This paper evaluates the incentive of firms to vertically integrate in a simple 2X2 Bertrand model of two substitutes that are each comprised of two complementary components. It confirms 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 four products are produced by independent firms (independent ownership). The reason for the change in the direction of 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. When the demand system is symmetric, total surplus is higher in parallel vertical integration, for all degrees of substitution among the products, even for the case when the goods are close substitutes and parallel vertical integration is not the equilibrium outcome. Thus, the market provides less vertical integration than is optimal from a social surplus maximizing point of view.
