Question

Suppose a firm purchases capital and labor in competitive markets at prices of r=6 and w=8, respectively. With the firm's current input mix, the marginal product of capital is 7 and the marginal product of labor is 10. Is this firm minimizing its costs? If so, explain how you know. If not, explain what the firm ought to do.

please write legibly and go step by step please and thank you

Answer 1

Marginal Rate of Technical Substitution (MRTS) is the rate at which one input can be exchanged for other input while producing the same amount of Output.

MRTS= Marginal Product of Labour/Marginal Product of Capital= 10/7= 1.43

Ratio of Prices of Input= w/r= 8/6= 1.33

Firm Produces optimally at a combination of Labour and Capital at which MRTS equals Ratio of Prices of Input. At that point, the cost of firm is minimised.

Here in this case, MRTS>Ratio of Prices of Input.

Therefore, the firm is not minimising its cost.

In this case, it will pay for the firm to substitute labour for capital. Thus, to minimise its cost, the firm must use more labour and less of capital until its MRTS becomes equal to Ratio of Prices of input.