CHAPTER 12 • Monopolistic Competition and Oligopoly 461 then their outputs cannot change It is also rational once they are in Cournot equilibrium because then neither firm will have any incentive to change its output When using the Cournot model, we must therefore confine ourselves to the behavior of firms in equilibrium The Linear Demand Curve—An Example Let’s work through an example—two identical firms facing a linear market demand curve This will help clarify the meaning of a Cournot equilibrium and let us compare it with the competitive equilibrium and the equilibrium that results if the firms collude and choose their output levels cooperatively Suppose our duopolists face the following market demand curve: P = 30 - Q where Q is the total production of both firms (i.e., Q = Q1 + Q2) Also, suppose that both firms have zero marginal cost: MC = MC = We can determine the reaction curve for Firm as follows To maximize profit, it sets marginal revenue equal to marginal cost Its total revenue R1 is given by R = PQ1 = (30 - Q)Q1 = 30Q1 - (Q1 + Q2)Q1 = 30Q1 - Q 21 - Q2Q1 Its marginal revenue MR1 is just the incremental revenue ⌬R1 resulting from an incremental change in output ⌬Q1: MR = ⌬R 1/⌬Q1 = 30 - 2Q1 - Q2 Now, setting MR1 equal to zero (the firm’s marginal cost) and solving for Q1, we find Firm 1=s reaction curve: Q1 = 15 - Q 2 (12.1) Q (12.2) The same calculation applies to Firm 2: Firm 2=s reaction curve: Q2 = 15 - The equilibrium output levels are the values for Q1 and Q2 at the intersection of the two reaction curves—i.e., the levels that solve equations (12.1) and (12.2) By replacing Q2 in equation (12.1) with the expression on the righthand side of (12.2), you can verify that the equilibrium output levels are Cournot equilibrium: Q1 = Q2 = 10