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

To find Firm 1's reaction function, we need to find the profit-maximizing quantity for Firm 1 given any quantity produced by Firm 2. To do this, we can use the first-order condition for profit maximization, which states that marginal revenue (MR) equals marginal cost (MC).

Firm 1's total revenue is TR = Pq1, where q1 is the quantity produced by Firm 1. Taking the derivative of TR with respect to q1, we get MR = P + q1(dP/dq), where dP/dq is the inverse demand curve slope. In this case, dP/dq = -50.

Firm 1's profit is π1 = TR - MC1q1 = (P - MC1)q1. Setting MR = MC1, we get P + q1(-50) = 100, which simplifies to q1 = 2 - 0.02q2 - 0.5q1. Solving for q1, we get q1 = 19 - 0.5q2. Therefore, Firm 1's reaction function is q1 = 19 - 0.5q2. Answer choice A is correct.

A Market Is Served by Two Firms in Cournot Competition