A firm's production function is given by Q = KL. The marginal products of labor and capital are, respectively, MP_L = K and MP_K = L. The wage rate of labor is w = $10 and the rental rate of capital is r = $20. What is the most efficient combination of labor and capital $ (L, K) $ that also yields a cost of exactly $1000? A) (10, 45) B) (25, 50) C) (50, 25) D) (20, 40)

Question

Quizplus · Accepted Answer

To minimize cost, the firm should equate the ratio of marginal products to the ratio of input prices: MP_L/w = MP_K/r. This gives K/10 = L/20, or K = 0.5L. Substituting into the cost equation 10L + 20K = 1000, we get L = 50 and K = 25.

A Firm's Production Function Is Given by Q = KL (L,K) (L, K) (L,K)

A Firm's Production Function Is Given by Q = KL $(L, K)$