Suppose the marginal rate of technical substitution for labor with capital is 5,the marginal product of labor is 8,and the marginal product of capital is 4.Assuming the law of diminishing marginal product applies to both labor and capital,this firm:
A) is minimizing the cost of producing its output.
B) could reduce costs by using fewer workers and more capital.
C) could reduce costs by using less capital and more workers.
D) could reduce the cost of producing the output by reducing workers and capital by the same proportion.

Question

Quizplus · Accepted Answer

The firm can reduce its costs by using fewer workers and more capital because the marginal rate of technical substitution (MRTS) is greater than the ratio of the marginal product of labor to the marginal product of capital (MPL/MPK).

MRTS measures the rate at which the firm can substitute one input for another while keeping the level of output constant. In this case, the MRTS is 5, meaning that the firm can reduce labor by 5 units and increase capital by 1 unit while keeping output constant.

Since MPL/MPK is 2 (8/4), and MRTS is 5, it is more efficient for the firm to use more capital and less labor. This is because each unit of capital can substitute for more than 2 units of labor, so the firm can produce the same level of output with fewer workers and more capital.

Therefore, the firm should reduce costs by using fewer workers and more capital.

Suppose the Marginal Rate of Technical Substitution for Labor with Capital