Merger Review for Markets with Buyer Power Simon Loertsher Leslie M. Marx September 6, 2018 Abstrat We analyze the ompetitive effets of mergers in markets with buyer power. Using mehanism design arguments, we show that without ost synergies, mergers harm buyers, regardless of buyer power. However, buyer power mitigates the harm to a buyer from a merger of symmetri suppliers. 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 are grateful to three anonymous referees of this journal and the editor, Emir Kamenia, for omments and suggestions that have helped us to improve the paper. We also thank Catherine Corbett, Eri Emh, Joe Farrell, Volker Noke, Patrik Rey, Mike Riordan, Carl Shapiro, 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 2018 Market Design Workshop at UTS, 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 gratefully aknowledged. Department of Eonomis, Level 4, FBE Building, 111 Barry Street, University of Melbourne, 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 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
suppliers partiipate. The suppliers osts are their private information, and so the buyer s 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 its 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 revealed preferene 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 it would from symmetri pre-merger suppliers. Thus, although buyer power an deter harmful mergers, it an 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. Regarding innovating, we show that the 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
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 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. 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 monopoly pries, and thus 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 of symmetri suppliers 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 at first, they have a lear and simple intuition. Without buyer power, the alloation is effiient before and after the merger. This explains the neutrality result for rivals. Beause a merger eliminates a 3
bid, the merger harms the buyer regardless of buyer power. Without buyer power, the elimination of a ompeting bid is the only effet of the merger on the merging suppliers beause the alloation is the same before and after merger, whih explains the profitability of the merger without buyer power. In general, the powerful buyer adjusts the alloation rule in response to the merger. 6 In our model of mergers without ost synergies, the merged entity s ost distribution is dominated in terms of the reverse hazard rate by eah merging supplier s 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 and the more aggressive reserve imply that the merger benefits rivals and potential entrants but may not be profitable for the merging suppliers when the buyer is powerful. 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 detrimental to buyers irrespetive of their power. 9 This motivates us to extend the analysis 6 The hange in the optimal alloation rule post merger makes it less obvious why the bid elimination harms the buyer. However, a revealed preferene argument shows that the merger harms even the powerful buyer: the buyer ould essentially use the post-merger optimal alloation rule before the merger and would be better off as a result of the additional ompetition between the two merging suppliers. Moving to the optimal pre-merger mehanisms leaves the buyer a fortiori better off without the merger. 7 See MAfee and MMillan (1987) on how optimal asending autions involve disrimination in favor of weaker bidders. 8 The OECD Roundtable on Monopsony and 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 4
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 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, the post-merger profit of the merged entity goes to zero as synergies approah 100 perent. 10 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 et al. (2017). Waehrer (1999) examines mergers in both asymmetri first-prie and seond-prie aution markets. 11 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 et al. (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 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 4). In ontrast to the Bulow and Klemperer thought experiment, a merger in our setting only eliminates a losing bid, but not a random draw. 10 As disussed later, the result for a buyer without power is sensitive to whether ost effiienies affet the upper support of the merged entity s ost distribution. 11 In addition, Dalkir et al. (2000) examine mergers in asymmetri first-prie autions using simulated equilibrium bidding strategies. Thomas (1999) examines mergers in asymmetri first-prie autions by deriving equilibrium bidding strategies for the binomial ost distribution. 5
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. 12 In addition, our framework extends to allow multi-produt firms that produe omplementary produts, as shown in the Online Appendix. 13 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 inrease in ross-ownership in a symmetri Cournot model with R&D spillovers. 14 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. 15 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. Setions 3 and 4 onsider mergers in the absene of ost effiienies. Setion 3 shows that mergers harm buyers. Setion 4 analyzes effets on all parties and on their inentives assuming ex ante symmetri suppliers. Setion 5 inorporates ost effiienies. Setion 6 briefly disusses the generalization to allow for ex ante asymmetries. Setion 7 onludes. 12 A related empirial literature is also grounded in models of Nash bargaining, inluding Crawford and Yurukoglu (2012), Gowrisankaran et al. (2015), and Collard-Wexler et al. (forthoming). 13 O Brien and Shaffer (2005) onsider mergers with multi-produt suppliers in a omplete information setup with Nash bargaining. 14 Noke and Whinston (2010) and Mermelstein et al. (2015) provide models of sequential mergers in the Cournot setup. 15 In the model of López and Vives (2016), when spillovers are 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 a orresponding redution in inentives for ost-reduing investment. 6
2 Setup In the baseline setup, we onsider one produt and one buyer. 16 In the 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 i with support [, ] and density g i that is positive on the interior of the support. Eah supplier is privately informed about its 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 refer to the model with G i = G for all i as the symmetri model, and the one where different suppliers have different distributions as the asymmetri model. Setion 3 applies to the more general asymmetri model. In Setions 4 and 5, we speialize to the symmetri model for larity of exposition, highlighting plaes where the assumption of symmetry is a restrition. In Setion 6 we disuss the extent to whih our results extend to the asymmetri model. 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. 17 We disuss the possibility of further ost effiienies from the merger in Setion 5. 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 }. We denote the distribution for the minimum of the pre-merger osts of suppliers 1 and 2 by Ĝ() 1 (1 G 1())(1 G 2 ()), with density ĝ. Under symmetry, we have Ĝ() = 1 (1 G()) 2. Thus, even if all 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. 18 Buyers and suppliers are risk neutral. A buyer s payoff is zero if it does not trade and is equal to its value minus the prie paid if trade does our. Similarly, a supplier s payoff is zero if it does not trade and is equal to the payment it reeives minus its ost if it does trade. 16 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. 17 This is the approah also taken by Salant et al. (1983), Perry and Porter (1985), Waehrer (1999), Dalkir et al. (2000), and Froeb et al. (1999). This type of merger is equivalent to effiient (observable) ollusion as disussed by Mailath and Zemsky (1991) and MAfee and MMillan (1992). 18 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. 7
The setup s merits inlude the assumption of private information and independently distributed private types. 19 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. 20 Modelling buyer power as the ability of a buyer with demand for a single unit to ommit to an optimal prourement is natural from a methodologial perspetive. 21 Although in a setup with single-unit demand there is no sope to meaningfully speak of large and small buyers, there are reasons why a real-world large buyer might be more likely to have suh ommitment power than a small buyer. 22 For example, large buyers are likely to be around longer, eteris paribus, so reneging on ommitments may be more ostly to their long-run reputation. Also, larger buyers are likely to be ative in more markets than smaller buyers, so again may obtain more value from building up a reputation and inur more ost from damaging that reputation by violating ommitments. Further, a large buyer may be more likely to have the sophistiation required to implement an optimal prourement. 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 19 Our prourement-based model highlights a differene between a setup in whih suppliers private information is ost versus one in whih it is quality. Although the suppliers payoffs an be modeled similarly in either ase, with private information regarding quality, the buyer s payoff would depend diretly on the trading supplier s private information. This would indue an element of interdependeny in valuations, whih in general renders very different (and arguably less pratial) mehanisms optimal (see Mezzetti, 2004, 2007). 20 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). 21 In priniple, the approah of Myerson (1981) extends straightfowardly to settings in whih the buyer has demand for multiple units with ommonly known values for these, provided the suppliers private information remains one-dimensional. However, a merger between two suppliers reates a multi-unit supplier that is most naturally thought of as having two-dimensional private information. If the buyer has demand for one unit only, the problem with multi-dimensional private information is moot. 22 For two ase studies of buyer power, see Roberts et al. (2011). 8
bound of the support of the ost distribution, that is, min{v, }. 23 This is an effiient mehanism. The ase of buyer power orresponds to a buyer using an optimal prourement mehanism, whih quite generally (for example, under the assumptions introdued in Setion 4) 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. The details of this implementation of the optimal prourement mehanism are provided in Setion 4 as they are not required in Setion 3. 3 Mergers harm buyers We define buyer surplus as the ex ante expeted surplus of the buyer, that is, the buyer s expeted value from obtaining the good minus the buyer s expeted payment. 24 We say that a merger harms the buyer if the buyer s expeted surplus is smaller after the merger than before. We first state a remarkably general result: Theorem 1. A merger without ost synergies harms the buyer. Proof. See the Appendix. Aording to Theorem 1, a merger without ost synergies harms the buyer irrespetive of whether the buyer has power and independently of any additional assumptions on the sellers ost distributions. The theorem has a lear intuition: A merger eliminates a bid, and that harms the buyer. This intuition is borne out in the proof. The proof is fairly straightforward when the buyer has no power beause then the alloation rule is effiient before and after merger, but there is one fewer bid after merger. However, with buyer power, the argument is more subtle and intriate. The mehanism design problems before and after a merger differ, and so does the powerful buyer s optimal prourement mehanism and alloation rule. Moreover, absent additional assumptions, we do not even know the struture of the optimal mehanisms. Fortunately, these obstales an be irumvented by taking the buyer s optimal mehanism after the merger as given. (From Myerson (1981), we know 23 The assumption that the aution starts at a prie no greater than only has an effet when there is only one supplier and v >. With two or more suppliers, Bertrand ompetition between them prevents pries from rising above. Tehnially, the assumption means that the individual rationality onstraint always binds for a supplier with the highest possible ost draw. 24 A formal definition is provided in Setion 4. 9
that this mehanism exists and an be derived using the tehniques developed there.) This mehanism an then be augmented and applied to the pre-merger market as follows: keep the alloation and payment rules for the nonmerging suppliers the same as in the optimal post-merger mehanism and have suppliers 1 or 2 produe in exatly the same instanes as the merged entity would under the optimal post-merger mehanism. To make this inentive ompatible for suppliers 1 and 2, the augmented mehanism needs to indue ompetitive bidding between suppliers 1 and 2 for the right to produe. Beause this additional bidding inreases the buyer s expeted surplus, it follows that the buyer must be better off before the merger even though the augmented mehanism is not optimal in the pre-merger market, it is available before the merger. Applying the optimal pre-merger mehanism only reinfores the onlusion that a powerful buyer is better off before the merger than after the merger. 4 Analysis of merger effets As shown in Theorem 1, merger harm to the buyer is general and not eliminated by buyer power. To analyze whether buyer power mitigates merger harm, and various other interations between buyer power and mergers, we now impose symmetry, that is, assume G i = G for all i, and additional strutural assumptions. We omment along the way whih of our results do not generalize to pre-merger asymmetri suppliers, at times distinguishing between whether or not the two merging suppliers are symmetri with eah other. We begin by analyzing the effets of a merger on market outomes 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. Before doing so, we introdue a regularity ondition inreasing virtual osts that renders a powerful buyer s optimization problem quasionave and thereby simplifies the analysis. The mehanism design onepts and results that we introdue, while seemingly of a tehnial nature, are key to the analysis and are the natural ounterparts to standard onepts familiar to industrial organization eonomists. Throughout this and the following setion, we assume that suppliers are symmetri before the merger and that the regularity ondition holds. 10
4.1 Preliminaries Let us start by onsidering the optimization problem for a buyer with value v that makes a take-it-or-leave-it offer to a single supplier that draws its ost from the distribution G: max(v p)g(p). p If, for example, v, the optimal prie offer is haraterized by the first-order ondition 0 = g(p) (v Γ(p)), where Γ() + G() g() is the supplier s virtual ost. If Γ is inreasing, the seond-order ondition is satisfied when the first-order ondition is, implying that the problem is quasionave. Thus, the assumption that Γ is inreasing is the optimal-prourement analog to the assumption of dereasing marginal revenue in models of industrial organization. In what follows, we assume that G is suh that both Γ and the merged entity s virtual ost ˆΓ() + Ĝ() ĝ() = + G() 2 G() g() 2(1 G()), (1) are inreasing. A suffiient ondition for this is that G/g is nondereasing. We assume that g() is finite, 25 but we allow the possibility that g is zero at the boundaries of the support. We define Γ() lim Γ() =, and analogously for ˆΓ. For x > Γ(), define Γ 1 (x). 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. 26 To do so, for 25 An impliation of this is that lim ˆΓ() =, and so v < ˆΓ(). Thus, the buyer exerts monopsony power as defined in the introdution (and disussed after Proposition 1 below) against the merged entity for some ost realizations. The assumption that g is finite at an be relaxed at the ost of adding more assumptions or ase distintions to Propositions 2, 6, and 11 as we disuss below. 26 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). Further, the EC Guidelines (para. 67) require that buyer power must also exist and remain effetive following the merger for it to be viewed as moderating merger harm, whih is onsistent with our assumption. That said, the EC Guidelines 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). If anything, our analysis suggests that a buyer s inentive to beome powerful inreases following a merger of two of its suppliers (see the disussion on p. 21). 11
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, a supplier s weighted virtual ost orresponds to its true ost, and when β = 1, to its virtual ost. If Γ β () is finite, then for x > Γ β (), define Γ 1 β (x), and analogously for ˆΓ β. Prourement autions and mehanisms We assume that the buyer uses an autionplus-final-offer proedure that onsists of an aution phase and a final take-it-or-leaveit offer phase defined as follows: In the aution phase, the buyer onduts a (possibly disriminatory) desending lok aution starting from a lok prie of min {v, }. As the lok prie dereases, partiipating suppliers an hoose to exit. When a supplier exits, the supplier beomes inative and remains so. The lok stops when only one ative supplier remains, with ties broken by 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 β (p) if i is an independent 1 supplier and p ˆΓ (p) if i is the merged entity, should the buyer hoose to trade with β that supplier. In the final offer phase, the buyer implements a supplier-speifi reserve of Γ 1 1 (v) for a nonmerged supplier and ˆΓ (v) for the merged entity as follows: If the β β aution prie is 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. A supplier s strategy speifies the prie at whih the supplier exits in the aution phase (as a funtion of the observed bidding history) and whether to aept or rejet any partiular final offer from the buyer. Clearly, in the final offer phase, the best response of a supplier with ost is to aept prie offers greater than and rejet those less than. In the aution phase, for a supplier with ost, remaining ative in the aution phase until the prie reahes Γ β () and then exiting weakly dominates other strategies. If a supplier with ost wins at a lok prie of p = Γ β (), then the supplier is obligated to supply at prie Γ 1 β (p) =. Exiting at a prie greater than Γ β() auses the supplier to forego the possibility of positive surplus, and remaining ative at a prie less than Γ β () only affets the supplier s surplus if it auses the supplier to win when it would not have otherwise, and in that ase leaves the supplier with nonpositive surplus (negative if trade ours at the prie determined by the aution phase and zero if the buyer makes a final offer that the supplier then rejets). 12
Thus, by standard aution 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 its weighted virtual ost and then exits, and if a supplier wins the aution, the supplier aepts a final offer from the buyer if and only if it is greater than or equal to the supplier s ost. For β = 0, the aution-plus-final-offer proedure orresponds to a desending lok aution with reserve min {v, }. 27 For β = 1, the aution is not disriminatory in the premerger market beause suppliers are symmetri. 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.28 To see this, observe that for all [, ], ĝ() Ĝ() = g() 2(1 G()) G() 2 G() g() G(), (3) with a strit inequality for in the interior of the support. 29 Consequently, for all [, ], 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 onepts from mehanism design theory. By the revelation priniple, the outome of this game an also be ahieved as the equilibrium outome of a diret mehanism that asks eah player i to report its type i to the mehanism and that makes the alloation and payments 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 pin down the interim expeted payments of every 27 To see this, 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. 28 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. 29 Dominane in terms of the reverse hazard rate implies first-order stohasti dominane, that is, (3) implies G() Ĝ(). 13
player. 30 Buyer and soial surplus The following is based on standard arguments from 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 [ n ] BS pre (q( )) E q i () (v Γ( i )), i=1 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 ] n SS post (ˆq( )) E [ˆq() (v min{ 1, 2 }) + 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 mehanism for a designer whose objetive is to maximize the expeted value of i=3 β(buyer surplus) + (1 β)(soial surplus), (4) subjet to inentive ompatibility and individual rationality. Proof. See the Appendix. 30 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). 14
Naturally, entral to our analysis is how a merger affets expeted buyer surplus, soial surplus, prie, and quantity, and how these hanges depend on buyer power. For given β {0, 1}, denote by q β ( ) and ˆq β ( ) the alloation rule implied by the aution-plusfinal-offer proedure pre and post merger, respetively. Letting BSpre β 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. From Theorem 1, it follows that BS 0 < 0 and BS 1 < 0. (5) 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 by ] [ n n ] P β E [ˆq β ()ˆΓ(min{ 1, 2 }) + ˆq β i ()Γ( i) + E q β i ()Γ( i), i=3 i=1 and by Q β the expeted hange in the quantity traded as a result of a merger, that is: ] n n Q β E [ˆq β () + ˆq β i () q β i (). i=3 i=1 4.2 Effets of a merger on market outomes 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 15
and without the merger. The alloation not being affeted by the merger means ˆq 0 () = q1() 0 + q2() 0 and, for i {3,..., n}, ˆq i 0 () = qi 0 (). 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, }. 31 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 one 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. 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), and a higher expeted payment by the buyer ( P 0 > 0). Proof. See the Appendix. In addition to the effets identified in Proposition 1, by Theorem 1, without buyer power, a merger results in lower expeted buyer surplus ( BS 0 < 0). 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 not have the lowest ost, and a buyer who exerts monopsony power may sometimes not purhase, even when the lowest ost is below the buyer s 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 its bargaining and monopsony power. Beause the pre-merger market is symmetri, a powerful buyer does not exert its bargaining power before the merger. After the merger, the 31 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. 16
extent to whih a powerful buyer exerts its 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 before the merger, and it an ause the merged entity to be paid less than supplier 1 or 2 would have been paid before the 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 its monopsony power against a supplier an be measured by the amount by whih the buyer s supplier-speifi reserve for that supplier falls below. 32 Relative to a buyer with a low willingness to pay, a buyer with a high willingness to pay will exert its monopsony power to a lesser extent, or possibly not at all. In partiular, a buyer with a value greater than Γ() never finds it optimal to make a final offer to a nonmerged supplier that might be rejeted. Thus, when Γ() is finite, whih implies that Γ() < ˆΓ(), a merger inreases the range of buyer values for whih the buyer exerts its monopsony power. In addition, beause v < ˆΓ(), 33 a merger inreases the extent to whih the buyer exerts its 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 in Theorem 1, mergers harm even powerful buyers. Figure 1 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 against both merged and nonmerged suppliers. As shown in panel (a), when n = 2, there is no bargaining power effet, but as a result of the exertion of monopsony power, a merger redues the set of types for whih trade ours (orresponding to the vertially hashed area). As shown in panel (b), when n 3, the merger not only redues the set of types 32 One ould quantify 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. 33 This follows from the assumption that g() is finite, whih implies that ˆΓ() is infinite. 17
for whih trade ours due to the additional exertion of monopsony power (represented by the vertially hashed area), 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 horizontally hashed area, 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. 2 v (a) Effets of a merger with n = 2 min{ 1, 2} v (b) Effets of a merger with n 3 Γ -1 v) Γ -1 v) trade with supplier 1 no trade Γ -1 (v) Γ -1 (v) trade with nonmerging supplier no trade Γ -1 (Γ()) trade with supplier 2 trade with merging supplier Γ -1 v) Γ 1 (v) v 1 =min{ 3,..., n} Γ 1 (v) v =min{3,...,n} Figure 1: Bargaining and monopsony power of a powerful buyer. Panel (a) refers to the ase of only two suppliers (merger to monopoly). The vertially hashed area indiates types for whih there is trade with the low-ost supplier prior to the merger but no trade after the merger, i.e., the buyer exerts more monopsony power after the merger than before. Panel (b) refers to the ase of three or more suppliers. When one of the merging suppliers trades, it is the lower ost of the two merging suppliers, and when one of the nonmerging suppliers trades, it is the lowest ost of the nonmerging suppliers. The vertially hashed area again indiates types for whih the buyer exerises additional monopsony power after the merger. The horizontally hashed area indiates types for whih after the merger the buyer exerts its bargaining power, trading with a merging supplier prior to the merger, but with a higher-ost nonmerging supplier after the merger. In both panels, the shaded area indiates types for whih the buyer exerises its monopsony power both before and after the merger. We summarize these results as follows: 34 Proposition 2. With buyer power, a merger results in a weakly lower expeted quantity traded ( Q 1 0) (stritly if n = 2 or if n 3 and v < Γ()) and stritly lower expeted soial surplus ( SS 1 < 0). In addition to the effets identified in Proposition 2, by Theorem 1, with buyer power, a merger results in lower expeted buyer surplus ( BS 1 < 0). 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 34 If we relax the assumption that g() is finite, then when n = 2, in order for the results in Proposition 2 for Q 1 and SS 1 to hold with a strit inequality, we require v < ˆΓ(). 18