Complementary Monopolies and Bargaining

How should complementarities affect antitrust merger policy? I introduce a two-stage strategic model in which complementary-input monopolists offer supply schedules to producers and then engage in bilateral bargaining with producers. The main result is that there is a unique weakly dominant strategy equilibrium, the equilibrium attains the joint-profit-maximizing outcome, and output equals that of a bundling monopoly. The result holds with perfect competition in the downstream market with both unit capacity and multiunit capacity.

The result also holds with oligopoly competition in the downstream market. The result contrasts with the Cournot effect, which states that complementary-input monopolists choose total prices that are greater than the bundled-monopoly level. The analysis shows that consumers’ surplus and total producers’ surplus are greater with supply schedules and bargaining than with posted-price competition. The analysis has implications for antitrust policy toward vertical and conglomerate mergers.