A firm's production process uses labor, L, and capital, K, and materials, M, to produce an output, Q according to the function Q = KLM, where the marginal products of the three inputs are MP_L = KM, MP_K = LM, and MP_M = KL. The wage rate for labor is w = 2, the rental rate of capital is r = 1, and the cost of materials is m = 4 per unit. What is the long run cost-minimizing level of capital that the firm must use to produce a target level of output, Q = 1000? A) K = 5 B) K = 10 C) K = 20 D) K = 40

Question

Quizplus · Accepted Answer

The long run cost-minimizing level of capital is found by solving the equation MP_K/r = MP_L/w = MP_M/m. Substituting the given values, we get LM/1 = KM/2 = KL/4. Solving for K, we get K = 20.

A Firm's Production Process Uses Labor, L, and Capital, K