Suppose a firm faces the demand function q = 800

Question

Suppose a firm faces the demand function q = 800 - 4P. The firm's total production costs are given by MC(q) = 9.5q + q². If the firm cannot price discriminate, its profit-maximizing price is $____. A) 200 B) 197.50 C) 175.25 D) 100

Quizplus · Accepted Answer

To find the profit-maximizing price, we first need to find the marginal revenue (MR) and set it equal to the marginal cost (MC). The demand function is q = 800 - 4P, which can be rewritten as P = 200 - 0.25q to find the inverse demand function. The total revenue (TR) is P*q = (200 - 0.25q)q. The marginal revenue (MR) is the derivative of TR with respect to q, which is MR = 200 - 0.5q. The given marginal cost (MC) is 9.5q + q^0, which simplifies to MC = 9.5 since q^0 is 1. Setting MR equal to MC to find the profit-maximizing quantity: 200 - 0.5q = 9.5, solving for q gives q = 381. Substituting q back into the inverse demand function to find P: P = 200 - 0.25*381, which gives P = 197.50.