The Incentive for Vertical Integration

We evaluate the incentive to integrate vertically in a simple 2X2 Bertrand model of two substitutes that are each comprised of two complementary components. We confirm that all prices fall as a result of a vertical merger. Further, we find that, when the composite goods are poor substitutes, producers of complementary components are better off after integration. Thus at equilibrium, each pair of complementary goods is produced by a single firm (parallel vertical integration). In contrast, when the composite goods are close substitutes, vertical integration reduces profits of the merging firms and is therefore undesirable. Thus, at equilibrium, all firms are independent (independent ownership). The reason for the change in the incentive to merge is that, as the composite goods become closer substitutes, competition between them reduces prices (in comparison to full monopoly) thereby eliminating the usefulness of a vertical merger in accomplishing the same price effect. We also find that, for intermediate levels of substitution, firms producing complementary components prefer to merge only if the substitute good is produced by an integrated firm. Thus, for intermediate levels of substitution, both parallel vertical integration and independent ownership are equilibria.