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. Struc- the theory (either Cournot or our theory), since tural models of vertically related markets typ- the theory suggests that, if the merging parties’ ically estimate markups under the assumption shares do not change, then the prices are unlikely that sellers post prices that buyers take as fixed to change as well. We advocate a more com- in a sequential vertical-pricing game.5 In our putationally intensive approach, which involves model, sellers and buyers move simultaneously estimating the capacities of the merging parties and the division of rents from market power from the pre-merger market share data. Given depends upon cost and demand functions. We those capacities, we then estimate the effect of investigate the conditions under which the first- the merger on the industry, taking into account order conditions of our model can be used to the incentive of the merged firm to restrict out- estimate demand and cost parameters. put (or demand, in the case of buyers). Horizon- Our model also provides an interesting alter- tal mergers among sellers in intermediate input native for studying spot electricity markets. The market, where buyers are manufacturing firms, operation of these markets closely resembles are more likely to raise price and be profitable our market game: generating firms submit sup- in our model than in the Cournot model because ply schedules, buyers report the demands of capacity reports of sellers are typically strategic their retail customers who face regulated prices, complements, not strategic substitutes. In whole- and an independent system operator chooses the sale markets, the buyers are retailers, and they spot price to equate reported supply to market typically respond to enhanced seller power by demand. Green and Newberry (1992) was the reducing their reported demand, thereby miti- first study of wholesale markets for electricity gating the effects of the merger and complicat- as a game in which firms’ strategies are their ing its impact on prices and profits. The model choices of supply functions.6 Empirical stud- treats horizontal mergers by buyers symmetri- ies of these markets have applied supply func- cally. Vertical mergers in our model generate tion models or Cournot models to predict the large efficiency gains because they eliminate potential for generating firms to exercise market two “wedges,” the markup by the seller and the power in spot electricity markets and to estimate markdown by the buyer. Foreclosure effects are their markups.7 Our model generates a markup important when the merging firms are large. equation that combines the advantages of the Structural models of homogenous good mar- supply function model with the simplicity of the kets with dispersed buyers use an ad hoc mod- Cournot model. ification of the Cournot first-order conditions to The second section presents a model of inter- estimate seller markups. They find that markups mediate good markets and derives the equilib- 4 are typically much lower than Cournot markups rium price/cost margins and the value/price mar- and attribute this finding to the Cournot model’s gins, which is the equivalent for buyers, for failure to account for a firm’s expectations of vertically separated markets and for vertically how rivals will respond to its output choices. In our model, each firm understands that reductions in its supply will be partially offset by increases 5. Several recent studies include Goldberg and Verboven (2001), Villas-Boas and Zhao (2005), and Villas-Boas and in the outputs of its rivals. Their response Hellerstein (2006). means that the elasticity of each firm’s resid- 6. Other studies include Anderson and Philpott (2002), ual demand function exceeds the elasticity of Anderson and Xu (2002, 2005), and Baldick et al. (2004). 7. The studies of markups include Borenstein and Bushnell (1999), Borenstein, Bushnell, and Wolak (2003), 3. Farrell and Shapiro (1990) and McAfee and Williams and Wolak (2003) on California; Hortacsu and Puller (2008) (1992) independently criticize the Cournot model while on Texas; Mansur (2007), Bushnell, Mansur, and Saravia using a Cournot model to address the issue. (2008) on California, New England, and Pennsylvania, New 4. See Bresnahan (1989) for a description of the method- Jersey, Maryland (PJM); Green and Newbery (1992), Green ology and a survey of a number of empirical studies. More (1996), Brunekreeft (2001), Sweeting (2007), and Wolfram recent studies include Genesove and Mullin (1998) and Clay (1999) on England and New Wales; and Wolak (2000, 2003, and Troesken (2003). 2007) on Australia. 394 ECONOMIC INQUIRY integrated markets. The third section extends oligopoly. A market with no vertically integrated the model to spot markets in electricity and firms is called a vertically separated market. wholesale markets in which buyers compete in a These markets can be further decomposed into downstream market. The fourth section analyzes oligopoly markets, in which sellers have market horizontal and vertical mergers. The fifth section power and buyers do not, and oligopsony mar- examines identification issues that would arise in kets, in which buyers have market power but trying to apply our model to market data. The sellers do not. A market with one or more ver- sixth section applies the model to the merger tically integrated firms is a vertically integrated of the west coast assets of Exxon and Mobil to market. illustrate the plausibility and applicability of the In what follows, we will need to distinguish theory. The final section concludes. between two kinds of intermediate good mar- kets based on the type of buyer. Markets in which buyers are manufacturing firms are called II. INTERMEDIATE GOOD MARKETS intermediate input markets. In these markets, We begin with a standard model of a market a buyer j combines the intermediate input qj for a homogenous intermediate good Q.There with capacity kj using a constant returns to scale are n firms, indexed by i from 1 to n. Each seller technology F(qj ,kj ) to produce a good yj that 10 i produces output xi using a constant returns to it sells at price r. Thus, its revenue function scale production function with fixed capacity γi . can be expressed as Thus, seller i’s production costs take the form = qi x V(qj ,kj ) rki f . C(x , γ ) = γ c i , ki (1) i i i γ i A manufacturing firm that has twice the capacity where c(·) is convex and strictly increasing.8 of another firm can produce twice as much at the Each buyer j consumes intermediate output same average productivity. qj and values that consumption according to Markets in which buyers are retail firms are a function V(qj ,kj ) where kj is buyer j’s called wholesale markets. In these markets, a capacity for processing the intermediate output. buyer j purchases qj to resell to final consumers = We assume that V is homogenous of degree one at price r.Hereyj qj and firm j’s valuation so that it can be expressed as of qj is given by qj = − qj (2) V(qj ,kj ) = kj v , V(qj ,kj ) rqj kj w k kj j where v(·) is concave and strictly increasing.9 qj qj = kj r − w A firm may be both a seller and a buyer, that kj kj is, it may produce the intermediate good and also consume it. Such firms are called vertically where w represents unit selling costs. A retailer integrated, although they may be net sellers or with twice as much selling capacity (e.g., num- net buyers. Letting p denote the market-clearing ber of stores) can sell twice as much at the same price in the intermediate good market, the profits unit cost. to a vertically integrated firm i are given by In the Cournot model of oligopoly markets, sellers submit quantities and the market chooses (3) price to equate reported supply to demand. q x The equilibrium price is equal to each buyer’s π = p (x − q ) + k v i − γ c i . i i i i k i γ marginal willingness to pay, but exceeds each i i seller’s marginal cost of supply. In the standard The profits to a firm if it is either a pure seller or oligopsony model, buyers submit quantities and a pure buyer can be obtained by setting qi = 0 the market chooses price to equate reported sup- or xi = 0, respectively. ply and demand. The equilibrium price is equal Markets in which both sellers and buy- to each seller’s marginal cost, but exceeds each ers exercise market power are called bilateral buyer’s true willingness to pay. In each of these
8. In addition, we assume that c (z) −→ ∞ as z −→ ∞ . 10. The production function could include other inputs 9. In addition, we assume v (z) −→ 0asz −→ ∞ . provided their quantities are proportional to qi . HENDRICKS & MCAFEE: THEORY OF BILATERAL OLIGOPOLY 395 models, one side of the market is passive and balance equation, the other side behaves strategically, anticipat- n n ing the market-clearing mechanism in order to = = = manipulate prices. Our interest, however, is in a (4) Q qi xi X market where both buyers and sellers recognize i=1 i=1 their ability to unilaterally influence the price and the marginal conditions, and behave strategically. In order to model this type of market, we extend the Klemperer and (5) Meyer model, in which sellers behave strategi- q x cally in submitting supply schedules, to allow j = = i = v p c γ ,i,j 1, .., n. buyers to behave strategically in submitting their kj i demand schedules. In adopting this model, however, we impose Note that, if everyone tells the truth, then the some restrictions on the schedules that the firms equilibrium outcome is efficient. Our model can can report. Sellers have to submit cost schedules be viewed as turning the market into a black which come in the form γc(x/γ), and buyers box, as in fact happens in the Cournot model, have to submit valuation functions which come where the price formation process is not mod- in the form kv(q/k). In a mechanism design eled explicitly. Given this black box approach, framework, agents can lie about their type, but it seems appropriate to permit the market to be they cannot invent an impossible type. The efficient when agents do not, in fact, exercise admissible types in our model satisfy (1) and unilateral power. Such considerations dictate the (2), and agents are assumed to be bound by competitive solution, given the reported types. this message space. For sellers, the message Any other assumption would impose inefficien- cies in the market mechanism, rather than having space is a one-parameter family of schedules inefficiencies arise as the consequence of the indexed by production capacity, and for buyers, rational exercise of market power by firms with the message space is a one-parameter family significant market presence. of schedules indexed by consumption capacity. Each firm anticipates the market mecha- Therefore, a seller’s type is a capacity γ,a nism’s decision rule in submitting its reports. buyer’s type is a capacity k, and if the firm From Equation (4), it follows that is vertically integrated, its type is a pair of capacities (γ,k). Agents (simultaneously) report ki Q γiQ their types to the market mechanism, but in (6) qi = ,xi = , doing so, they do not have to tell the truth. K A seller can exaggerate its costs by reporting a where capacity γ that is less than what it is in reality, n n and a buyer can understate its willingness to (7) K = k , = γ . pay by reporting a capacity k that is less than i i = = what it is in reality.11 Values and costs are not i 1 i 1 well specified at zero capacity. However, the Thus, given the firms’ reports, market output solution can be calculated for arbitrarily small Q( , K) solves the equation but positive capacities and zero capacity handled as a limit. Firms with zero capacity would then Q Q (8) v = c , report zero capacity. K Given the agents’ reports, the market mecha- nism chooses price p to equate reported supply which depends only on the aggregate production and reported demand, and allocates the output and consumption capacity reports. Market price efficiently. The solution is characterized by the p( , K) is obtained by substituting Q( , K) into the marginal conditions of Equation (5), and the output is allocated to sellers and buyers using the market share Equation (6). 11. A buyer’s marginal willingness to pay for another The firms’ actual types are common knowl- unit of input at q units of input is measured by v q .Since k edge to the firms. Thus, in choosing their reports, v is concave, this derivative is increasing in k. Therefore, a buyer understates its willingness to pay by underreporting firms know the true types of other firms. Then its capacity. the payoff to a vertically integrated firm i from 396 ECONOMIC INQUIRY