A market is served by two firms in Cournot competition, each with a constant marginal cost of $100. The market inverse demand curve is P = 2,000 - 50Q, where Q is the total market output produced by the two firms, q₁ + q₂. What is Firm 1's reaction function?

Question

Quizplus · Accepted Answer

Firm 1's reaction function is derived by maximizing its profit given the output of Firm 2. The inverse demand function P = 2000 - 50Q, where Q = q1 + q2, can be used to find the total revenue of Firm 1, which is TR = P*q1 = (2000 - 50(q1 + q2))q1. The marginal revenue of Firm 1 is then MR = 2000 - 100q1 - 50q2. Setting MR equal to marginal cost (MC = 100) and solving for q1 gives q1 = 19 - 0.5q2, which matches choice A.

A Market Is Served by Two Firms in Cournot Competition