Suppose that a firm's production function can be specified as .Which of the following accurately describes this firm's long run total cost function?

Question

Suppose that a firm's production function can be specified as  .Which of the following accurately describes this firm's long run total cost function?

Quizplus · Accepted Answer

The long run total cost (LRTC) function can be obtained by finding the minimum cost of producing any given output level in the long run. This is achieved by choosing the input levels that minimize the cost at each output level. Since we do not know the factor prices, we cannot derive the LRTC function directly from the production function. However, the mathematical relationship between the production function and the LRTC function is given by the cost function: C(w,r,Q) = wL + rK, where w is the wage rate, r is the rental rate of capital, L is labor, K is capital, and Q is output. The cost function can be used to find the LRTC function by solving for the optimal input levels (L,K) that minimize C, subject to the constraint that Q = f(L,K). The LRTC function is therefore given by: LTC(Q) = min{C(w,r,Q)}, where the minimum is taken over all possible combinations of L and K that yield Q. In this case, we do not have enough information to solve for the LRTC function exactly, but we can eliminate some of the answer choices based on their mathematical properties. Choices A, B, and D all contain different terms than the production function, which suggests that they are incorrect. Choice C contains the same functional form as the production function, so it is the best choice. However, we cannot derive the exact coefficients without more information about the factor prices.

Suppose That a Firm's Production Function Can Be Specified as