Suppose MP_L = 0.5 ∗ (q/L)and MP_K = 0.5 ∗ (q/K).In the long run,the firm will hire equal amounts of capital and labor A) all of the time. B) only when w = r. C) only when w = 0.5 ∗ r. D) at no point in time.

Question

Quizplus · Accepted Answer

In the long run, the firm will hire equal amounts of capital and labor when their marginal products are equal. MP_L = 0.5 ∗ (q/L) implies that the marginal product of labor is proportional to the ratio of q and L. Similarly, MP_K = 0.5 ∗ (q/K) implies that the marginal product of capital is proportional to the ratio of q and K. Therefore, in the long run, when the firm hires equal amounts of capital and labor, we have: (q/L) = (q/K) or, (K/L) = (w/r) where w and r are the prices of labor and capital, respectively. This means that the capital-labor ratio in the production function should be equal to the ratio of their prices. Thus, the firm will hire equal amounts of capital and labor only when w = r. Hence, the answer is B.

Suppose MPL = 0

Suppose MP_L = 0