Find the least cost output assuming that MPL = R100 and MPK = R200

Question

Quizplus · Accepted Answer

The least cost output can be determined by equating the marginal products of labor and capital with their respective prices. In this case, MPL = R100 and MPK = R200.

To minimize the cost of producing a given output, the firm should hire labor and capital in such a way that the marginal product per rand spent is equal for both. This means that the firm should allocate its spending on labor and capital in such a way that

MPL/PL = MPK/PK

where PL is the wage rate and PK is the rental rate of capital.

Let's consider the options:

A) Total cost of labor R2,000 and total cost of capital R2,000.

If the total cost of labor is R2,000 and MPL = R100, then the firm is hiring 20 units of labor (R2,000/R100). If the total cost of capital is also R2,000 and MPK = R200, then the firm is hiring 10 units of capital (R2,000/R200).

The marginal product per rand spent on labor is MPL/PL = R100/R100 = 1. 
The marginal product per rand spent on capital is MPK/PK = R200/R200 = 1.

Therefore, this allocation of labor and capital does not satisfy the condition of MPL/PL = MPK/PK, and it is not the least cost output.

B) Total cost of labor R2,000 and total cost of capital R4,000.

If the total cost of labor is R2,000 and MPL = R100, then the firm is hiring 20 units of labor (R2,000/R100). If the total cost of capital is R4,000 and MPK = R200, then the firm is hiring 20 units of capital (R4,000/R200).

The marginal product per rand spent on labor is MPL/PL = R100/R100 = 1. 
The marginal product per rand spent on capital is MPK/PK = R200/R200 = 1.

This allocation of labor and capital satisfies the condition of MPL/PL = MPK/PK, and it is the least cost output.

C) Total cost of labor R4,000 and total cost of capital R2,000.

If the total cost of labor is R4,000 and MPL = R100, then the firm is hiring 40 units of labor (R4,000/R100). If the total cost of capital is R2,000 and MPK = R200, then the firm is hiring 10 units of capital (R2,000/R200).

The marginal product per rand spent on labor is MPL/PL = R100/R100 = 1. 
The marginal product per rand spent on capital is MPK/PK = R200/R200 = 1.

Therefore, this allocation of labor and capital does not satisfy the condition of MPL/PL = MPK/PK, and it is not the least cost output.

D) It can't be done.

This answer is not correct. It is possible to determine the least cost output by equating MPL/PL = MPK/PK, as shown in option B.

Find the Least Cost Output Assuming That MPL = R100