A THEORY OF BILATERAL OLIGOPOLY KENNETH HENDRICKS and R. PRESTON MCAFEE∗ In horizontal mergers, concentration is often measured with the Hirschman– Herfindahl Index (HHI). This index yields the price–cost margins in Cournot com- petition. In many modern merger cases, both buyers and sellers have market power, and indeed, the buyers and sellers may be the same set of firms. In such cases, the HHI is inapplicable. We develop an alternative theory that has similar data requirements as the HHI, applies to intermediate good industries with arbitrary numbers of firms on both sides, and specializes to the HHI when buyers have no market power. The more inelastic is the downstream demand, the more captive production and consump- tion (not traded in the intermediate market) affects price–cost margins. The analysis is applied to the merger of the gasoline refining and retail assets of Exxon and Mobil in the western United States. (JEL L13, L41) I. INTRODUCTION in a bilateral oligopoly market in evaluating the competitiveness of the market? Merging a net The seven largest refiners of gasoline on buyer with a net seller produces a more bal- the west coast of the United States account anced firm, bringing what was formerly traded for over 95% of the production of California in the intermediate good market inside the firm. Air Resources Board (CARB) certified gasoline Will this vertical integration reduce the exercise sold in the region. The seven largest brands of of market power and produce a more compet- gasoline also account for over 97% of retail sales itive upstream market? Or will the vertically of gasoline. Thus, the wholesale gasoline market integrated firm restrict supply to other nonin- on the west coast is composed of a number tegrated buyers, particularly if they are rivals in of large sellers and large buyers who compete the downstream market? against each other in the downstream retail There is a voluminous theoretical literature market. What will be the effect of a merger of that addresses these questions. Most of the vertically integrated firms on the wholesale and literature considers situations in which one or retail markets? This question has relevance with two sellers supply one or two buyers who the mergers of Chevron and Texaco, Conoco and compete in a downstream market and models Phillips, Exxon and Mobil, and BP/Amoco and their interactions as a bargaining game.1 Sellers Arco, all of which have been completed in the negotiate secret contracts with buyers specifying past decade. a quantity to be purchased and transfers to When monopsony or oligopsony faces an be paid by the buyer. The bilateral bargaining oligopoly, most analysts consider that the need in these models is efficient, so there is no for protecting buyers from the exercise of mar- distortion in the wholesale market. Gans (2007) ket power is mitigated by the market power of uses the model of vertical contracting to derive the buyers and vice versa. Thus, even when the buyers and sellers are separate firms, an analysis 1. See Rey and Tirole (2008) for a survey of this based on dispersed buyers or dispersed sellers literature. Several of the main papers in this literature is likely to err. How should antitrust authori- are Hart and Tirole (1990), McAfee and Schwartz (1994), ties account for the power of buyers and sellers O’Brien and Shaffer (1992), Segal (1999), and de Fontenay and Gans (2005). *We thank Jeremy Bulow and Paul Klemperer for their useful remarks and for encouraging us to explore downstream concentration. ABBREVIATIONS Hendricks: Department of Economics, University of Texas CARB: California Air Resources Board at Austin, Austin TX 78712. HHI: Hirschman–Herfindahl Index McAfee: Yahoo! Research, 3333 Empire Blvd., Burbank, CA MHI: Modified Hirschman–Herfindahl Index 91504. Phone 818-524-3290, Fax 818-524-3102, Email [email protected] 391 Economic Inquiry doi:10.1111/j.1465-7295.2009.00241.x (ISSN 0095-2583) Online Early publication November 12, 2009 Vol. 48, No. 2, April 2010, 391–414 © 2009 Western Economic Association International 392 ECONOMIC INQUIRY a concentration index that measures the amount Moreover, our model will suffer from the same of distortion in the vertical chain as a result of flaws as the Cournot model in its application both horizontal concentration among buyers and to antitrust analysis. Elasticities are treated as sellers and the degree of vertical integration. constants when they are not, and the relevant However, the vertical contracting models do elasticities are taken as known. However, the not describe intermediate good markets like the analysis can be applied to markets with arbitrary wholesale gasoline market in the western United numbers of sellers and buyers, who individually States. The market consists of more than two have the power to influence price, and buyers sellers and two buyers, and trades occur at a who may compete against each other in a down- fixed, and observable, price. Other papers study stream market. The analysis is simple to apply, vertical mergers by assigning the market power and permits the calculation of antitrust effects in either to buyers or to sellers, but not both.2 a practical way. These models are excellent for assessing some Our approach is based on the Klemperer and economic questions, including the incentive to Meyer (1989) market game. In their model, sell- raise rival’s cost, the effects of contact in several ers submit supply functions and behave strate- markets, or the consequences of refusals-to-deal. gically, buyers are passive and report their true But they do not address the implications of demand curves, and price is set to clear the mar- bilateral market power that we wish to study ket. We allow the buyers to behave strategically in this paper. in submitting their demand functions, and apply Traditional antitrust analysis presumes dis- a similar concept of equilibrium as Klemperer persed buyers. Given such an environment, the and Meyer. As is well known, supply function Cournot model (quantity competition) suggests models have multiple equilibria. Klemperer and that the Hirschman–Herfindahl Index (HHI), Meyer (1989) reduce the multiplicity by intro- which is the sum of the squared market shares of ducing stochastic demand, and they show that, the firms, is proportional to the price–cost mar- if the support is unbounded, then the equilib- gin, which is the proportion of the price that rium is unique. More recently, Holmberg (2004, is a markup over marginal cost. Specifically, 2005) has shown that capacity constraints and the HHI divided by the elasticity of demand a price cap can lead to uniqueness. A number equals the price–cost margin. The HHI is zero of authors (e.g., Turnbull 1981; Green 1996, for perfect competition and one for monopoly. 1999; and Akgun 2005) obtain uniqueness by The HHI has the major advantage of simplicity restricting the supply schedules to be linear. Our and low data requirements. In spite of well- approach is similar but we do not require lin- publicized flaws, the HHI continues to be the earity. In our model, sellers can select from workhorse of concentration analysis and is used a one-parameter family of nonlinear schedules by both the U.S. Department of Justice and the indexed by production capacity, and buyers can Federal Trade Commission. The HHI is inap- select from a one-parameter family of nonlinear plicable, however, to markets where the buyers schedules indexed by consumption or retailing are concentrated, particularly if they compete in capacity. Thus, sellers can exaggerate their costs a downstream market. by reporting a capacity that is less than it in fact Our objective in this paper is to offer an is, and buyers can understate demand. The main alternative to the HHI analysis that applies to advantage of restricting the selection of sched- homogenous good markets with linear pricing ules is that it allows us to study the strategic where buyers are concentrated and with (i) sim- interaction between sellers and buyers. ilar informational requirements, (ii) the Cournot In a traditional assessment of concentration model as a special case, and (iii) an underly- according to the U.S. Department of Justice ing game as plausible as the Cournot model. Merger guidelines, the firms’ market shares The model we offer suffers from the same are intended, where possible, to be shares of flaws as the Cournot model. It is highly styl- capacity. This is surprising in light of the fact ized and static. It uses a “black box” pricing that the Cournot model does not suggest the use mechanism motivated by the Cournot analysis. of capacity shares in the HHI, but rather the share of sales in quantity units (not revenue). 2. See, for example, Hart and Tirole (1990), Ordover, Like the Cournot model, the present study Saloner, and Salop (1990), Salinger (1988), Salop and suggests using the sales data, rather than the Scheffman (1987), Bernheim and Whinston (1990). An alternative to assigning the market power to one side of capacity data, as the measure of market share. the market is Salinger’s sequential model. Capacity plays a role in our theory, and indeed HENDRICKS & MCAFEE: THEORY OF BILATERAL OLIGOPOLY 393 a potential test of the theory is to check that demand, so markups are lower in our model than actual capacities, where observed, are close to in the Cournot model. Furthermore, the rivals’ the capacities consistent with the theory. responses are determined by their marginal The merger guidelines assess the effect of the costs, so markups depend upon cost elasticities merger by summing the market shares of the as well as the demand elasticity. Larger firms merging parties.3 Such a procedure provides a have higher markups, and markups are higher in useful approximation, but is inconsistent with markets where marginal costs are steep.