RETAIL MERGERS AND BUYER POWER

Transcription

1 RETAIL ERGERS AND BUYER POWER by Ncola azzarotto CCR and School of Economc and Socal Studes Unversty of East Angla CCR Worng Paer CCR 04-3 Abstract Suler-retaler barganng s analysed over alternatvely lnear rces and to-art tarffs n a contet here retalers are horzontally dfferentated. Comarng dfferent nds of mergers shos that hat determnes changes n the retalers ost-merger buyer oer s the etent to hch the artes are veed by the manufacturer as alternatve ays of channellng her roduct to fnal consumers. Ths contradcts a commonly held ve that the sze of the buyer s a good roy for ts buyer oer. The results sho that dverson ratos can rovde a better ndcaton of a merger s effect on the artes buyer oer than maret shares. Arl 004 JEL Classfcaton: L4; L0; L40. Key ords: Buyer Poer; ergers; Dverson Ratos; Barganng; Retal Sector Acnoledgements: I ould le to than Bruce Lyons and orten Hvd for gudance and helful suggestons on earler drafts. I ould also le to than semnar artcants at UEA and at the IIOC 003 conference at Northeastern Unversty Boston for helful comments. Any remanng shortcomngs are my on. Fnancal suort from the ESRC s gratefully acnoledged. Contact detals: Ncola azzarotto Cometton Commsson Vctora House Southamton Ro London WCB 4AD Telehone 44 (0) ISSN The author s an Economc Advser at the Cometton Commsson London UK. The research resented n ths artcle s not related to any or conducted by the author as an advser at the Cometton Commsson and the ves eressed are the author s on and do not necessarly reresent the ves of any of the members of the Cometton Commsson.

2 RETAIL ERGERS AND BUYER POWER. INTRODUCTION In the ast ten years Euroean anttrust authortes have been faced th a shar ncrease n the trend of mergers and acqustons thn the retal sector and the food retal sector n artcular. The arallel ncrease n concentraton has attracted attenton thn both the academc orld and among anttrust racttoners. As a result a ave of theoretcal or on the economcs of the retal sector th an eye to anttrust mlcatons has folloed n art sonsored drectly by anttrust agences and nternatonal organsatons 3. One ssue that has been gven artcular emhass s the one of buyer oer that s: the maret oer that retalers or buyers n general ossess vs-à-vs ther sulers. The resence of buyer oer at some stage n the suly chan s no a maret feature that s taen nto serous consderaton also n anttrust roceedngs 4. From the ont of ve of theoretcal research a relatvely bg amount of attenton has been devoted to the effects that buyer oer can have on the orng of manufacturng or retal ndustres and to the elfare mlcatons of ts resence. Comaratvely lttle attenton on the other hand has been devoted to analysng the orgn of buyer oer. In other ords lttle theoretcal or emrcal research has focused on hat features confer to a frm more buyer oer than ts comettors have. The latter s an mortant ssue not only because t does someho logcally recede the former but because n anttrust roceedngs t s necessary to sho that a frm or grou of frms See Clare et al. (00) table The follong are ust a fe eamles: general or sonsored by anttrust agences nclude Dobson et al. (998) Dobson Consultng (999) OECD (999) FTC (000); on retalers countervalng oer see von Ungern-Sternberg (996) and Dobson and Waterson (997); on vertcal restrants: Comanor and Rey (000); on secfc contractual clauses (slottng fees) see Shaffer (99) and Sullvan (997) and for case studes and statstcal analyss see Clare et al. (00). 4 See NERA (999) the Ree-enl Decson: Decson 999/674/EC Ree/enl (OJ L 74/ 3/0/999) and other EC Decsons quoted theren.

3 actually enoys a certan degree of buyer oer before one can move on to assess ts elfare mlcatons. It s also arguably a queston that needs to be addressed from a theoretcal standont rather than an emrcal one. The reason for ths s that buyer oer s almost ntrnscally an ssue that concerns ntermedate marets here rces are not ublcly observed thereby rulng out the oton for eamle of an emrcal SSNIP test to defne the relevant maret. One ossble reason for the relatve absence of theoretcal or on the determnants of buyer oer s that there has develoed on ths matter a conventonal ve hch s more or less mlctly emloyed by economc theorsts and anttrust racttoners ale. Ths ve roughly seang states that buyer sze determnes buyer oer. In other ords: the bgger customer ays the loer rce. In ths aer I argue that ths ve though havng an ntutve aeal s not ft to descrbe the orng of modern retal urchase marets because t does not tae nto account the ay n hch retalers comete for consumers. The formal analyss that follos shos that hen the localsed nature of retal dstrbuton marets s taen nto account smaller retal chans can have more barganng oer than bg ones th resect to the same manufacturer f they serve a dstrbuton maret that s suffcently more nsulated from cometton than the one of ther larger comettors. Furthermore t s also shon that the nature of the contracts beteen retalers and ther sulers can mae a dfference for the ncentves retalers have to merge.. RETAIL COPETITION Retalers do not sell a homogeneous good. In fact the roduct they offer to ther consumers s a rather comle one. It ncororates varous tyes of servces (e.g. arng facltes n-store staff etc.) and t also dffers accordng to the actual range of roducts on the shelves. There are grous of retalers though for hch these varables are more of less homogeneous for eamle suermarets and hyermarets. Nevertheless one varable n artcular revents treatng retalers as sellers of a homogeneous good: stores locaton. Accordng to numerous surveys hat s by far the most mortant reason for shong at a artcular outlet s not hether rces are loer or the staff s frendler but smly here the shos are located n relaton to consumers homes or orlaces.

4 Table belo here convenence s to be ntended n a geograhcal sense as nversely related to transort costs gves a better dea of ths fact 5. Table : Factors affectng the choce of grocery store ost mortant factor Proorton of resondents % Convenence 54 Product range/ selecton 4 Lo rce 3 ualty 9 Cleanlness Frendly staff Handy oenng hours Others 6 Total 00 Source: London Economcs (997) ost of the lterature that treats formally the ssue of buyer oer does so by loong at dfferent maret structures here all retalers are symmetrc and comares stuatons n hch there s a hgher or loer number of retalers 6. Although ths frameor may be a useful aromaton n the analyss of some asects of buyer-suler relatons t does not lend tself to the analyss of the determnants of buyer oer. In fact the symmetry hyothess cannot but somehat cloud the ssue. For eamle von Ungern-Sternberg states that the holesale rce equlbrum outcome n hs model [ ] catures the conventonal dea that large retalers have more barganng oer. The roducer cannot afford to lose ther hgh sales volume and s thus llng to accet loer holesale rces. But retalers n a symmetrc frameor are all equally large; a symmetrc frameor cannot gve ndcatons as to the mortance of sze relatve to other otental determnants of buyer oer such as for eamle the ntensty of donstream cometton. The model ntroduced n the net secton ll consder alternatve merger scenaros n a settng here retalers are horzontally dfferentated th the urose of analysng the mortance of sze n determnng a retaler s buyer oer. The results ndcate that there can be small retalers th a hgher barganng oer than ther bgger comettors deendng on donstream comettve condtons. 5 Clare et al. (00) reort fgures by INSEE for France shong an even more sgnfcant role for convenence n consumers choce see. 0. 3

5 .. FORALISATION OF RETAIL COPETITION A number n of stores are located around a crcle of unt crcumference so that the dstance beteen to neghbourng stores s alays the same. All stores sell one and the same good. Consumers are unformly dstrbuted th densty one around the crcle and each ont around the crcle corresonds to one atomstc consumer. Preferences of each and every consumer over the good are reresented by the same demand functon q ( P ). Ths functon s decreasng n hch s the generalsed rce for the good and n turn deends ostvely on the rce charged by P store and by transort costs: P t. Fnally consumers buy only from the store chargng the loer generalsed rce for ther locaton. Theoretcal or that analyses mergers n a satal settng such as ths one n general reresents ndvdual consumers references by a unt demand 7. Ths assumton does smlfy the analytcal settng sgnfcantly. In the resent model I do not mae ths assumton. The reason beng that contrary to most of ths lterature the focus here s hat haens n the ntermedate maret (rather than n the fnal or dstrbuton maret) after a retal merger. As ll become clear later from the manufacturer s ont of ve t s mortant ho much the retalers ll sell ost merger at any gven holesale rce. Assumng a unt demand for each ndvdual consumer ould n other ords hde much of the acton n the barganng rocess. Under assumtons that are set out n aend each store faces a demand ) hch deends negatvely on rce at store and ostvely on rces charged at ( neghbourng locatons. Gven ths demand t s ossble to rte don the retalers roft functon: Π ( ) ( ) C( ( )) () Ths equaton smly defnes rofts as equal to revenues mnus costs. In order to rte don the cost functon assumtons have to be made as to the ay n hch retalers trade th ther sulers. The secfc nature of contracts that are suosed to regulate suler-retaler transactons s the subect of debate. In artcular there s no general consensus on hether they are better descrbed by a lnear holesale rce or by a to-art tarff. In order to avod deendence of the 6 E.g. Dobson and Waterson (997) and von Ungern-Sternberg (996). 7 See for eamle Brad (986) and Levy and Retzes (99). 4

6 results on a secfc formalsaton and also because t s ossble that dfferent forms of contracts may coest n the maret I ll loo n turn at a to-art tarff and at a lnear rce. In any case hether or not a retaler s suosed to ay a fed fee to ts suler s rrelevant as far as the frst order condton for roft mamsaton s concerned 8. Wth the further assumton that the costs of conductng a retalng busness be constant and normalsed to zero the only cost that these retalers ncur s the amount they ay to buy the goods they sell. Ths mles that under both tyes of contracts the Frst Order Condton (FOC) for mamsaton at each store locaton s equal to: Π ( ) 0 ;... n () From these n condtons equlbrum rces and quanttes are derved that deend on the holesale rces ad by each retaler. These quanttes can be rtten as: ( ) and as shon n Lemma A. n aend they deend resectvely ostvely and negatvely on the holesale rce ad by the same retaler. ( )... n and.. EFFECT OF RETAIL ERGERS IN THE FINAL ARKET FOR GIVEN CONTRACT TERS 9 Defne as the status quo a stuaton n hch each store around the crcle corresonds to one frm. In ths contet all frms are symmetrc th resect to both ther costs and ther demand and therefore gven the same contract terms th the manufacturer they ll all charge the same rce at equlbrum.... Non contguous stores Wth resect to ths status quo consder the merger of to non-contguous stores say store and store here ±. Call the merged entty frm A. Frm A s rofts are smly the sum 8 As the frst dervatve of the (constant) fed-fee s zero. 9 Contract terms refer to the value of the holesale rce and n case of the fed-fee that have been agreed uon n the ntermedate maret. 5

7 of the rofts of the to stores: A Π Π Π. The FOC for A s roft mamsaton s 0 Π Π A A and can therefore be rtten as: ( ) ( ) ( ) 0 Π Π Π Π A (3) ( ) ( ) ( ) 0 Π Π Π Π A The fact that the mergng stores are non-contguous means that the rce level at one of the to stores does not affect rofts at the other store. In formal terms the equalty n the mddle of the to equatons (3) s due to the fact that the second term of the sum on the left hand sde s zero thereby shong that the mamsaton roblem s dentcal to the one the mergng retalers face n the status quo. Ths mles the follong: Result : for gven contract terms n the ntermedate maret a merger beteen non contguous stores leaves fnal rces quanttes and rofts er-store unchanged.... Contguous stores Consder no a merger beteen to contguous outlets say stores and and call ths merged entty frm B. Agan B s rofts are the sum of the rofts earned at the to outlets and mamsaton s comuted over ths sum. The FOC s therefore: ( ) ( ) 0 Π Π Π B (4) ( ) ( ) 0 Π Π Π B 6

8 These equatons sho that rofts at the to stores deend on the rce charged at the neghbourng locaton. The effect of the merger on fnal rces can be derved from equatons () and (4) by rtng elctly the dervatve of the roft functons: ( ) ( ) 0 Π B Π ( ) ( ) 0 B (5) In the re-merger status quo roft mamsaton taes the form of the FOC gven n equaton (). Wth resect to that equaton ths merger scenaro brngs about an etra term n the frst order condton. Under the hyothess that retalers oerate th a strctly ostve mar-u and gven that demand deends ostvely on the rce charged at neghbourng locatons the thrd term of the sum s ostve. Ths mles that the rce that as charged re-merger s no too lo. In order to restore equalty n the FOC the frst to terms of the sum.e. the sloe of each store roft functon has to become negatve. As the follong fgure llustrates ths means that rces have to rse: Π Ths sums u n the follong: 7

9 Result : for gven contract terms n the ntermedate maret a merger beteen contguous stores loers the quantty sold and rases fnal rces and rofts er store at all neghbourng locatons. These results are consstent th the fndngs of most of the lterature on mergers beteen rce-settng frms. Denecere and Davdson (985) sho that n a rce settng monoolstcally comettve ndustry mergers ll lead to hgher rces and rofts for all frms. In a satal settng here consumers have nelastc unt demands Levy and Retzes (99) also sho ho rces and rofts rase for all retalers follong a merger beteen contguous outlets hle they reman unchanged f non-contguous stores merge. Results and therefore smly etend some of the fndngs of Levy and Retzes (99) to the case here consumers have donard slong ndvdual demands. 8

10 3. THE INTEREDIATE ARKET The revous secton has descrbed the ay n hch retalers comete for fnal consumers for gven contract terms. The art that follos ll turn to loo at ho these contract terms are determned n the ntermedate maret. Consder the follong vertcal chan of roducton. A sngle frm s the monoolst manufacturer of a good. The manufacturer can sell ts roduct to n retalers ho n turn ll sell the same roduct to fnal consumers n the ay secfed n the revous secton. The assumton of a sngle manufacturer s common to most related lterature (e.g. Dobson and Waterson 997 or von Ungern-Sternberg 996). Ths assumton s mantaned here n order to rovde a smle benchmar aganst hch to analyse the shft n the retalers barganng oston that can follo a retal merger 0. The assumton of a sngle monoolstc manufacturer s clearly not a satsfactory aromaton for all urchase marets. For eamle t s not an arorate assumton hen manufacturng ndustres are very comettve and unconcentrated le n the case of fresh roduce. On the other hand t s a good aromaton hen manufacturers suly roducts that consumers do not erceve as easly substtutable such as some must-stoc branded goods. Furthermore assume that along the hyothessed vertcal chan trade occurs n the follong to stages.. The manufacturer and the retalers bargan over the terms of a contract.. The retalers comete for fnal consumers gven the terms of that contract. Ths to-stage structure s agan a common feature n models that analyse buyer-suler barganng. It s usually consdered an arorate frameor n marets here nut rces are negotated uon less frequently than fnal maret comettve varables can be adusted. The UK s Cometton Commsson s recent reort on Suermarets (Cometton Commsson 000) rovdes some nsghts as of the tycal duraton of contracts beteen retal 0 An olgoolstc ustream ndustry already rovdes a contet n hch smaller retalers can be n a better barganng oston than ther bgger comettors see the eamles quoted n Scherer and Ross (990). See for eamle Horn and Wolnsy (988). 9

11 chans and ther sulers. The nqury shoed that Contracts tend to be oen-ended or ongong and there s no standard length to them. Four ees notce s normal to termnate arrangements. Furthermore t aears that n many cases oral day-to-day negotatons are used to agree on rce and quantty. There aear though to be sgnfcant dfferences n the ay negotatons are conducted across dfferent manufacturng ndustres. The man suermarets nvolved n the Commsson s nqury stated that hle rce and quantty of ershable goods are negotated on a eely bass th rces beng nfluenced by maret fluctuatons the same s not true for the roducers of so-called must stoc tems. For these roducts negotatons seem to be sgnfcantly less frequent 3. Ths evdence on the frequency of negotatons therefore seems to ustfy the use of a to-stage structure for the same categores of manufacturng ndustres for hch the snglemanufacturer hyothess s more arorate that s roducers of must stoc branded goods 4. The follong formalsaton of the barganng rocess beteen the manufacturer and the retalers s dvded n to arts. The frst ll analyse the case n hch a to-art tarff s emloyed n trade contracts and the second the case n hch the contracts secfy only a lnear rce. These contracts are assumed to be bndng BARGAINING OVER A TWO-PART TARIFF A barganng roblem s defned by three elements: a set of agents a set of ayoff ars and a status quo or dsagreement ont. Follong most of the lterature that analyses smlar vertcal structures 6 negotatons beteen retalers and the manufacturer are treated here as consttutng n ndeendent and smultaneous barganng roblems; hence the agents n each barganng roblem are to: the manufacturer and each ndvdual retaler. The soluton concet adoted s the symmetrc Nash Barganng Soluton (NBS) The barganng roblem In ths settng ayoff ars concde th the rofts that can be earned by tradng th the counterart. The manufacturer s assumed to roduce the good thout f costs and at a constant Cometton Commsson (000) ara See Cometton Commsson (000) ara Furthermore the focus here s on the dfferences beteen re and ost-merger barganng ostons and t does not seem narorate to ostulate that after a merger the artes ould ant to renegotate the general terms of ther agreement even th those sulers th hom they mght have establshed a tradton of day-to-day negotatons. 5 Ths rules out all ssues of renegotatons as rased for eamle by O Bren and Schaffer (99) 6 For eamle: cafee and Schartz (994) Horn and Wolnsy (988). 0

12 margnal cost. Therefore n the case of to-art tarff contracts f the manufacturer trades th all retalers n the ntermedate maret the rofts she earns are gven by the follong eresson: Π n F (6) Where the manufacturer s margnal cost s assumed constant and s normalsed to zero thout further loss of generalty s the holesale rce and F s the fed fee. Conversely each retaler s rofts tae the follong form: ( ) F ; n Π (7) R... By defnton the coordnates of the dsagreement ont are the rofts earned by the manufacturer and by the retaler f no agreement s reached. Snce the manufacturer s n ths settng the sole suler of the only good retalers can sell the retalers dsagreement rofts are set to zero. On the other hand f the manufacturer does not reach an agreement th any one retaler she can stll sell to the other n remanng retalers. The anufacturer s dsagreement rofts can therefore be rtten n the follong ay: Π [ d () ] F d () < (8) The dea behnd ths eresson s the follong. If the manufacturer does not trade th retaler she ll lose the sales that as revously mang through that outlet. Yet f negotatons th retaler ere to brea don gven the assumton that retalers sell no substtutes to the manufacturer s good the effect ould be dentcal to retaler etng the donstream maret. Ths n turn ould mact uon the sales of the remanng retalers. Equaton (8) defnes the manufacturer s dsagreement ayoff n a ay that does not constran the retalers (ndrect) quantty choce n the dstrbuton maret to any secfc resonse. The terms d () smly allo eressng the quantty that each remanng retaler ll buy from the manufacturer as a roorton of the sales that she ould have made va retaler.

13 The condton that the sum of these terms be less than one s requred for the manufacturer to have an ncentve to reach an agreement at all th any one retaler. If ths condton as volated the mlcaton ould be that the manufacturer ould mae more sales f as not n the maret and ould therefore lac an ncentve to trade. The arameter values for hch ths condton s satsfed n ths artcular model are derved n Aend and bascally requre that all retalers stll be actve comettors even after s et. Ths s therefore assumed. In a ay these terms are analogous to hat Sharo (995) calls dverson ratos. These are defned th resect to any to dfferentated frms n a maret. If one of these to frms rases the rce of ts roduct t ll lose a certan amount of sales. The dverson rato ndcates hat fracton of the lost sales ll be recuerated va ncreased sales to the other frm. A hgh dverson rato therefore ndcates that the to frms are close comettors and vce versa. In equaton (8) the dverson ratos are defned th resect to a frm etng the maret or equvalently th resect to a rce rase above all consumers reservaton rce. The mlcatons of ths latter defnton for the value these ratos can assume ll be consdered belo The Nash Barganng Soluton (to-art tarff) The symmetrc NBS mles that agreement s reached for a holesale rce and a fed fee such that 7 : R ( F ) arg ma{ Π Π } (9) F 7 The second order condton for ths mamsaton roblem s analysed n Aend 3.

14 The mamand on the rght hand sde s the roduct of to quanttes that corresond to the ncentve that each agent has to trade and t s commonly referred to as the Nash Barganng Product (NBP). ore recsely these magntudes corresond to the ncremental rofts that retaler and manufacturer can earn by agreeng to the terms of a contract. For the manufacturer after some manulaton these can be rtten as: Π Π Π F d () F g ( ) (0) Here g ) s defned for convenence as the functon of nsde the square arenthess. Note that n the symmetrc status quo ths functon taes lo values f retalers are close comettors e.g. f travel costs are lo or the number of stores s hgh so that follong the et of any one store the quantty sold by that store s almost fully absorbed by the remanng outlets and d (). ( The ncremental rofts for the retaler are equal to: R R ( ) F Π Π () From equaton (9) the FOC th resect to the fed-fee can be rtten as: R R Π Π Π Π () F F Snce the dervatves th resect to the fed-fee of the ncremental rofts are for the manufacturer and the retaler resectvely equal to and the FOC for the fed-fee mles: R ( F ) Π Π : (3) 3

15 hch states that the fed fee s chosen to equate the ncremental rofts of the to agents. The FOC th resect to the holesale rce s 89 : NBP (4) R ( ): g ( ) Π Π 0 Gven equaton (3) ths mles: g ( ) d ( ) 0 (5) hch n turn requres that the holesale rce be set at: 0 (6) Fnally substtutng ths bac nto equaton (3) gves the value of the fed fee: F (7) Equaton (7) states that the fed fee ll be set at a value eactly equal to a half of the retaler s rofts. Ths s a standard result. A to-art tarff elmnates the double margnalzaton eternalty and restores barganng effcency by allong agents to set a holesale rce equal to the margnal cost of roducng the good n ths case normalsed to zero and a fed fee so to slt the rofts beteen the barganng artes 0. ( ) 8 g Here. Ths corresonds to the assve belefs assumton used dely n related lterature [e.g. cafee and Schartz (994); O Bren and Schaffer (99); Horn and Wolnsy (988)] accordng to hch the barganng beteen the manufacturer and each retaler taes lace smultaneously and ndeendently and holdng constant at the equlbrum values the outcomes of the other bargans. R 9 Π Note also that the Enveloe Theorem mles that. 0 In ths case the rofts are slt n half. The NBS can suort any other rato for dfferent eogenously set levels of barganng oer. Ths does not affect the qualtatve results. 4

16 3..3. The effects of retal mergers on the ntermedate maret (to-art tarff) The results of the revous secton are suffcent to dra the frst mortant conclusons regardng the sources of buyer oer n the ntermedate maret. Startng from a status quo such as the one descrbed n secton. let any number say four of non-contguous stores merge. Snce the holesale rce s alays set to equal the margnal cost of roducton by vrtue of Result above fnal rces quanttes and rofts er store are unchanged by the merger. In terms of equaton (7) ths means that the ne frm ll ay a fed fee hch s eactly four tmes hgher than the one that each store used to ay ndvdually n the status quo. In other ords: Result 3: Wth to-art tarff contracts a merger beteen any number of non contguous stores leaves holesale rces fnal rces and quanttes unchanged; the fed fee ncreases to leave rofts er store unchanged. On the other hand f th resect to the same status quo any number say to of contguous stores s to merge Result states that the effect ll be to rase fnal rces and rofts at each neghbourng locaton and to reduce quantty. Equaton (7) mles that the merged frm ll also ay a hgher fed fee er-store but ths s don to the fact that the total rofts of the vertcal chan are ncreased. As a consequence the merged frm although t ll ay a hgher fed fee to the manufacturer ll stll enoy hgher rofts er store. Ths translates to: Result 4: Wth to-art tarff contracts a merger beteen contguous stores leaves the holesale rce unchanged loers the quantty sold rases fnal rces and rofts er-store as ell as the value er-store of the fed fee. When to art tarffs are emloyed a defnton of buyer oer s more dffcult because the holesale rce s alays left unchanged and the fed fee s alays chosen to slt the rofts n half. Havng sad ths hat can be assessed n ths contet s hether any tye of retal merger ould confer to the mergng artes a comettve advantage th resect to ther rvals. The conventonal ve on buyer oer onts to the concluson that the larger buyer tends to get the better deal therefore retal mergers that lead to the creaton of a large layer n the ntermedate maret are looed at suscously because of the advantage n terms of urchase costs that sze s suosed to confer. Results 3 and 4 have strong mlcatons th resect to these ssues. 5

17 They sho that f to-art tarffs are emloyed the sze of the buyer s a msleadng ndcator hen t comes to determnng hether a retaler enoys a comettve advantage. To see ths tae as above four (or ndeed any hgher number) non-contguous mergng stores as oosed to only to contguous outlets. The amount that the former urchase from the manufacturer s more than tce the one bought by the latter. Yet t s the to contguous stores that ll enoy hgher rofts er store n the ost merger scenaro. It s them ho ll enoy a comettve advantage. One clarfcaton s due at ths ont concernng economes of scale n retalng. The tyes of mergers I consder here are beteen retal frms that are suosed to enoy the same level of economes of scale that come from buyng n large quanttes e.g. n dstrbuton. It s a roven fact that those economes are sgnfcant and therefore there may ell be cases here a merger beteen many non cometng outlets ould enable the mergng artes to get better deals hereas small local monoolstc shos could ay more for ther sules because of hgher urchase and dstrbuton costs. 6

18 3.. BARGAINING OVER A LINEAR PRICE Wth resect to the to-art tarff case the barganng roblem s here changed n the set of ayoff ars. In the absence of a fed fee the manufacturer s rofts are: Π n (8) and analogously the retaler s rofts: R ( ) Π (9) If the manufacturer does not reach an agreement th retaler her rofts ll be: Π [ d () ] (0) And therefore the ncremental rofts that the manufacturer gans by reachng an agreement th retaler are n ths case: Π Π Π d () g () As n the revous case the retaler s dsagreement ayoff s zero mlyng that her ncremental rofts are equal to the rofts gven n equaton (9). 7

19 3... The Nash Barganng Soluton (lnear rce) Gven equatons (8) () the outcome of the barganng rocess can be comuted. Adotng once more the NBS the outcome of the barganng rocess s a lnear rce such that : R { Π Π } arg ma () The FOC for ths mamzaton can be rtten n the follong ay: Π Π Π Π R R (3) Whch gven the revous eressons can n turn be rtten as: g ( ) (4) g ( ) Ths equlbrum condton eresses the retaler s mar u as a functon of the degree of cometton beteen retalers. If cometton s hgh (e.g. transort costs are lo) n the symmetrc status quo then g ( ) s lo and to ths scenaro corresonds a loer mar u Retal mergers beteen to non-contguous stores (lnear rce) Consder a merger beteen stores at locatons and here ±. Call the holesale rce over hch the merged entty ll bargan th the manufacturer. In ve of the symmetry of any to outlets around the crcle the equlbrum rce and quantty er store ll be the same for every gven holesale rce.e. ( ) ( ) and ( ) ( ). Furthermore gven the non contguty of the mergng outlets Result mles that the equlbrum rce and quantty er store ll be the same functon of the holesale rce as they ere for each of the mergng outlets n the status quo. The second order condton for ths mamsaton roblem s analysed n Aend 3. 8

20 In ve of these consderatons the ne frm ll mamze the follong rofts: ( ) ( ) ( ) ( ) ( ) ( ) R Π (5) The merger ll change the manufacturer s dsagreement ayoff: () ( ) [ ] Π d d (6) Because of the symmetry of the model for any to stores and around the crcle t has to be the case that. Usng ths and equaton () e can rte the manufacturer s ncentve to agree th the merged entty n a ay that ll mae t easy to comare t to the status quo ( ) ( d d ) ] 3 : () () ( ) [ ) ( d g d d Π (7) and ts dervatve s: ( ) ( ) [ Π d g ] (8) These formulae allo rtng the FOC for the NBS for the merged entty as: ( ) ( ) ( ) ( ) [ ] ( ) ( ) [ ] ( ) d g d g (9) Comarng ths condton th equaton (4) referrng to the status quo shos that n the ost merger scenaro the rght hand sde of the FOC s hgher for all values of the holesale rce 4. Convety of retaler s rofts n and concavty of the manufacturer s rofts n are suffcent 3 One thng to ee n mnd s that because of the symmetry n the status quo ( ) ( g g ). Recall also that the holesale rce that aears n the formula s not the holesale rce the artes are barganng over t s the equlbrum holesale rce ad n the status quo to retaler. 4 Ths s the case f. For a dscusson of the mlcatons of ths requrement see Aend. () 0 > d 9

21 condtons for the left hand sde to be a decreasng functon of the holesale rce and for the rght hand sde to be an ncreasng one. On ths bass t s ossble to dra some conclusons about the effects of the merger. The merged stores ll oerate th a hgher mar u than before and the mar u ll be hgher the hgher the value of d (). In other ords f the mergng outlets are relatvely close comettors they ll oerate n the ost-merger scenaro th a hgher mar u; vce versa f the to outlets do not closely comete ther ost merger mar u ll be only slghtly hgher. Ths hgher mar u ll be acheved by a decrease n the holesale rce ad to the manufacturer. The fnal rce ll also decrease but less than roortonally to the holesale rce. To sum u: Result 5: Wth lnear rces a merger beteen to non-contguous retalers loers the holesale rce n a measure nversely roortonal to the comettve dstance beteen the artes. The fnal rce s also loer but less than roortonally to the decrease n the holesale rce. Ths result shos that hen barganng s not effcent the cture changes drastcally. In ths case non contguous retalers do have an ncentve to merge because the merger shfts the status quo n the barganng roblem gvng the manufacturer a bgger ncentve to reach an agreement th the merged stores. Ths n turn mles that the merged retalers get a better deal n the form of a loer holesale rce. The source of ths ncreased buyer oer resdes n the term ( ) d. The merger maes a dfference to the manufacturer because she loses one alternatve. In other ords the to mergng stores ll get a better deal only to the etent that they reresent alternatve ays for the manufacturer to channel her goods to the same fnal consumers. If ths ere not the case the term d () ould be zero and the barganng roblem ould not change. For these reasons agan t s not the sze of ther urchases from the manufacturer that mroves the merged stores barganng oston th resect to ther comettors but rather ther strategc nterdeendence n the status quo. One thng to note s that snce they are not drect comettors but stll face ndeendent stores on each sde the loer holesale rce obtaned n the ntermedate maret translates nto 0

22 loer rces for fnal consumers too 5. The merger rases buyer oer but snce donstream cometton s stll strong art of the dscount s assed on to fnal consumers CONCLUSION In secton 3 a number of dfferent tyes of mergers have been analysed n ther effects on the relatve barganng oston of the mergng artes and ther suler. The results sho that n no case the conventonal ve on buyer oer hch lns ts source to buyer sze s ft to gve even an ndcatve dea of the outcome of negotatons. On the contrary t can be a serously msleadng ndcator of relatve barganng strength of the mergng artes or of a suosed cost advantage over ther comettors. The eamles taen nto eamnaton sho that t s the etent to hch the mergng artes reresent alternatve ays for the manufacturer to channel her goods to fnal consumers that drves a change n the retalers barganng oston follong a merger. In ths sense the results etend to urchase marets the dea already dely shared for dstrbuton marets that n the assessment of mergers beteen frms ho sell dfferentated roducts dverson ratos n Sharo s terms rather than maret shares s hat should be taen nto account. Fnally by loong at dfferent tyes of contractual arrangements t emerges that hether or not the ntermedate maret adots contracts conducve to barganng effcency does mae a dfference n terms of the ncentves that retalers have to merge. Whle th a to-art tarff a merger s only roftable f the artes are drect comettors n the dstrbuton maret hen lnear rces are adoted even non-contguous stores have an ncentve to merge. REFERENCES Brad R Stacelberg rce leadersh n satal cometton Internatonal Journal of Industral Organzaton Cometton Commsson 000. Suermarets: a reort on the suly of groceres from multle stores n the Unted Kngdom. htt://.cometton-commsson.org.u/nqures/archve.htm 5 The analyss of non-contguous merger scenaros s suffcent for dervng the man results. The analyss of a merger beteen contguous outlets resents sgnfcantly hgher comutatonal dffcultes thout addng sgnfcant nsghts to the analyss and s therefore not consdered here. 6 Ths result s n accordance th other or on Countervalng Poer. E.g. Dobson and Waterson (997) and von Ungern-Sternberg (996).

23 Clare R. Daves S. Dobson P. and Waterson. 00. Buyer Poer and Cometton n Euroean Food Retalng Cheltenham UK and Northamton A USA: Edard Elgar. Comanor W.S. Rey P Vertcal Restrants and the aret Poer of Large Dstrbutors Reve of Industral Organzaton Cometton Commsson 000. Suermarets: A reort on the suly of groceres from multle stores n the Unted Kngdom..Cometton-Commsson.org.u. Denecere R. and Davdson C Incentves to form coaltons th Bertrand cometton Rand Journal of Economcs Dobson Consultng 999. Buyer Poer and ts mact on cometton n the Food Retal Sector of the Euroean Unon Reort reared for the Euroean Commsson DGIV. Study Contract No. IV/98/ETD/078. Dobson P.W. and Waterson Countervalng oer and consumer rces Economc Journal Dobson P.W. Waterson. and Chu A The Welfare Consequences of the Eercse of Buyer Poer OFT Research Paer No. 6. FTC 000. Slottng Alloances and other grocery maretng ractces. FTC Publc Worsho. htt://.ftc.gov/bc/slottng/nde.htm. Horn H. and Wolnsy A Blateral monooles and ncentves for merger RAND Journal of Economcs Levy D.T. and Retzes J.D. 99. Antcomettve effects of mergers n marets th localzed cometton Journal of La Economcs and Organzaton Lyons B.R. 00. Could oltcans be more rght than economsts? A theory of merger standards CCR Worng Paer CCR 00-. London Economcs 997. Cometton n Retalng OFT Research aer No. 3. cafee R.P. and Schartz Oortunsm n multlateral vertcal contractng: nondscrmnaton eclusvty and unformty Amercan Economc Reve NERA 999. erger arasal n olgoolstc marets OFT Research aer No. 9.

24 Novshe W Equlbrum n Smle Satal (or Dfferentated Product) odels Journal of EconomcTheory O Bren D.P. Shaffer G. 99. Vertcal control th blateral contracts RAND Journal of Economcs OECD 999. Buyng Poer of ultroduct Retalers Cometton olcy roundtable n.3. htt://.oecd.org/daf/cl/roundtables/buyng00.htm. Scherer F.. and Ross D Industral maret structure and economc erformance Boston a: Houghton ffln. Shaffer G. 99. Slottng Alloances and Resale Prce antenance: A Comarson of Facltatng Practces RAND Journal of Economcs. Sharo C ergers th dfferentated roducts Address before the Amercan Bar Assocaton. htt://.usdo.gov/atr/ublc/seeches/sharo.sc.tt Sullvan.W Slottng alloances and the maret for ne roducts Journal of La and Economcs XL Von Ungern-Sternberg T Countervalng oer revsted Internatonal Journal of Industral Organzaton

25 APPENDIX : EUILIBRIU AND DEAND FUNCTIONS IN RETAIL COPETITION The formal analyss of cometton among retalers conducted above conssts of comarng dfferent equlbra that are not elctly derved n ths aer. For a formal roof of estence of the equlbrum n ths model the reader s referred to Novshe (980). Here the man assumtons of Novshe s aer are mantaned. In artcular crucal to the estence of an equlbrum n a satal maret of ths tye s the fact that frms must not have the oton of caturng the hole of ther rval s maret by undercuttng ther rvals mll rce. Novshe rules out ths ossblty by assumng a modfed Zero Conectural Varaton strategy that s: ndvdual frms assume the rces charged by ther rvals not to change n resonse to ther on rce changes unless the rval s undercut at hs store s locaton n hch case (s)he reles by loerng the rce. The model n secton of the aer follos Novshe n assumng aay mll rce undercuttng. Novshe also shos that f there are enough frms around the crcle so that they all drectly comete th one another then there s only one equlbrum and t s symmetrc n both rce and locaton. Furthermore n equlbrum all frms are at an nteror roft-mamsng soluton and hence frst and second order condtons can be used to characterse the equlbrum. Here the attenton s confned to the case n hch all frms actvely comete th one another (.e. no frm s at a monooly soluton). In ths contet Novshe s results vndcate the assumton of equally saced frms around the crcle and allo the follong analyss of the roertes of the demand functon based on frst order condtons. a b P If each ndvdual consumer around the crcle has a demand for the good ( ) q P hch s a donard slong functon of P t that s the delvered or generalsed rce for the good at locaton then the margnal consumer ho s ndfferent beteen buyng at the successve locatons and s dentfed by the follong equaton: ( t ) a b t a b (A.) n 4

26 hch mles that: t n (A.) Ths shos ho movements n frm s rce and n the rce of neghbourng frms affect the maret area covered by the frms. Ths defnton together th the analogous one for the margnal consumer to the left of frm can be used to rte don elctly the demand that retaler faces: ( ) a b ( t) d a b ( t)d 0 (A.3) 0 On the bass of equatons (A.) and (A.) t s ossble to derve some roertes of the aggregate demand facng each retaler. Consder frst a rse n the rce charged by store. Ths has to effects: on one hand as can be seen n eq. (A.) t reduces the maret area served by thereby shortenng both ntegraton ntervals n eq. (A.3) and on the other hand t loers at each ont the value of the ntegrated functon. Therefore the aggregate demand deends negatvely on the on rce. Conversely a rse n the rce charged at ether neghbourng locatons etends the ntegraton nterval by shftng the margnal consumer. Ths rases the derved demand at store by ncreasng the value of ether of the to terms of the sum on the left hand sde of equaton (A.3). Wth these roertes of the demand functon n mnd t s ossble to move on to analyse some comaratve statcs relatve to the retal-cometton equlbrum quanttes and rces. The frst order condton for roft mamsaton that as gven n the man tet as (3) s here reeated as (A.4): Π ( ) 0 ;... n (A.4) As mentoned above ths system of equatons has a unque and symmetrc soluton corresondng to the equlbrum rces (... )... n that deend on the holesale rces n hch are n ths case fed and equal for all frms. In the analyss of the aer some roertes of these functons are used. These are roved n the follong: 5

27 Lemma A.: The rce charged by a retaler deends ostvely and ts outut negatvely on the holesale rce ad to the manufacturer. Proof: Totally dfferentatng the FOC (A.4) gves: Π d Π d 0 (A.5) hch mles that: d d ( ) (A.6) here the second dervatve of the roft functon th resect frst to the on rce and then to the on holesale rce s equal to the dervatve at the numerator on the rght hand sde by vrtue of the Enveloe Theorem. The denomnator of the fracton n (A.6) s negatve because the second order condton holds n equlbrum 7. Therefore: d sgn sgn (A.7) d Snce quantty as elaned above s nversely related to the on rce ths equalty mles that the equlbrum rce rses n resonse to an ncrease n the holesale rce ad to the manufacturer. As a corollary to ths the quantty roduced ll fall n resonse to a rase n the holesale rce [ED]. 7 See Novshe (980) for a formal roof. 6

28 APPENDIX : DIVERSION RATIOS In the model retal mergers change the artes barganng ostons vs-à-vs ther suler because they change the manufacturer s dsagreement ayoff. An mortant element of the formalsaton of the barganng roblem set out n secton 3 s therefore the ay n hch the manufacturer s dsagreement rofts are rtten. The dverson ratos ntroduced n eq. (8) and reeated belo as (A.) reflect the fact that hen retalers are horzontally dfferentated they do not comete th all other retalers th the same ntensty. On the contrary the ntensty th hch one retaler cometes for fnal consumers aganst another one deends on the retalers oston n the maret.e. ts locaton. d Π [ d () ] F d () < (A.) In order to better understand the mlcatons of ths settng for the ntermedate maret the ( ) dverson ratos d t mlctly defned n eq. (A.) can be rtten elctly n the follong ay here ndcates the amount that retaler ll roduce follong s et: d (A.) ( t) The dverson ratos eress the change n retaler s outut that follos s et n terms of the amount revously sold by. From the ont of ve of the manufacturer they ndcate hat roorton of retaler s sales ould be absorbed by retaler f retaler as to et the maret. The fact that retalers comete more closely th some and less closely th others n the dstrbuton maret means that hen a retaler stos stocng the manufacturer s roduct (n ths model: ets the maret) the retalers that ere hs closest comettors are also the ones that ll ncrease ther outut the most. 7

29 In hat follos t ll be shon that after an et the total quantty sold n the maret ll fall as rces are rased at all actve locatons. Ths roves that the manufacturer ll alays have an ncentve to reach an agreement th a retaler. It should be noted that n ths settng the value of the factor s not constraned to be ostve. It s concevable that after an et the effect of dmnshed cometton on rces s so strong that at least some frms end u sellng less than before. Ths mars a sgnfcant dfference beteen dverson ratos defned relatve to a rces ncrease that ees the frm n the maret or as n the resent case over an et. Nevertheless f substantal cometton s reserved n the dstrbuton maret even n absence of one artcular retaler some of the sales that ere revously made by the eted retaler ll be recuerated va ncreased sales through other outlets. Ths latter case s the one on hch the resent analyss focuses. d () RETAIL COPETITION Consder as the status quo the one descrbed n secton th n equally saced outlets sellng ndeendently the same roduct to fnal consumers that are unformly dstrbuted around a crcle of unt length. Consder retaler n the rocess of negotatng a contract th the manufacturer. What determnes the coordnates of the status quo ont n ths barganng roblem and hence the strength or the eaness of s barganng oston s the amount the manufacturer ll stll be able to sell n case ets the maret. Sales n ths latter case ll only be made to retaler s comettors ho by assumton do not have the ossblty of relocatng once has eted the maret. Retaler le all other retalers around the crcle has to drect comettors one on each sde of ts store; these are: retaler - to ts left and to ts rght. Because the status quo s symmetrc n rce and retalers are all at the same dstance the analyss of say - s resonse to s et ll be suffcent to no s behavour as ell. As far as retaler - s concerned t s useful to thn of ts sales as dvded n to halfmarets: one to the left and the other to the rght of - store s locaton 8. The left half-maret ll not be affected by s et but the rght one obvously ll be. In artcular hat ll haen s that at the status quo rce - ll fnd that t s no servng many more consumers on ts rght. To be more recse f rces are unchanged from the status quo and consumers are assumed to all urchase some quantty of the good somehere (.e. to have a hgh enough reservaton rce for all frms to stll comete even after s et) - ll fnd that the margnal consumer on ts rght has 8 A smlar aroach s used n Lyons (00) A.. 8

30 no moved further aay to the oston revously occued by s store. Ths s shon n fgure A.. belo. Fgure A..: - here reresents n fg. A. the margnal consumer beteen - and and the arros ndcate the drecton n hch the margnal consumer shfts (for - and ) hen ets the maret. The effect of s et on - can therefore be analysed th reference to a shft to the rght of the margnal consumer. ore recsely ths shft to the rght s caused by a reducton n the number of frms; therefore the et can be analysed by reference to the arameter n. The demand that - faces n ts rght hand sde half-maret s: a b( 0 t) d (A.3) 9

31 here t n s the eresson ndcatng the margnal consumer to the rght of - hen s resent n the maret. Note that: ( ) { } ( ) 0 t q d t q (A.4) and: ( ) n t q n n (A.5) and fnally that: ( ) ( ) n t q t q n n (A.6) Wth these eressons t s no ossble to move on to loo at the rce elastcty of demand n the rght hand sde half maret for retaler -. Ths elastcty s by defnton: η (A.7) and n order to be able to analyse the effect of s et to the rce charged and the quantty sold by - t s necessary to calculate the dervatve of ths elastcty th resect to n the number of frms. The formula s: ( ) n n n η (A.8) 30

32 In order to fnd the drecton of change n the rce level after s et t s suffcent to no the sgn of ths dervatve hch s gven by: n n sgn n sgn η (A.9) Gven equatons (A.5) and (A.6) the condton for the sgn of ths dervatve to be ostve can be rtten n the follong ay: ( ) ( ) ( ) > t q t q t q (A.0) To verfy f and hen ths nequalty holds let s assume the same lnear ndvdual demand as n Aend that s ( ) ( ) t b a t q. Consder frst the sum on the left hand sde. The frst term of ths sum s the value of the dervatve of the ndvdual consumer s functon th resect to the mll rce calculated at the dstance of the margnal consumer. Clearly ths value s alays equal to mnus b regardless of the secfc locaton at hch t s calculated. The second term on the other hand s alays equal to b hch mles that the left hand sde of condton (A.0) s alays equal to b. To calculate the value taen by the rght hand sde roduct t s useful to rte the terms n a dfferent ay. Smle manulaton shos that for the lnear ndvdual demand secfed above and rtng ( ) ( ) t q q for smlcty the follong equaltes hold: ( ) bt q q (A.) q (A.) and: 3

33 3 bt q t (A.3) On the bass of these last three equatons t s ossble to re-rte the (A.0) n the follong ay: < 3 q bt bt q bt (A.4) that can be further smlfed to: 0 3 > q bt q (A.5) Ths n turn mles that: 0 3 > bt q (A.6) Fnally recallng equaton (A.) the condton for the sgn of the dervatve to be ostve eressed n the (A.0) s equvalent for the lnear ndvdual demand to the follong: ( ) ( ) > q bt q (A.7) Ths condton moses a restrcton on the value of the ndvdual consumer s reservaton rce. It requres that consumers that are further aay from - than the margnal consumer by a fracton 3 ll stll ant to urchase a ostve amount from -. It s therefore assumed that consumers have a hgh enough reservaton rce for (A.7) to hold. 3

34 Under condton (A.7) hen a store ets the maret ts mmedate comettors ll see ther elastcty of demand decrease and ll therefore rase ther rces. As a consequence because of the strategc comlementarty of rces all frms ll rase ther rces ost et and therefore total quantty roduced ll fall. 33

35 APPENDIX 3: SECOND ORDER CONDITIONS Ths aend eamnes the second order condtons for the mamsaton roblems resented n secton 3. They relate to the Nash Barganng Products n the barganng roblems over a to-art tarff and a lnear holesale rce. TWO-PART TARIFFS Consder the NBP for the to-art tarff case n eq. (9). The second order condton th resect to the fed-fee s satsfed as both terms of the NBP are lnear n the fed fee and ther frst dervatves are equal to lus and mnus one. As a consequence t s straghtforard to sho that: NBP F (A3.) As for the holesale rce the second dervatve of the NBP th resect to the holesale rce drong for notatonal ease the subscrts s: NBP F g Π R ( ) Π Π (A3.) Ths eresson can be smlfed recallng that the FOC requres that Π Π R and that. After smle manulaton equaton (A3.) can be re- g 0 hch n turn mly that rtten as: Π NBP F 3 Π R < 0 (A3.3) 34

36 As shon n Lemma A. the dervatve of quantty th resect to the holesale rce s negatve and as a consequence so s the rght hand sde of eq. (A3.3). LINEAR PRICES Consder no the NBP for the case of a lnear rce n eq. (). The second dervatve of the NBP th resect to the holesale rce s the same eresson as n eq. (A3.): NBP g Π R ( ) Π Π (A3.4) The term n square bracets on the rght hand sde s the second dervatve of the ncremental rofts earned by the manufacturer by reachng an agreement th retaler. For ths term to be negatve t s suffcent that quantty s not too conve n the holesale rce; ths s assumed. In order to establsh the sgn of the second and thrd terms n the sum on the rght hand sde of eq. (A3.4) consder the FOC eressed n eq. (3). Ths can be rtten as: Π Π R Π (A3.5) Whch mles that here the FOC holds Π has to be greater than zero as all the other terms n the equalty are strctly ostve. Consder the last to terms of the sum n (A3.4) n solaton. Call the sum of these to terms A. A can be rtten as: Π A Π R (A3.6) 35