Suppose a firm's inverse demand curve is P = 100

Question

Suppose a firm's inverse demand curve is P = 100 - Q, and its marginal cost is constant at $20. What is the value of the Lerner index at the profit-maximizing quantity?

Quizplus · Accepted Answer

The Lerner index is defined as (P - MC) / P, where P is the price and MC is the marginal cost. At the profit-maximizing quantity, the marginal revenue equals the marginal cost. The marginal revenue curve is the derivative of the inverse demand curve, which is MR = 100 - 2Q. Setting MR = MC, we get 100 - 2Q = 20, which implies Q = 40. The price at this quantity is P = 100 - Q = 100 - 40 = 60. Therefore, the Lerner index is (60 - 20) / 60 = 0.67.