A firm's long-run total cost curve is given by LTC = 2,000Q - 10Q² + 1/3Q³, and long-run marginal cost is given by LMC = 2,000 - 20Q + Q². What is the quantity of output that minimizes long-run average total cost? A) 15 B) 165 C) 500 D) 210

Question

Quizplus · Accepted Answer

To minimize long-run average total cost, we need to find the quantity of output where long-run marginal cost equals long-run average total cost. LMC = LTC/Q2,000 - 20Q + Q² = 2,000/Q - 10 + 1/3Q²Q³ - 60Q² + 6,000Q - 6,000 = 0(Q - 15)(Q² - 45Q + 400) = 0Q = 15 or Q = 200Since Q = 200 is not feasible, the quantity of output that minimizes long-run average total cost is Q = 15.

A Firm's Long-Run Total Cost Curve Is Given by LTC