Question

A firm’s production function is given by Q = K^L. The marginal products of labor and capital are, respectively, MPL=K^2 and MPK=2KL. Further, the wage rate is r=20 and the rental rate of capital is w=10. In a short run the firm capital is fixed on K=10 and they hire 80 units of labor to minimize their cost. How much more the firm can cut its costs in the long run to produce the same level of output?

A. 400
B. not enough information
C. 600
D. 1000

Answer 1

In the long run, a firm can change both capital and labor to minimize costs, but without further details on production and costs, we cannot determine the exact amount of potential cost savings. The correct option is B.

Step-by-step explanation:

The question revolves around a firm's production function Q = KL and explores cost minimization in the short and long run. Given the marginal products of labor and capital, MPL=K2 and MPK=2KL, along with the wage and rental rates, the firm seeks to minimize cost while maintaining the same level of output. In the short run, with capital fixed at K=10 and 80 units of labor, we see a certain cost. However, in the long run, when capital is no longer fixed, the firm can adjust both inputs (labor and capital) to achieve cost minimization.

In the long run, the firm can substitute capital for labor or vice versa to reach an optimal mix that minimizes costs further. We do not have enough information to pinpoint exactly how much more the firm can reduce its costs without additional details about the production function's specific form and the exact costs associated with varying levels of labor and capital. Thus, the correct answer is B. not enough information.