Suppose that a firm's production function of output Q is a function of only two inputs, labor (L) and capital (K) and can be written Q = 25LK with marginal products MP_L = 25K and MP_K = 25L. Let the wage rate for labor be w = 1 and the rental rate of capital be r= 1. If the firm produces 100 units of output, how many units of labor will it use? A) 1 B) 2 C) 3 D) 4

Question

Quizplus · Accepted Answer

To maximize profits, the firm should hire labor and use capital until the marginal product of each input equals its price. In this case, the wage rate for labor is 1 and the rental rate for capital is also 1. MP_L = 25K = w = 1 25K = 1 K = 1/25 MP_K = 25L = r = 1 25L = 1 L = 1/25 So, the firm will hire 1/25 units of labor and 1/25 units of capital to produce 1 unit of output: Q = 25LK 100 = 25L(1/25) 100 = L Therefore, the firm will use 100 units of labor to produce 100 units of output, which is equivalent to choice B.

Suppose That a Firm's Production Function of Output Q Is