A Price Theory of Vertical and Lateral Integration under Productivity Heterogeneity∗

Abstract

We develop a model of organizational choice in a perfectly competitive product market with heterogeneous firms and incomplete contracts. Successful production requires two inputs that are supplied by two different firms. Firms are vertically heterogeneous with respect to their productivity. Each supplier from one side matches endogenously in a stable equilibrium with one supplier from the other side. After they match, and taking the market price as given, they decide whether to integrate or stay as separate units. Each supplier cares about firm profits and private benefits. Organization decisions involve a trade-off between firm profits and private benefits. An important feature of our model is the endogenously determined, through matching, bargaining powers, which as we show have a profound effect on organizational design in a market. We study the interplay between market price, firm productivity and firm boundaries. Integration decisions can be non-monotonic in overall firm productivity. More specifically, it may be the low productivity firms that have stronger incentives to integrate. A higher market price can induce more firms to disintegrate, yielding an industry supply curve that is backward-bending. These results generate new empirical implications