Factor substitutability, monopoly, and vertical integration: a heuristic analysis.

• Author: Hamilton, James L.

1. Introduction

   A monopolist of an intermediate good can extract profit from final consumers only indirectly, since it only sells to other firms, which in turn produce final products. If those final producers substitute other inputs for the one the monopolist sells, they would not see that their substitution cuts into the monopolist's profit. Because of this "vertical externality"[10, 179], the monopolist would earn less than the maximum monopoly rent. Although the final producers would minimize their nominal costs, their input combination would be suboptimal. Vernon and Graham [11] showed that the monopolist would increase both its profit and economic welfare by vertically integrating to reverse such input substitution (for a given final output). Schmalensee[9] then investigated what portion of a perfectly competitive final product industry the input monopolist would acquire. While he found that complete integration would maximize profits, Schmalensee also discovered that the integration would affect final output and its price, but that the effect was ambiguous. Obviously, the welfare gain from lower real costs would be offset partially or entirely, if integration also reduced output. This ambiguity differed from analyses that had assumed a fixed input proportion in final production. With fixed proportions, integration never would reduce output and always would increase welfare.(1) The many refinements of Schmalensee's analysis have shown that whether integration by the monopolist would increase or decrease final production depends on the elasticities of final demand and input substitution[3; 6; 7; 12; 13]. The ambiguous effect on output that occurs when inputs are substitutable has become part of the lore about vertical integration and has been an element in the debates about antitrust policy toward vertical integration[2, 168].

   This literature is very technical and does not have any single clear result comparable to that in the fixed proportions case. For that reason it is difficult to convey intuitively. This paper takes a heuristic approach that adds to this literature in several ways. First, the two components in the anatomy of integration are derived explicitly for the first time. "The first is a change in input proportions so as to reduce real costs. The second is a broadening of monopoly"[8, 27]. Each of these components can affect final output. Revealing the anatomy shows that the component due to the change in the input proportions in final production not only reduces real cost, it always contributes an increase in final output, while the component due to broadening of monopoly always tends to reduce final output. In this anatomy, the ambiguous effect of integration on output is due to ambiguity about the comparative magnitudes of the two component effects. Second, the anatomy demonstrates that an assumption that is crucial to the ambiguity about output is the pure input monopoly assumption. In the pure monopoly model, integration "broadens the monopoly" only because input substitutability affects the elasticity of the derived demand for the intermediate good relative to the elasticity of the final demand. Finally, in models of noncompetitive equilibrium in which the elasticity of final demand does not affect pricing decisions at all, the monopoly power component disappears. Then, vertical integration to reduce suboptimal input proportions has the intuitive and unambiguous result of lowering real costs and increasing final output.

2. The Model

   The model here encompasses the essential traits of previous studies. Let the consumers' inverse demand for a final product Q be P = D (Q), with [D.sub.Q]

   A perfectly competitive industry produces Q from inputs X and Y. Input Y is available in perfectly elastic supply at price r. A pure monopoly produces X at constant cost k and sells it at a linear price w. Final producers are price takers with respect to both w and r. They have a linear...