Buyer Power and Industry Structure

Transcription

1 Buyer Power and Industry Struture David E. Mills Departent of Eonois P.O. Box University of Virginia Charlottesville, VA (phone) (fax) February, 2010 Forthoing in Review of Industrial Organization Final publiation available at 1

2 Abstrat This paper investigates the exerise of arket power by a large buyer who eerges via growth, erger, or group purhasing. It explores the effiieny and redistributive effets of suh an event when a opetitive fringe of sall buyers reains in the arket. Ters of trade, inluding those for sall buyers, depend on strutural onditions on the supply side of the arket and the nature of interations between the newly eerged doinant buyer and suppliers. Predited aggregate welfare effets have ipliations for antitrust. Key Words Antitrust, Buyer Power, Doinant Buyer, Waterbed Effet 2

3 I. Introdution Large, powerful buyers an be found in any arkets. Exaples inlude health plans, in their dealings with physiians or hospitals; produers of food and beverage ingredients, in their dealings with agriultural oodity growers; airraft anufaturers, in their dealings with airraft engine anufaturers; and hospital group purhasing organizations, in their dealings with the suppliers of health are produts. When a large buyer exerises arket power to influene the ters of trade with its suppliers, the fir is said to possess buyer power. This ter applies to a variety of situations. 1 A uniquely large buyer ay eerge by growth or erger. Or the large buyer ay be a ooperative assoiation of sall buyers, suh as a group purhasing organization or even a buyer artel. The starting point for this paper s analysis is an input or interediate produt arket with any sall buyers who are not diret downstrea opetitors. 2 Next a doinant buyer eerges in the arket beause one of the buyers grows large in relation to the rest, or beause a signifiant nuber of buyers erge or for a group purhasing organization. The doinant buyer exerises its arket power to obtain favorable ters fro sellers. But this ondut ay affet sellers ters to the reaining buyers. The doinant buyer s effets on pries, quantities and welfare depend on strutural onditions on the supply side of the arket and on the interations between the doinant buyer and suppliers. If the good is produed by a perfetly opetitive industry with infinitely elasti supply, then a doinant buyer annot influene the good s prie. But if industry supply is upward 1 Inderst and Shaffer (2008, p. 1612) define buyer power as the ability of buyers to obtain advantageous ters of trade fro their suppliers. Siilarly, Noll (2005, p. 589) defines it as the irustane in whih the deand side of a arket is suffiiently onentrated that buyers an exerise arket power over sellers. 2 The odel also applies to retail distribution where buyers are retailers and where the doinant buyer does not opete in the sae geographi arket as other retailers. 3

4 sloping, the doinant buyer an indue a lower prie by reduing its deands. In this senario, the low prie that the doinant buyer fores on sellers beoes the arket prie, so the welfare effet of the doinant buyer s eergene is positive for all buyers. The welfare effet on suppliers is negative, and the aggregate welfare effet is negative as well beause unit sales derease. The doinant buyer s eergene reates a dead weight loss. Outoes are different for buyers who purhase an input or interediate produt fro a onopolist or the supplier of a strongly differentiated good. This is beause a doinant buyer ay negotiate ters of trade that do not apply to sall buyers. In what follows, the doinant buyer s dealings with the seller are odeled as a Nash bargaining gae. With this, the eergene of a doinant buyer has no effet on sall buyers if the seller has onstant arginal osts. But if the seller has inreasing arginal osts, Nash bargaining reates a waterbed effet on pries: The doinant buyer pays a lower prie than if it were a passive prie-taker and the reaining prie-taking buyers pay a higher prie. In this senario, the welfare effet of the doinant buyer s eergene is negative for non-doinant buyers, but aggregate welfare ay inrease or derease. The likelihood that a doinant buyer inreases aggregate welfare is greater where the supplier s arginal osts do not inrease rapidly and where the sall buyer segent is sall. The predited effets on aggregate welfare have ipliations for antitrust. Buyers who purhase inputs or interediate produts fro suppliers in a opetitive arket should be prohibited fro erging or foring group purhasing organizations solely to reate a doinant buyer. If the input or interediate produt is sold by a onopolist, however, the foration of a doinant buyer should not be prohibited in every instane. Lenieny ay be warranted if arket onditions portend a positive effet on aggregate welfare. 4

5 II. Copetitive Sellers Consider a hoogeneous good that is produed and sold in a perfetly opetitive industry. Let the industry s inreasing and ontinuously differentiable supply funtion be y S( p ) for p p. There are any buyers, eah of whose deand for the good is dereasing and ontinuously differentiable on the interval( 0, p ), where p p. Aggregate deand y D( p ) is dereasing and ontinuously differentiable on the sae interval, so the opetitive prie and output level ( p, y )are uniquely deterined by y D( p ) S( p ), with y 0and p ( p, p ). Now suppose that a group of sall, independent buyers erge to for a single doinant buyer whose deand x f ( p ) is dereasing and ontinuously differentiable on the interval (0, p ). In the alternative, the doinant buyer ay be a group purhasing organization onsisting of independent buyers whose obined deand is f ( p ). 3 In either ase, the reaining independent buyers aggregate deand is y g( p ), where g( p ) D( p ) f ( p ). These assuptions iply that f ( p ) 0 and g( p ) 0. If the doinant buyer is large enough in relation to the rest, it is plausible that the fir s size and proinene give it soe influene over pries in the arket. Indeed aquiring this influene ay be the raison d être of the doinant buyer. A buyer suh as this is unlikely to exhibit the passive, prie-taking behavior of atoisti buyers in a opetitive arket. To fous on the iediate welfare effets of a doinant buyer, assue that this fir does not opete diretly with other buyers in a downstrea arket. (Whether non-doinant 3 For onveniene, the doinant buyer will be referred to as a fir even if it is a group purhasing organization. 5

6 buyers opete with eah other downstrea is iaterial.) This assuption applies to several senarios. The good ay be an interediate produt where buyers are produers of unrelated or strongly differentiated final goods. Or the good ay be a loally produed interediate produt that is purhased by loal produers of a final good that is sold in a global arket in whih even the doinant buyer has no arket power. Finally, non-doinant buyers ay be dealers or retailers who distribute the good in different arketing hannels or at different loations than does the doinant buyer. In none of these senarios is a sall buyer s deand for the good dependent on the prie paid by the doinant buyer. This odel is an exat deand-side analogy of the failiar doinant fir odel that has a uniquely large seller in a arket with any sall sellers. In that odel, the doinant seller hooses a prie to axiize its own profit on the presuption that sall, opeting sellers are passive prie-takers (e.g., Stigler, 1965). This exerise of arket power sustains a prie that is higher than the opetitive prie. In the doinant buyer ase, a large buyer uses its prie-setting ability to ipose a lower than opetitive prie (Blair and Harrison, 1993). The doinant buyer s ability to ipose suh a prie stes fro the fir s ability to redue signifiantly the total quantity deanded at any prie. 4 To see how a doinant buyer affets outoes in the industry, note that the residual supply of the good available to the doinant buyer is x S( p ) g( p ). This quantity is positive 4 This paper ephasizes the effets of group purhasing organizations that are fored to exerise onopsony power. Other papers have ephasized the ability of group purhasing organizations to exploit nonlinear priing or vertial restraints. Marvel and Yang (2008, p. 1091) show that a buying group ay for to eliit disounts fro opeting suppliers and extrat attrative pries fro suppliers not through enhaned bargaining power, but rather through their ability to obtain [nonlinear] tariffs that pit suppliers against one another effetively. In a odel that is an extension of O Brien and Shaffer s (1997) analysis of interations between a onopsonist and a duopoly, Dana (2006) shows that buying groups ay organize in order to win disounts fro duopolists by oitting to purhase exlusively fro the supplier who offers the lower prie. 6

7 for any prie greater than p, where p ( p, p ) is defined by S( p ) g( p ). 5 For any prie less than or equal to p, the residual supply is zero beause produers would not even supply enough output to eet the deands of the sall buyers. The doinant buyer s residual supply funtion is inreasing and ontinuously differentiable on the interval( p, p ). By the inverse funtion theore, this funtion ay be inverted to give a funtion p ( x )that is inreasing and ontinuously differentiable on the interval (0,S( p )). Aordingly, the doinant buyer ay purhase any quantity x ( 0,S( p )) of the good for a total ost of ( x ) x. 1 The doinant fir s inverse deand funtion p f ( x ) is dereasing and ontinuously differentiable on the interval (0, f (0 )). The fir s surplus fro aquiring x units is x 1 0 f ( z )dz ( x ) x. To axiize this surplus, the doinant buyer purhases x* units, where x* uniquely satisfies the first-order ondition: 1 ( x*) '( x*) x* f ( x*). (1) The fir pays the prie p* y* g( p*) units. ( x*) for these units. At this prie, the reaining buyers purhase The ain effets of the doinant buyer s eergene are suarized in: 6 Proposition 1: p* < p, x* < f(p ), y* > g(p ) and x* +y* < y. The doinant buyer auses a prie derease by withholding purhases to support the lower prie. This eans that the doinant buyer purhases fewer units than if the fir ated as a passive prie-taking buyer. The reaining buyers are passive benefiiaries of the doinant buyer s 5 The existene of a unique p is assured by previous assuptions about and S( p ) g( p ). 6 Proofs of the propositions are in the Appendix. 7

8 arket power beause they buy ore units of the good at a lower prie than before the doinant buyer eerged. The welfare effet of an eerging doinant buyer is positive for every buyer in the arket. For produers, the welfare effet is negative beause total output falls; they sell fewer units at a lower prie. The aggregate welfare effet is negative beause the produers loss exeeds the buyers gain. With perfetly opetitive suppliers, the eergene of a doinant buyer reates dead-weight loss in the arket. The preditions in Proposition 1 hinge on the assuption that the industry supply funtion is inreasing. The prie effets are saller the ore elasti is S( p ). If the industry supply funtion is infinitely elasti, a doinant buyer would have no ipat on arket outoes beause it ould not fore a lower prie on sellers by purhasing fewer units. There would be no power buyer inentive for buyers to erge or for group purhasing organizations if supply is infinitely elasti. Profitably exerising arket power on the buyers side of the arket requires a less-than-infinitely elasti industry supply. III. A Single Seller Now onsider a good produed and sold by a onopolist. In the alternative, the good ay be produed and sold by a single fir in an industry with several firs whose produts are strongly differentiated. The seller s ost funtion C( y )is inreasing and ontinuously differentiable with C''( y ) 0 for all y 0. Aggregate deand y D( p ) is the sae as before, 7 1 and ay be inverted to give p D ( y ) for all y (0,D(0 )). The seller s profit funtion is 7 If the good is a differentiated produt, D( p ) depends on the pries of opeting brands, although ross prie elastiities are assued to be sall. This dependene is suppressed in the notation. 8

9 . The fir s profit-axiizing output level y is given by '( y ) 0, 1 ( y ) D ( y ) y C( y ) 1 and its prie by p D ( y ). Call the seller s resulting profit ( y ). As before, suppose that a group of buyers erge to for a single doinant buyer or organize a group purhasing organization with deand x f ( p ). The obined deand of the reaining buyers is y g( p ). An exaple of a doinant buyer and a single seller ight be a health plan (the buyer) and a regional hospital (the seller) where the health plan purhases hospital servies for a large fration of the patients who reside in the region served exlusively by the hospital. Another exaple ight be an airline (the buyer) and an airport (the seller) where there are no other nearby airports and where the airline aounts for a signifiant fration of the airport s fees and lease payents for flight-related servies. The eergene of a doinant buyer in this situation has different effets on arket outoes than with opetitive suppliers. In partiular, seller opetition no longer prevents an outoe in whih the doinant buyer pays a different prie than others. The relationship between the doinant buyer and the seller resebles a bilateral onopoly. Sine this arrangeent an be vulnerable to the double arginalization distortion, the firs have strong inentives to reah utually benefiial ters of trade to extrat as uh surplus as possible fro their transation. 8 Assue that the doinant buyer and the seller negotiate a ontrat in a bilateral bargaining gae instead of an arrangeent where the buyer hooses a quantity after the seller sets the prie. In arket strutures where there is both a buyer and a seller with arket power, and where the firs ontrat in isolation under onditions of 8 Inderst and Shaffer (2008) distinguish arket strutures where firs interat via a arket interfae versus a bargaining interfae. In the forer, ipersonal arket fores set pries. In the latter, pries are set in bilateral bargaining between individual buyers and sellers. 9

10 oplete inforation, Whinston s (2006, p. 139) bilateral ontrating priniple predits that the firs will reah an agreeent that axiizes their joint payoff. 9 In aordane with this priniple, the doinant buyer and the seller negotiate a ontrat that axiizes the su of the doinant buyer s surplus and the seller s profit. The arket struture assued here is distinguished fro a bilateral onopoly beause there is a opetitive fringe of sall buyers. Although they are passive, the latent surplus of these buyers affets bilateral negotiations between the doinant buyer and the seller. It is natural to assue that the firs ontrat reflets endogenous effets on the seller s profit fro sales to its reaining buyers. Let the ters of the ontrat between the firs be those predited by the Nash bargaining solution. The doinant buyer and the seller negotiate a ontrat for x units of the good and a total 1 payent of T. This ontrat antiipates sales of y units to sall buyers at the prie g ( y ). With Nash bargaining, the output levels ˆ ˆ ( x, y )are those that axiize: The division of x 1 1 M( x, y ) f ( z )dz g ( y ) y C( x y ) 0. (2) M ( xˆ, yˆ) between the doinant buyer and the seller is ahieved by the doinant buyer s payent ˆT. With Nash bargaining, ˆT depends on eah fir s bargaining power and their outside options: the firs payoffs should an agreeent not be reahed. 9 The insight that buyers and sellers with arket power an ahieve the vertially integrated solution is invoked by Bernhei and Whinston (1998), Chipty and Snyder (1999), Mathewson and Winter (1987), Capbell (2007), and Tirole (1988), aong any others. Blair and Harrison (1993) disuss the idea s anteedents in early eonoi theory. Baker, Farrell, and Shapiro (2008) are less sanguine about the generality of the vertially integrated solution beause of obstales raised by asyetri inforation and inoplete ontrats. 10

11 Assue that if the firs failed to reah an agreeent, the seller would harge the prie p to all buyers and the doinant buyer would purhase profit would be and the doinant buyer s surplus would be: f ( p )units. With this, the seller s x 1 0 v f ( x )dx p x. (3) Based on these outside options, the firs joint gain fro bilateral bargaining is: Let (0,1) M ( xˆ, yˆ) v. (4) designate the bargaining power of the doinant buyer and1 the bargaining power of the seller. The Nash bargaining solution predits that the ontrat between the firs fixes ˆT so that the doinant buyer retains the fration of expression (4) and the seller gets the rest. This division iplies that the seller s profit ˆ, the doinant buyer s surplus ˆv, and the payent ˆT are jointly deterined by: ˆ ˆp ˆy Tˆ C( ˆx ˆy ) y ˆx 1 ˆv f ( x )dx Tˆ 0. (5) T ˆ (1 ) ( ˆ vˆ v ) Under the ontrat( ˆx,T ˆ ), the doinant buyer pays the seller an effetive prie of ˆp x Tˆ ˆx. The ain effets of the doinant buyer s eergene are: Proposition 2: If = = = C'' 0, then p ˆ < p p ˆ, x ˆ > f(p ), yˆ g(p ) and x ˆ + y ˆ > y > < < x y. The first result to notie is that the ontrat between the seller and the doinant buyer alls for a lower prie and ore output than if the buyer had instead ated as a passive prietaker. The seond result to notie is that the doinant buyer s eergene inreases total unit 11

12 sales in the arket. The final result to notie is that the doinant buyer s ipat on sall buyers depends on the seller s osts. Sall buyers are unaffeted by the doinant buyer s eergene if the seller has onstant arginal osts. But if the seller s arginal osts are inreasing, the doinant buyer reates a waterbed effet on pries. That is, the prie paid by sall buyers inreases while the doinant buyer s prie dereases. By negotiating superior ters with the seller, the doinant buyer seures a lower effetive prie than p. But this preipitates a higher prie than 12 p for sall buyers. In effet, the doinant buyer wrests a disount fro the seller. But this disount triggers a prie inrease for reaining sall buyers beause supplying ore output to the doinant buyer inreases the inreental ost of supplying the rest. The soure of the waterbed effet in this odel is the seller s inreasing arginal osts. This priing phenoenon arises for different reasons in soe other odels. Inderst and Valletti (2006) identify a waterbed effet that stes fro the fixed osts that buyers ay bear if they searh for or swith to a bakup soure for the seller s good, or if they integrate upstrea to produe the good theselves. In that odel, a seller ust offer a lower prie to a large buyer than to sall buyers to indue the large buyer to forgo alternatives. Majudar (2005) deonstrates a waterbed effet in a odel with two suppliers who have dereasing arginal osts. In that odel, a large buyer eliits a low prie by inviting bids to beoe its sole supplier. One the large buyer selets a sole supplier, opetition between the suppliers for sales to the reaining buyers supports a higher prie than the large buyer pays. Mathewson and Winter (1996) show that if a group of independent buyers in a onopolistially opetitive arket for a group purhasing organization to negotiate exlusive ontrats with a subset of the suppliers, they will pay lower pries than do outside buyers. Sale eonoies of one kind or another play a

13 role in eah of these odels. But in the present analysis, the waterbed effet is aused by diseonoies of sale. The only prie or quantity in Proposition 2 that depends on the relative bargaining power of the seller and the doinant buyer is p ˆ x. The quantities ˆx and ˆyand the sall buyers prie ˆp y are not affeted by a hange in. The doinant buyer s payent ˆT varies inversely with, so the effetive prie pˆ x paid by that buyer dereases as its bargaining power inreases. 10 The payent ˆT is bounded above and below as follows: First, litˆ ˆx p, (6) 0 beause ˆv would be less than v if the doinant buyer paid an effetive prie of p for ˆx f ( p ) units of the good. This would be unaeptable to the doinant buyer. Also, ˆ 1 ˆ ˆ 1 lit x f ( x ), (7) beause ˆ would be less than if the doinant buyer paid an effetive prie of 13 f ( x ) for ˆx units of the good. An effetive prie this low would award the entire inreental surplus reated by inreasing x to the doinant buyer while reduing the seller s profit fro sales to the sall buyers. This would be unaeptable to the seller. These bounds on ˆT ean that the doinant buyer s effetive prie is never as high as p and never as low as f ( x ). 1 ˆ 1 ˆ While the welfare effet of a doinant buyer on sall buyers is positive when there are any sellers, the sae does not hold when there is a single seller with arket power. With a single seller, the welfare effet on the seller and on those buyers who grow, erge, or organize is positive; but the welfare effet on the reaining buyers is non-positive. This is beause sall 10 Inderst and Shaffer (2008) provide an extensive disussion of fators that affet the value of firs outside options and oparative bargaining power in bilateral negotiations between buyers and sellers with arket power.

14 buyers annot free ride on the advantageous ters negotiated by the doinant buyer when there is a single seller. If the seller s arginal osts are onstant, the doinant buyer has no effet on sall buyers. In this instane the aggregate welfare effet of the doinant buyer is positive beause the ontrat between the doinant buyer and the seller redues dead weight loss. But if the seller s arginal osts are inreasing, the welfare effet on sall buyers is negative beause of the waterbed effet on pries. Even if sall buyers are losers when the doinant buyer eerges, the aggregate welfare effet of the doinant buyer still ay be positive. This ours if the sall buyer segent is sall relative to the doinant buyer, 11 or if C''( y )is suffiiently sall. Either ondition would ake the loss inurred by sall buyers less than the gain jointly aptured by the doinant buyer and the seller. Proposition 2 applies where the doinant buyer and the seller negotiate an effiient ontrat. But ost of the prie and quantity relationships predited in the Proposition apply ore generally. Suppose that there are obstales to effiient ontrating between the firs, whih auses the to strike a bargain( x,t )that is suboptial in the sense that their joint payoff is less than M ( xˆ, y ˆ). 12 Any suh ontrat would be utually benefiial to the doinant buyer and the seller. A utually benefiial ontrat( x,t )between the doinant buyer and the seller is one that has: where ( x ) and v( x ) v, with at least one strit inequality, (8) 11 At the liit, if there were no sall buyers, this would be an instane of bilateral onopoly/onopsony, and any negotiated outoe between the two parties ust iprove the welfare of both parties and thus iprove aggregate welfare. 12 See Baker, Farrell, and Shapiro (2008) for a disussion that hallenges the feasibility of effiient ontrating in these kinds of oerial relationships. 14

15 and where ( x ),v( x ), and T( x ) jointly satisfy: h( x ) arg ax[ M( x, y )], (9) y 1 ( x ) g ( h( x ))h( x ) T( x ) C( x h( x )) x 1 v( x ) f ( z )dz T( x ) 0. (10) T( x ) (1 ) ( ( x ) v( x ) v ) Under suh a ontrat, the doinant buyer pays an effetive prie 1 onopolist harges sall buyers the prie p g ( h( x )). y p x T( x ) / x, and the Any utually advantageous ontrat between the seller and an eergent doinant buyer has the following effets: Proposition 3: If = C'' 0, then > = = p x < p p y, x > f(p ) and y g(p ) for any ontrat < < (x,t(x)) that satisfies (8). This Proposition indiates that if the seller has onstant arginal osts, any utually benefiial bargain that a seller strikes with a doinant buyer leaves sall buyers untouhed. The aggregate welfare effet of the doinant buyer s eergene in this instane is positive beause the ontrat redues dead weight loss. If the seller s arginal osts are inreasing, the Proposition indiates that any utually benefiial ontrat between the two firs brings on a higher prie and fewer unit sales for sall buyers. The size of the waterbed effet, and the sign of the effet on aggregate welfare, depends on the ters of the ontrat, the relative size of the sall buyer segent, and the agnitude of C''(y). IV. Poliy Ipliations 15

16 In reent years, several Federal Trade Coission onferenes and reports have studied potential antitrust probles related to the purhasing praties of doinant firs in industries as diverse as e-oere, health are, and petroleu. 13 There is general reognition that the exerise of arket power on the deand side of a arket ay reate alloative ineffiieny that is siilar to arket power on the supply side. Beause the effets of onopsony and onopoly are basially the sae, Noll (2005) argues that antitrust poliy should be syetrial (p. 623). The relevane of antitrust for onopsony was underlined reently by the Supree Court s deision in Weyerhaeuser Co. v. Ross-Sions Hardwood Luber Co., In., 549 U.S. 312 (2007). 14 The analysis in this paper suggests that the eergene of doinant buyers is probleati in soe irustanes but not all. 15 Insofar as antitrust is guided by the goal of prooting eonoi effiieny, input and interediate produt buyers should be prohibited fro erging or foring group purhasing organizations to ahieve doinane when purhasing fro suppliers in a opetitive arket. But the orret presription is less lear-ut when the doinant buyer s trading partner is a seller with arket power. If the seller has onstant arginal osts, the eergene of a doinant buyer is soially benefiial and does not har sall buyers. An event like this does not all for antitrust intervention. However, if the seller has 13 Noll (2005) suarizes these studies and reviews the ipliations of buyer power for antitrust poliy. 14 In Weyerhaeuser the plaintiff (a sall buyer) laied that the defendant (a large buyer) bid pries up so as to ipose losses on the plaintiff; i.e., the behavior was allegedly predatory. In the present analysis, the doinant buyer s ondut redues its own prie but ay raise the prie that sall buyers pay beause of the seller s diseonoies of sale. 15 The notion that the ountervailing power of a doinant buyer an subdue the arket power of a large seller and iprove arket perforane has a long history, beginning with Galbraith (1952, 1954). Galbraith s ain hypothesis was that the ountervailing power of a doinant retailer lowers retail pries. Chen (2003), Dobson and Waterson (1997), and von Ungen-Sternberg (1996) eah have found speialized strutural onditions and other features of retail arkets that support this hypothesis. The ehaniss and qualifiations that they identify are different, but all of the rely on vigorous opetition aong retailers to transfer benefits downstrea to onsuers. The analysis in this paper indiates that ountervailing power ay pit the interests of one lass of buyers against another, whether or not it iproves arket perforane. 16

17 inreasing arginal osts, the doinant buyer s eergene ay or ay not be soially benefiial. This is beause the doinant buyer s eergene reates a waterbed effet that redues the welfare of sall buyers. If the effet on the sall buyer segent is suffiiently large, intervention to prohibit a erger or the foration of a group purhasing organization to ahieve doinane would be warranted. The two fators that raise a red flag for antitrust under this senario are if the seller has signifiant diseonoies of sale and if the size of the buyer segent left to absorb the waterbed effet is relatively large. These onlusions ust be qualified by two onsiderations. The first qualifiation is that soe doinant buyers ay not be reated by growth or by the erger or group purhasing of a large nuber of sall buyers. Soe ay be reated when two oligopsonists erge who already are large enough to exert soe influene over their ters of sale with the seller. With this kind of erger, soe of the gains unloked by utually advantageous ontrats between a doinant buyer and the seller ay already have been aptured. This redues the inreental welfare gains, if any, that would arise if the buyers erged. Also, the analysis and onlusions in this paper do not aount for distortions, if any, that ay arise if the doinant buyer opetes downstrea with the sall buyers. Where this happens, sall opetitors inur a ost disadvantage beause of the waterbed effet. If there is downstrea opetition (e.g., buyers are opeting retailers), this disadvantage ight reate a viious yle where upstrea arket power onfers a downstrea ost advantage that bolsters downstrea arket power. This, in turn, aplifies the fir s upstrea arket power, and so on (Dobson and Inderst, 2008). In extree ases, it is possible that this hain of events ight ulinate in the exlusion of downstrea rivals, or deterrene of downstrea entrants. Appendix 17

18 Proof of Proposition 1: Reall that 1 f ( x ) is dereasing on (0, f (0 )). To show that * ( ) x f p, it is suffiient to show that the doinant fir s inreental surplus would be negative if the fir purhased f ( p )units. When purhasing x units, the doinant fir s inreental surplus is: d dx f ( z )dz ( x ) x f ( x ) ( x ) '( x ) x. (11) x Evaluating the r.h.s. of this expression at x f ( p )gives: p ( f ( p )) '( f ( p )) f ( p ). (12) Next, inverting both sides of f ( p ) S( p ) g( p )gives: ( f ( p )) p. (13) Substituting (13) into (12) siplifies (12) to '( f ( p )) f ( p ), whih is negative. This establishes that x* f ( p ). It follows fro x* f ( p ) that ( x*) ( f ( p )) and hene that p* p. Further, beause p* p and g'( p ) 0, we have y* g( p*) g( p ). Finally, S( p*) S( p ), (14) beause p* p and S'( p ) 0. Inequality (14) iplies that x* y* y. 18

19 Proof of Proposition 2: Without a doinant buyer, those buyers who otherwise erge would purhase f ( p ) units of the good, and the reaining buyers would purhase g( p )units. These quantities satisfy: 1 1 df ( f ( p )) f ( f ( p )) f ( p ) C'( f ( p ) g( p )) dx. (15) 1 1 dg ( g( p )) g ( g( p )) g( p ) C'( f ( p ) g( p )) dy The first order onditions for axiizing M( x, y )are: 1 dg ( y ) f ( ˆx ) C'( xˆ ˆy ) and g ( ˆy ) ˆy C'( xˆ ˆy ). (16) dy 1 1 ˆ Suppose ˆx ˆy y. Beause C''( ) 0, this relationship would iply: C'( ˆx ˆy ) C'( y ). (17) 1 1 Beause f ( x ) and g ( y ) are dereasing, and beause y f ( p ) g( p ), (15) - (17) iply that ˆx f ( p ) and ŷ g( p ). This establishes a ontradition and shows that: ˆx ˆy y. (18) Next, (18) iplies that: = C'( ˆx ˆy ) C'( f ( p ) g( p )) > if = C'' 0 >. (19) Equations (15) and (16) together with (19) iply that: = ŷ g( p ) < if = C'' 0 >. (20) Beause g( ) is dereasing, (20) iplies that: 19

20 pˆ y = p > if = C'' 0. (21) > Together with (18), (20) also establishes that buyer would prefer( p, f ( p ))to( p,x ˆ )for any p p. ˆx f ( p ). Finally pˆ x p beause the doinant Proof of Proposition 3: For (8) to hold, it is straightforward that x f ( p ). This inequality iplies that px p beause otherwise satisfy: v( x ) v, whih ontradits (8). For any x, (9) requires that y h( x ) ust 1 1 dg ( y ) g ( y ) y C'( x y ). (22) dy = = = With x f ( p ), equation (22) iplies that p p y and y g(p ) if C'' 0 < < > beause g( p )is dereasing. 20

21 Aknowledgeents The author thanks the General Editor, two referees, Sion Anderson, Federio Ciliberto, Kenneth Elzinga, Maxi Engers, and Nathan Larson for helpful oents, and the Bankard Fund for Politial Eonoy at the University of Virginia for finanial support. 21

22 Referenes Baker, J. B., J. Farrell, and C. Shapiro (2008). Merger to Monopoly to Serve a Single Buyer: Coent. Antitrust Law Journal, 75, Bernhei, B. D. and M. D. Whinston (1998). Exlusive Dealing. Journal of Politial Eonoy, 106, Blair, Roger D. and Jeffrey L. Harrison (1993). Monopsony: Antitrust Law and Eonois. (Prineton: Prineton University Press) Capbell, T. (2007). Bilateral Monopoly in Mergers. Antitrust Law Journal, 74, Chen, Z. (2003). Doinant Retailers and the Countervailing-Power Hypothesis. RAND Journal of Eonois, 34, Chipty, T., and C. M. Snyder (1999). Buyer Size and Bargaining Power. Review of Eonois and Statistis, 81, Dana, J. (2006). Buyer Groups as Strategi Coitents. Retrieved February 10, 2010, fro The Center for the Study of Industrial Organization at Northwestern University Web site: Dobson, P. W. and Inderst, R. (2008). The Waterbed Effet: Where Buying and Selling Power Coe Together. Wisonsin Law Review, 2008, Dobson, P. W. and M. Waterson (1997). Countervailing Power and Consuer Pries. The Eonoi Journal, 107, Galbraith, J. K. (1952). Aerian Capitalis: The Conept of Countervailing Power. (Boston: Houghton Mifflin) (1954). Countervailing Power. Aerian Eonoi Review, 44, 1-6 Inderst, R. and G. Shaffer (2008). Buyer Power in Merger Control. (In W. D. Collins (ed.), Issues in Copetition Law and Poliy, Vol. II (pp ). Chiago: Aerian Bar Assoiation.) Inderst, R. and T.M. Valletti (2009). Prie Disriination in Input Markets. RAND Journal of Eonois, 40, 1-19 Majudar, A. (2005). Waterbed Effets and Buyer Mergers. Retrieved February 10, 2010, fro ESRC Centre for Copetition Poliy at University of East Anglia Web site: 22

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