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

Multiple Choice

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. Let materials input be fixed now at M = 2. What is the cost minimizing level of capital that the firm must use to produce a target level of output, Q = 1600?

A) K = 5
B) K = 10
C) K = 20
D) K = 40