A firm's production function is given by Q = KL, where MP_L = K and MP_K = L. The wage rate (W) = $50, and the rental per unit of capital (R) is $12.50. In the short run, capital (K) is fixed at 10 units. The short-run average total cost of producing 100 units of output is _____, and the long-run average total cost of producing 100 units of output is _____. A) $14.75; $8.80 B) $6.25; $5 C) $6.25; $4.20 D) $14.75; $9

Question

Quizplus · Accepted Answer

In the short run, with K fixed at 10, L = Q/K = 100/10 = 10. Short-run total cost = (W * L) + (R * K) = (50 * 10) + (12.50 * 10) = 625. Short-run average total cost = 625/100 = $6.25. In the long run, K = L = sqrt(Q) = sqrt(100) = 10. Long-run total cost = (W * L) + (R * K) = (50 * 10) + (12.50 * 10) = 625. Long-run average total cost = 625/100 = $5.

A Firm's Production Function Is Given by Q = KL