Suppose a firm has a Cobb-Douglas weekly production function Q = F(L,K)= 25L^0.5K^0.5,where L is the number of workers and K is units of capital.The wage rate is $900 per week,and a unit of capital costs $400 per week.Assuming no fixed costs,what is the firm's total cost of production if it uses least-cost input combination to produce 675 units of output? A) $48,600 B) $43,650 C) $35,100 D) $32,400

Question

Quizplus · Accepted Answer

To minimize cost, the firm should use inputs such that the marginal product per dollar is equal for both inputs. For Cobb-Douglas, this means L/K = w/r, where w is the wage rate and r is the rental rate of capital. Here, w = 900 and r = 400, so L/K = 900/400 = 2.25. Solving the production function for L and K given Q = 675 and L/K = 2.25, we find L = 25 and K = 11.11. Total cost = 900L + 400K = 900(25) + 400(11.11) = $32,400.

Suppose a Firm Has a Cobb-Douglas Weekly Production Function Q