Merger Review for Markets with Buyer Power Simon Loertsher Leslie M. Marx January 1, 2018 Abstrat We analyze the ompetitive effets of mergers in markets with buyer power. Using mehanism design arguments, we show that without ost synergies, buyer power an mitigate, but never eliminate, harm from mergers. With buyer power, a merger inreases inentives for entry, inreases investment inentives for rivals, and an inrease investment inentives for merging parties. Beause buyer power redues the profitability of a merger, it inreases the profitability of perfet ollusion relative to a merger. Cost synergies an eliminate merger harm, but also render otherwise profitable mergers unprofitable. Keywords: unilateral effets, ost effiienies, innovation, autions versus negotiations JEL Classifiation: D44, D82, L41 We thank Joe Farrell, Volker Noke, Patrik Rey, Mike Whinston, and seminar partiipants at the Australian Competition & Consumer Commission, Commere Commission in New Zealand, Diretorate- General for Competition of the European Commission, Penn State University, Swiss Competition Commission, Università della Svizzera Italiana, University of Western Australia, Weil, Gotshal& Manges LLP, Russell MVeagh, and partiipants in the 2017 Hal White Antitrust Conferene, Ninth Annual Federal Trade Commission Miroeonomis Conferene, 2017 Organizational Eonomis Workshop in Sydney, and 2016 Asia Paifi Industrial Organization Conferene for helpful omments. Edwin Chan provided exellent researh assistane. Finanial support by The Samuel and June Hordern Endowment is also gratefully aknowledged. DepartmentofEonomis,Level4,FBEBuilding,111BarryStreet,UniversityofMelbourne,Vitoria 3010, Australia. Email: simonl@unimelb.edu.au. The Fuqua Shool of Business, Duke University, 100 Fuqua Drive, Durham, NC 27708, USA: Email: marx@duke.edu.
1 Introdution Buyer power features prominently in the antitrust analysis of mergers. That buyer power will prevent merging suppliers from being able to negotiate higher pries is a frequent merger defense. 1 As one observer put it, buyer power is sometimes embraed by ourts as if it had talismani power. 2 Beause powerful buyers an withstand upward prie pressure from mergers of suppliers, so this appealing argument goes, they are not harmed by suh mergers. 3 In large part beause the most ommonly used models in merger review, whih are based on Cournot or Bertrand ompetition, do not aommodate powerful buyers, it is often not lear what exatly is meant by buyer power. However, this does not mean that buyer power laks empirial plausibility. For example, omputer manufaturers suh as Dell and HP proure omponents from upstream suppliers using ompetitive prourements and fae-to-fae negotiations. Although these buyers might value having the latest generation of a omponent, they may also be willing to ontinue to manufature using a prior generation in the absene of a suffiiently low prie for the new generation. Or they may be willing to take a tough negotiating stane with the low-ost supplier, even if it means the possibility of ultimately having to purhase from a higher-ost supplier. As another ase in point, oil ompanies suh as Shell, Exxon-Mobil, and BP proure oilfield servies for their wells using ompetitive prourements and negotiations in whih they play oilfield servies providers off against one another. Likewise, muniipalities prouring road improvements, park landsaping, and other ity servies sometimes anel prourements in the fae of what they view as insuffiiently ompetitive priing. 4 The use of ompetitive prourement proesses by the buyers in these examples makes it natural to model buyer power in the ontext of a prourement. This is the approah we take in this paper. We view the buyer as designing a prourement mehanism in whih suppliers partiipate. The suppliers osts are their private information, and so the buyer s 1 See, e.g., Steptoe (1993) and Carlton and Israel (2011). 2 As stated by Steptoe (1993, p. 494), Although the strong-buyer defense may be valid in a variety of irumstanes, I believe that the ourts have sometimes embraed it as if it had talismani power that ured all doubts about a merger. 3 Aording to the U.S. Horizontal Merger Guidelines (hereafter U.S. Guidelines) whih guide ourts in the United States in how to evaluate the potential antiompetitive effets of a merger, The Agenies onsider the possibility that powerful buyers may onstrain the ability of the merging parties to raise pries. (U.S. Guidelines, p. 27) Merger guidelines in other jurisditions provide a similar treatment of buyer power. The European Commission s Guidelines on the Assessment of Horizontal Mergers (hereafter EC Guidelines) disuss the possibility that buyer power would at as a ountervailing fator to an inrease in market power resulting from the merger. (para. 11) The Australian Competition and Consumer Commission s Merger Guidelines view ountervailing power as a ompetitive onstraint that an limit merger harms. (paras. 1.4, 5.3, 7.48) 4 See Kumar et al. (2015, online appendix). 1
mehanism is onstrained by inentive ompatibility and individual rationality for the suppliers. Similar to Bulow and Klemperer s (1996) approah to modeling environments with and without a powerful seller, in our model a buyer with no buyer power must rely on the outome of an effiient aution among potential suppliers, with no ability to further negotiate. In ontrast, a powerful buyer an demand disriminatory disounts from suppliers and negotiate with the aution winner, thereby implementing the buyer surplus maximizing mehanism, subjet to inentive ompatibility and individual rationality. Our approah aptures, in a general way, prourement markets, where purhasing an involve ombinations of requests for proposals, autions, and negotiations. It ombines this generality with a disiplined, prinipled analysis of buyer power, without being subjet to a pitfall of omplete information models that bargaining is always effiient. 5 Our prourement-based approah allows us to build on insights from the theory of optimal autions and to exploit results from mehanism design. The framework aounts for market power beause eah supplier is treated as having a monopoly over her private information. Yet, suppliers are oligopolisti in the sense that when there are more of them, the market power of eah individual supplier dereases. We model a merger without ost synergies as allowing the merged entity to produe at a ost equal to the minimum of the osts of the merging suppliers. Using mehanism design arguments, we show that without ost synergies, a merger of suppliers is harmful for a buyer regardless of buyer power, despite the fat that the buyer demands a lower prie from the merged entity than he would from symmetri pre-merger suppliers. Although buyer power an deter harmful mergers, it an thus never eliminate harm if mergers our. We also analyze the effet of a merger on inentives to merge, enter, and innovate. Absent buyer power, mergers without synergies are neutral for rivals and potential entrants and profitable for the merging suppliers. With buyer power, a merger of symmetri suppliers is benefiial for rivals and inreases the expeted profits of entrants. Buyer power does not neessarily render a merger unprofitable for the merging suppliers, but it an, in some ases even for a merger to monopoly. Related to innovation, we show that the effet on inentives for ost reduing investment depends on buyer power and differs for the merging and nonmerging suppliers. Without buyer power, a merger does not affet inentives for investment by nonmerging suppliers and inreases inentives for investment 5 For an early ritiism of omplete information model, see, for example, Samuelson (1985, p. 322), who writes: In pursuit of a preferred agreement, one party may threaten the other and, for redibility s sake, bind himself to arry out the threat some portion of the time. When he does, effiieny fails. Alternatively, the parties may adopt the standard negotiation bluff, insisting on ultrafavorable (and inompatible) terms of agreement. If agents persist in these demands, a mutually benefiial agreement may be lost. Although proponents of the Coase presumption may regard these ations as irrational, it is no less true that suh behavior (e.g., strikes, the arrying out of ostly threats) frequently ours. Moreover, it is unrealisti to suppose that the bargaining setting is one of perfet information. 2
by merging suppliers. With buyer power, a merger inreases inentives for investment by nonmerging suppliers and, in some ases, inreases inentives for investment by merging suppliers. A natural view is that mergers and perfet ollusion are equivalent. Although this way of thinking is orret without buyer power, it is misleading in its presene. First, mergers are publi events, while ollusion happens under the surfae. Powerful buyers an thus be expeted to take defensive ations against the inreased market power of a merged entity, but not neessarily against a artel. 6 Therefore, buyer power makes ollusion more profitable relative to mergers, assuming the ollusion is not deteted (or suspeted). Moreover, beause buyer power indues more aggressive prie demands by the buyer, losing bids above these prie demands are more likely with buyer power even with ompetitive bidding, making ollusive bidding involving deliberately losing bids harder to detet. Consequently, buyer power makes ollusion not only more profitable, but also more diffiult to detet. This ontrasts with Carlton and Israel (2011), who argue that powerful buyers may atually be harmed more by a merger than buyers without buyer power. They base this on the possibility that, in the absene of powerful buyers, suppliers ould ollude to set monopolypries, andthus a merger would have no effet. But, so the argument goes, with powerful buyers, pries would be below monopoly levels before the merger and therefore inrease as a result of a merger. They onlude that there is no theoretial neessity that the presene of powerful buyers must always lessen the prie effets from a merger. (Carlton and Israel, 2011, p. 132) Although we do not disagree with the letter of this statement, we show that the presene of powerful buyers is more likely to invite ollusion than the absene of buyer power and that, in our prourement setting, it is a theoretial neessity that powerful buyers are less affeted by a merger than those without buyer power. Thus, our results are onsistent with empirial evidene that ollusion in, for example, produts suh as disk drives, LCD panels, and auto parts, negatively affeted seemingly powerful buyers, like Dell, HP, Mirosoft, and major auto manufaturers. While the results desribed above may strike one as surprising and ounterintuitive at first, there is a lear and simple intuition for them. Without buyer power, the alloation is effiient before and after the merger. This explains the neutrality result for rivals. Beause a merger eliminates a ompeting bid for the merged entity, it follows that the merger is profitable for the merging suppliers and harmful to the buyer, whose expeted payments inrease. Turning to the ase with buyer power, in our model of mergers without 6 If olluding firms an make side payments and an alloate whih firm is to win effiiently, then ollusion and mergers have the same effet in aution markets if and only if both the ollusion and the merger is observed by the buyer. However, landestine ollusion has a different effet from merger beause of the differene in reation by the buyer. See MAfee (1994) and Kumar et al. (2015). 3
ost synergies, the merged entity s ost distribution is dominated in terms of the reverse hazard rate by the pre-merger distribution. This means that, like the seller in Myerson s optimal aution who disriminates against strong bidders, a powerful buyer disriminates against the merged entity in its ompetition with the other suppliers and applies a more aggressive reserve prie to the merged entity. 7 But this disrimination implies that the merger benefits rivals and potential entrants when the buyer is powerful. Although the powerful buyer an mitigate some of the harm from a merger, a simple revealed preferene argument implies that harm annot be eliminated. It is useful to think of buyer power as onsisting of both bargaining power, whih aptures the ability of the buyer to disriminate among suppliers, and monopsony power, whih is the buyer s ability to set a binding reserve prie. In our framework, bargaining and monopsony power do not vary with the merger; however, their optimal exertion does. For example, it may be that the buyer optimally exerts neither of these powers before a merger and optimally exerts both after a merger. These two omponents of buyer power not only resonate with notions that fare prominently in urrent antitrust ommentary, but also take on a preise meaning within our framework in a way that aptures the spirit of the antitrust usage. 8 In addition, the notion of bargaining and monopsony power as omponents of buyer power proves useful for explaining many of the key results, as will beome lear in what follows. The results summarized above imply that, without ost synergies, mergers are always detrimentaltobuyersirrespetiveoftheirpower. 9 Thismotivatesustoextendtheanalysis to aount for suh ost effiienies. We model ost effiienies as a ommonly known perentage derease in the ost of the merged entity relative to the minimum ost of the two merging suppliers before the merger. The assumption that this perentage is known is based on ost effiienies being part of a merger review and therefore information that both the buyer and the merging suppliers have. We show that, as expeted, ost effiienies make mergers unambiguously less harmful to the buyer and, if the effiienies are large enough, an ause the buyer to welome the merger. However, arguments based 7 See MAfee and MMillan (1987) on how optimal asending autions involve disrimination in favor of weaker bidders. 8 The OECDRoundtable on Monopsonyand Buyer Power(p. 9) found: There are two types of buyer power: monopsony power and bargaining power.... Both types of buyer power result in lower pries, though the lower prie obtained from monopsony power is ahieved through the at of purhasing less, whereas the lower prie obtained from bargaining power is ahieved through the threat of purhasing less. 9 The lassi result of Bulow and Klemperer (1996) that a revenue maximizing seller is better off with an additional bidder and an effiient mehanism than with an optimal aution suggests that in our setup the prourer would prefer having no merger and no buyer power to having the merger our and being a powerful buyer. However, this is intuition is not orret in general (as we explain in detail in Setion 3). In ontrast to the Bulow and Klemperer thought experiment, a merger in our setting only eliminates a losing bid, but not a random draw. 4
on ost synergies do not onstitute a slam-dunk defense: The ost synergies required to make a merger aeptable to the buyer may make it unprofitable to the merging suppliers. Indeed, whether the buyer is powerful or not, post-merger profit of the merged entity goes to zero as synergies approah 100 perent. Although ost synergies redue osts, they also squeeze suppliers informational rents and thereby profits. Eventually, the latter effet dominates. There is a related literature on merger analysis based on aution models, inluding Waehrer(1999), Waehrer and Perry(2003), Miller(2014), and Froeb, Mares, and Tshantz (2017). Waehrer (1999) examines mergers in both asymmetri first-prie and seondprie aution markets. 10 Waehrer and Perry (2003) fous on open autions and allow the optimal reserve to adjust post merger. Our approah differs in onsidering optimal prourements with asymmetri bidders and allowing varying buyer power. Miller (2014) onsiders a prourement setting in whih buyers purhase from suppliers of differentiated produts using a variant of a seond-prie aution and develops a stohasti model that an be alibrated to estimate merger effets. Froeb, Mares, and Tshantz (2017) onsider effets of a merger between bidders in an optimal (asending) aution when bidders draw their values from a family of power-related distributions, where eah bidder s value an be viewed as the maximum of some number of draws from a ommon distribution. They show that a merger redues the autioneer s expeted revenue and that, under ertain onditions, a merger to monopoly is not profitable for the merging bidders. Related work on buyer power and its role in merger analysis inludes papers in the vertial ontrating literature in the tradition of Dobson and Waterson (1997), Horn and Wolinsky (1988), and Inderst and Wey (2007). These are omplete information models with Nash or other bilateral bargaining protools, whih do not exhibit the tradeoff between effiieny and rent extration that arises in a prourement-based model suh as ours. 11 In addition, our framework extends to allow multi-produt firms that produe omplementary produts, as shown in the Online Appendix, while O Brien and Shaffer (2005) onsider mergers with multi-produt suppliers in a omplete information setup with Nash bargaining. Other authors have onsidered the effet of a merger on inentives for investment. Motta and Tarantino (2017) show that in a Bertrand oligopoly with differentiated produts, absent effiieny gains, a merger lowers total output and as a result lowers total investment in ost redution. López and Vives (2016) fous on the effet of a symmetri 10 In addition, Dalkir, Logan, and Masson (2000) examine mergers in asymmetri first-prie autions using simulated equilibrium bidding strategies. Thomas (1999) examines mergers in asymmetri firstprie autions by deriving equilibrium bidding strategies for the binomial ost distribution. 11 A related empirial literature is also grounded in models of Nash bargaining, inluding Crawford and Yurukoglu (2012), Gowrisankaran, Nevo, and Town (2015), and Collard-Wexler, Gowrisankaran, and Lee (forthoming). 5
inrease in ross-ownership in a symmetri Cournot model with R&D spillovers. 12 They show that an inrease in ross-ownership inreases ost-reduing investment for high levels of R&D spillovers but dereases investment for low levels of R&D spillovers. 13 Our model has no R&D spillovers (investment by one supplier has no effet on other suppliers osts), but we fous on the hange in ross-ownership resulting from a merger, whih neessarily involves asymmetries. Although we do not pursue it here, our approah an also be extended to aount for ross-ownership among suppliers along the lines of Lu (2012). The paper is strutured as follows. Setion 2 defines the setup. Setion 3 analyzes a merger in the absene of ost effiienies, assuming ex ante symmetri suppliers. Setion 4 inorporates ost effiienies. Setion 5 generalizes the analysis by allowing for ex ante asymmetries. Setion 6 onludes. 2 Setup In thebaseline setup, we onsider one produt and onebuyer. 14 Inthe pre-merger market, there are n 2 suppliers, indexed 1,...,n. Eah supplier i {1,...,n} draws a ost i independently from a ontinuously differentiable distribution G with support [, ] and density g that is positive on the interior of the support. (We relax the assumption of symmetry in Setion 5.) Eah supplier is privately informed about her type, and so the suppliers types are unknown to the buyer. The buyer has value v > for one unit of the produt. All of this is ommon knowledge. We let suppliers 1 and 2 be the merging suppliers. Like Farrell and Shapiro (1990), we model a merger as allowing the merging suppliers to rationalize prodution by produing using the lower of their two osts. 15 We disuss the possibility of further ost effiienies from the merger in Setion 4. Thus, given pre-merger osts = ( 1,..., n ), in the orresponding post-merger market, the nonmerging suppliers have the same ost as before the merger, and the merged entity has ost = min{ 1, 2 }. 12 Noke and Whinston (2010) and Mermelstein, Noke, Satterthwaite, and Whinston (2015) provide models of sequential mergers in the Cournot setup. 13 In the model of López and Vives (2016), when spilloversare high, the dominant effet of the derease in ompetition assoiated with ross-ownership is to allow investing firms to better appropriate the benefits of their investments, inreasing inentives for investment. However, when spillovers are low, the dominant effet of inreased ross-ownership is a redution in output and orresponding redution in inentives for ost-reduing investment. 14 The assumption of one buyer is onservative from the perspetive of providing the senario in whih buyer power is most likely to enable a buyer to remedy merger harms. 15 This is the approah also taken by Salant, Switzer, and Reynolds (1983), Perry and Porter (1985), Waehrer (1999), Dalkir, Logan, and Masson (2000), and Froeb, Tshantz, and Crooke (1999). This type of merger is equivalent to effiient (observable) ollusion as disussed by Mailath and Zemsky (1991) and MAfee and MMillan (1992). 6
We denote the distribution for the minimum of the pre-merger osts of suppliers 1 and 2 by Ĝ() 1 (1 G())2, with density ĝ. Thus, although suppliers are ex ante symmetri in the pre-merger market, in the post-merger market they are not beause the merged entity draws its ost from a different distribution. 16 We denote a nonmerged supplier s virtual ost funtion by Γ() + G() g(), and the merged entity s virtual ost funtion by ˆΓ() + Ĝ() ĝ() = + G() g() 2 G() 2(1 G()), (1) where the equality uses the definition of Ĝ(). 17 We impose the standard regularity assumption that Γ and ˆΓ are inreasing. A suffiient ondition for this is that G/g is nondereasing. Beause we allow the possibility that the densities are zero at (and also possibly ), define Γ() lim Γ() =, and analogously for ˆΓ. If Γ() is finite, then for x > Γ(), define Γ 1 (x), and analogously for ˆΓ. Buyers, suppliers, and the designer are risk neutral. A buyer s payoff is zero if he does not trade and is equal to his value minus the prie he pays if he does trade. Similarly, a supplier s payoff is zero if she does not trade and is equal to the payment she reeives minus her ost if she does trade. The setup s merits inlude the assumption of private information and independently distributed private types. This neither presumes nor preludes effiieny and results in a tradeoff between effiieny and rent extration when the buyer is powerful. It also means that the optimal Bayesian mehanism provides a pratial benhmark. 18 16 If one pereives a merger as an aquisition of one firm by another, then the aquiring firm might view itself as more effiient beause it draws its ost from Ĝ rather than G; however, beause the distribution of the minimum ost aross all firms is unhanged, it seems appropriate to refer to this as an aquisition/merger without ost effiienies. 17 As noted by Bulow and Roberts (1989), the virtual ost funtion an be interpreted as a supplier s marginal ost, treating the (hange in the) probability of trade as the (marginal hange in) quantity. To see why this is so, interpret q = G(p) as the quantity supplied by a seller who draws his ost from G at prie p. The inverse supply funtion of this seller is then P(q) = G 1 (q). Consequently, the ost of of prouring quantity q from this seller is C(q) = qp(q), whose derivative is C (q) = qp (q) +P(q). Substituting P (q) = 1/g(G 1 (q)) and q = G(p) then gives C (q) = Γ(G 1 (q)). 18 The assumption of independently distributed types is made on theoretial grounds and aptures the notion that there may be a trade-off between profit and effiieny. With orrelated types, no matter how small the degree of orrelation, profit maximization and effiieny are in no onflit, as shown by Crémer and MLean (1985, 1988), but this requires mehanisms that involve gambles that do not seem plausible or realisti; see, for example, Kosmopoulou and Williams (1998) and Börgers (2015). At the ost of additional notation, the assumption of private value ould easily be relaxed by allowing for 7
The buyer uses a prourement proedure to selet a supplier and determine a purhase prie. We adapt the approah used by Bulow and Klemperer (1996) to our prourement setup and extend it to aommodate asymmetri suppliers. Bulow and Klemperer (1996) model a seller without power as using a seond-prie aution and a seller with power as using an asending aution followed by a take-it-or-leave-it offer by the seller to the aution winner, whih is an optimal sales mehanism in their setup. In our prourement ontext, the ase of no buyer power orresponds to a buyer using a desending lok aution with a reserve (or starting prie) equal to the minimum of the buyer s value and the upper bound of the support of the ost distribution, that is, min{v,}. This is an effiient mehanism. The ase of buyer power orresponds to a buyer using an optimal prourement mehanism, whih an be implemented as a disriminatory desending lok aution possibly followed by a final take-it-or-leave-it offer by the buyer to the aution winner. It will be useful to define a single prourement proess parameterized by β {0,1} that nests the ases with (β = 1) and without (β = 0) buyer power. 19 To do so, for β {0,1}, we define weighted virtual ost funtions by Γ β () (1 β)+βγ() and ˆΓ β () (1 β)+βˆγ(). (2) By onstrution, when β = 0, the weighted virtual ost orresponds to the true ost, and when β = 1, to the supplier s virtual ost. If Γ β () is finite, then for x > Γ β (), define Γ 1 β (x), and analogously for ˆΓ β. We assume that, given β {0, 1}, a buyer uses an aution-plus-final-offer proedure that onsists of an aution phase and a final take-it-or-leave-it offer phase defined as follows: In the aution phase, the buyer onduts a (possibly disriminatory) desending lok aution. The lok prie starts at prie min{v,}. 20 As the lok prie dereases, partiipating suppliers an hoose to exit. When a supplier exits, she beomes inative and remains so. The lok stops when only one ative supplier remains, with ties broken by interdependent values along similar lines as Myerson (1981). 19 We assume that buyer power itself is not affeted by a merger among suppliers, whih seems natural if buyer power derives from the size and/or sophistiation of the buyer, as suggested by the EC Guidelines(para. 65), or from the ability to vertially integrate upstream or sponsor entry, as suggested by the U.S. Guidelines(p. 27). However, the EC Guidelines also raise the possibility that a merger ould redue buyer power beause a merger of two suppliers may redue buyer power if it thereby removes a redible alternative. (EC Guidelines, para. 67) 20 The assumption that the aution starts at a prie no greater than only has an effet when there is only one supplierer and v >. With two or more suppliers, Bertrand ompetition between them will prevent pries from rising above. Tehnially, the assumption means that the individual rationality onstraint always binds for a supplier with the highest possible ost draw. 8
randomization. The aution is potentially disriminatory in that ativity by supplier i at a lok prie of p obligates supplier i to supply the produt at the lok prie p less a supplier-speifi disount of p Γ 1 1 β (p) if i is an independent supplier and p ˆΓ β (p) if i is the merged entity, should the buyer hoose to trade with that supplier. 21 In the final offer phase, the buyer implements a supplier-speifi reserve of Γ 1 β (v) for a nonmerged supplier and (v) for the merged entity as follows: If the aution prie is ˆΓ 1 β below the reserve, then trade ours at the aution prie. Otherwise, the buyer offers the reserve, take-it-or-leave-it, to the aution winner. If the offer is aepted, trade ours at the aepted prie, and if it is rejeted, there is no trade. By the usual logi, in the essentially unique equilibrium in non-weakly dominated strategies of the aution-plus-final-offer proedure, eah supplier remains ative until the lok prie reahes her weighted virtual ost and then exits, and if she wins the aution, she aepts a final offer from the buyer if and only if it is greater than or equal to her ost. For β = 1, the aution is not disriminatory in the pre-merger market beause suppliers are symmetri. 22 However, in the post-merger market, the merged entity is subjet to a larger disount off the lok prie relative to the nonmerged suppliers beause Ĝ is dominated by G in terms of the reverse hazard rate. 23 To see this, observe that for all [,], ĝ() Ĝ() = g() 2(1 G()) G() 2 G() g() G(), (3) withastrit inequality forintheinterior ofthesupport. 24 Consequently, forall [,], we have ˆΓ() Γ() and hene, for all p, ˆΓ 1 (p) Γ 1 (p), with strit inequalities for (,) and p (,ˆΓ()), respetively. Thus, with buyer power, the buyer behaves more aggressively towards the merged entity than towards nonmerged suppliers, demanding greater disounts from the merged entity in the aution phase and applying a lower reserve to the merged entity in the final offer phase. It is useful to relate the aution-plus-final-offer proedure desribed above to standard 21 In the extension to asymmetri suppliers in Setion 5, we allow ost distributions to differ for eah supplier. In that ase, supplier speifi disounts would be defined analogously, but based on the supplier speifi virtual ost funtions. 22 To see that for β = 0, the aution-plus-final-offer proedure indeed redues to a desending lok aution with reserve equal to min{v,}, reall first that, for β = 0, the weighted virtual ost funtions are the identity funtions. This means that the aution phase has disounts of 0 and so is not disriminatory. In addition, when β = 0, the supplier-speifi reserves are just min{v,}, whih is the starting prie for the aution phase. 23 Reall that the reverse hazard rate for a distribution F() with density f() is f()/f() and that F() dominates G() in terms of the reverse hazard rate if f()/f() g()/g() for all. 24 Dominane in terms of the reverse hazard rate implies first-order stohasti dominane, that is, (3) implies G() Ĝ(). 9
onepts from mehanism design theory. By the revelation priniple, the outome of this gameanalsobeahievedastheequilibriumoutomeofadiretmehanismthataskseah playeritoreporthistype i tothemehanismandthatmakesthealloationandpayments a funtion of the olletion of reports. Given an alloation rule q() = (q 1 (),...,q n ()) pre merger and ˆq() = (ˆq(),ˆq 3 (),...,ˆq n ()) post merger, where q i (),ˆq(),ˆq i () [0,1], n i=1 q i() 1, and ˆq()+ n i=3 ˆq i() 1, with values of 1 (0) meaning that a player does (does not) produe, inentive ompatibility (and binding individual rationality onstraints for the least effiient seller types) then pins down the(interim expeted) payments of every player. 25 The following is based on standard arguments mehanism design theory; see, e.g., Krishna (2009). Given inentive ompatibility and binding individual rationality onstraints for sellers of type, pre-merger expeted buyer surplus given alloation rule q( ) is BS pre (q( )) E [ n i=1 q i ()(v Γ( i )) ], while post merger, expeted buyer surplus given alloation rule ˆq(.) is ( BS post (ˆq( )) E [ˆq() v ˆΓ(min{ ) 1, 2 }) + ] n ˆq i ()(v Γ( i )). Given the alloation rules, soial surplus pre and post merger is given, respetively, as SS pre (q( )) E [ n i=1 i=3 q i ()(v i ) ] and SS post (ˆq( )) E [ˆq()(v min{ 1, 2 })+ ] n ˆq i ()(v i ). As disussed above, when β = 0, the aution-plus-final-offer proedure maximizes soial surplus. As shown in the proof of the following lemma, when β = 1, the proedure is optimal for the buyer in the sense of maximizing expeted buyer surplus. Lemma 1 The equilibrium outome of the aution-plus-final-offer proedure orresponds to the alloation and payments in the dominant strategy implementation of the optimal i=3 25 There are transfers that make a mehanism with alloation rule q(), respetively ˆq(), inentive ompatible if and only if for all i and all, q i (), respetively ˆq i (), is noninreasing in i ; see, e.g., Krishna (2009). 10
mehanism for a designer whose objetive is to maximize the expeted value of β(buyer surplus) +(1 β)(soial surplus), (4) subjet to inentive ompatibility and individual rationality. Proof. See the Appendix. Naturally, entral to our analysis below will be how a merger affets expeted buyer surplus, soial surplus, prie, and quantity, and how these hanges depend on buyer power. Letting BS β pre BS pre(q β ( )) and BS β post BS post (ˆq β ( )), we denote by BS β BS β post BS β pre the differene in expeted buyer surplus post and pre merger, where, for given β {0,1}, q β ( ) and ˆq β ( ) denote the alloationrule implied by the aution-plus-final-offer proedure pre and post merger, respetively. Analogously, we denote by SS β E [ˆq β ()(v min{ 1, 2 })+ ] [ n n ] ˆq β i ()(v i) E q β i ()(v i) i=1 i=3 the hange in expeted soial surplus as a result of a merger. We denote by P β the hange in the buyer s expeted payment as result of a merger, whih is given as P β E [ˆq β ()ˆΓ(min{ 1, 2 })+ ] [ n n ] ˆq β i ()Γ( i) +E q β i ()Γ( i), i=1 i=3 and by Q β the expeted hange in the quantity traded as a result of a merger, that is: 3 Merger analysis Q β E [ˆq β ()+ ] n n ˆq β i () q β i (). i=3 We begin by analyzing the effets of a merger on pries, quantities, and buyer surplus, assuming no ost effiienies from the merger or other ountervailing effets. Then we onsider suppliers inentives to merge, enter, or invest in ost-reduing innovation. In Setion 5, we allow merger-related ost effiienies. i=1 11
3.1 Merger effets A merger has two key effets on the supply side of the market. First, the number of suppliers is redued by one. Seond, as noted above, the merged entity has a better ost distribution than any of the individual suppliers, that is, Ĝ() G() for all [, ]. Beause of the hange in distribution, the merger affets the aution-plus-final-offer proedure for a powerful buyer, as we disuss below. We first address the ase without buyer power. Beause a buyer without buyer power uses an effiient mehanism before and after the merger, the alloation is effiient with and without the merger. The alloation not being affeted by the merger means ˆq 0 () = q 0 1 ()+q0 2 () and, for i {3,...,n}, ˆq0 i () = q0 i (). If 1 = min{}, then supplier 1 wins in the pre-merger market and reeives payment min{v, 2,.., n }, and the merged entity wins in the post-merger market, but reeives the weakly larger payment min{v, 3,..., n,}. 26 Beause the merger eliminates a bid, the only effet of a merger is to inrease the buyer s payment in ases in whih the pre-merger outome would have involved one of the merging suppliers winning and the other determining the prie. Thus, although the alloation is not affeted by the merger when there is no buyer power, the expeted payment by the buyer inreases, and so the merger dereases expeted buyer surplus. Proposition 1 In the absene of buyer power, a merger results in the same alloation for any realization of osts (implying that Q 0 = 0 and SS 0 = 0), a higher expeted payment by the buyer ( P 0 > 0), and lower expeted buyer surplus ( BS 0 < 0). Proof. See the Appendix. Proposition 1 highlights a ontrast with the results of Farrell and Shapiro (1990), who show that under Cournot ompetition, in the absene of ost synergies, a merger auses the quantity to derease and the prie to inrease. In our setup, there an be a prie effet without a quantity effet. Next we analyze the ase with buyer power. As mentioned in the introdution, we an deompose buyer power into bargaining power, the ability to optimally disriminate among suppliers in the aution phase, and monopsony power, the ability of a buyer to ommit in the final offer phase to a take-it-or-leave-it offer that is less than min{v,}. A buyer who exerts bargaining power may sometimes purhase from a supplier who does 26 Likewise, if 2 = min{}, then supplier 2 wins in the pre-merger market and reeives payment min{v, 1, 3,.., n }, and the merged entity wins in the post-merger market, but reeives the weakly larger payment min{v, 3,..., n,}, where we add to this last expression to aount for the ase of n = 2. 12
not have the lowest ost, and a buyer who exerts monopsony power may sometimes not purhase, even when the lowest ost is below his willingness to pay. In our framework, bargaining power and monopsony power do not vary with a merger. However, a merger affets the extent to whih it is optimal for the buyer to exert his bargaining and monopsony power. Beause the pre-merger market is symmetri, a powerful buyer does not exert his bargaining power before the merger. After the merger, the extent to whih a powerful buyer exerts his bargaining power is driven by the presene of rivals and the differene between virtual ost funtions Γ and ˆΓ. Beause Γ() < ˆΓ() for all (,), the buyer disriminates against the merged entity relative to rivals in the aution phase by requiring larger disounts of the merged entity. Thus, in the presene of rivals, the exertion of bargaining power an ause the merged entity not to trade when supplier 1 or 2 would have traded pre merger, and it an ause the merged entity to be paid less than supplier 1 or 2 would have been paid pre merger. However, in the ase of merger to monopoly, bargaining power has no effet there is no sope for disrimination before the merger beause suppliers are symmetri and none after the merger beause there is only one supplier. The extent to whih a powerful buyer exerts his monopsony power against a supplier an be measured by the amount by whih the buyer s supplier-speifi reserve for that supplier falls below. 27 Relative to a buyer with a low willingness to pay, a buyer with a high willingness to pay will exert his monopsony power to a lesser extent, or possibly not at all. In partiular, a buyer with a value greater than Γ() (respetively ˆΓ()) never finds it optimal to make a final offer to a nonmerged supplier (respetively merged entity) that might be rejeted. Thus, when Γ() is finite, whih implies that Γ() < ˆΓ(), a merger inreases the range of buyer values suh that the buyer exerts his monopsony power. In addition, if v < ˆΓ(), then ˆΓ 1 (v) < Γ 1 (v), whih implies that a merger inreases the extent to whih the buyer exerts his monopsony power against the merged entity relative to a nonmerged supplier, as refleted in a more aggressive final offer to the merged entity. The powerful buyer s inreased inlination to exert monopsony power post merger resonates with the popular view that powerful buyers will withstand upward prie pressure due to a merger. Nevertheless, as shown below, mergers harm even powerful buyers. Figure?? illustrates the mehanis at work. Panel (a) shows the effets of a merger with buyer power and n = 2, and panel (b) shows the effets of a merger with buyer power and n 3. Both panels assume v < Γ(), so that the buyer exerts monopsony power 27 One ould quantity the extent to whih a powerful buyer exerts monopsony power against a nonmerged supplier by ( Γ 1 (v))/( ) and against the merged entity by ( ˆΓ 1 (v))/( ), both of whih vary from 0 (no exertion of monopsony power) to 1 (maximal exertion of monopsony power) as v varies from to. 13
against both merged and nonmerged suppliers. As shown in panel (a), when n = 2, there isno bargaining power effet, but asaresult of theexertion of monopsony power, amerger redues the set of types for whih trade ours. As shown in panel (b), when n 3, the merger not only redues the set of types for whih trade ours due to the exertion of monopsony power, but also shifts trade away from the merged entity and towards higher ost nonmerged suppliers due to the exertion of bargaining power. In partiular, for types in the lighter shaded region along the diagonal, one of the merging suppliers trades before the merger, but inreased disrimination against the merged entity results in a higher ost nonmerged supplier trading after the merger. (a) Effets of a merger with n = 2 (b) Effets of a merger with n 3 buyfrom1 no trade buyfroma nonmerging supplier no trade 2 min{1,2} buyfrom2 buyfroma merging supplier 1 min{ 3,..., n} Figure 1: Bargaining and monopsony power. With buyer power, a revealed preferene argument implies that the buyer s expeted surplus is redued by the merger: In the pre-merger market, the buyer ould use the same alloation rule as in the post-merger market by prouring from the lower-ost supplier of suppliers 1 and 2 whenever he would purhase from the merged entity after the merger, in whih ase the additional ompeting bid would inrease his pre-merger expeted buyer surplus. 28 Adopting the pre-merger mehanism that is optimal for the buyer an only further inrease pre-merger expeted buyer surplus. We summarize these results as follows: Proposition 2 With buyer power, a merger results in a weakly lower expeted quantity traded ( Q 1 0) (stritly if n = 2 and v < ˆΓ() or if n 3 and v < Γ()), lower expeted buyer surplus ( BS 1 < 0), and weakly lower expeted soial surplus ( SS 1 0) (stritly if n 3 or v < ˆΓ()). 28 Of ourse, the language of using the same alloation rule is loose beause the set of agents varies. What we mean by keeping the alloation rule the same is made preise in the proof of Theorem 1 in the Appendix. 14
Proposition 2 implies that soial surplus dereases stritly with a merger in the presene of buyer power if n 3,i.e., the merger is not amerger tomonopoly, or v < ˆΓ(), i.e., the buyer exerts monopsony power against the merged entity. To appreiate the breadth of the onditions under whih SS 1 < 0, observe that the buyer exerts monopsony power against the merged entity under the fairly weak onditions that v is finite and the ost distribution is suh that g()(1 G()) = 0, whih holds whenever g() is finite. 29 The derease in quantity in Proposition 2 is partiularly notable beause merger review tends to fous on the prie effets of a merger, with little onsideration to effets on quantity. For example, after a merger to monopoly, the buyer who exerts monopsony power against the merged entity may pay a lower prie. 30 Despite this lower offer, whih might be pereived as a redution in the prie paid by the buyer, the buyer is stritly worse off as a result of the merger. Thus, in this example, a fous on prie effets leads to the wrong onlusion regarding the effets of the merger on the buyer. In both our setup with buyer power and that of Farrell and Shapiro (1990), a merger results in a shift in quantity away from the merged entity and towards other suppliers (or towards zero if n = 2). In Farrell and Shapiro, the internalization of externalities by the merging suppliers results in a derease in their equilibrium quantity, and a orresponding inrease in the equilibrium quantities of nonmerging suppliers. The resulting derease in total quantity implies an inrease in prie. In ontrast, in our setup with buyer power, a merger auses the buyer to protet himself from the inreased market power of the merged entity by exerting his bargaining power to more aggressively disriminate against the merged entity relative to rivals and by exerting his monopsony power to make a more aggressive final offer to the merged entity. This response by the buyer results in a derease in quantity for the merged entity, both due to a greater probability of no trade at all, and a shift towards trade with nonmerged suppliers. But, despite the buyer s more aggressive stane towards the merged entity, the loss of ompetition auses a derease in the buyer s expeted surplus. Carlton and Israel(2011) argue that beause the threat from a buyer s outside option for example, due to vertial integration that allows the buyer to produe in-house is not diminished by a merger of suppliers, a merger of suppliers may have little effet on pries. In ontrast, Proposition 2 shows that even when buyer power is derived from an outside option that leaves the buyer with the same willingness to pay (equal to v) before the merger and after the merger, the harmful effets of the merger on the buyer are not 29 Beause ˆΓ() = + G() 2 G() g() 2(1 G()),g()(1 G()) = 0 implies lim ˆΓ() = and hene v < ˆΓ(). 30 In the example of merger to monopoly, the post-merger final offer ˆΓ 1 (v) is the transation prie. For v suffiiently small, Γ 1 (v) is a good proxy for the transation prie before the merger, but beause it is higher, the transation is both more likely and more expensive before the merger. On balane, the buyer is made worse off by the merger. 15
eliminated. Propositions 1 and 2 also provide an interesting ontrast with a lassi result from the autions literature due to Bulow and Klemperer (1996). This result says that a seller is better off with n + 1 bidders drawing their types from idential distributions and no power than having only n bidders and maximal power. This suggests the following thought experiment in our setting: Would the buyer prefer faing the merged entity and having buyer power to having no merger and no buyer power? Intuition based on Bulow and Klemperer might suggest that the buyer is better off with no merger and no buyer power. However, this intuition is wrong in general beause, in a nutshell, a merger only eliminates a losing bid, not a ost draw, whih is the key differene relative to the Bulow and Klemperer thought experiment. If a powerful buyer s value is suffiiently large that he does not exert his monopsony power, then a Bulow-Klemperer-like result does hold beause, in that ase, the powerful buyer and the powerless buyer have the same pre-merger payoff (both buy from the low-ost supplier at a prie equal to the seond-lowest ost). Thus, for v suffiiently large, BSpre 0 (v) = BS1 pre (v) > BS1 post (v), where we add the argument v to highlight the dependene of buyer surplus on v and where the inequality follows from the result that BS 1 < 0. Intuitively, if a powerful buyer does not exert his monopsony power, then he is left with only his bargaining power, whih is less valuable than having an additional bid. However, as shown in the proof of Proposition 3, for v suffiiently small that the powerful buyer does exert his monopsony power (and under the tehnial ondition that g() > 0), the opposite of the Bulow-Klemperer result holds: buyer power dominates ompetition in the sense that BSpre 0 (v) < BS1 post (v). Proposition 3 Assuming g() > 0, there exists v > suh that for all v (,v ), BS 0 pre(v) < BS 1 post(v). Proof. See the Appendix. As shown in Figure 2, in both the framework of Bulow and Klemperer (1996) and in our framework, the autioneer is better off with power than without and better off with more bidders than fewer. However, in Bulow and Klemperer s setup, where an entire draw of a bidder s type is lost and the assumed symmetry eliminates any benefit to the autioneer from disrimination, the harm to the autioneer from a redution in the number of bidders dominates power. In ontrast, in our framework, only a losing bid is lost and a powerful buyer exerts both bargaining and monopsony power, with the result that the benefit of buyer power an dominate. 16
(a) Bulow and Klemperer framework (b) Prourement-based merger framework n+1 n pre-merger post-merger no BP 0.5 0.333 no BP 0.5 0.417 BP 0.531 0.417 BP 0.531 0.511 Figure 2: Comparison of Bulow and Klemperer (1996) and a prourement-based merger framework. Panel (a): Expeted autioneer revenue in an asending aution with and without bargaining power for an autioneer with zero ost faing n + 1 = 3 or n = 2 bidders. Panel (b): Expeted buyer surplus in a prourement-based merger model with and without buyer power for a buyer with value v = 1 faing 3 pre-merger suppliers or a merged entity and one other supplier. Both panels assume that (pre-merger) types are drawn from the uniform distribution on [0, 1]. As we show below, buyer power mitigates some harmful effets of a merger but exaerbates others. Propositions 1 and 2 imply that 0 = Q 0 Q 1 and 0 = SS 0 SS 1 with strit inequalities in the ases desribed in Proposition 2. Thus, quantity and soial surplus effets are exaerbated by buyer power. In ontrast, buyer power mitigates the effet of a merger on expeted buyer surplus, as shown in the proof of the following proposition: Proposition 4 0 = Q 0 Q 1 and 0 = SS 0 SS 1 and 0 > BS 1 > BS 0. Proof. See the Appendix. The effet on expeted buyer surplus desribed in Proposition 4 implies that, although a merger harms a buyer with buyer power, that harm is less than the harm to a buyer without buyer power. Another relevant question is how the number of rivals affets the harm from mergers. Competition authorities typially view the presene of large numbers of nonmerging suppliers as a fator that mitigates the harm from a merger. 31 We now show that without buyer power this is indeed the ase in our setup. Furthermore, as n goes to infinity, it is also true for powerful buyers. Under the tehnial onditions that (i) ((1 G()) n 2 (1 G(Γ 1 (min{ˆγ(),}))) n 2 )max{v ˆΓ(),0}dĜ(), 31 For models of vertial integration in whih harm inreases with the ompetitiveness of the industry, see Riordan (1998) and Loertsher and Reisinger (2014). 17
is nondereasing in n and (ii) (Ĝ() Ĝ(ˆΓ 1 (Γ())))max{v Γ(),0} is noninreasing in, we an also show that merger harm dereases in n for powerful buyers. Proposition 5 With no buyer power, buyer harm dereases in n, i.e., BS 0 inreases in n. With buyer power, buyer harm and harm to soial surplus go to zero as n goes to infinity, lim n BS 1 = 0 and lim n SS 1 = 0. Moreover, with buyer power, under onditions (i) and (ii), buyer harm monotonially dereases in n, i.e., BS 1 monotonially inreases in n. Proof. See the Appendix. Although Proposition 5 leaves open the possibility that buyer surplus ould hange nonmonotonially with n when buyers are powerful, numerial alulations show that harm to buyers dereases monotonially in n for a variety of distributions, inluding the uniform distribution. 3.2 Merger-related inentives As we show, the inentives to merge, enter, and innovate are affeted by buyer power. Inentives to merge A well-known result for mergers in the Cournot model is that a merger without ost synergies always benefits rival firms, but is not profitable for the merging firms unless it is a merger to monopoly (see Salant, Switzer, and Reynolds (1983) and Perry and Porter (1985)). 32 As we now show, in our prourement model, things are starkly different. As already foreshadowed by the preeding analysis, without buyer power, mergers are always profitable for the merging suppliers and neutral for the rivals. In the absene of buyer power, a merger either does not hange or inreases the joint surplus of the merging suppliers. The inrease ours when, before the merger, one of the merging suppliers wins and is paid the ost of the other merging supplier, whih ours with positive probability. Then, after the merger, the merged entity wins but reeives a larger payment. In other ases, no supplier s quantity or payment is affeted by the merger. 32 For the Bertrand model, mergers have been shown to be more benefiial for outsiders than for the merging firms; see Denekere and Davidson (1985). 18