Question

1. The following table provides data related to the production technology of a firm that use only two inputs – labor and capital – to produce output. Both inputs are variable.

Production with Two Variable Inputs
			Labor Input
Capital Input	1	2	3	4	5
1	40	80	110	130	150
2	80	120	150	170	180
3	110	150	180	200	210
4	130	170	200	220	230
5	150	180	210	230	240

1. Keeping capital on the y-axis and labor on the x-axis, draw an isoquant map for the firm’s production technology (At least 3 isoquant maps)
2. Does this production technology exhibit diminishing marginal returns to labor? Justify your answer.
3. Does this production technology exhibit diminishing marginal returns to capital? Justify your answer.
4. Does this production technology exhibit diminishing MRTS? Justify your answer.

Answer 1

Answer

The above figure is the isoquant map of the table given in the question. In this figure labor(L) is measured on the horizontal axis, and the capital(K) is measured on the vertical axis.Seven isoquants are presented in the figure.All the isoquants represents different quantities of output.Higher the iisoquant, higher is the amount of output. Each isoquant shows the given quantity of output that can be produced with different combinations of input; like,the second isoquant, which shows 80 units of output, that can be produced by either 1 unit of labor and 2 units of capital , or 2 units of labor and 1 unit of capital.

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b. To know that if this production technology exhibits diminishing marginal returns to labor, we have to calculate the marginal productivity of labor(MP_L) , keeping capital constant.

MP_L = Change in quantity of output / change in one extra unit of a labor.

The following table,Table-1 shows, MP_L, when capital is constant at 1 unit.

Table-1

Quantity of output	Labor	Marginal productivity of Labor (MPL)
40	1	-
80	2	40
110	3	30
130	4	20
150	5	20

From the Table-1, we see that MPL is gradually decreasing, and it is constant at 5 units of labor.

Now, keeping capital constant at 2 units, and increasing labor by 1 unit for all the additional production,we get the following table for MP_L,

Table -2

Quantity of output	Labor	Marginal productivity of Labor (MPL)
80	1	-
120	2	40
150	3	30
170	4	20
180	5	10

In Table-2 also we see that MP_L is gradually decreasing.

We can prove the similar by keeping capital constant at 3,4, and 5 units. So the production technology here exhibits the diminishing marginal returns to labor.

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c. To know that if this production technology exhibits diminishing marginal returns to capital (K) we have to calculate the marginal productivity of capital(MP_K) , keeping labor constant.

MP_K = Change in quantity of output / change in one extra unit of a capital.

The following table,Table-1 shows, MP_K, when labor is constant at 1 unit.

Table-3

Quantity of output	Capital	Marginal productivity of Capital (MPK)
40	1	-
80	2	40
110	3	30
130	4	20
150	5	20

From the above table, we see that MP_K is gradually diminishing,and is constant at 5 units of capital.

Now, keeping labor constant at 2 units, and increasing capital by 1 units for higher production, we get MP_K, represented in the following table, Table-4.

Table-4

Quantity of output	Capital	Marginal productivity of Capital(MPK)
80	1	-
120	2	40
150	3	30
170	4	20
180	5	10

From the above table, we see that the MP_K is gradually diminishing , keeping labor at 2 units.

The diminishing MP_K can be proved from the given production table in question, by keeping labor constant at , 3, 4, and 5 units also. So we can say that the production technology here shows the diminishing marginal returns to capital.

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d. Yes, the production technology exhibits the diminishing MRTS(marginal rate of technical substitution).

The marginal rate of technical substitution(MRTS) shows that keeping the output constant, if we want to increase one unit of one input, we must sacrifice certain amount of other input. The rate of sacrifice is called, MRTS.

From tables of MP_L and MP_{K ,} we see, that , both the MP_L and MP_K are decreasing with the increase in output , and the isoquants are convex to origin. All the isoquants show, that keeping the quantities constant, if we want to increase one input, we must decrease the other input. Say, for production of 80 units of output, i.e. the second isoquant, if we increase labor from 1 to 2 units, we must sacrifice capital from 2 to 1 unit.This indicates the diminishing MRTS. So the production technology here exhibits the diminishing MRTS.

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