Endogenous Pre-Trade Equilibria and Trade Liberalisation in Differentiated-Goods Oligopoly Models Cillian Ryan * and Toby Kendall Abstrat Tis paper provides a general model for te study of merger inentives and te effets of globalisation in oligopolisti marets. Employing a differentiated goods version of a standard Cournot model and allowing for te possibility of now-ow transfer, we study a variety of mergers were te target firm as a ontinuing maret presene post-merger. Te paper explores te partners oie between an independent division strategy tus ommitting to apaity and a oint-operation maret-onentrating strategy and identifies wi firms will ave te greatest inentive to merge. We establis onditions for te initial equilibrium, identify trigger maret-onentration levels and study te effet of unilateral and bilateral tariff anges on merger inentives. JEL Classifiation F1, F13, L11, L13 * COTACT AUTHOR, European Resear Institute and Department of Eonomis, University of Birmingam, Edgbaston, Birmingam, B15 TT, UK. Email:.ryan@bam.a.u Department of Eonomis, University of Birmingam, Edgbaston, Birmingam, B15 TT, UK. Email: t.endall@bam.a.u 18/08/006 1 14:11
1. Introdution Wit te progressive, multilateral removal of impediments to trade under te WTO, some poliy maers and on-governmental Organisations GOs in partiular ave raised onerns about te riss of agglomeration by large firms. Poliy disussions ave been partiularly onerned about te ris of inreases in maret onentration in oligopolisti industries. International trade variants of te standard Cournot maretonentration model ave tended to support tese onerns, tus promoting te sear for appropriate national or supra-national ompetition poliies to ounterat tis possible downside of globalisation. 1 Te idea tat maret onentration may be a problem also exists in te literature were governments oose trade poliies to obtain te optimal level of maret onentration from te national perspetive, toug typially tis literature neglets te firms inentives. However, wereas te bul of te earlier omogeneous goods literature onsidered mergers wi result in te target being losed down, tis paper is onerned instead wit mergers or strategi partnersips between firms produing differentiated goods, were te firm wi is taen over ontinues to ave an endogenous maret presene, eiter as a possibly revamped plant produing its differentiated produt or as an independent division, franise or liensee. 3 Examples of aquisitions wi fit tis model, were te firms differed onsiderably in size and degree of tenial effiieny, are Volswagen's purase of Soda and Seat and BMW's purase of parts of Rover, wile examples were te merging partners were seen to be loser in terms of size and effiieny would be te merger of Grand Met wit Guinness and latterly Seagram to form Diageo, Coors and Molson breweries ea wit 1 For example, Long and Vousden 1995, Falvey 1998 and Falvey and atananan 00 all employ variants of te Salant et al. 1983 model of mergers to sow tat liberalisation leads to undesirable inreases in maret onentration. In Ryman 000, for example, governments pi te number of firms and ten trade poliy to maximise welfare in trade ompetition wit a seond ountry in a tird maret. Head and Ries 1997 study mergers between similar firms, wi result in a single entity tat redues eiter fixed osts or ex ante idential marginal osts and ten onsider te appropriateness or oterwise of domesti or supranational regulation of te merger given te impliations for domesti and world welfare. In Horn and Levinson 001 governments use merger poliy to oose te optimal level of maret onentration and examine ow tis is influened by trade poliy. Horn and Levinson also provide an exellent and more extensive review of te literature and Ryan 006 identifies a wider range of te salient anteedents to tis paper. 3 Deneere and Davidson, 1985 also study differentiated goods in te ontext of a Bertrand model. 18/08/006 1 14:11
independent management HQs, and most reently Arelor and Mittal Steel. In addition, te sorts of partnersip studied ere araterise many of te 1980's mergers were orporate raiders and as-ri tobao and oil ompanies purased a wide range of disparate firms, on te grounds tat tey were bringing superior management teniques to oter industries. Tis paper employs a simple variant of te Salant et al. 1983 model were firms of varying levels of effiieny produe a differentiated good and merging firms ave te option of eiter setting output as one integrated firm or letting ea entity at as an independent division. Te partnersip may also allow tem aess to better nowow weter tat be superior tenologial, proess or management nowledge. 4 Tis model is apable of generating a wide range of equilibria were firms may sequentially oose different organisational forms and/or partners depending on te ost and feasibility of te tenology transfer and/or te degree of produt differentiation. Our framewor tus allows for a wider range of mergers tan previous wor and ene for a rier set of results. One important differene to te earlier literature is tat te most effiient largest firm will no longer always merge wit te least effiient smallest firm, but in some irumstanes will find it more profitable to merge wit te next most effiient. Additionally, we identify limits on maret size and oter variables wi mae firms swit from mergers were entities are operated as independent divisions to tose were te firm operates as a single oint operation enterprise. Tese new results allow us to explain te various mergers disussed earlier in a single framewor. Having araterised te endogenous equilibrium, te paper moves on to onsider some trade impliations of te model and demonstrate tat multilateral liberalisation is liely to redue potentially less effiient tariff-umping mergers and, at te margin, to promote more Independent-Division rater tan Joint-Operation mergers, resulting in lower pries, and inreased output, onsumer surplus and aggregate produer welfare. Tus te number of ases properly of onern to ompetition autorities may 4 Resear by MKinsey and te LSE MKinsey and Co. 005 suggests tat 70% of all effiieny gains are proess rater tan tenology driven. For tis reason we prefer te term Know-How Transfer to Tenology Transfer.
diminis rater tan grow as a onsequene of globalisation. Conversely tis paper points to mu greater merger-inentive problems in te presene of trade barriers. Given te wide range of literature related to tis topi we do not aim to provide an exaustive survey ere, but in addition to te Salant et al. 1983 tradition tere are two furter strands wi are ey to te model. Te Joint-Operation option wen tenology is transferable is similar to Perry and Porter 1985, were a merged firm grows in size relative to its ompetitors by virtue of aess to a larger apital sto and enoys redued prodution osts. 5 However, wile te Perry and Porter firm is larger, in te sense of aving more pysial apaity, overall maret output falls relative to te initial state and tere is maret onentration. Tis is one, but not te only, possibility in tis paper. Te oter important strand relevant to tis paper is in te tenology-transfer literature. 6 Marit et al. 000 study te inentive for firms to liense teir superior tenology in a multi-firm setting. Te model we employ wereby firms purase a target and operate it as an independent division employing te superior tenology, is observationally equivalent. However, in addition we allow for te possibility of sequential mergers, employ an international setting, ave differentiated goods and introdue te alternative oint-operation option. 7 Te remainder of te paper is set out as follows. Setion of te paper sets out te basi model, establises a benmar equilibrium, and sets out te merger and tenology transfer proesses. Setion 3 onsiders indiative Independent-Division and Joint-Operation mergers and onsiders te sequential merger proess in ea ase. Setion 4 examines te interation between te two ases and details a five-firm example. Setion 5 onsiders te trade impliations of te model, wile Setion 6 onludes. 5 Oter papers in tis tradition are Barros and Cabral 1994, Levinson 1996 and Head and Ries 1997. 6 Long and Vousden refer to ost transfers as te lower ost of produing output transferred to te lowost firm following te losure of te target. Here tenology transfer refers to te use by te target of te superior tenologial or management proesses of te parent. 7 In addition Kabira and Marit 003 examine te inentive effet on tenology transfers of tariff anges in a two-ountry, two-firm, omogeneous good model and te fous is on optimal tariffs and development. Tis paper studies te n-firm eterogeneous-goods ase of mergers involving tenology transfers in an international setting and onsiders te impat of anges in tariffs on te inentive of firms to merge. An alternative interpretation of tis paper is tat it is an international trade variant of 3
. Preliminaries.1. Te Model Te model is a partial-equilibrium Cournot oligopoly model wit differentiated produts and differing osts. Te superior tenology or management tenique assoiated wit te differenes in osts may be transferable between firms via te merger proess, albeit imperfetly. We assume tat tere is a small, initially fixed, number of firms,, produing a differentiated produt. 8 We assume tat firm i faes onstant marginal ost, i, tat marginal osts differ aross firms, and firms are raned su tat > if >. For simpliity we assume no fixed osts assoiated wit prodution. 9 Firms play a two-stage game as follows. In stage one a firm deides weter it wises to remain as it is, or to enter into a partnersip wit a rival. If it opts to engage in a strategi partnersip or merger ten it employs its superior management or tenial ability if appropriate. 10 In addition te partnersip ooses weter to operate two independent divisions ompeting against ea oter ea maximising its own profits, or to operate te divisions togeter, taing a oint-output, profit-maximising, deision. 11 Te profitability of ea of tese options will depend on ow oter players reat to te firm s strategy. In stage two te Baye et al. 1996 wit differentiated goods and eterogeneous firm osts, owever te general equilibrium formulation in tat paper yields intratable results in tis ontext. 8 In ommon wit te literature in tis area, we are taing te initial number of firms as fixed, altoug in equilibrium te number of surviving firms is determined endogenously. Tus, te initial may be determined via a random alloation of marginal osts and, depending on demand, a seletion of potential firms is able to produe profitably but after tat mergers are endogenous. Tus, taing te initial number of firms in te industry as given, we are foussing on te strategi and tenologial motives for a merger, franise or liensing agreement. 9 It is typially possible to generate a wider range of results by employing fixed prodution osts, owever, witout minimising teir signifiane, we want to fous on te underlying maret onentration divisionalisation issue in tis paper. We do, owever, allow later for a fixed ost arising from te merger proess. 10 For expositional onveniene, it is intuitively easier to disuss te paper in terms of a merger, owever te analysis, partiularly tat of Independent Divisions, applies equally to a franise or liensing arrangement. Te only restrition is tat one partnersip does not prelude te possibility of anoter tat is we are not onsidering exlusive lienes as in Marit et al. 000. 11 We ould also inlude ere te possibility of starting a new division equivalent to developing a new brand. In te ontext of tis model, tis option will always be dominated by taing over an operating rival sine taing over a ompeting rival redues te number of players by one. Starting a new division 4
firms, inluding any independent divisions, deide teir level of output in te maret via Cournot ompetition. 1 Te number of independent firms and divisions depends endogenously on deisions made in te previous stage of te game and te game is potentially repeated until an equilibrium is reaed... A Benmar Equilibrium Due to te omplexity of te game, tere is no simple funtion to desribe payoffs in stage two of tis game and it is tus neessary to solve te payoffs from ea strategy separately and ompare tem in stage one. In order to aid te analysis, we initially derive a benmar final-stage output rule assoiated wit te ase were tere are independent, single-plant, firms. We ten onsider ow te various partnersip options influene firm outputs and profits. Foussing initially on demand, te representative onsumer as a utility funtion of te form: 1 = i= 1 * 1 u, AH H i were A is a positive onstant, i is te sales of a firm, H i i= 1 and is a substitution index between varieties of te good ranging from 0 independent goods to 1 omogeneous goods. From te above utility funtion, te inverse demand funtion faing firm i is given by: pi = A 1 i i 1, = 1 were p i is te prie. Te profit maximisation problem for a representative firm is is equivalent to taing over a non-operating rival one wose osts are above te ritial minimum level required for profitable partiipation in te maret. 1 In Setion 5, we extend te model to te ase were firms sell in two marets. 5
Max p i i i wit respet to i : Max A i 1 i yielding first order onditions: 3 p i i = i. =1 i i By suessive substitutions of tis yields 4 p i 0 A C 1 0 = 0 i were C = n = 1, and z = z-1, for z = 0, 1,,,. Output of plant i is terefore: 0 A C 5 i i =. 0 Firm division profit is given by 6 π = p =. i i i i i Given tis single-plant firm benmar we next need to onsider te potential profitability of te various options a firm an pursue su as an independent-division or a oint-operation merger or a new division..3. Mergers We will onsider te following merger or partnersip proess: 13 1. Mergers are bilateral.. At any point in time all possible mergers are eligible for onsideration, but only one will our. 3. A merger between firms i and involves a profit saring pat between te two firms regarding te distribution of te ange in profits, Δπ = πˆ π π, were πˆ i are te profits tat arue to te merged firm. 14 i i 13 Te merger proess ould be eiter a ooperative merger or a ostile taeover, te two being equivalent ere as we are not onerned wit te distribution of profits between te firms. However, for ease of exposition we will periodially refer to te iger-ost firm as te target. Te atual identity of te instigator of any merger as no bearing on our analysis. 14 Alternatively, one firm an mae a tae-it or leave-it offer, or we ould ave a as bargaining game over te prie and/or allow for outside offers, owever, te distribution of merger profits is unimportant for te positive analysis. 6
4. Te most profitable merger ours at ea unture. 5. Steps 1-4 are repeated until equilibrium is establised..4. Te Know-How Transfer Proess Following a merger, te low-ost firm may ave te possibility of transferring its superior now-ow as follows. Te low-ost firm an transfer its superior now-ow δ to te target aording to te funtion, ~ = were ~ indiates te target s post-merger marginal ost, 0, 1 is a measure of produt differentiation, equivalent to te substitution index in prodution above wit = 1 indiating perfet substitutes and = 0 representing independent produts, δ 0, is a measure of te transferability of now-ow were δ = 0 indiates perfet transferability and δ = indiates tat now-ow transfer is not possible. 15 In evaluating te potential profitability of a merger te partners must onsider te ange in profit plus possibly a fixed ost, M. One interpretation of M is tat it is te one-off ost as opposed to te feasibility, δ of implementing te now-ow transfer, but it may also inlude legal fees and/or te ost of an anti-monopoly inquiry. It ould be argued tat tis ost may vary aording to te relative size of te merging firms, te differene in pre-merger proesses, and/or te degree of onentration of te industry, but we will disuss tese refinements in due ourse. 3. Independent Divisions versus Joint-Operations We start tis analysis of te various merger options by first examining an indiative merger of ea type relative to te benmar equilibrium, before exploring te onsequene of a sequene of mergers of ea type inluding te possibility of typeswiting during te sequene. 15 Tis framewor is more general tan tat used in most of te previous literature, wose assumptions about te transferability or not of ost advantages are enompassed by tis approa. For example, wen ost advantages are not transferable, as in te models of Long and Vousden 1995, Falvey 1998 and Falvey and atananan 00, tis is equivalent to = 1 and δ = 1. Leay 00 loos at properties of te demand and ost funtion in a very general setting, and te Cournot version is equivalent to δ = 0, 1, wile Ryan 006, assuming ostless tenology transfer and omogeneous goods, is equivalent to = 1 and δ = 0. Tis paper allows for 0, 1 and δ 0,. 7
3.1. An indiative Independent-Division Merger In tis setion we onsider te strategy were te merged firm opts to run te newly aquired target as a separate division and allows it to set its own output to maximise its divisional profits on te assumption tat all oter firms or divisions are independent - oter possibilities will be onsidered in due ourse. Tus ea firm and division solves te same maximisation problem as in Setion.1 wit te modifiation tat te marginal ost faing te target plant is now ~ δ =, were 0, 1, δ 0,. Tis yields: Lemma 1. Te prie level falls for all goods due to te inreased ompetitiveness of te target and output of te target s produt rises as does te merged-firm s overall output. Proof: Te post-merger prie level of good is: 7 p R p C A p < δ = δ = 0 0 1 0 0 ˆ were 0 R =. Similarly, te post-merger prie of good is now: p R p p p < δ δ = = 1 1 0 ˆ ˆ 8 R > = 1 ˆ δ δ and te output of te merged firm is 9 [ ] == R R 1 ˆ ˆ δ δ δ R > = 1 δ δ 8
Proposition 1. In te absene of any additional merger ost, an independent-division merger is always profitable for 3. Proof: Te ange in profits from te Independent-Division merger is ID p p p p δ = π Δ ˆ ˆ ˆ ˆ ˆ [ ] [ ] ˆ ˆ ID = Δπ, wi yields 10 R R ID δ δ δ δ δ δ = Δπ 1 1 For 3 tis expression is positive. 16 Corollary 1. Profits are positively related to te pre-merger ost gap for 3 and, wen now-ow is perfetly transferable, negatively related to te degree of produt differentiation for 4. Proof: 11 0 1 1 δ δ δ δ δ δ = Δπ R R ID wi is positive for 3. Similarly for δ = 0 16 Te profit of a non-merging firm falls sine were ˆ ˆ r r = π r r r r R C C A < δ = δ = 0 * 0 ˆ. Te marginal nonmerging firm may leave te maret ere requiring a realulation and tis is eed in all te simulations below. 9
Δπ ID 1 = [ 3 6 7 ] R [ 3] R 0, for 4. In te absene of te fixed merger ost M disussed earlier, te ange in profits is always positive for 3 and ene su a ost may be neessary to establis an internal equilibrium. In tis senario, for all values of and δ, te most profitable merger involves te most effiient firm taing over te least effiient, transferring its superior tenology and running it as an independent division or franise. Peraps surprisingly, Corollary 1 tells us tat te ange in profits is greater wen te merger involves two firms selling similar goods. Te intuition is tat te inreased output of te new former ig-ost division, wile reduing te original low-ost division s output, also as te effet of reduing te output of all te non-merging outside firms. Tis latter effet is greatest wen is igest, yielding greater profits for te merger. Tis is equivalent to te merged firm squeezing ompetitors by maing a ommitment to apaity via te now-ow transfer. From Lemma 1 and Proposition 1 we get: Corollary. As δ approaes, te ange in profits goes to zero and tus some degree of now-ow transfer is essential for an independent-division merger to be profitable. Proof: Follows immediately from equation 10. Tis result is intuitive as an independent-division merger as no effet on maret struture and ene an only be profitable if it leads to a ost redution. Corollary 3. An independent-division merger is always welfare enaning if tenology is perfetly transferable. Proof: Sine prie falls, and bot te output of te merged firm and aggregate output unambiguously rise, welfare rises. 17 17 ote tat te Herfindal-Hirsman index as risen as a onsequene of te merger despite te fat tat it is welfare enaning. Tis merely reinfores te point made by Farrell and Sapiro 1990 tat 10
δ δ 13 Δ CS = H > 0 1 1 Were now-ow is perfetly transferable, aggregate firm profits also rise, sine te additional output displaes less effiient produers. 14 δ δ Δπˆ ˆ Δπr = 1 δ δ R r= 1, δ 1 δ [ H ] R > 0 18 3.. Sequential Independent Division Mergers Te results in Proposition 1 and Corollary 1 are suffiient to allow us to use steps 1-4 as set out in Setion.3 to identify te initial merger. Te next question we must as ourselves in tis setion is, given tat te most profitable merger as ourred between ten most and least effiient firms 1 and, ow are subsequent merger inentives affeted by tis merger tat is, wat is te sequene in step 5 of te merger proess? It is important to note ere tat in te ase of Independent Divisions te general form of te output equation is onveniently unaffeted by te number of firms wi ave already merged, or te number of plants assoiated wit ea partner, or indeed outsiders. All tat is required is a modifiation of te individual and aggregate ost omponent C in equation 5. It follows from tis and te analysis above tat: te Herfindal-Hirsman index may not always be an appropriate measure of te welfare effets of a merger. 18 Tere may be some ost to te now-ow transfer but as long as its transfer is perfetly feasible δ =0 and tere are positive profits tis is suffiient to ensure a rise in overall welfare. Tis ase differs from Lairi and Ono 1988, in tat we are not dealing wit a marginal ange in tenology of te weaest firm. Rater, post-merger, te less effiient firm,, assumes te tenology of te most effiient firm, i, ~ = i. Tus, in tis ase we ave a ase of a new more effiient division displaing less effiient produers,..., -1. Sine overall output rises, aggregate osts are lower and te prie falls, aggregate welfare unambiguously rises. In te more general ase were δ > 0, te merger wit te less effiient target migt result in only a marginal improvement in its osts and ene its inreased output migt merely displae more effiient produers and aggregate welfare may fall as in Lairi and Ono. 11
Corollary 4. For any given previous set of mergers by te most effiient firm, 1, wit,-1 up to 1, denoted [1,, -1,, ] 1, a subsequent independentdivision merger between te most effiient firm and any oter firm denoted [1,, -1,, 1], is more profitable tan any oter independent-division merger involving te target and any oter firm m, given -1, -,, 3,, oter independent ompeting firms. Tat is, ˆ π ID [ 1n11... 1] > ˆ π [1,n,n 1..., 1, ] ID m [,m] [1,n,n 1 : 1,..., 1]...: 3 : 1 :...: 3 :,m { 1,...3, } were [ 1,n,n 1..., 1, ] 1:...: 3 : and [,m] [1,n,n 1,..., 1] 1 :...: 3 : indiate te respetive new maret strutures. Proof: Follows from Corollary 1 by indution. Tus, in te absene of any oter fores in partiular ignoring te possibility of Joint- Operation mergers, we would observe in equilibrium tat te most effiient firm would operate several divisions wi were formerly relatively ineffiient independent firms. Hig-ost targets always ave an inentive to oin te oalition as tey stand to lose if te low-ost firm engages in an alternative merger sine Independent-Division mergers reate a negative externality for non-partiipants wose output and profits fall. 19 Te grand oalition of te most effiient firm and its, sequentially, least-effiient targets is terefore only limited by te size of te merger ost, M. Tere are no retaliatory Independent-Division mergers as te profits from su a merger are always less tan tose assoiated wit any feasible merger for te most effiient firm. If instead of a fixed merger ost M, we assumed tat te merger ost was proportional to te prodution ost gap -, ten a rier merger pattern for independentdivision mergers ould be generated. 0 We will return to te issue of suessive and multi-firm mergers wen we disuss te full equilibrium. 19 See footnote 16. ote tat te fat tat outsiders lose avoids te first mover inentive problems in Horn and Persson 001 0 However, as we will see in Setion 5, even wit a fixed M it is possible to generate a multiple multifirm equilibrium simply by adding tariffs. 1
3.3. An Indiative Joint-Operation Merger In tis setion a merging firm follows an alternative strategy. Te two merging partners operate as a single firm, maing a oint-prodution deision. Tus ea plant produes its variant of te differentiated produt, taing into aount te effet of its sales deisions on te sales of te firm s oter plant. We start by examining te simplest ase first, were a single-plant low-ost firm is ontemplating an arrangement wit a single-plant iger-ost firm before moving on to te general ase were te partners and non-merging ompetitors outsiders ave multiple plants. Te new maximisation problem involves oosing and to 15 Max p p wit respet to, and, yielding first order onditions 1 16 p = p =. Tis yields, for example, a new level of ome maret output indiated by supersript ~ by te lower-ost firm s original plant,, of : 17 ~ 0 A C = δ { } { 1} 1 Te partners post-merger outputs in terms of teir pre-merger outputs te benmar establised in Setion. are: 18 ~ 3 = 1 { } { } δ 41 { 1} { } 1 Subet to te new being positive. If it is negative, we simply need to ompute te effet of a taeover and lose merger as in te standard maret onentration literature. 13
19 ~ 3 = 1 { } { } δ 3 { 4 3 } 4 1 { } Te intuition beind equations 18 and 19 is as follows. Ignoring ost differenes and now-ow transfer, as long as produts are not ompletely independent = 0 a merged Joint-Operation firm will tend to redue output in bot plants so as to redue ompetition and exploit maret power. Tis redution is aptured by te first term in equations 18 and 19 above, wi is a fration less tan one of te original level of output and depends on. It tells us te amount by wi output would fall if osts were omogeneous aross firms and tis term is te differentiated-good equivalent of te losure of te target firm in Salant et al. 1983. Te seond term in 18 tells us te additional fall in te original low-ost firm s output, indued as a onsequene of an inrease in te target s output, were osts differ ex ante, >, and tenology is perfetly transferable. Te tird term in 18 orrets for te potential diffiulty in tenology transfer, and indiates a smaller redution in te low-ost firm s output as te diffiulty δ in transferring te superior now-ow to te target inreases. Te orresponding seond and tird terms in 19, te output of te target plant, are of opposite sign and larger sine all oter firms redue teir output in response to te tenology transfer and tus te terms in 18 are only a fration of tose in 19. ote tat in te ase were osts are different but tenology is not transferable = δ, te final term in ea equation dominates and te low-ost firm wile utting overall output of te two plants sifts prodution from te ig ost firm s produt towards its own good. 3 From equation 16 we an write te expression for te ange in profit as a result of tis two-firm two-plant merger as: JO ~ ~ ~ ~ ~ ~ Δπ = M Δπ JO ~ = ~ ~ ~ t M Wit omogeneous goods te optimal strategy is for te more effiient plant to produe te entire output of te good, sine in te absene of apaity onstraints tere will never be an inentive to produe an undifferentiated produt at two loations wit different onstant marginal osts. 14
Tis equation does not readily simplify into a simple redued form and unlie te independent-division mergers it annot be unambiguously signed, even for M = 0, witout reourse to parameterisation. Te equation beomes even more omplex wen we introdue te possibility of sequential mergers. Tus in te rest of tis setion and later setions we rely on simulation analysis. 4 Tese Joint-Operation merger simulations igligt two ey differenes relative to te Independent-Division ase. Table 1 reports simulations wi demonstrate tat profits are maximised at intermediate values of dar squares rater tan wen =1 as we saw in Setion 3.1, wile Table reports an example were te most effiient firm, firm 1, would prefer to merge wit te next most-effiient, firm, rater tan te least-effiient firm firm 4 in tis example as in te previous setion. Te simulations in Table 1 report te results of a Joint-Operation merger between te most and least effiient firm for a maret onsisting of various numbers of firms from 0 down to 3 wen now-ow is perfetly transferable. Wit te exeption of te = 0 ase, te reported output falls in ea ase but profits inrease and depend positively on R and ene on te ost differene between te firms, but in ontrast to te Independent-Division ase in equation 1 te greatest inrease in profits in perentage terms ours wit internal values of. Table 1: Simulation of Joint-Operation Merger between firm 1 and for various values of wit δ=0, A=10000 and i =50i: gamma 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 % fall in Output -.7 -.93-3.15-3.36-3.57-3.79-4.01-4.5-4.54 % Cange in profit 14.06 5.77 34.16 38.93 40.19 38.9 33.75 7.11 18.96 13 % fall in Output 3.03 0.04 17.10 14.1 11.35 8.5 5.71.90 0.0 % Cange in profit -0.46 5.54 10.01 13.05 14.73 15.15 14.37 1.49 9.65 11 % fall in Output 7.83 4.33 0.90 17.53 14.0 10.9 7.67 4.40 1.06 % Cange in profit -7.0-1.48 3.08 6.5 8.84 10.06 10.19 9.30 7.50 9 % fall in Output 31.37 7.50 3.7 0.0 16.39 1.80 9.5 5.67 1.98 3 Tis is te differentiated good equivalent of wat Long and Vousden 1995, in te omogeneous goods ontext, refer to as te ost-reduing effet of a merger meaning te sifting of some prodution to te lower-ost produer following te losure of te less effiient target. 4 An Exel file is available from te autor. 15
% Cange in profit -13.06-7.30 -.49 1.34 4.16 5.97 6.77 6.60 5.58 7 % fall in Output 33.43 9.37 5.43 1.59 17.83 14.1 10.43 6.69.79 % Cange in profit -16.68-10.88-5.98 -.00 1.01 3.07 4.18 4.40 3.90 5 % fall in Output 33.44 9.50 5.69 1.99 18.38 14.79 11.18 7.46 3.48 % Cange in profit -16.06-10.70-6.5 -.74-0.14 1.59.51.74.46 3 % fall in Output 9.46 6.41 3.46 0.56 17.63 14.6 11.43 7.96 4.06 % Cange in profit -5.48 -.55-0.44 0.96 1.76.06 1.98 1.65 1.5 Te reason for tis result is tat te onentration effet is non-linear. Te more substitutable te goods, te weaer is te benefit from reduing output due to te inrease in output by outsider firms in response to te merger onentration. Conversely, for low values of te pre-merger equilibrium already reflets most of te desirable onentration and te additional onentration attributable to te merger is very small. Tese two effets give an internal equilibrium in tis ase. If we extend te analysis to allow for imperfet now-ow transfer δ > 0 tis redues te potential profitability of all mergers and te tresold value of required for a profitable merger is redued, altoug te maximum is unaffeted, tat is, te profit urve as a funtion of is sifted down. We inlude in tis table te ase were = 0 as a merger between firms 1 and 0 results in te now-ow transfer effet dominating te onentration effet and aggregate output rises, as in te Independent- Division ase. 5 Table reports te anges in profits relative to te initial Cournot equilibrium for te full set of possible Joint-Operation first-round mergers and illustrates te oter feature of equation 0. Unlie in te omogeneous goods literature see for example Ryan 006, eary 003 or Falvey and atananan 00 te relationsip between merger profitability and R is not stritly inreasing in tis model. In te omogeneous goods literature te most profitable merger always involves te most effiient and least effiient firms, and wen now-ow is fully transferable δ = 0 a similar result obtains ere. However, in Table we see tat wen δ is ig and is low, te most effiient firm, firm 1, would prefer to merge wit te next most effiient, firm, wit 3 and 4 independent merger [1,] 3:4, rater tan te least effiient firm 4 16
[1,4] :3. Tus wen tenology transfer is diffiult and goods are not easily substitutable, te inrease in maret power is more important and te two losest firms ave te most to gain. Table: Example of profits being larger if firm 1 merges wit nearest low ost firm, firm, rater tan ig ost firms 3 or 4 wen tenology is OT transferable = 4, A = 1000, i =50i and δ = =0.9 =0.8 =0.7 =0.6 =0.5 =0.4 =0.3 =0. =0.1 Cange in profits for 14 from [1,4] :3-18.04-13.16-9.06-5.81-3.37-1.70-0.68-0.118-0.0881 Cange in profits for 13 from [1,3] :4-17.43-1.53-8.49-5.31 -.96-1.37-0.44-0.053-0.0103 Cange in profits for 1 from [1,] 3:4-16.79-11.90-7.9-4.8 -.55-1.04-0.0 0.1045 0.0670 Cange in profits for 3 from [,3] 1:4-16.80-11.91-7.93-4.83 -.56-1.05-0.0 0.1034 0.0665 Cange in profits for 34 from [3,4] :4-16.81-11.9-7.94-4.84 -.56-1.05-0.1 0.10 0.0661 Cange in profits for 4 from [,4] 3:4-17.46-1.56-8.51-5.33 -.97-1.38-0.45-0.0555-0.0113 3.4. Sequential Joint-Operation Mergers Te analysis above only involves a single-plant firm merging wit anoter singleplant firm and all oter firms are autonomous single-plant firms. However, more generally, we must allow for te possibility tat tere are F independent firms indexed r 1,..., F ea wit a different number Sr of plants, ea indexed S rm, wit F m 1,..., Sr and S r =. We wis to onsider te ase were two firms, i and, r=1 wi ave already aumulated Si and S plants, respetively, want to engage in a new strategi partnersip or merger, wit S = S S ~ te level of output for firm i s most effiient plant i1 satisfies: i i plants. In tis general ase, 5 As one migt expet, simulations onfirm tat wenever te tenology transfer effet dominates tat is te aggregate merged firm s output rises merger profits are positive. However, in tis ase a Joint-operation merger will always be dominated by an Independent-Division merger. 17
0 { S A i i1 δ 1 1} F r= 1 Si S i m= r { S I r= 1 Si im F i1 { S { S r i1 } i 1 { S r } F r } ~ i } r r= 1 Si m= = i r im i1 r= 1 Si m= m= S S rm 1 r1 S rm r1 All outputs of oter firms and plants, rm, an be readily derived from tis and employed in te oint-operation, multi-plant firm simulations reported in Setion 4 below. Profits must be similarly adusted, inreasing wit te number of plants due to inreased maret power and, as before, dereasing in te degree to wi now-ow is transferable. Si im 1 i 1 πi 1 = 1 Si 1 i 1 δ i1 m= 1 4. An Illustrative Sequential Equilibrium wit Independent-Division and Joint- Operation Mergers: In tis setion we use te analysis developed in Setion 3 above to investigate te potential sequene of mergers required to determine te equilibrium maret struture, tat is we onsider Step 5 of te merger proess identified in Setion.3. In Setion 3.1 we identified te merger sequene for a maret were Independent- Division mergers are possible. We now tat in su a maret we will ave, eteris paribus, a sequene of mergers involving te most effiient firm and te least effiient remaining independent firm. We now wis to reonsider tis sequene and offer te most effiient firm te option of oosing a Joint-Operation merger rater tan an Iindependent-Division merger at ea unture. If te firm first ooses an Independent-Division merger, ten subsequently it will ompare a new Independent- Division merger wit a oint operation involving its two existing independent plants and te target. Tus at ea step, a firm wit S - 1 existing divisionalised plants onsiders weter to engage in a oint-produt merger and gain JO π onverting all 18
its S - 1 existing plants plus te target into an S-plant/produt Joint-Operation firm, or to engage in a furter Independent-Division merger for a return of. For simpliity in tis setion we assume tat now-ow is perfetly transferable and onsider te impat of imperfet now-ow transfer non-zero δ in te disussion. ID π We are interested in finding te point in te merger sequene at wi: π JO = S 1 S 1 ~ ˆ > S l = π ID ote tat given te simplifying assumption on now-ow transfer, te post-merger outputs of te merging partners are equalised, ~ ~ = i and ˆ = ˆ. Tus from 8 and 1 te respetive ondition we require is i 0 A C ID ˆ π = S i i = Si = S 1 1 i Si 0 m= 1 i 0 A C i i im ii m= 1 { { S } { S } S } i i i S i i im S ii < π i JO = S i 1 S i ~ 1 i wi, wen S,, te number of plants owned by te target, equals 1, redues to: Proposition : If δ = 0, a firm will oose a Joint-Operations rater tan an Independent Division merger iff [{ { S } { S } S }] < 1 S 1 0 i i i i Proof: Follows from rearranging te above inequality. Table 3 below identifies te first merger for wi it pays for te merging multi-plant firm to swit from an Independent-Division strategy to a Joint-Operation merger, 19
depending on te number of firms in te maret and. Tus tis table tells us te point at wi te Independent-Division merger sequene in Corollary 4 gives way to a Joint-Operation merger. Table 3: Wit firms in te industry te swit involving all plants from an Independent-Division to a Joint-Operation Merger to S-plant firm will our on te S-1 t Merger in te table below = 0.1 = 0. = 0.3 = 0.4 = 0.5 = 0.6 = 0.7 = 0.8 = 0.9 3 1 st 1 st 1 st 1 st 1 st nd nd nd nd 4 1 st 1 st 1 st nd nd nd nd nd 3 rd 5 1 st 1 st nd nd 3 rd 3 rd 3 rd 3 rd 3 rd 6 1 st nd nd 3 rd 3 rd 3 rd 4 t 4 t 4 t 7 1 st nd 3 rd 3 rd 4 t 4 t 4 t 5 t 5 t 8 1 st nd 3 rd 4 t 4 t 5 t 5 t 5 t 6 t 9 nd 3 rd 4 t 5 t 5 t 6 t 6 t 6 t 7 t 10 nd 3 rd 4 t 5 t 6 t 6 t 7 t 7 t 7 t 11 nd 4 t 5 t 6 t 7 t 7 t 7 t 8 t 8 t 1 nd 4 t 6 t 6 t 7 t 8 t 8 t 9 t 9 t 15 3 rd 6 t 7 t 9 t 9 t 10 t 11 t 11 t 1 t 0 5 t 9 t 11 t 1 t 13 t 14 t 15 t 15 t 16 t 5 7 t 1 t 14 t 16 t 17 t 18 t 19 t 0 t 0 t To interpret tis table onsider te ase of = 0.5. If initially tere were = 1 firms in te industry ten, subet to te merger inreasing profits by more tan M, a sequene of independent-division mergers will our until on te sevent merger a seven-independent- division firm attempts to merge wit te next firm in te sequene to reate an eigt division firm. Tus, π ID [1,1,11,10,9,8,7] :3:4:5:6 > π JO [1,1,11,10,9,8,7] :3:4:5:6 but π JO [1,1,11,10,9,8,7,6] :3:4:5 > π ID [1,1,11,10,9,8,7,6] :3:4:5. ote tat if a firm as already ad seven independent-division mergers ten all seven will be involved in te oint-operation merger wit firm 8, sine it follows from tat it is less profitable for only a subset of te divisions to be involved in te Joint- Operation deision. Intuitively, tis maes sense sine one a firm opts to exploit its maret power for a given it maes sense to employ tis strategy aross all divisions simultaneously. Finally, te swit-over point, S JO, is a positive funtion of S JO JO S and. Tat is > 0 and > 0 for 0,1]. One tis swit taes plae we ave to examine a more omplex range of potential Joint-Operation mergers to assess te next merger in te sequene. In te next setion 0
we analyse a five-firm example, were we examine a range of subsequent possible oint-operation onfigurations as well as te Independent-Division options in ea ase. Tese Joint-Operation senarios for te five-firm ase are represented by te saded line in Table 3, wi tells us tat te swit from an Independent-Division merger strategy to a Joint-Operation merger strategy will our on te tird merger to reate a four-plant firm for = 0.7, and on te seond merger to reate a treeplant firm for = 0.4, wile te first merger to reate a two-plant firm will be a Joint-Operation merger in te ase of = 0.. Finally, note tat for = 0 te two types of merger yield equal profits sine tere is no interation between produts anyway, wile for = 1 an Independent-Division merger dominates for all >. 6 4.1. An illustrative five-firm equilibrium: We ave now identified te pay-off assoiated wit ea expansion strategy, te onditions under wi tey may be profitable and te irumstanes under wi one form will dominate anoter. However, wile te analysis above illustrates te pertinent issues, tere learly is no simple result in te absene of greater parameterisation of te problem. In tis setion, by way of illustration, we onsider te payoffs assoiated wit a five-firm version of te game, were A = 10000, i = 50i and δ = 0. We investigate all te possible merger and de-merger ombinations at ea stage, and report te most salient outomes in Table 4. [Table 4 about ere see end] Again, wen traing merger istory we invoe te ey assumption tat te most profitable merger ours at ea stage, altoug of ourse te omplete set of payoffs allows us to see te result of an immediate ump to any onfiguration inluding te ore-grand-oalition of [1:5:4:3:]. We report te payoffs wit M set to zero, owever te atual observed equilibrium will depend on te value of M. Te table is broen into tree setions. Setion 1 reports te ange in profits for an Independent- Division [1,5] merger line 1, te effet on all firms of a Joint-Operation [1,5] merger 6 See Ryan 006. 1
lines -5 plus, by way of omparison, te results for a Joint-Operation [1,] merger line 6. Te first point to note is tat te payoffs beave as desribed in Table 3 above wit an Independent-Division merger being preferred for greater tan 0. and a Joint Operation for 0. or less. As we an see, a Joint-Operation merger strategy auses te outsiders profits to rise. So for example, for = 0.4 te ange in profits for firm from a [1,5] merger π JO [] [1:5],,3,4 = 653368 is greater tan te profits for firms 1 and 5 from te same merger π JO [1:5] [1:5],,3,4 = 38711. Tis outsider inentive effet is te ey issue tat leads to te diffiulty in identifying te equilibrium in te omogeneous goods ase su as in Horn and Persson 001. However, in tis example, for all te relevant mergers were π JO > π ID te profits for outsiders wile positive are less tan tose for insiders, maing su mergers less suseptible to inentive problems. 7 Setion A reports te possible outomes assoiated wit a retaliatory [,3] or [,4] merger. Comparing tese results wit tose in Setion B, wi reports te ange in profits from te alternative [1,5,4] merger relative to te relevant previous Independent-Division or Joint-Operation [1,5] merger, we see tat te returns for te relevant [1,5,4] merger dominates te returns for eiter te [,3] or [,4] retaliation. ote in addition tat, as reported in Table 3, if =0.4 te move from [1,5] to [1,5,4] leads to a swit from an Independent-Division strategy, were te ange in profits is π ID [1,5,4] [1,5,4]::3 = 33967, to a Joint-Operation merger, were te profits relative to te previous Independent-Division ase line 15 are π JO/ ID = [1,5,4] [1,5,4]:3:- π πjo ID [1,5] [1,5]:4:3:- π ID 4 [1,5]:4:3: = 6856. Line 16 gives te relevant ange in te Joint Operation profits relative to te previous Joint Operation [1,5] wi is te relevant ompassion for = 0. or less. Lines 18 and 19 ompare te profits from te relevant [1,5,4] merger wit te base profits of te individual firms wen all firms were independent. Comparing tese profits wit te sum of tose obtained via a step-wise merger proess, we observe tat te latter an yield different results to one were te multiple [154] merger an our 7 But note tat δ < is ruial for tis alternative Independent-Division effet.
simultaneously. For example, were te initial merger is an Independent Division merger, su as wen = 0.5, te ange in profits from te sequene of mergers Δπ ID [1,5] [1,5]::3:4 = 488611 and Δπ ID [1,5,4] [1,5,4]::3 =304531 exeeds te ange in profits from te same merger relative to te base =71448 from line 18. Tis ours beause te initial Independent-Division merger redues te profits of te outsider firm 4, wi te subsequent [1,5,4] merger weter Independent-Division or Joint-Operation reovers. So te step-wise merger proess biases aeptane of mergers tat migt not our in a multilateral merger setting wen te initial merger is an Independent-Division merger. By ontrast, for = 0. te sum of te individual profits of te sequene of Joint-Operation mergers is lower tan te base ase beause of te positive externality on outsiders, wi is lost wen a subsequent merger inludes te outsider, tus biasing reetion relative to a base omparison in a multilateral merger. Setion 3 reports a seletion of results for a retaliatory [,3] merger, te next merger in te [1,5,4,3] sequene and an alternative [1,5,4,] merger. Again te results beave as expeted, wit te Joint-Operation format replaing te previous Independent- Division mergers for in te 0.9-0.5 range. Wat will te preise equilibrium be in tis model? Tere are a number of possible ontenders. In te absene of a merger ost M, eiter te proess iterates to te grand Joint-Operation oalition of [1,5,4,3,] or alternatively te merger proess ends one te Independent Divisions merger proess exausts itself beause of te Insider- Outside inentive onflits wit te Joint-Operation merger. 8 For all oter possible equilibria, some substantial merger ost is essential. Tus, for example, wit = 0.5, if we invoe a merger ost of M = 400,000, we will only observe te merger [1,5]::3:4 and not [1,5,4]::3, even toug te subsequent Joint-Operation [1,5,4,3]: would be igly profitable. By ontrast, if = 0.4, bot te [1,5] and [1,5,4] mergers would be feasible. However, if M is not a fixed number, and as we noted previously tere are good reasons to tin tat it migt not be, ten te value of M assoiated wit [1,5,4]::3 migt be signifiantly iger tan tat assoiated wit 3
[1,5]::3:4 if te relevant regulatory body were to laun a long and expensive merger investigation. Similarly, it migt be more ostly to merge wit a firm wit a mu lower level of now-ow rater tan wit one wit a similar level. Tus for = 0. te Joint-Operation merger [1,5]::3:4 would not our if M 15 = 650,000, wile te merger [,3]:[1,5]:4 wit M 3 =190,000 would appen. Tis is a different issue to te ase were = δ reported in Table. Hene tis framewor is potentially apable of generating equilibria wit a wide variety of arateristis one we ave te appropriate merger ost, M, plus produt differentiation, marginal ost and now-ow transfer parameters. Observations from te five-firm equilibrium Observation 1: For ig levels of substitutability, an Independent-Division merger is liely to dominate. Observation : It is possible to identify onditions under wi Joint-Operation mergers dominate Independent-Division mergers and for ea level of substitutability, tere is a ritial merger su tat an Independent-Division merger gives way to a Joint-Operation merger. Tus, a Joint-Operation merger beomes progressively more liely as falls and/or a sequene of Independent Division mergers as already ourred Observation 3: Tere is tus a natural sequene of inentive-ompatible Independent-Division mergers before we get to a Joint-Operation merger wit its attendant problem of outsider inentives. Te onlusion of tis sequene of Independent-Division mergers may represent a natural benmar equilibrium against wi anges in poliy su as te removal of tariffs to be disussed below may be measured. 8 Altoug, as we noted above, at all points were te Joint-Operation profits atually dominate Independent-Division profits, te returns to insiders dominate te returns to outsiders, so tis may not be as problemati in tis model. 4
Observation 4: We now tat for M = 0, Independent-Division mergers are always profitable as long as δ < and R > 0, tat is, tere is some marginal ost gap between te firms and te superior tenology or management proesses are at least imperfetly transferable. Hene Joint-Operation mergers tat dominate Independent Division mergers must always be profitable. Furtermore, it appears tat su a Joint-Operation merger tat atually our yield iger profits to insiders tan outsiders. 9 Observation 5: Were te initial merger is an Independent-Division merger, te sum of te ange in profits assoiated wit a merger sequene will be boosted relative to a omparison wit te ange in profits from te same simultaneous multilateral merger, sine losses experiened by an outsider in as step-wise merger sequenes will be reovered one absorbed into a merged firm. Hene a sequene of mergers wi absorbs previous outsiders individually may involve more partners and terefore be larger tan a simultaneous multi-firm merger. Table 5: Case summary approaing 1 approaing 0 δ=0 δ= Independent Division mergers more liely between most and LEAST effiient o merger, some degree of now-ow transfer essential Joint Operation mergers more liely between most and LEAST effiient Joint Operation mergers more liely between most and EXT MOST effiient 5. Tariffs and Merger Ativity As well as allowing te new insigts already explained into merger inentives in a losed eonomy, te model set out above also failitates an analysis of te impat of 9 Due to te omplexity of te model, spae onstraints prevent us from exploring welfare effets of a Joint-Operation merger ere. We now from Corollary 3 tat an Independent-Division merger yields unambiguous benefits under free trade as long as δ = 0. We now from te omogeneous goods literature see for example Falvey 1998 tat Joint-Operation mergers are more omplex as te inreased onentration and prie sifts surplus from produers to onsumers and te onditions for a welfare gain are more restritive tan in te Independent-Division ase. 5
inreased globalisation on onentrated marets were evidene suggests tat te target tends to ave a maret presene post-merger. Spae onstraints prevent a ompreensive analysis of all te possible ases, but te purpose of tis setion is to identify te main fators in te analysis from wi te full range of possibilities an be dedued. 30 In tis setion we assume te world is omposed of two ountries, ome and foreign wose variables are denoted by an asteris. Again we assume tat ea ountry as a small, initially fixed, number of firms n and n* respetively, and n n* =, ea produing a differentiated produt, and te two marets are segmented wit ea firm selling in bot marets. In te analysis below we tae as given some initial equilibrium as establised via te proess disussed in Setion 4 above, given te existing set of tariffs or trading osts, and onsider te effets of a ange in te trade regime. In partiular, we are interested in anges in te inentives for te two types of merger as a onsequene of relaxing trade impediments. For simpliity, we again tae as our initial equilibrium te benmar -firm equilibrium were we impose a trading ost su as a tariff or additional tenial requirement of t on imports into te ome maret from foreign firms. Tis modifiation is equivalent to an inrease in te marginal ost faed by foreign firms, and ene tis term rises in all te relevant equations in Setion 3. We start by reexamining te benmar output and prie equations before detailing te effets on merger profits. Te trading ost tariff inlusive prie is: * n t p it = pi > p 0 i and a domesti firm s sales to te domesti maret rise to it * it * n t = i, wile a foreign firm s sales to te domesti maret fall to 0 [ 0 n] * t = i. Tat is, te output of all ome firms rises by te same 0 absolute amount * n t, wile sales of ea foreign firm to te domesti maret 0 30 A sligt modifiation to te equations, depending on wi ountry is imposing te tariff and te loation of ea of te merger andidates, allows for oter ases to be onsidered. See Ryan 006 for some examples. 6