Double marginalization and vertical integration: new lessons from extensions of the classic case.

• Author: Hamilton, James L.

1. Introduction

   Although firms have a variety of motives for vertical merger and other vertical restrictions, a traditional issue, which permeates much of the literature on vertical integration, is how the existence of horizontal market power in one or more vertically-related industries creates motives for them to vertically integrate [13, 187-89]. The classic case is double marginalization. Suppose that an upstream industry sells an intermediate good to a downstream industry, which in turn produces a final product that it sells to consumers. Then, because the upstream and downstream industries independently engage in noncompetitive pricing, the firms in each industry only see the effect of their output restriction on their own profits, and do not see that their output restriction also affects the profits of the firms in the other industry. This myopia creates a "vertical externality" that vertical integration would internalize. In the simplest case, when the products are homogeneous and final production has fixed input proportions, the conventional wisdom about double marginalization is that ". . . the integrated industry makes more profit than the nonintegrated industry, and the consumer price is lower in the case of the integrated industry. These two properties are very general . . ." [15, 175]. The implication is that integration of two noncompetitive industries would not be anticompetitive, contradicting the traditional antitrust hostility toward vertical integration.

   In fact, what is crucial for double marginalization to have any relevance for antitrust policy is the conjunction of the welfare and profitability properties. No matter how beneficial or damaging a particular behavior might be, if that behavior is unprofitable it has little relevance for antitrust policy, because it either would not occur or would be self-correcting. Rational public policy would not be concerned about what firms have no incentive to do. Consequently, profitability is a crucial methodological requirement of models that analyze vertical integration.

   PROFITABILITY CRITERION. Since vertical integration is a voluntary merging of firms, in a model vertical integration must be profitable for each participant.

   This conjunction of greater welfare and greater profits is shown here not to be a general property of classic double marginalization. Models that have shown this conjunction have assumed that the upstream industry (at least) is a pure monopoly [4; 8], which is a highly restrictive concept of noncompetitive behavior, because it is empirically rare. The models analyzed here use the conjectural variation (CV) concept of noncompetitive equilibrium in both industries. In these CV models, eliminating double marginalization by vertical integration always increases economic welfare, but profitability is not a general condition. In the CV models, whether or not integration adds to profits depends crucially on the noncompetitive market structure and conduct that are assumed. In fact, many CV models of double marginalization do not satisfy the Profitability Criterion for vertical integration and are not relevant for analyzing policy issues.

   Double marginalization is an inherent phenomenon in any model of successive noncompetitive industries. Because of this ubiquity, the analytical effects of double marginalization in these CV models, where it is the only vertical phenomenon, are relevant to a much wider class of models that include other vertical phenomena and other motives for vertical integration. Whatever other vertical relationships a model may include, the effects of eliminating double marginalization will be an element of the measured effect of vertical integration of the industries.

   The reasons for analyzing CV models are three. First, in spite of its unrealistic naivete about interfirm dynamics, Cournot's special null case of a CV noncompetitive equilibrium has been used in models of vertical integration.(1)

   Second, CV models easily impose a methodological requirement that integration be purely vertical.

   VERTICALITY CRITERION. Since the analytical issue is how pre-existing horizontal market power in the nonintegrated industries would create double marginalization and vertical externalities, in a model the measured effect of vertical integration must not include changes in that horizontal market power.

   Every noncompetitive industry has some basis in its horizontal structure and interfirm conduct for whatever horizontal market power exists in that industry. If the acquiring industry has a less competitive structure or conduct, it will impose them on the industry acquired. Such changes in structure or conduct are horizontal effects, because such changes are possible by means other than vertical integration. As Abiru [1] and Wu [17] point out, when a model of vertical integration builds in such changes in horizontal market power among firms, the model confounds the purely horizontal effects of this merger with the purely vertical effect of internalizing an externality. Since horizontal market power in a CV equilibrium depends only on the structure and conduct parameters of the industries, the model shows the pure vertical effects of double marginalization by holding constant both the market structure parameter (the number of firms) and the market conduct parameter (the coefficient of conjectural variation). In this way, the analysis can abstract from the kind of horizontal market power effects of vertical integration that have been built into some previous models of integration of successive oligopolies. For example, both Greenhut and Ohta [5] and Salinger [14] assumed different numbers of finns in the two industries.(2) Thus, in those models horizontal effects remain confounded with the vertical effects of integration. While discovering the overall effect of such compound events is a valid inquiry, the purpose here is to analyze the purely vertical effect. In such compound cases, Hamilton and Lee [8] show how to identify and isolate the effect of horizontal changes as a component of the total measured effect of integration. In CV models the pure vertical component would, then, be the case here of setting identical and constant structure and conduct parameters.(3)

   A third reason for using CV models is that they are more general than Cournot models and can portray any degree of pre-existing market power. The price-cost margin in an industry can take any value from pure monopoly to perfect competition, depending on the values assigned to the market structure parameter or the market conduct parameter. For a given horizontal structure, Cournot models impose a special case of pre-existing price-cost margins by assuming a special case of competitive conduct.

   Among CV models that satisfy the Verticality Criterion, how vertical integration can fail to satisfy the Profitability Criterion is shown in two ways. First, an industry-level method of analysis in section III assumes that some or all firms are integrated and compares the resulting integrated equilibrium with the nonintegrated equilibrium that is presented in section II. This comparison of industrial equilibria shows that vertical integration is profitable for CV equilibria only if the pre-existing market power is sufficiently great. Consequently, vertical integration is unprofitable for a wide range of cases, including the Cournot case.

   Second, a firm-level method of analysis in section IV does not impose integration a priori: the expected profitability of integration is analyzed for a pair of nonintegrated firms. This method has a dimension that does not exist in the industry-level method. Analyzing the integration decision at the firm-level demonstrates that a pair must make an additional conjecture in order to assess the profitability of integration: the pair must have a conjecture about whether or not it expects rival pairs also will integrate. Thus, whether or not a pair of firms would expect vertical integration to be profitable depends, as before, on the pre-existing horizontal market structure and conduct in the CV model, but it also depends on whether a pair expects that other pairs also will integrate, or not. This firm-level method shows that a pair of nonintegrated firms might see their own integration as profitable, without seeing that integration generally would reduce industry profitability. If so, the two industries would integrate piecemeal.

   Both industry-level and firm-level analyses of CV models show that the existence of double marginalization does not always create a situation in which vertical integration would increase both welfare and profits. The limits on when integration is profitable are the limits on the policy relevance of the double marginalization phenomenon. In the CV models, those limits are not robust among model assumptions and analytic methods. These results have methodological implications for the analysis of vertical integration, which are in section V.

2. A Model of Nonintegrated Oligopolies

   This section presents a conjectural variations model of two successive nonintegrated industries. The noncooperative equilibrium of this nonintegrated model is the benchmark used in sections III and IV to show the impact of vertical integration on profits and economic welfare. The assumptions in this CV model generally encompass those in previous studies of Cournot and pure monopoly models in which classic double marginalization is the sole vertical phenomenon.

   The Verticality Criterion is implemented by assuming that the intermediate and final goods industries have the same horizontal structure (number of firms n) and the same noncompetitive conduct (coefficient of conjectural variation [Lambda]) and that vertical integration does not change either parameter.(4) In order for the integrated industry to have the same horizontal structure as the two nonintegrated industries, integration is by pairs of firms, one from each industry.

   The upstream...