A firm with market power faces the demand function q = 1,000 - P. The firm's total cost function is TC(q) = 5q + q² + 500. If the firm behaves as a single-price monopoly, the firm's optimal output level is ____. A) 751.25 B) 510.45 C) 326.75 D) 248.75

Question

Quizplus · Accepted Answer

To find the optimal output level for a monopoly, set marginal revenue (MR) equal to marginal cost (MC). The inverse demand function is P = 1000 - q, so TR = P*q = 1000q - q^2. MR is the derivative of TR, MR = 1000 - 2q. The MC is the derivative of TC, MC = 5 + 2q. Setting MR = MC: 1000 - 2q = 5 + 2q, solving gives q = 248.75.

A Firm with Market Power Faces the Demand Function Q