Mergers in Multidimensional Competition

Transcription

1 Mergers n Multdmensonal Cometton Carl Davdson Mhgan State Unversty and GEP, Unversty of Nottngham Ben Ferrett GEP, Unversty of Nottngham ABSTRACT In realty, horzontal mergers are often drven by the oortuntes they reate for the exlotaton of R&D omlementartes. An examle s the BP/ ARCO mega-merger, aroved n 000, where a entral justfaton was that ntegraton by ommttng the frms to sharng ther aumulated tehnal exertse would sgnfantly redue extraton osts at the enormous Prudhoe Bay ol feld n Alaska. We nvestgate the ostve features of a ror blateral merger to exlot R&D omlementartes n a game where olgoolsts omete both n roess R&D and on the rodut market. For a nontrval degree of omlementarty between frms R&D stoks, we show that a blateral merger has the followng ntutvely-aealng features ndeendently of the assumed strateg varable n market ometton re vs. uantty: a nsders beneft; b outsders are harmed; and nsders end u larger than outsders. These results ontrast sharly wth the fndngs of tradtonal models of merger to aheve market ower alone, whh are well known to be both ounterntutve and hghly senstve to the unobservable mode of rodut market ometton. Keywords: horzontal merger; R&D omlementartes; endogenous R&D; merger aradox. JEL lassfaton: L, L4, 03.

2 . Introduton A key feature of the results of R&D nvestment s ther ubl good.e. nonrval aset both wthn and aross frms: use of a new tehnology n one lant does nothng to relude ts alaton to roduton elsewhere. Indeed, the total return to an R&D nvestment s n general greater, the more wdely ts results are dssemnated aross roduton lants. The ororate struture of Brtsh Petroleum Amoo BP, the world s seond-largest ntegrated ol omany, learly reveals the roftablty gans from nformaton oolng and the role layed by ntegraton n faltatng t: BP omrses around 00 sem-autonomous busness unts, whh are enouraged to share nformaton extensvely through eer asssts.e. busness unts an all on ersonnel from other unts to hel solve oeratng roblems. More sefally, t aears that, n the real world, horzontal mergers are often drven by the oortuntes they reate va knowledge transfers between lants for the exlotaton of R&D omlementartes. The exerene of BP agan llustrates ths: a entral justfaton for the BP/Atlant Rhmond ARCO mega-merger, aroved by the Federal Trade Commsson n 000, was that by ommttng the frms to sharng ther aumulated tehnal exertse t would sgnfantly redue extraton osts at the enormous Prudhoe Bay ol feld n Alaska. 3 Although a gven frm wll be harmed f a rval aesses ts stok of roess R&D and frms R&D stoks are not erfet substtutes, jont rofts rse as the general level of margnal osts falls. Ths smle ont takes R&D stoks as gven. The mortant ssue of the mat of the soe of dssemnaton on R&D nvestment nentves s dsussed below. That BP mantans extremely lean headuarters s evdene of the oeratonal dsreton granted to ts onsttuent busness unts. See Holmström and Roberts 998,. 9 for more on the BP ase and other relevant examles. 3 BP and ARCO ersuasvely argued that over twenty years of ontratual exerments to gan the benefts of nformaton oolng had faled see Bulow and Sharo, 00; Farrell and Sharo, 00, The Farrell/ Sharo artle gves other examles of mergers to exlot R&D omlementartes.

3 Usng a framework of multdmensonal.e. two-stage ometton where frms omete both n roess R&D and on the rodut market, ths aer analyses the use of horzontal mergers to exlot R&D omlementartes between frms. A key ontrbuton s that the sze of the synergy beneft of merger, aused by the exstene of R&D omlementartes, s endogenously determned. We are rmarly onerned wth the ondtons under whh suh arrangements are roftable for the artatng nsde frms and wth the mlatons of mergers motvated by the exstene of R&D omlementartes for the relatve oston of non-artatng outsde frms. Deste the aarently wdesread use of horzontal merger to exlot omlementartes n frms R&D stoks, the formal lterature on R&D oolng has foused almost exlusvely on the vehle of researh jont ventures RJVs whereby frms dede to share tehnologal knowledge whle, n rnle, ontnung to omete aganst eah other n the rodut market. 4 In addton to ther emral relevane, we justfy our fous on horzontal mergers beause, n many ases, RJVs may rove mossble to form, forng frms to searh for other methods of exlotng R&D omlementartes. For examle, frms artatng n an RJV learly have a strong nentve not to reveal all ther R&D results to ther artners. If an RJV s to aheve dfferent results from thoroughgong non-ooeratve behavor, ths roblem must be Moreover, t s well establshed n the emral lterature that synerges from ombnng frms R&D stoks an motvate merger Andrade, Mthell and Stafford, Usng a two-stage model of roess R&D followed by rodut market nteraton, Kamen, Muller and Zang 99 rovde a thorough analyss of RJVs, ontrastng the ases of RJV ometton frms ool R&D results but behave non-ooeratvely at both stages and RJV artelzaton oolng of R&D results wth ooeratve determnaton of R&D nvestment but ometton n the subseuent market stage. Suzumura 99 ontans a losely related analyss. D Asremont and Jauemn 988 do allow for merger.e. artatng frms ool R&D results and ooerate n both stages of the game; however, as wth Kamen/ Muller/ Zang, all frms n the ndustry two, n ther ase are assumed to artate, whh makes an assessment of the relatve oston of nsders versus outsders, a key ontrbuton of our analyss, mossble. For analyses of ometton n R&D followed by olluson n oututs, see Fershtman and Gandal 994 and Brod and Shvakumar 999.

4 overome. In rnle, a soluton s for the artants to ontrat out all R&D atvtes to a thrd arty; however, n rate, ontrats are lkely to be rohbtvely ostly to establsh and enfore. In suh ases, horzontal merger, whh reommts artatng frms to sharng all ther R&D oututs wth all other nsders jont roft maxmzaton, wll be an attratve alternatve to formng an RJV. 5, 6 We model horzontal mergers motvated by the exlotaton of R&D omlementartes n a two-stage game layed by olgoolst frms, eah rodung a substtute brand of a dfferentated good. In the frst stage the frms hoose how muh to nvest n roess R&D, and n the seond stage they omete on the rodut market. We solve the game bakwards to solate ts sub-game erfet Nash eulbrum n ure strateges. Asde from our modelng of R&D omlementartes, our set-u s standard to allow for straghtforward omarsons wth the exstng formal lterature. 7 The margnal ost of a frm that s not merged wth another deends only on ts own R&D nvestment.e. there are no nter-frm sllovers. However, a merged frm s margnal ost s dereasng both n ts own R&D level and at a slower rate n the ombned R&D sendng of other nsders. We restrt attenton to a sngle blateral merger, where two 5 See Hernán, Marín and Sots 003 for an emral assessment of determnants of frm artaton n RJVs. Note also that asymmetr RJVs e.g. where one artant undertakes the bulk of R&D atvty are lkely to be muh more dffult to establsh than symmetr ones dental artants beause fnanal transfers to the R&D-ntensve nsder from ts artners wll be neessary to ensure that all frms beneft from the RJV. The dlemma s that the artners wll be unwllng to ontrbute muh towards the nnovatng frm s R&D budget untl the ualty of ts new R&D results has been verfed; however, verfaton may reure dstrbutng the new tehnology amongst nsders for free. Reeated nteratons and ontratng may hel to allevate ths roblem, but n many ases ntegraton wll rove a more straghtforward alternatve. 6 It should be noted that the RJV/ merger omarson s only lkely to be nterestng under Cournot ometton, sne mergers are generally roftably under Bertrand for market ower reasons alone. 7 Margnal osts are onstant and dereasng n R&D at a onstant rate. The margnal ost of R&D s strtly nreasng. The system of demand funtons s symmetr and lnear. We allow for both Cournot and Bertrand ometton n stage two. 3

5 frms o-oerate n both the R&D and roduton stages. 8 Therefore, R&D omlementartes are refleted n the fat that a merged frm s effetve R&D stok s a weghted sum of ts own R&D sendng and that of the other nsder; ths s the synergy effet of merger. The weght on the merger artner s R&D sendng.e. the degree of R&D omlementarty deends on the tehnal loseness between brands. If roduton roesses are ute smlar e.g. beause brands are only dstngushed by some non-tehnal attrbute suh as olor, then we would exet a merged frm s effetve R&D stok to be aroxmately the unweghted sum of both nsders sendng on R&D. On the other hand, f roduton roesses are ute heterogeneous e.g. beause ute dfferent mahnery s used to rodue dfferent brands, then we would exet an nsder s effetve R&D stok aroxmately to eual ts own R&D sendng. 9 Our results stem from a omarson between the game s sub-game erfet Nash eulbra wth and wthout a blateral merger. They an be nterreted n relaton to the fndngs of the anonal analyses of horzontal mergers under Cournot ometton Salant, Swtzer and Reynolds, 983 and Bertrand ometton Denekere and Davdson, 985, both of whh took frms margnal osts as dental and exogenously gven. Moreover, a key ontrbuton of our modelng aroah, the novelty of whh s that mergers affet ometton n two dmensons.e. n R&D and on the rodut 8 Ths an be justfed by assumng, for examle, that the sunk ost of admnsterng a merger s strtly onvex and nreasng n the number of artatng frms. 9 Two mlt assumtons should be reognzed. Frst, we assume that the smlarty between frms R&D atvtes s ndeendent of that between ther roduton roesses.e. the tehnal loseness between brands. If frms wth dental roduton roesses undertook dental R&D atvtes wth dental results, then there would obvously be no advantage from oolng R&D results. Ths follows the Kamen/ Muller/ Zang 99,. 98 assumton that R&D atvty nvolves tral and error t s a multdmensonal heurst rather than a one-dmensonal algorthm roess wth eah frm ursung several avenues of researh smultaneously, only some of whh ay off. Seond, we assume that the dfferentaton between brands n the eyes of onsumers s ndeendent of the tehnal loseness between brands roduton roesses: seemngly dental brands may be rodued very dfferently. 4

6 market, s that t ermts a soluton to the well-known merger aradox. The merger aradox refers to the dffulty of onstrutng a model of horzontal mergers where a nsders generally gan; b outsders generally lose; and nsders are larger n sales terms than outsders n the ost-merger eulbrum. We regard a, b and as ntutvely-aealng roertes that any reasonable model of horzontal mergers should be aable of satsfyng. Proertes a and b seem desrable beause, n realty, mergers are both freuently roosed by frms and nvarably ferely oosed by outsders. We advoate beause, as Perry and Porter 985,. 9 argue, t seems rght that a merger, by oolng the nsders assets, should make the ntegrated frm larger than ts rvals. Unfortunately, when frms omete n only one dmenson.e. on the rodut market, models of horzontal mergers under both Cournot and Bertrand ometton have been unable smultaneously to satsfy rtera a, b and. 0 In artular, whle nsders generally lose from merger under Cournot ometton, under Bertrand they generally gan. These onverse roftablty effets for nsders are artularly troublng beause they hnge on an unobservable haraterst of the market, the strateg varable n ometton. To gan an ntutve feelng for our results on the roftablty effets of merger, onsder how a merger affets the market eulbrum n stage two eters arbus. For a gven dstrbuton of R&D sendng aross brands, a merger exerts two oosng nfluenes on the nsders behavor n market ometton. Frst, the tradtonal market 0 That reresents the reord rather euhemstally. In fat, under Cournot ometton Salant, Swtzer and Reynolds, 983 a, b and all fal, whereas under Bertrand ometton Denekere and Davdson, 985 only a holds. For a very dfferent aroah to the merger aradox that also reles on nformaton sharng wthn the merged frm, see Creane and Davdson 004 and Huk, Conrad and Mueller 004. For alternatve analyses of merger where margnal osts are endogenously determned although by ute dfferent mehansms to that adoted here, see Perry and Porter 985 and Gowrsankaran

7 ower or strateg effet reflets the nsders attemts to move towards the monooly soluton. As s well known, under both Cournot and Bertrand ometton, the market ower effet makes the nsders less aggressve. The seond effet of merger on market ometton, whh works n the ooste dreton, s the R&D oolng effet. Under both Cournot and Bertrand behavour, ths makes the nsders more aggressve as they exlot R&D omlementartes between gven R&D stoks and ther margnal osts fall. Whh of the two effets domnates, and the onseuent net dreton of shft n the nsders best rely funtons, s determned by the degree of tehnal loseness between brands.e. R&D omlementarty, whh governs the strength of the R&D oolng effet relatve to the market ower effet. In our lnear model, uanttes are strateg substtutes under Cournot ometton but res are strateg omlements under Bertrand. Therefore, under Bertrand ometton, the R&D oolng effet benefts nsders but harms outsders, whereas the market ower effet benefts both tyes. Beause both effets beneft nsders under Bertrand ometton, the only ueston s whether outsders gan or lose from merger. For low levels of tehnal loseness R&D omlementarty, the market ower effet domnates, so all frms gan from merger; we label ths the Pareto Gan ase. As brands beome tehnally loser.e. the degree of R&D omlementarty rses, the R&D oolng effet strengthens relatve to the market ower effet. Put dfferently, the market ower effet shfts the nsders ombned best rely funton nwards n uantty sae Cournot, but t shfts eah nsder s best rely funton uwards n re sae Bertrand. Both shfts reflet nsders wshes to move u ther brand demand funtons towards the monooly soluton. 6

8 Eventually, for suffently tehnally lose brands, the R&D oolng effet domnates, so nsders gan from merger but outsders lose; we label ths the Intutve Outome. The roftablty effets of merger are more omlex under Cournot ometton beause the nsders do not always gan. As wth Bertrand, the R&D oolng effet benefts nsders but harms outsders under Cournot ometton. However, the market ower effet now works n resely the ooste dreton, harmng nsders but beneftng outsders. The olar ases, where one of the two effets of merger on market eulbrum obvously domnates, are lear: for low levels of tehnal loseness, the market ower effet domnates and nsders lose from merger but outsders gan, the Salant, Swtzer and Reynolds ase; and for suffently tehnally lose brands, the R&D oolng effet domnates and nsders gan from merger but outsders lose, the Intutve Outome agan. In between, for ntermedate levels of tehnal loseness R&D omlementarty, the market ower and R&D oolng effets are of roughly eual strength, and all frms gan from merger, the Pareto Gan outome reeated. 3 Our entral result on the roftablty effets of merger s that, for suffently tehnally lose brands, blateral mergers n multdmensonal ometton beneft the nsders but harm outsders ndeendently of the strateg varable n market ometton. We refer to a ost-merger eulbrum wth these features as the Intutve Outome beause t fulfls reasonable rtera a and b ntrodued above. The largeness of the areas n both strategy and arameter sae over whh our model generates the Intutve Moreover, we show that the rtal degree of tehnal loseness that makes outsders ndfferent to a merger s very small under Bertrand ometton, so the Intutve Outome ours for most of arameter sae. 3 Under Cournot ometton, there are two rtal levels of tehnal loseness to onsder, one to make nsders ndfferent to merger and a seond for outsders. It s mossble for them to be ranked suh that, for some arameters, all frms lose from merger. Intutvely, sne merger redues ometton n the ndustry, average frm rofts rse. 7

9 Outome beomes a artularly valuable feature when ontrasted wth the roftablty effets generated by tradtonal models of merger to aheve market ower alone, whh are well known to be both ounterntutve and hghly senstve to the unobservable mode of rodut market ometton. Our results on the mlatons of merger for frm sze an be understood by onsderng the determnaton of roess R&D levels n stage one. The roftablty of extra R&D nvestment deends on the sze of the resultng roess nnovaton and on the level of outut to whh that nnovaton wll be aled n roduton. A merger does not alter the relatonsh between R&D nvestment and ost reduton for outsders, but t enhanes the effeny of R&D nvestment for nsders beause both own-brand and merger-artner margnal osts are redued. The effet of merger on frm oututs follows from the dsusson above of roftablty effets. In sales volume terms, the greater the degree of tehnal loseness between brands, the larger wll be nsders relatve to outsders n rodut market eulbrum beause the stronger wll be the R&D oolng effet relatve to the market ower effet. 4 Ths feature s ndeendent of the hoe between Cournot and Bertrand ometton. 5 These outut effets of merger mean that an nsder s R&D nentve margnal return s nreasng n the degree of tehnal loseness between brands, whle that for outsders s dereasng. 6 Therefore, for nsde brands, the volumes of both roess R&D and outut are nreasng n tehnal 4 Moreover, assume that R&D er brand s at ts symmetr eulbrum level wth no merger. Then, relatve to the no-merger eulbrum oututs, a merger dereases nreases nsders roduton but nreases dereases that of outsders for low hgh degrees of tehnal loseness. 5 In Cournot ometton nreased tehnal loseness rases nsder outut and uts outsder outut strateg substtuton, whle under Bertrand t redues the relatve re of nsders.e. all res fall due to strateg omlementarty but outsders do not resond euroortonately to nsders re uts. 6 Of ourse, merger also enhanes the nsders R&D nentves by ermttng the ubl good haraterst of R&D outut to be exloted. 8

10 loseness, whereas both are dereasng n tehnal loseness for outsde brands. 7 Ths gves our fnal key result, the ondtons under whh reasonable rteron are satsfed: ndeendently of the strateg varable n market ometton, nsders are larger than outsders n ost-merger eulbrum for suffently tehnally lose brands. Furthermore, ombnng ths result wth our fndngs on the roftablty effets of merger, our modelng struture s aable smultaneously of fulfllng all our reasonable rtera.e. roftable mergers; harmed outsders; and nsders larger than outsders under both Cournot and Bertrand ometton when brands are suffently tehnally lose. The remander of the aer s organzed as follows. In the next two setons we solve for the eulbrum outomes of multdmensonal ometton under, suessvely, Cournot and Bertrand ometton n the market stage. We ay artular attenton to atalogung the roftablty effets of merger by omarng the no-merger and ostmerger eulbra. Fnally, seton 4 onludes.. Quantty Cometton We onsder a market oulated by N ntally dental frms that omete n two-stages of ometton. In the frst stage, they nvest n R&D whh lowers ther margnal ost of roduton. In the seond stage, one margnal osts have been determned and revealed, they omete n uanttes. We frst alulate the eulbrum 7 We show that, for a non-trval degree of tehnal loseness between brands, the R&D oolng effet and an nreased level of R&D nvestment work together to nrease the sze outut volume of nsders followng merger. Moreover, followng merger, both nsde and outsde frms otmally hoose the symmetr eulbrum no-merger R&D level for nteror degrees of tehnal loseness. 9

11 outome under the assumton that the frms reman ndeendent and then omare ths wth the outome generated when frms and merge before stage ometton begns. We assume that market demand s lnear wth = A where and denote frm s re and outut, resetvely, and j j. Wthout nvestment n R&D, we assume that eah frm would fae a onstant margnal ost of. Furthermore, n the absene of a merger, any frm that sends x on R&D an lower ts margnal ost to x, so that there are no nter-frm sllovers from R&D. Frm 's total ost of R&D s assumed to be / x γ. If a merger between frms and takes lae, then there are two mlatons. Frst, the merged frms hoose R&D and outut levels to maxmze ther jont rofts. Seond, the merged frms share the results of ther researh and ths generates wthn-frm sllover effets. In artular, we assume that the frms margnal osts beome x θx = and = x θx where θ measures the degree of tehnal loseness between brands, whh determnes the magntude of wthn-frm sllovers followng merger. The bas dea that we are tryng to ature s that the blateral merger enables the ntegrated frm to exlot the tehnal loseness between brands by alyng R&D onduted on one brand to the roduton roess of the other brand t owns. The magntude of θ therefore deends uon the tehnal loseness of the brands offered by the two frms. For examle, f the roduton roesses are ute heterogeneous e.g., dfferent mahnery s used to rodue the dfferent brands then we would exet θ to be ute small. On the other hand, f the roduton roesses are ute smlar so that 0

12 the brands are dstngushed by some non-tehnal attrbute suh as olor, then we would exet R&D atvty to generate onsderable wthn-frm sllovers. We begn by desrbng the Sub-game Perfet Nash Eulbrum SPNE n the absene of the merger. To smlfy the exoston that follows, we ntrodue the followng notaton: Q ; C ; 0 N ; and 0. Then, n the seond stage of the game, frm s goal s to hoose outut,, to maxmze rofts from sales wth R&D exendtures held fxed; or, max A j j wth = x and x fxed. Straghtforward alulatons yeld the followng symmetr stage two eulbrum outomes A C 0 3 = 0 4 Q AN C 0 Turn next to stage one n whh the frms ndeendently hoose ther R&D levels. For frm, the goal s to hoose x to maxmze rofts; or, 5 max A j j γ x x where and j are gven n 3. Carryng out the maxmzaton and alyng symmetry yelds the followng eulbrum outome: 0 A 6 x = γ 0 0

13 Profts an then be obtaned by substtutng 6 nto 3 and then usng the fat that, at Cournot eulbrum, 7 5. x γ π =. For 3, 6 and 7 to reresent an eulbrum, t must be the ase that 0 0 > γ and > γ A. The frst neualty ensures that the frms seond-order-ondtons hold and the seond neualty ensures that 6 s omatble wth non-negatve margnal osts. Now, suose that frms and merge ror to the stage ometton. Then n stage, the outsders stll solve whle the nsders hoose and to solve 8 > > max j j j j A A Carryng out the maxmzaton and solvng the frst-order ondtons yelds the followng stage outomes = C A 0.5 > = C A.5 = C A N Q Turn next to the frst stage n whh the frms omete n R&D. Sne R&D now reates sllovers for the nsders, the margnal osts for the frms beome ; x x θ = ; x x θ = and > = x

14 Eah outsder hooses x to maxmze 7 wth the oututs gven n 9 and 0 and the osts gven by ; whereas the nsders hoose x and x to maxmze jont rofts, or 3 π π =.5γ x x If we use x m to denote the R&D hoe of eah frm nvolved n the merger and use x o to denote the hoe by a tyal outsder, then arryng out the maxmzaton, alyng symmetry for nsders x m x = x and outsders xo x for all >, and solvng yelds 4 x m a = 3 b ab A a b 3 3 a b 5 x o = a A a 3 a x m where we have defned a ; a a ; a γ a ; b θ 0 θ 3 ; b θ N 0 ; and b 3 γ θ 0. Eulbrum rofts for the outsders an then be alulated by substtutng 0,, 4, and 5 nto 7. Smlarly, eulbrum rofts for the merged frm an be obtaned form 9 and -5. Our results are summarzed n Fgure where the arameter sae s dvded nto 3 regons. The degree of rodut dfferentaton s measured on the horzontal axs, wth a value of zero reresentng ndeendent goods and a value of one reresentng erfet substtutablty aross brands. The level of merger-ndued R&D sllovers s measured on the vertal axs, wth hgher values ndatng stronger omlementartes n R&D aross the merged frm s brands. The urve labeled θ M shows ombnatons of and θ for whh the nsders earn the same rofts wth and wthout the merger. Thus, 3

15 below ths urve the R&D sllovers are not strong enough to generate gans for the nsders. The urve labeled θ O shows ombnatons of and θ for whh the outsders earn the same rofts wth and wthout the merger. Above ths urve, the R&D sllovers for the merged frm are strong enough that the outsders are harmed by the merger. It follows that n the regon labeled SRR, we get the standard Salant, Swtzer and Reynolds 983 result: the nsders are harmed by the merger whle the outsders gan. In the regon labeled PG for Pareto Gan, both the nsders and the outsders beneft from the merger. 8 Fnally, n the regon labeled IO for Intutve Outome, we fnd that the nsders gan from the merger whle the outsders are harmed. The fores that generate our results an be exlaned wth the ad of Fgure, whh shows the aggregate outut rodued by the nsders Q and the outsders Q n the seond stage of the game. Of ourse, sne uanttes are strateg substtutes, these values vary nversely wth eah other. The sold blak lnes reresent best-resonse oututs n the absene of the merger, so that the no-merger Nash eulbrum s reresented by ther nterseton. We begn by fousng on the nsders outut hoe n the seond stage of ometton, holdng brand R&D levels fxed at the eulbrum nomerger level. When the nsders merge, t s n ther olletve nterest to rodue less outut than they would n the absene of the merger n order to ush re u towards ts ollusve level thus, ther total outut would be lower than t would be wthout merger. Ths hange n behavor s refleted by the downward shft of the * m * o * Qm urve to the dashed 8 Ths regon ould be sub-dvded based on whether the nsders or the outsders gan more. In the lower orton of the PG regon, the outsders gan more; yeldng an outome ualtatvely dental to that obtaned n Denekere and Davdson s 985 study of mergers wth re ometton. Thus, wth twodmensonal ometton, t s ossble to get the Denekere-Davdson outome when frms omete n uanttes. In the uer-orton of the PG regon, t s the nsders that beneft more from the merger than the outsders. 4

16 red lne n Fgure. Sne best-rely funtons are downward slong under uanttyometton, ths shft results n hgher aggregate outut by the outsders. As a result, the merger leaves the nsders wth a lower market share and a slghtly hgher re; but, beause the nrease n re s damened by the exanson of the outsders, the nsders tyally lose. On the other hand, the outsders wnd u sellng more outut at a hgher re, so that they always gan. Ths s the tradtonal market ower effet of a horzontal merger that drves the results n Salant, Swtzer and Reynolds 983 the merger auses the nsders to rodue less. Ths usually harms the nsders whle beneftng the outsders. In addton to the market ower effet, there s another fore at work that alters the outome n the seond stage. Sne the merger generates R&D sllovers for the nsders, f we hold the frms R&D nvestments at ther no-merger levels, then the merger lowers the margnal osts of the nsders as the nsders R&D stoks are ooled wthn the merged frm. Ths shfts u ther best rely funton toward the blue dashed lne n Fgure, tendng to nrease nsder outut but to ut that by outsders. We refer to ths hange n behavor due to R&D oolng by the nsders as the R&D oolng effet. Whh of the market ower and R&D oolng effets domnates, and the onseuent net dreton of shft n the nsders best rely funton, s determned by the degree of tehnal loseness between brands θ, whh governs the relatve strength of the R&D oolng effet. Now, turn to the frst stage of ometton. The mat of the merger on R&D sendng by the nsders s not obvous. The roftablty of extra R&D nvestment deends both on the sze of the resultng roess nnovaton and on the level of outut to 5

17 whh that nnovaton wll be aled n roduton. On the one hand, sne the merger reates sllovers n R&D for the nsders.e. a larger roess nnovaton, there s an nentve for the nsders to send more on R&D followng the merger than they would n ts absene. Ths s the synergy effet of merger on R&D nvestment, whh results from the oolng of the nsders R&D stoks followng merger. On the other hand, for a gven level of brand R&D sendng, the mat of merger on nsders outut s ambguous and deends uon whh of the market ower and R&D oolng effets domnates n stage. When merger-ndued R&D sllovers are very weak, merger works to redue the outut of nsde brands.e. the market ower effet domnates the R&D oolng effet n stage, and ths effet tself outweghs the weak synergy effet so that the margnal return to R&D for nsders falls and merger leads to a reduton n R&D sendng by the nsders. As the level of merger-ndued R&D sllovers rses, the market ower effet n stage weakens relatve to the R&D oolng effet so that nsders outut for gven R&D nvestments tends to rse followng merger. By tself, exandng outut makes extra R&D nvestment roftable, and ths tendeny s renfored by a strengthenng of the synergy effet as θ rses. Therefore, only modest sllovers are reured for merger to rase the margnal return to nsders of R&D nvestment, mlyng that for most values of θ, the merger leads the nsders to send more on R&D than they would otherwse. Inreased R&D nvestment leads to lower margnal osts for all nsders and renfores the R&D oolng effet n stage, shftng the nsders best rely funton n Fgure u to the dashed blue lne. 9 We refer to hanges n behavor due to hanges n the frst stage of ometton as the R&D nvestment effet. Note that, as long as merger ermts a 9 Moreover, even f the nsders resond to the merger by redung R&D exendtures, ther margnal osts are stll lkely to be redued by the merger-ndued R&D sllovers. 6

18 non-trval degree of R&D sllovers, the R&D oolng and R&D nvestment effets work n the same dreton they both make the nsders more aggressve and shft u ther ombned best rely funton. For future referene, we refer to the ombnaton of these two as the total R&D effet of the merger. If the R&D effet were the only mat of the merger, the nsders would end u rodung more, the outsders would end u rodung less, the nsders would gan, and the outsders would lose. It follows that the R&D effet works n the ooste dreton to the tradtonal market ower effet t auses the nsders aggregate outut to nrease. Ths benefts the nsders whle harmng the outsders. When the goods are almost ndeendent.e., when s low the market ower effet of merger s weak and t only takes a low level of R&D sllovers for the R&D effet to domnate. When ths ours, we have the Intutve Outome. As nreases.e., the goods beome more smlar, the market ower effet beomes more mortant and a hgher value of θ s reured to generate the Intutve Outome. When R&D sllovers are weak.e., θ s low, then the market ower effet domnates for even low values of and we have the standard SSR outome. However, as θ nreases, the R&D effet beomes more mortant and a hgher value of s then needed for the market ower effet to domnate. For ntermedate values of θ and, the two effets roughly balane out and all frms beneft from the merger. In ths ase, the outsders beneft beause the market ower effet makes the nsders olletvely less aggressve when hoosng ther outut levels; whereas the nsders beneft beause the R&D effet results n greater R&D sendng and lower margnal osts of roduton. 7

19 The urves n Fgure orresond to the ase n whh there are 0 frms n the ndustry. If there are fewer frms, then, holdng all else eual, a blateral merger generates larger ostve benefts for the outsders, mlyng that strong R&D sllovers for the nsders are reured to make the outsders ndfferent towards the merger. Thus, as N falls, the θ O urve shfts u. As for the nsders, as N falls, a blateral merger s more lkely to be roftable solely for market ower reasons there are fewer outsders to nrease outut n resonse to the merger. Thus, as N falls, the θ M urve shfts to the rght. As a result, for low values of N, the PG regon s ute large. Ths regon shrnks as N nreases, wth the SSR and IO regons beomng larger. In multdmensonal ometton where rodut market nteraton s Cournot, we have shown that some frms n an ndustry must beneft from a blateral merger. The dentty of the wnners outsders only SSR, all frms PG, or nsders only IO deends on the degree of omlementarty between the nsders R&D stoks, θ. The greater the degree of R&D omlementarty that merger allows the nsders to exlot, the more lkely t s that a merger wll toughen ometton on the rodut market deste ts market ower effets and, onseuently, beneft nsders but harm outsders. Ths s our Intutve Outome beause, n realty, we observe that mergers are both freuently roosed by frms and nvarably ferely oosed by outsders. Moreover, when the degree of R&D omlementarty s suffently hgh, the nsders end u larger n roduton volume terms than the outsders after a merger. Ths ntutvely-aealng sze advantage, whh ontrasts wth the sze dsadvantage tradtonally redted e.g. by SSR, ours beause a merger enhanes the effeny of the nsders R&D stoks n delverng margnal ost redutons and, onseuently, enourages the nsders to nvest 8

20 more n R&D. In the next seton we examne the robustness of these fndngs by assumng nstead that frms omete n res on the rodut market. 3. Pre Cometton To faltate omarson wth the lterature, we adot the same demand urve used by Denekere and Davdson 985 n ther study of mergers wth re ometton. Thus, demand s gven by 6 = A λ where N j j denotes he average re harged n the ndustry. All other assumtons are dental to those made n our analyss of uantty ometton. For λ notatonal onvenene, we defne the followng new terms: z ; λ z; and N N j j, so that s the average margnal ost n the ndustry. We begn by analyzng the seond stage of ometton when the frms reman ndeendent. Wth the margnal osts already determned, frm 's roft from sales wth R&D exendtures held fxed s gven by 7 π = [ A λ ] The frm s frst-order ondton s then 8 A λ λ = 0 Summng 8 over allows us to solve for the average re n the ndustry n the Bertrand eulbrum. We obtan 9

21 9 A = We an now use 8 and 9 to solve for frm 's eulbrum re; however, for later use, t s more onvenent to reort the eulbrum dfferene between re and margnal ost. We obtan 0 λ A λ = λ λ. Turn next to the R&D stage of ometton when the frms are all ndeendent. We begn by notng that the 8, the frm s frst-order ondton n the re stage, an be wrtten as =. It follows that we an wrte frm 's total rofts as π = γx.5 where = x. Dfferentatng wth reset to x yelds the followng frst-order ondton = γx x We an now make use of 0, aly symmetry and solve to obtan the eulbrum level of R&D exendture for eah frm. We obtan 3 λ A x =. γ λ λ Eulbrum rofts an then be obtaned by substtutng 0 and 3 nto. We now turn to the ase n whh frms and merge before R&D exendtures are hosen. Sne the ualtatve nature of the outsders rng deson remans the same, ther frst-order ondton s stll gven by 8. However, the nsders now make 0

22 ther seond-stage rng desons wth jont rofts n mnd. Thus, ther frst-order ondtons beome 4 0 = z z A λ λ λ 5 0 = z z A λ λ λ Summng the frst-order ondtons for all of the frms allows us to solve for the average ndustry re n the ost-merger re game. We obtan 6.5 z N z A N z = λ. Substtuton of 6 nto 8 and 4-5 then yelds the eulbrum res for the outsders and the nsders n the ost-merger re game 7 ] [.5 z z z A = λ λ 8 ] [.5 ] [ z z z A j j = λ λ λ λ for, j Fnally, we turn to the ost-merger R&D ometton. For the outsders, the frstorder ondton s stll gven by, although we know must use 8 for the eulbrum re as oosed to e. 0. For the nsders, t s straghtforward to show that ther frstorder ondtons from the re stage mly that z = and z =. Ths mles that the merged frm s rofts an be wrtten as 9.5 ] [ x x z = γ π π wth x x θ = and x x θ =. Dfferentatng 9 wth reset to x yelds the followng frst-order ondton

23 30 [ z ] [ z ] = γx x x Imosng symmetry, ths redues to [ ] 3 z = γx x If we use x m to denote R&D exendtures by a tyal nsder and use x o to denote the R&D exendtures for a tyal outsder, then we an use 7, 8, the defntons of j, and, and symmetry to rewrte the frst-order ondtons n and 3 n a more useful fashon. We obtan 3 λ A z θ [ z λ] x m = δ o xo 33 λ A z N x o = δ m xm γ λ [ z ] where ψ ; δ o ψ { z N λ[ z ]}; λ[ z ] z γ [ z ] and δ m θ [ z ]. Euatons 3 and z θ [ z ] 33 an be solved for the eulbrum values of xm and x o, whh an then be used wth 7, 8 and the defntons of osts to alulate the rofts of the outsders as gven n e. and the merged frm as gven n e. 9. Our results for the re game are summarzed n Fgure 3, whh s dvded nto two regons. Fgure 3 has one less regon than Fgure beause wth re ometton, the nsders always beneft from the merger. Conseuently, there s no θ M λ urve n Fgure 3. As wth Fgure, the λ urve shows ombnatons of λ and θ for whh the θ O outsders earn the same rofts wth and wthout the merger. For hgher values of θ, the outsders are harmed by the merger. It follows that, as wth uantty ometton, n the

24 PG regon all frms gan from the merger whle n the IO regon the nsders gan from the merger whle the outsders are harmed. The most surrsng result from Fgure 3 s that the PG regon s ute small, so that for almost all arameter values we get the ntutve outome. And, although Fgure 3 s drawn for the ase n whh there are 0 frms n the ndustry, ths feature remans even when there are only 3 frms n the ndustry. Thus, wth only weak R&D sllovers a model n whh frms omete n roess-orented R&D followed by Bertrand ometton yelds redtons about horzontal mergers that aord well wth our bas ntuton. The fores that generate our results an be exlaned wth the ad of Fgure 4, whh shows the re harged by a tyal nsder P and a tyal outsder P n the seond stage of the game. Of ourse, sne res are strateg omlements, these values vary dretly wth eah other. The sold blak lnes reresent these roftmaxmzng values n the absene of the merger, so that the no-merger Nash eulbrum s reresented by ther nterseton. We begn by fousng on the nsders re deson n the seond stage of ometton, holdng brand R&D levels fxed at the no-merger eulbrum level. When the nsders merge, t s n ther olletve nterest to nrease ther res toward the ollusve level. Thus, the merger leads the nsders to harge hgher res than they would n the absene of the merger. Ths hange n behavor s refleted by the uward * m * o shft of the * Pm urve to the dashed red lne n Fgure. Sne best-rely funtons are uward slong under re-ometton, ths shft results n hgher res for the outsders as well. As a result, the merger auses all frms to nrease ther res, wth the nsders res nreasng by a greater amount than the outsders for stablty. All frms 3

25 beneft from the merger, but the outsders beneft by a greater amount. Ths s the market ower effet of a horzontal merger that drves the results n Denekere and Davdson 985 the merger auses the nsders to harge hgher res and ths benefts both the nsders and the outsders. In addton to the market ower effet, there s another fore at work that alters the outome n the seond stage. Sne the merger generates R&D sllovers for the nsders, f we hold the frms R&D nvestments at ther no-merger levels, then the merger lowers the margnal osts for the nsders. Ths shfts down ther best rely funtons toward the blue dashed lne n Fgure. As wth Cournot ometton, we refer to ths hange n behavor due to R&D oolng by the nsders as the R&D oolng effet. Now, turn to the frst stage of ometton. The ualtatve mat of the merger on R&D sendng s the same as t s under uantty ometton. On the one hand, there s a synergy effet: beause the merger reates sllovers n R&D for the nsders, there s an nentve for the nsders to send more on R&D followng the merger than they would n ts absene. On the other hand, the mat of merger on the sze of the outut base over whh nsders roess nnovatons wll be sread s, as wth uantty ometton, ambguous. As wth uantty ometton, when merger-ndued sllovers are very weak, the synergy effet s domnated by the ontraton n nsders oututs, and the merger leads to a reduton n R&D sendng by the nsders. However, only modest merger-ndued sllovers are reured for merger to rase the margnal return to R&D for nsders, mlyng that for most values of θ, the merger leads the nsders to send more on R&D than they would otherwse. 0 Ths leads to lower margnal osts for all nsders 0 As under Cournot ometton, nreases n θ strengthen the synergy effet of merger on R&D nvestment and nrease for any gven level of R&D an nsder s outut level. 4

26 and shfts down ther best rely funtons for the seond stage of ometton. As a result, ther res fall, as refleted by the shft down to the dashed blue lne n Fgure 4. Ths s the same R&D nvestment effet that we enountered under uantty ometton. As before, the R&D nvestment effet smly renfores the shft n the best rely funton aused by the R&D oolng effet. As a result, we have an overall R&D effet whh auses the nsders to beome more aggressve n the seond stage of ometton. If the overall R&D effet were the only mat of the merger, all frms would end u hargng lower res, the nsders would gan from the reduton n osts whle the outsders would lose. It follows that the overall R&D effet works n the ooste dreton to the market ower effet t auses the nsders res to fall. Ths benefts the nsders whle harmng the outsders. As Fgure 3 learly ndates, t takes only weak merger-ndued R&D sllovers for the overall R&D effet to domnate the market ower effet so that for almost all arameter values we obtan the Intutve Outome. As wth uantty ometton, the level of sllovers reured for ths nreases n λ, sne the market ower effet s stronger when the goods are more substtutable. In multdmensonal ometton where rodut market nteraton s Bertrand, we have shown that nsde frms always beneft from a blateral merger. Whether outsders gan PG or lose IO deends on the degree of omlementarty between the nsders R&D stoks, θ. For a non-trval degree of R&D omlementarty, we generate ntutvely-aealng results under Bertrand ometton: a nsders gan from merger; b outsders lose; and nsders end u larger than outsders n roduton volume As noted n footnote 9, even f the nsders resond to the merger by redung R&D exendtures, ther margnal osts are stll lkely to be redued by the merger-ndued R&D sllovers. 5

27 terms. The toughenng of rodut market ometton aused by the merger-ndued exlotaton of R&D omlementartes aounts for a and b, and t ontrbutes together wth the synergy effet of merger to. Moreover, a omarson of our Cournot and Bertrand results shows that, for a suffently large degree of R&D omlementarty, we obtan ths Intutve Outome ndeendently of the strateg varable n market ometton. Ths feature reresents a sgnfant advane on the fndngs of exstng models of merger to aheve market ower alone, whh are well known to be hghly senstve to the assumed mode of rodut market ometton. In ontrast, the strateg varable n market ometton, an unobservable haraterst of real-world rodut markets, lays no role n ths mortant ualtatve result. 4. Conluson The motvaton for our analyss was the emral rooston that horzontal mergers often aear to be motvated by a desre to exlot omlementartes between the nsders R&D stoks. The merger n 000 between BP and ARCO, whh was justfed on the grounds that the resultng oolng of tehnal knowledge would sgnfantly redue ol extraton osts, rovdes a sold examle of ths mehansm. We studed the eulbrum outomes of multdmensonal ometton, where frms omete n roess R&D and then on the rodut market, and the ostve effets of a ror blateral merger. Our modelng struture nororated two dstnt motves for merger: frst, a tradtonal market ower or strateg motve; and seond, a novel R&D oolng motve to reflet the emral drver of mergers noted above: a merged frm an aly the roess R&D onduted on one nsde brand to the roduton of the 6

28 merger-artner s brand, thereby exlotng the ubl good nature of R&D outut to generate extra roess nnovatons from gven R&D stoks. The game was solved bakwards, generatng redtons for the effets of merger on both roess R&D nvestments and rodut market atons. In artular, beause R&D nvestments are endogenously determned and merger allows R&D omlementartes to be exloted, our model an be nterreted as rovdng an aount of the sze of the synergy benefts of merger. Our most sgnfant results our whenever the degree of R&D omlementarty or tehnal loseness between brands s non-trval. In ths ase, relatve to the symmetr no-merger eulbrum, a blateral merger has the followng ostve roertes: a nsders.e. merger artants beneft; b outsders.e. nonartants are harmed; and nsders end u larger than outsders. We desrbe the onjunton of these three features as the Intutve Outome beause t aords wth our bas ntuton on the effets of merger. The mehansm behnd these results s that a non-trval degree of R&D omlementarty smultaneously enourages extra roess R&D nvestment by the nsders and, by toughenng ometton on the rodut market, dsourages R&D sendng by the outsders. Imortantly, we obtan these ntutvelyaealng results ndeendently of the strateg varable n market ometton re vs. uantty. Ths reresents a sgnfant advane on the fndngs of exstng models of merger to aheve market ower alone, whh are well known to be both extremely ounterntutve and hghly senstve to the assumed mode of rodut market ometton. In ontrast, the strateg varable n market ometton, an unobservable 7

29 haraterst of real-world rodut markets, lays no role n our entral ualtatve results. An assumton of our analyss s that merger reresents the only means of exlotng R&D omlementartes. In artular, we ruled out nter-frm ontratual methods, suh as RJVs. In many ases, ths s an arorate assumton: ontrats are often extremely ostly both to wrte and to enfore, and atalogung desred atons n all arorate states of the world s a formdably omlex task. In ths onnexon, t s nterestng to note that BP and ARCO had tred, before fnally mergng n 000, to exlot the omlementartes between ther stoks of tehnal exertse va ontratual means for over twenty years wthout suess Farrell and Sharo, 00, However, an nterestng extenson of our analyss eseally n the ase of Bertrand ometton on the rodut market would be to allow for RJVs alongsde merger and to omare the roftabltes of those two alternatve vehles for exlotng R&D omlementartes. 8

30 Referenes Andrade, G., Mthell, M. and Stafford, E. 00. New Evdene and Persetves on Mergers. Journal of Eonom Persetves 5: Brod, A. and Shvakumar, R Advantageous sem-olluson. Journal of Industral Eonoms 47: -30. Bulow, J. and Sharo, C. 00. The BP Amoo/ARCO Merger: Alaskan Crude Ol. Researh Paer No. 739, Graduate Shool of Busness, Stanford. Creane and Davdson 004. Multdvsonal Frms, Internal Cometton and the Merger Paradox. Canadan Journal of Eonoms 374: D Asremont, C. and Jauemn, A Cooeratve and Nonooeratve R&D n Duooly wth Sllovers. Ameran Eonom Revew 785: Denekere, R. and Davdson, C Inentves to Form Coaltons wth Bertrand Cometton. Rand Journal of Eonoms 64: Farrell, J. and Sharo, C. 00. Sale Eonomes and Synerges n Horzontal Merger Analyss. Anttrust Law Journal 68: Fershtman, C. and Gandal, N Dsadvantageous semolluson. Internatonal Journal of Industral Organzaton : Gowrsankaran, G A Dynam Model of Endogenous Horzontal Mergers. Rand Journal of Eonoms 30: Hernán, R., Marín, P., and Sots, G An Emral Evaluaton of the Determnants of Researh Jont Venture Formaton. Journal of Industral Eonoms 5: Holmström, B. and Roberts, J The Boundares of the Frm Revsted. Journal of Eonom Persetves 4: Huk, Konrad and Mueller 004. Proftable Horzontal Mergers Wthout Cost Advantages: The Role of Internal Organzaton, Informaton and Market Struture. Eonoma 7: Kamen, M., Muller, E., and Zang, I. 99. Researh Jont Ventures and R&D Cartels. Ameran Eonom Revew 85: Perry, M. and Porter, R Olgooly and the Inentve for Horzontal Merger. Ameran Eonom Revew 75:

31 Salant, S., Swtzer, S., and Reynolds, R Losses from Horzontal Merger: The Effets of an Exogenous Change n Industry Struture on Cournot-Nash Eulbrum. Quarterly Journal of Eonoms 98: Suzumura, K. 99. Cooeratve and Nonooeratve R&D n an Olgooly wth Sllovers. Ameran Eonom Revew 85:

32 θ IO θ O θ M PG SSR Fgure Outomes wth Quantty Cometton Notes: Forθ = θo, the outsders earn the same rofts wth and wthout the merger. For θ = θ M, the nsders earn the same rofts wth and wthout the merger. In the SSR regon we have the Salant, Swtzer and Reynolds outome; n the PG regon all frms gan from the merger so there s a Pareto Gan; and, n the IO outome we have the Intutve Outome the nsders gan from the merger whle the outsders lose. The urves n Fgure orresond to the ase n whh N = 0, γ =, A = 3, and =. 3

33 Q m Q * o Q m * Q m Q o Q o Fgure The Imat of the Merger wth Quantty Cometton Notes: The sold blak lnes show how aggregate outut by the nsders and the outsders vary wth eah other n the no-merger ase. Ther nterseton determnes the no- merger Nash outome. The shft down to the dashed red lne s due to the market ower effet of the merger. The shft u to the dashed blue lne s due to the R&D oolng effet of the merger. 3

34 θ IO λ θ o PG λ Fgure 3 Outomes wth Pre Cometton Notes: Forθ = θo, the outsders earn the same rofts wth and wthout the merger. In the PG regon all frms gan from the merger so there s a Pareto Gan; and, n the IO outome we have the Intutve Outome the nsders gan from the merger whle the outsders lose. The urves n Fgure 3 orresond to the ase n whh N = 0, γ =, A = 3, and =. 33

35 P m P * o P m * P m P o P o Fgure 4 The Imat of the Merger wth Pre Cometton Notes: The sold blak lnes show how the re of a tyal nsder and a tyal outsder vares wth eah other n the no-merger ase. Ther nterseton determnes the no- merger Nash outome. The shft u to the dashed red lne s due to the market ower effet of the merger. The shft down to the dashed blue lne s due to the R&D oolng effet of the merger. 34