462 PART • Market Structure and Competitive Strategy Q1 30 Firm 2’s Reaction Curve F IGURE 12.5 DUOPOLY EXAMPLE The demand curve is P = 30 − Q, and both firms have zero marginal cost In Cournot equilibrium, each firm produces 10 The collusion curve shows combinations of Q1 and Q2 that maximize total profits If the firms collude and share profits equally, each will produce 7.5 Also shown is the competitive equilibrium, in which price equals marginal cost and profit is zero Competitive Equilibrium 15 Cournot Equilibrium 10 Collusive Equilibrium 7.5 Firm 1’s Reaction Curve Collusion Curve 7.5 10 15 30 Q2 The total quantity produced is therefore Q = Q1 + Q2 = 20, so the equilibrium market price is P = 30 − Q = 10, and each firm earns a profit of 100 Figure 12.5 shows the firms’ reaction curves and this Cournot equilibrium Note that Firm 1’s reaction curve shows its output Q1 in terms of Firm 2’s output Q2 Likewise, Firm 2’s reaction curve shows Q2 in terms of Q1 (Because the firms are identical, the two reaction curves have the same form They look different because one gives Q1 in terms of Q2 and the other gives Q2 in terms of Q1.) The Cournot equilibrium is at the intersection of the two curves At this point, each firm is maximizing its own profit, given its competitor’s output We have assumed that the two firms compete with each other Suppose, instead, that the antitrust laws were relaxed and the two firms could collude They would set their outputs to maximize total profit, and presumably they would split that profit evenly Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost, which in this example is zero Total revenue for the two firms is R = PQ = (30 - Q)Q = 30Q - Q Marginal revenue is therefore MR = ⌬R/⌬Q = 30 - 2Q Setting MR equal to zero, we see that total profit is maximized when Q = 15 Any combination of outputs Q1 and Q2 that add up to 15 maximizes total profit The curve Q1 + Q2 = 15, called the collusion curve, therefore gives all pairs of outputs Q1 and Q2 that maximize total profit This curve is also shown in