The firm's long-run total cost is given by LTC = 100Q - 10Q² + (1/3)Q³, and long-run marginal cost is given by LMC = 100 - 20Q + Q². At what output level does the firm have economies of scale? A) Q

Question

The firm's long-run total cost is given by LTC = 100Q - 10Q² + (1/3)Q³, and long-run marginal cost is given by LMC = 100 - 20Q + Q². At what output level does the firm have economies of scale? A) Q < 15 B) Q < 175 C) Q < 4,000 D) Q < 88

Quizplus · Accepted Answer

Economies of scale occur when an increase in output leads to a decrease in long-run average costs, which happens when the long-run marginal cost (LMC) is less than the long-run average cost (LAC). Given the LMC formula, economies of scale are present when the derivative of LTC (which gives us LMC) is decreasing. The condition for economies of scale is when LMC is decreasing with an increase in Q, which, based on the given LMC formula, happens when Q is less than a certain threshold. Without the exact LAC calculation, we infer economies of scale from the point where LMC starts to increase, which is not directly given but can be inferred to be at the lowest Q value provided among the options, as LMC is increasing with Q in the formula.

The Firm's Long-Run Total Cost Is Given by LTC =