 10 24 40 50 56 57
5 0 12 29 46 56 58 59
6 0 13 33 50 57 59 60
2020-21
Page 3


Chapter 3
P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs
A Firm Effort
In the previous chapter, we have discussed the behaviour of the
consumers. In this chapter as well as in the next, we shall examine
the behaviour of a producer. Production is the process by which
inputs are transformed into ‘output’. Production is carried out by
producers or firms. A firm acquires different inputs like labour,
machines, land, raw materials etc. It uses these inputs to produce
output. This output can be consumed by consumers, or used by
other firms for further production. For example, a tailor uses a
sewing machine, cloth, thread and his own labour to ‘produce’
shirts. A farmer uses his land, labour, a tractor, seed, fertilizer,
water etc to produce wheat. A car manufacturer uses land for a
factory, machinery, labour, and various other inputs (steel,
aluminium, rubber etc) to produce cars. A rickshaw puller uses a
rickshaw and his own labour to ‘produce’ rickshaw rides. A
domestic helper uses her labour to produce ‘cleaning services’.
We make certain simplifying assumptions to start with. Production
is instantaneous: in our very simple model of production no
time elapses between the combination of the inputs and
the production of the output. We also tend to use the
terms production and supply synonymously and often
interchangeably.
In order to acquire inputs a firm has to pay for them.
This is called the cost of production. Once output
has been produced, the firm sell it in the market and
earns revenue. The difference between the revenue
and cost is called the firm’s profit. We assume that
the objective of a firm is to earn the maximum profit
that it can.
In this chapter, we discuss the relationship between
inputs and output. Then we look at the cost structure of
the firm. We do this to be able to identifiy the output at which
firms profits are maximum.
3.1  PRODUCTION FUNCTION
The production function of a firm is a relationship between inputs
used and output produced by the firm. For various quantities of
inputs used, it gives the maximum quantity of output that can be
produced.
2020-21
Consider the farmer we mentioned above. For simplicity, we assume that the
farmer uses only two inputs to produce wheat: land and labour. A production
function tells us the maximum amount of wheat he can produce for a given
amount of land that he uses, and a given number of hours of labour that he
performs. Suppose that he uses 2 hours of labour/ day and 1 hectare of land to
produce a maximum of 2 tonnes of wheat. Then, a function that describes this
relation is called a production function.
One possible example of the form this could take is:
q = K × L,
Where, q is the amount of wheat produced, K is the area of land in hectares,
L is the number of hours of work done in a day.
Describing a production function in this manner tells us the exact relation
between inputs and output. If either K or L increase, q will also increase. For
any L and any K, there will be only one q. Since by definition we are taking the
maximum output for any level of inputs, a production function deals only with
the efficient use of inputs. Efficiency implies that it is not possible to get any
more output from the same level of inputs.
A production function is defined for a given technology. It is the technological
knowledge that determines the maximum levels of output that can be produced
using different combinations of inputs. If the technology improves, the maximum
levels of output obtainable for different input combinations increase. We then
have a new production function.
The inputs that a firm uses in the production process are called factors of
production. In order to produce output, a firm may require any number of
different inputs. However, for the time being, here we consider a firm that produces
output using only two factors of production – labour and capital. Our production
function, therefore, tells us the maximum quantity of output (q) that can be
produced by using different combinations of these two factors of productions-
Labour (L) and Capital (K).
We may write the production function as
q = f(L,K)    (3.1)
where, L is labour and K is capital and q is the maximum output that can be
produced.
A numerical example of production function is given in Table 3.1. The left
column shows the amount of labour and the top row shows the amount of
capital. As we move to the right along any row, capital increases and as we move
down along any column, labour increases. For different values of the two factors,
37
Production and Costs
Table 3.1: Production Function
Factor Capital
0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 3 7 10 12 13
2 0 3 10 18 24 29 33
    Labour 3 0 7 18 30 40 46 50
4 0 10 24 40 50 56 57
5 0 12 29 46 56 58 59
6 0 13 33 50 57 59 60
2020-21
38
Introductory
Microeconomics
the table shows the corresponding output levels. For example, with 1 unit of
labour and 1 unit of capital, the firm can produce at most 1 unit of output; with
2 units of labour and 2 units of capital, it can produce at most 10 units of
output; with 3 units of labour and 2 units of capital, it can produce at most 18
units of output and so on.
In our example, both the inputs are necessary for the production. If any of
the inputs becomes zero, there will be no production. With both inputs positive,
output will be positive. As we increase the amount of any input, output increases.
3.2 THE SHORT RUN AND THE LONG RUN
Before we begin with any further analysis, it is important to discuss two concepts–
the short run and the long run.
In the short run, at least one of the factor – labour or capital – cannot be
varied, and therefore, remains fixed. In order to vary the output level, the firm
can vary only the other factor. The factor that remains fixed is called the fixed
factor whereas the other factor which the firm can vary is called the variable
factor.
Consider the example represented through Table 3.1. Suppose, in the short
run, capital remains fixed at 4 units. Then the corresponding column shows the
different levels of output that the firm may produce using different quantities of
labour in the short run.
Isoquant
In Chapter 2, we have learnt about indifference curves. Here, we introduce a
similar concept known as isoquant. It is just an alternative way of
representing the production function. Consider a production function with
two inputs labour and capital. An
isoquant is the set of all possible
combinations of the two inputs
that yield the same maximum
possible level of output. Each
isoquant represents a particular
level of output and is labelled with
that amount of output.
Let us return to table 3.1
notice that the output of 10 units
can be produced in 3 ways (4L,
1K), (2L, 2K), (1L, 4K). All these
combination of L, K lie on the
same isoquant, which represents the level of output 10. Can you identify
the sets of inputs that will lie on the isoquant q = 50?
The diagram here generalizes this concept. We place L on the X axis and
K on the Y axis. We have three isoquants for the three output levels, namely
q = q
1
, q = q
2 
and q = q
3
. Two input combinations (L
1
, K
2
) and (L
2
, K
1
) give us
the same level of output q
1
. If we fix capital at K
1 
and increase labour to L
3
,
output increases and we reach a higher isoquant, q = q
2
. When marginal
products are positive, with greater amount of one input, the same level of
output can be produced only using lesser amount of the other. Therefore,
isoquants are negatively sloped.
2020-21
Page 4


Chapter 3
P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs
A Firm Effort
In the previous chapter, we have discussed the behaviour of the
consumers. In this chapter as well as in the next, we shall examine
the behaviour of a producer. Production is the process by which
inputs are transformed into ‘output’. Production is carried out by
producers or firms. A firm acquires different inputs like labour,
machines, land, raw materials etc. It uses these inputs to produce
output. This output can be consumed by consumers, or used by
other firms for further production. For example, a tailor uses a
sewing machine, cloth, thread and his own labour to ‘produce’
shirts. A farmer uses his land, labour, a tractor, seed, fertilizer,
water etc to produce wheat. A car manufacturer uses land for a
factory, machinery, labour, and various other inputs (steel,
aluminium, rubber etc) to produce cars. A rickshaw puller uses a
rickshaw and his own labour to ‘produce’ rickshaw rides. A
domestic helper uses her labour to produce ‘cleaning services’.
We make certain simplifying assumptions to start with. Production
is instantaneous: in our very simple model of production no
time elapses between the combination of the inputs and
the production of the output. We also tend to use the
terms production and supply synonymously and often
interchangeably.
In order to acquire inputs a firm has to pay for them.
This is called the cost of production. Once output
has been produced, the firm sell it in the market and
earns revenue. The difference between the revenue
and cost is called the firm’s profit. We assume that
the objective of a firm is to earn the maximum profit
that it can.
In this chapter, we discuss the relationship between
inputs and output. Then we look at the cost structure of
the firm. We do this to be able to identifiy the output at which
firms profits are maximum.
3.1  PRODUCTION FUNCTION
The production function of a firm is a relationship between inputs
used and output produced by the firm. For various quantities of
inputs used, it gives the maximum quantity of output that can be
produced.
2020-21
Consider the farmer we mentioned above. For simplicity, we assume that the
farmer uses only two inputs to produce wheat: land and labour. A production
function tells us the maximum amount of wheat he can produce for a given
amount of land that he uses, and a given number of hours of labour that he
performs. Suppose that he uses 2 hours of labour/ day and 1 hectare of land to
produce a maximum of 2 tonnes of wheat. Then, a function that describes this
relation is called a production function.
One possible example of the form this could take is:
q = K × L,
Where, q is the amount of wheat produced, K is the area of land in hectares,
L is the number of hours of work done in a day.
Describing a production function in this manner tells us the exact relation
between inputs and output. If either K or L increase, q will also increase. For
any L and any K, there will be only one q. Since by definition we are taking the
maximum output for any level of inputs, a production function deals only with
the efficient use of inputs. Efficiency implies that it is not possible to get any
more output from the same level of inputs.
A production function is defined for a given technology. It is the technological
knowledge that determines the maximum levels of output that can be produced
using different combinations of inputs. If the technology improves, the maximum
levels of output obtainable for different input combinations increase. We then
have a new production function.
The inputs that a firm uses in the production process are called factors of
production. In order to produce output, a firm may require any number of
different inputs. However, for the time being, here we consider a firm that produces
output using only two factors of production – labour and capital. Our production
function, therefore, tells us the maximum quantity of output (q) that can be
produced by using different combinations of these two factors of productions-
Labour (L) and Capital (K).
We may write the production function as
q = f(L,K)    (3.1)
where, L is labour and K is capital and q is the maximum output that can be
produced.
A numerical example of production function is given in Table 3.1. The left
column shows the amount of labour and the top row shows the amount of
capital. As we move to the right along any row, capital increases and as we move
down along any column, labour increases. For different values of the two factors,
37
Production and Costs
Table 3.1: Production Function
Factor Capital
0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 3 7 10 12 13
2 0 3 10 18 24 29 33
    Labour 3 0 7 18 30 40 46 50
4 0 10 24 40 50 56 57
5 0 12 29 46 56 58 59
6 0 13 33 50 57 59 60
2020-21
38
Introductory
Microeconomics
the table shows the corresponding output levels. For example, with 1 unit of
labour and 1 unit of capital, the firm can produce at most 1 unit of output; with
2 units of labour and 2 units of capital, it can produce at most 10 units of
output; with 3 units of labour and 2 units of capital, it can produce at most 18
units of output and so on.
In our example, both the inputs are necessary for the production. If any of
the inputs becomes zero, there will be no production. With both inputs positive,
output will be positive. As we increase the amount of any input, output increases.
3.2 THE SHORT RUN AND THE LONG RUN
Before we begin with any further analysis, it is important to discuss two concepts–
the short run and the long run.
In the short run, at least one of the factor – labour or capital – cannot be
varied, and therefore, remains fixed. In order to vary the output level, the firm
can vary only the other factor. The factor that remains fixed is called the fixed
factor whereas the other factor which the firm can vary is called the variable
factor.
Consider the example represented through Table 3.1. Suppose, in the short
run, capital remains fixed at 4 units. Then the corresponding column shows the
different levels of output that the firm may produce using different quantities of
labour in the short run.
Isoquant
In Chapter 2, we have learnt about indifference curves. Here, we introduce a
similar concept known as isoquant. It is just an alternative way of
representing the production function. Consider a production function with
two inputs labour and capital. An
isoquant is the set of all possible
combinations of the two inputs
that yield the same maximum
possible level of output. Each
isoquant represents a particular
level of output and is labelled with
that amount of output.
Let us return to table 3.1
notice that the output of 10 units
can be produced in 3 ways (4L,
1K), (2L, 2K), (1L, 4K). All these
combination of L, K lie on the
same isoquant, which represents the level of output 10. Can you identify
the sets of inputs that will lie on the isoquant q = 50?
The diagram here generalizes this concept. We place L on the X axis and
K on the Y axis. We have three isoquants for the three output levels, namely
q = q
1
, q = q
2 
and q = q
3
. Two input combinations (L
1
, K
2
) and (L
2
, K
1
) give us
the same level of output q
1
. If we fix capital at K
1 
and increase labour to L
3
,
output increases and we reach a higher isoquant, q = q
2
. When marginal
products are positive, with greater amount of one input, the same level of
output can be produced only using lesser amount of the other. Therefore,
isoquants are negatively sloped.
2020-21
39
Production and Costs
In the long run, all factors of production can be varied. A firm in order to
produce different levels of output in the long run may vary both the inputs
simultaneously. So, in the long run, there is no fixed factor.
For any particular production process, long run generally refers to a longer
time period than the short run. For different production processes, the long run
periods may be different. It is not advisable to define short run and long run in
terms of say, days, months or years. We define a period as long run or short run
simply by looking at whether all the inputs can be varied or not.
3.3 TOTAL PRODUCT, AVERAGE PRODUCT AND MARGINAL PRODUCT
3.3.1 Total Product
Suppose we vary a single input and keep all other inputs constant. Then
for different levels of that input, we get different levels of output. This
relationship between the variable input and output, keeping all other inputs
constant, is often referred to as Total Product (TP) of the variable input.
Let us again look at Table 3.1. Suppose capital is fixed at 4 units. Now in
the Table 3.1, we look at the column where capital takes the value 4. As we
move down along the column, we get the output values for different values of
labour. This is the total product of labour schedule with K
2
 = 4. This is also
sometimes called total return to or total physical product of the variable
input. This is shown again in the second column of table in 3.2
Once we have defined total product, it will be useful to define the concepts of
average product (AP) and marginal product (MP). They are useful in order to
describe the contribution of the variable input to the production process.
3.3.2 Average Product
Average product is defined as the output per unit of variable input. We calculate
it as
L
L
TP
AP
L
=
    (3.2)
The last column of table 3.2 gives us a numerical example of average product
of labour (with capital fixed at 4) for the production function described in
table 3.1. Values in this column are obtained by dividing TP (column 2) by
L (Column 1).
3.3.3 Marginal Product
Marginal product of an input is defined as the change in output per unit of
change in the input when all other inputs are held constant. When capital is held
constant, the marginal product of labour is
 = 
L
Changeinoutput
MP
Changeininput
        
L
TP
L
?
=
?
    (3.3)
where ? represents the change of the variable.
The third column of table 3.2 gives us a numerical example of Marginal
Product of labour (with capital fixed at 4) for the production function described
in table 3.1. Values in this column are obtained by dividing change in TP by
2020-21
Page 5


Chapter 3
P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs
A Firm Effort
In the previous chapter, we have discussed the behaviour of the
consumers. In this chapter as well as in the next, we shall examine
the behaviour of a producer. Production is the process by which
inputs are transformed into ‘output’. Production is carried out by
producers or firms. A firm acquires different inputs like labour,
machines, land, raw materials etc. It uses these inputs to produce
output. This output can be consumed by consumers, or used by
other firms for further production. For example, a tailor uses a
sewing machine, cloth, thread and his own labour to ‘produce’
shirts. A farmer uses his land, labour, a tractor, seed, fertilizer,
water etc to produce wheat. A car manufacturer uses land for a
factory, machinery, labour, and various other inputs (steel,
aluminium, rubber etc) to produce cars. A rickshaw puller uses a
rickshaw and his own labour to ‘produce’ rickshaw rides. A
domestic helper uses her labour to produce ‘cleaning services’.
We make certain simplifying assumptions to start with. Production
is instantaneous: in our very simple model of production no
time elapses between the combination of the inputs and
the production of the output. We also tend to use the
terms production and supply synonymously and often
interchangeably.
In order to acquire inputs a firm has to pay for them.
This is called the cost of production. Once output
has been produced, the firm sell it in the market and
earns revenue. The difference between the revenue
and cost is called the firm’s profit. We assume that
the objective of a firm is to earn the maximum profit
that it can.
In this chapter, we discuss the relationship between
inputs and output. Then we look at the cost structure of
the firm. We do this to be able to identifiy the output at which
firms profits are maximum.
3.1  PRODUCTION FUNCTION
The production function of a firm is a relationship between inputs
used and output produced by the firm. For various quantities of
inputs used, it gives the maximum quantity of output that can be
produced.
2020-21
Consider the farmer we mentioned above. For simplicity, we assume that the
farmer uses only two inputs to produce wheat: land and labour. A production
function tells us the maximum amount of wheat he can produce for a given
amount of land that he uses, and a given number of hours of labour that he
performs. Suppose that he uses 2 hours of labour/ day and 1 hectare of land to
produce a maximum of 2 tonnes of wheat. Then, a function that describes this
relation is called a production function.
One possible example of the form this could take is:
q = K × L,
Where, q is the amount of wheat produced, K is the area of land in hectares,
L is the number of hours of work done in a day.
Describing a production function in this manner tells us the exact relation
between inputs and output. If either K or L increase, q will also increase. For
any L and any K, there will be only one q. Since by definition we are taking the
maximum output for any level of inputs, a production function deals only with
the efficient use of inputs. Efficiency implies that it is not possible to get any
more output from the same level of inputs.
A production function is defined for a given technology. It is the technological
knowledge that determines the maximum levels of output that can be produced
using different combinations of inputs. If the technology improves, the maximum
levels of output obtainable for different input combinations increase. We then
have a new production function.
The inputs that a firm uses in the production process are called factors of
production. In order to produce output, a firm may require any number of
different inputs. However, for the time being, here we consider a firm that produces
output using only two factors of production – labour and capital. Our production
function, therefore, tells us the maximum quantity of output (q) that can be
produced by using different combinations of these two factors of productions-
Labour (L) and Capital (K).
We may write the production function as
q = f(L,K)    (3.1)
where, L is labour and K is capital and q is the maximum output that can be
produced.
A numerical example of production function is given in Table 3.1. The left
column shows the amount of labour and the top row shows the amount of
capital. As we move to the right along any row, capital increases and as we move
down along any column, labour increases. For different values of the two factors,
37
Production and Costs
Table 3.1: Production Function
Factor Capital
0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 3 7 10 12 13
2 0 3 10 18 24 29 33
    Labour 3 0 7 18 30 40 46 50
4 0 10 24 40 50 56 57
5 0 12 29 46 56 58 59
6 0 13 33 50 57 59 60
2020-21
38
Introductory
Microeconomics
the table shows the corresponding output levels. For example, with 1 unit of
labour and 1 unit of capital, the firm can produce at most 1 unit of output; with
2 units of labour and 2 units of capital, it can produce at most 10 units of
output; with 3 units of labour and 2 units of capital, it can produce at most 18
units of output and so on.
In our example, both the inputs are necessary for the production. If any of
the inputs becomes zero, there will be no production. With both inputs positive,
output will be positive. As we increase the amount of any input, output increases.
3.2 THE SHORT RUN AND THE LONG RUN
Before we begin with any further analysis, it is important to discuss two concepts–
the short run and the long run.
In the short run, at least one of the factor – labour or capital – cannot be
varied, and therefore, remains fixed. In order to vary the output level, the firm
can vary only the other factor. The factor that remains fixed is called the fixed
factor whereas the other factor which the firm can vary is called the variable
factor.
Consider the example represented through Table 3.1. Suppose, in the short
run, capital remains fixed at 4 units. Then the corresponding column shows the
different levels of output that the firm may produce using different quantities of
labour in the short run.
Isoquant
In Chapter 2, we have learnt about indifference curves. Here, we introduce a
similar concept known as isoquant. It is just an alternative way of
representing the production function. Consider a production function with
two inputs labour and capital. An
isoquant is the set of all possible
combinations of the two inputs
that yield the same maximum
possible level of output. Each
isoquant represents a particular
level of output and is labelled with
that amount of output.
Let us return to table 3.1
notice that the output of 10 units
can be produced in 3 ways (4L,
1K), (2L, 2K), (1L, 4K). All these
combination of L, K lie on the
same isoquant, which represents the level of output 10. Can you identify
the sets of inputs that will lie on the isoquant q = 50?
The diagram here generalizes this concept. We place L on the X axis and
K on the Y axis. We have three isoquants for the three output levels, namely
q = q
1
, q = q
2 
and q = q
3
. Two input combinations (L
1
, K
2
) and (L
2
, K
1
) give us
the same level of output q
1
. If we fix capital at K
1 
and increase labour to L
3
,
output increases and we reach a higher isoquant, q = q
2
. When marginal
products are positive, with greater amount of one input, the same level of
output can be produced only using lesser amount of the other. Therefore,
isoquants are negatively sloped.
2020-21
39
Production and Costs
In the long run, all factors of production can be varied. A firm in order to
produce different levels of output in the long run may vary both the inputs
simultaneously. So, in the long run, there is no fixed factor.
For any particular production process, long run generally refers to a longer
time period than the short run. For different production processes, the long run
periods may be different. It is not advisable to define short run and long run in
terms of say, days, months or years. We define a period as long run or short run
simply by looking at whether all the inputs can be varied or not.
3.3 TOTAL PRODUCT, AVERAGE PRODUCT AND MARGINAL PRODUCT
3.3.1 Total Product
Suppose we vary a single input and keep all other inputs constant. Then
for different levels of that input, we get different levels of output. This
relationship between the variable input and output, keeping all other inputs
constant, is often referred to as Total Product (TP) of the variable input.
Let us again look at Table 3.1. Suppose capital is fixed at 4 units. Now in
the Table 3.1, we look at the column where capital takes the value 4. As we
move down along the column, we get the output values for different values of
labour. This is the total product of labour schedule with K
2
 = 4. This is also
sometimes called total return to or total physical product of the variable
input. This is shown again in the second column of table in 3.2
Once we have defined total product, it will be useful to define the concepts of
average product (AP) and marginal product (MP). They are useful in order to
describe the contribution of the variable input to the production process.
3.3.2 Average Product
Average product is defined as the output per unit of variable input. We calculate
it as
L
L
TP
AP
L
=
    (3.2)
The last column of table 3.2 gives us a numerical example of average product
of labour (with capital fixed at 4) for the production function described in
table 3.1. Values in this column are obtained by dividing TP (column 2) by
L (Column 1).
3.3.3 Marginal Product
Marginal product of an input is defined as the change in output per unit of
change in the input when all other inputs are held constant. When capital is held
constant, the marginal product of labour is
 = 
L
Changeinoutput
MP
Changeininput
        
L
TP
L
?
=
?
    (3.3)
where ? represents the change of the variable.
The third column of table 3.2 gives us a numerical example of Marginal
Product of labour (with capital fixed at 4) for the production function described
in table 3.1. Values in this column are obtained by dividing change in TP by
2020-21
40
Introductory
Microeconomics
Average product of an input at any level of employment is the average of all
marginal products up to that level. Average and marginal products are often
referred to as average and marginal returns, respectively, to the variable input.
3.4 THE LAW OF DIMINISHING MARGINAL PRODUCT AND
THE LAW OF VARIABLE PROPORTIONS
If we plot the data in table 3.2 on graph paper, placing labour on the X-axis and
output on the Y-axis, we get the curves shown in the diagram below. Let us
examine what is happening to TP. Notice that TP increases as labour input
increases. But the rate at which it increases is not constant. An increase in labour
from 1 to 2 increases TP by 10 units. An increase in labour from 2 to 3 increases
TP by 12. The rate at which TP increases, as explained above, is shown by the
MP. Notice that the MP first increases (upto 3 units of labour) and then begins to
change in L. For example, when L changes from 1 to 2, TP changes from 10 to
24.
MP
L
= (TP at L units) – (TP at L – 1 unit)    (3.4)
Here, Change in TP = 24 -10 = 14
Change in L = 1
Marginal product of the 2
nd
 unit of labour = 14/1 = 14
Since inputs cannot take negative values, marginal product is undefined at
zero level of input employment. For any level of an input, the sum of marginal
products of every preceeding unit of that input gives the total product. So total
product is the sum of marginal products.
Table 3.2: Total Product, Marginal product and Average product
 Labour TP MP
L
AP
L
0 0 - -
1 10 10 10
2 24 14 12
3 40 16 13.33
4 50 10 12.5
5 56 6 11.2
6 57 1 9.5
2020-21
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