Suppose a firm faces the demand function q = 600

Question

Suppose a firm faces the demand function q = 600 - 6P. The firm's total production costs are given by MC(q) = 5q / 6 + q². Further suppose that the firm can perfectly price discriminate. The output level that maximizes profit for the firm is ____. A) 12.64 B) 10.89 C) 9.51 D) 7.63

Quizplus · Accepted Answer

To maximize profit under perfect price discrimination, set marginal cost equal to marginal revenue. The inverse demand function is P = 100 - q/6. The marginal revenue is the same as the demand curve under perfect price discrimination, so MR = 100 - q/6. Set MR = MC: 100 - q/6 = 5q/6 + q^2. Solving this equation gives q ≈ 9.51.