A monopolist with a marginal cost of MC = 20Q faces the inverse demand curve P = 90 - 5Q. The profit-maximizing price is $_____.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, we first need to find the quantity where marginal revenue (MR) equals marginal cost (MC). The inverse demand curve is P = 90 - 5Q, so the total revenue (TR) is P*Q = (90 - 5Q)Q = 90Q - 5Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 90 - 10Q. Setting MR equal to MC to find the profit-maximizing quantity: 90 - 10Q = 20Q => 90 = 30Q => Q = 3. Substituting Q = 3 into the demand curve to find the price: P = 90 - 5(3) = 90 - 15 = 75.

A Monopolist with a Marginal Cost of MC = 20Q