Vertical or Horizontal: Endogenous Merger Waves in Vertically Related Industries

Transcription

1 Vertcal or Horzontal: Endogenous Merger Waves n Vertcally Related Industres Zhyong Yao and Wen Zhou March 2, 202 Abstract Endogenous merger waves n vertcally related ndustres are studed assumng frms can engage n both vertcal and horzontal mergers. The analyss explans why and how merger waves occur endogenously so that the market structure transforms from one stable confguraton n whch no frm s merged, to another n whch many frms are merged. Merger waves are shown to be possble wth or wthout any fundamental change n the underlyng economc condtons. Whether a merger wave s vertcal or horzontal depends on the balance between vertcal and horzontal externaltes, and the balance between upstream and downstream competton. Keywords: merger waves, endogenous mergers, vertcal mergers, horzontal mergers, stable market structure JEL Code: L3, L42, D43 Introducton It has been well documented that mergers occur n waves, clusterng n tme and by ndustry (e.g., Andrade et al. 200; Mtchell and Mulhern, 996). Some merger waves are horzontal, consstng manly of mergers between competng frms n the same ndustry, whle some others are vertcal, made up manly of mergers between supplers and customers. For example, the frst great merger wave n the U.S. (890s 904) was horzontal. Consoldaton between compettors generated corporate gants n the steel, telephone, ol, mnng, ralroad, and other major manufacturng and servce ndustres. The second great merger wave (90s 929), by contrast, was manly vertcal. Ford and General Motors emerged as the major automoble manufacturers through vertcal ntegraton, acqurng every busness along the supply chan from ron and coal mnng Yao: yzy@fudan.edu.cn, School of Management, Fudan Unversty, 670 Guoshun Road, Shangha, Chna. Zhou (correspondng author): wzhou@busness.hku.hk, School of Busness, The Unversty of Hong Kong, Pokfulam Road, Hong Kong. We would lke to thank Jmmy Chan, Yongmn Chen, Zhq Chen, Stephen Chng, Km Sau Chung, Ncholas Economdes, Duozhe L, and Nng Sun for helpful comments and suggestons. Fnancal support from the Hong Kong General Research Fund (HKU75790H), HKU-Fudan IMBA Jont Research Fund, and the NET Insttute s gratefully acknowledged.

2 to ralroads and water transportaton, steel mlls, all the way to fnshed vehcles (Lpton, 2006; Martynova and Renneboog, 2008). In the U.S., the cement and ready-mxed concrete ndustres underwent at least two waves of vertcal ntegraton n the 960s and 980s (Hortacsu and Syverson, 2007). More recently, n February 20 Noka and Mcrosoft announced a comprehensve plan to ally vertcally n the smartphone area n response to the success of Apple s Phone. Several months later, Google acqured Motorola Moblty n a smlar move. Horzontal mergers may cluster not only n a sngle ndustry, but also across several ndustres that are vertcally related. For example, a seres of mergers n the US pharmaceutcal ndustry occurred n 2007 to counteract the ncreased barganng power n the downstream health care ndustry, where consoldaton had been takng place. Furthermore, a wave of ntegraton along one dmenson may follow a wave of dsntegraton along another. In other words, the market may swtch between vertcal and horzontal ntegratons. Semconductor companes used to be vertcally ntegrated. Wth rsng costs and a changng cost structure, economes of scale became more mportant, and frms started to dsntegrate vertcally and merge horzontally. 2 These examples hghlght the need to study horzontal and vertcal mergers together, as a merger wll alter the ncentves for other mergers, and the mpacts are lkely to be dfferent dependng on whether the mergers are vertcal or horzontal. Gven the observed regularty of horzontal and vertcal merger waves, the followng questons mmedately emerge: Why do mergers cluster? What causes a merger wave to occur n the frst place? And what determnes whether the wave s vertcal or horzontal? There have been some economc studes on horzontal merger waves (n a sngle ndustry) and a few on vertcal merger waves, but vrtually none n whch the two are consdered together. Ths research studed mergers n vertcally related ndustres and s therefore well postoned to address the last queston. In dong so, the analyss has shed new lght on the answers to the frst two questons. Consder two vertcally related ndustres, each consstng of two frms that may engage n both horzontal and vertcal mergers. 3 Although merger decsons are made smultaneously, the soluton concept s such that each frm consders possble responses from other frms when contemplatng a merger. A merger wave s an equlbrum phenomenon whch satsfes two condtons. Frst, t s stable for multple frms to merge, meanng that the frms merger ncentves must be analyzed together. Second, mergng s endogenous, meanng that the orgnal market structure,.e., all frms remanng Meanderng gants, The Economst, March 24, Under new management, The Economst, Aprl 2, Snce each ndustry has only two frms, a horzontal merger wave n ths context would be horzontal mergersnbothndustres,whchsslghtlydfferent from the usual meanng of multple mergers n a sngle ndustry. 2

3 ndependent, must also be stable. Therefore, a merger wave s a change n the market structure from one stable confguraton to another. The analyss wll show that any stable market structure results n ether no merger or multple mergers, so mergers always occur n waves. Dependng on whether the two structures are stable under dfferent or dentcal condtons, a merger wave may be trggered n two ways. Market structure may change because the underlyng condtons have changed, or the wave may be a swtch between equlbra wthout any change n the fundamentals. The frst case corresponds, for example, to an economc shock that changes the cost, demand, or regulatory stuaton, so the trgger s tangble. In the second case, the trgger may be ntangble, correspondng to somethng trval or totally unrelated to the underlyng economc condtons, such as rumors or changes n mood or expectatons. The man contrbuton of ths study was to lnk the two trggers to demand and cost propertes, and to dentty the condtons determnng whether a merger wave s horzontal or vertcal. It was found that these condtons affectstablemarketstruc- ture through the relatve ntensty between vertcal and horzontal externaltes, and the relatve ntensty of competton n the upstream and downstream ndustres. Vertcal mergers elmnate vertcal externaltes (double markup) but ntensfy horzontal externaltes (competton n the downstream ndustry). Horzontal mergers lessen horzontal externaltes n both ndustres but exacerbate vertcal externaltes. If the two externaltes are balanced, one wll mtgate the other as long as all four frms reman ndependent. Ths explans why frms may refran from mergng, a necessary component for the endogenzaton of merger waves. If the balance s dsrupted,.e., f the externaltes become more severe along ether dmenson, frms wll start to merge. For example, when the demand for the fnal product becomes more convex, double markup s more damagng, and frms have an nventve to merge vertcally. Whle the externaltes manly affect the four frms total profts, the relatve ntensty of competton n the two ndustres affects how the total proft s dstrbuted among them. When competton n the two ndustres s balanced, frms tend to reman ndependent or merge vertcally. When the balance s dsrupted, frms wll merge horzontally. For example, when the fnal products become closer substtutes, horzontal competton s ntensfed and frms merge horzontally n both ndustres. So competton n one ndustry may nduce mergers n a vertcally related ndustry. Not mergng and vertcal mergers tend to share the same condtons whle horzontal mergers correspond to dfferent condtons, so vertcal merger waves are more lkely to be assocated wth ntangble trggers, whle a horzontal merger wave tends to be assocated wth a tangble trgger. Research has long establshed that mergers tend to occur n waves, and scholars have usually explaned the waves n terms of economc shocks at the ndustry or econ- 3

4 omy level (Andrade et al. 200; Andrade and Stafford, 2004; Harford, 2005; Jensen, 993; Jovanovc and Rousseau, 2002; Mtchell and Mulhern, 996; Shlefer and Vshny, 2003). In the ndustral organzaton lterature, there are only a few theoretcal papers on merger waves, all n the same ndustry. Nlssen and Sorgard (998) analyzed sequental horzontal mergers to demonstrate ther temporal nterdependence. Faul-Oller (2000) studed sequental mergers among frms wth asymmetrc costs, and found that a merger s proftablty s affected by both the demand level and mergers among other frms. Frdolfsson and Stennek (2005) showed that a merger may nduce further mergers due to the negatve mpact a merger exerts on other frms. Qu and Zhou (2007) and Toxvaerd (2008) endogenzed multple mergers and attrbuted merger waves to economc shocks. Ths paper s manly nterested n a settng where both horzontal and vertcal mergers are possble, and we have found equlbrum condtons that are ndeed unque to such settngs: the balance between vertcal and horzontal externaltes and between upstream and downstream competton. Toxvaerd (2008) has shown that mergng and not mergng can be unque or multple equlbra under dentcal or dfferent condtons. Although not dscussed explctly, Toxvaerd s result mples the possblty of tangble and ntangble trggers. Nevertheless, hs reason for why no merger and multple merger co-exst s very dfferent from ours. We have further related the two trggers to the types of merger waves and the specfc demand and cost condtons. Colangelo (995) studed vertcal and horzontal mergerstogether,buthsmergergamesverydfferent from the one consdered here. Colangelo was manly nterested n exclusve, sngle mergers that are assumed to be substtutes, whle ths study consders multple mergers that turn out to be complements. Hs merger decsons are sequental wth an exogenous target and ordered moves, whle n ths study everythng ncludng the merger process s endogenous (.e., the pre-merger and post-merger market structures must both be at equlbrum). Greenhut and Ohta (979) have demonstrated that successve duopolsts would both merge vertcally, but Bonanno and Vckers (988) and Ln (988) showed that frms may choose vertcal dsntegraton n order to dampen downstream competton. Our model syntheszes these contradctory results, as we show that both market structures can be stable even under the same condtons. Lke Greenhut and Ohta (979), we emphasze the role of double markup n drvng vertcal mergers. Lke Bonanno and Vckers (988) and Ln (988), we show that frms may refran from proftable vertcal mergers because vertcal dsntegraton generates a vertcal externalty that mtgates the horzontal externalty assocated wth horzontal competton. Unlke ther settng n whch the only alternatve to not mergng s vertcal ntegraton, frms n our model have the addtonal opton of horzontal merger. In applyng the equlbrum concept for one-to-one matchng games wth externaltes 4

5 (Sasak and Toda, 996; Hafalr, 2008), 4 our smultaneous merger game provdes a useful framework for merger studes. The equlbrum concept s able to justfy both no merger and multple mergers as stable confguratons and thereby dentfy an ntangble trgger of endogenous merger waves. It also captures the essental nterdependence of frms merger ncentves wthout havng to specfy detals such as the order of moves, whch so often wll greatly affect the equlbrum outcome. The plan of the paper s as follows. Secton 2 presents the major fndngs n a baselne model wth specfc assumptons about demand, cost, and the nature of competton. The next secton relaxes and generalzes these assumptons and demonstrates that the fndngs are robust. More mportantly, varatons n the settng put the fndngs n perspectve and help us relate merger waves to specfc demand and cost condtons. Fnally Secton 4 concludes. 2 Model 2. Setup Consder two vertcally related ndustres. The upstream ndustry conssts of two dentcal frms, A and B, and the downstream ndustry also conssts of two dentcal frms, and 2. A homogeneous nput s produced by the upstream frms at constant margnal cost, c, and sold through arm s-length transacton to the downstream frms, whch then transform t nto a homogeneous fnal product at zero extra cost on a one-for-one bass. Frms compete à la Cournot n both ndustres. Each downstream frm regards the nput prce, denoted t, as gven and chooses ts output based on the demand for the fnal product, p = α Q, whereq s the total output produced by the downstream frms. The downstream Cournot equlbrum wll gve rse to Q as a functon of t, whch s then nverted to generate the nverse demand for the nput,.e., t as a functon of Q. Facng ths derved demand, the upstream frms engage n ther Cournot competton. 5 The frms play a two-stage merger game. In stage one, each frm chooses smultaneously a merger partner. A frm can commt to ndependence by choosng tself as the partner. A merger can be ether horzontal (between two downstream frms or two upstream frms) or vertcal (between a downstream frm and an upstream frm), and t takes place f and only f two frms choose each other as partners. A merged entty s not allowed to partcpate n any further mergers. 6 The merger decsons result n a market 4 Work on coalton formaton wth externaltes (Bloch 996; Ray and Vohra, 999) has borrowed and modfed varous equlbrum concepts from cooperatve game theory, but those concepts lead to ether a very large set of equlbra or an empty set, therefore are not sutable for the questons studed here. 5 The successve Cournot olgopoly settng has been wdely used. See Greenhut and Ohta (976), and Salnger (988) for examples. 6 Ths s to avod tral monopoles. 5

6 confguraton, whch s publcly announced. The game then proceeds to stage two. Gven the market confguraton from the frst stage, all the resultng frms compete à la Cournot, choosng ther quanttes n order to maxmze ther payoffs. Wthn a merged entty, the two partners share the merger surplus equally, 7 where the surplus s calculated assumng a fxed confguraton among the other frms. For example, a merger between frms A and n N {A, B;, 2} leads to S {B; A, 2}, soπ S A = πn A + 2 π S A π N A πn and π S = π N + 2 π S A π N A πn, where A denotes the entty resultng from a merger between frms A and, andπ X s frm s payoff n confguraton X wth X. Aconfguraton s stable f no devaton by any ndvdual frm or par of frms s proftable. A devaton s proftable f all devators are better off (strctly for at least one) for any possble confguraton among the other frms. Once stablty s characterzed, a transton from one stable confguraton n whch no frm s merged to another n whch all frms are merged wll be an endogenous merger wave. Ths s essentally a one-to-one matchng game, so both unlateral devatons by ndvdual frms and collectve devatons by a par of frms are allowed (e.g., Roth and Sotomayor, 990). Snce a merger nvolves two frms, collectve devaton must also be consdered, as devatng nto a new merger requres two frms to change ther strateges smultaneously. Furthermore, because a merged entty s profts depend on other frms merger structures, ths merger game s essentally a one-to-one matchng wth externaltes. Followng Sasak and Toda (996), our equlbrum concept requres a devaton to be proftable under all possble confguratons among the remanng frms. Such a requrement s obvously suffcent to justfy the devaton. Sasak and Toda (996) have proved the exstence of such an equlbrum n the context of one-to-one matchng wth externaltes, and t works well for ths merger game, as the equlbrum set thus generated s small but not empty. 2.2 Analyss The game s solved by backward nducton. Suppose that at the begnnng of stage two themarketconfguraton contans v vertcally ntegrated frms, u ndependent upstream frms, and d ndependent downstream frms. Because margnal costs are constant and dentcal wthn an ndustry, a horzontal merger s equvalent to elmnatng one of the mergng frms. A vertcally ntegrated frm partcpates only n the downstream competton, 8 and t dffers from an ndependent downstream frm n that ts nput s 7 Ths assumpton can be justfed by mplementng alternatng-offer barganng à la Rubnsten (982). 8 Salnger (988) has ponted out that a vertcally ntegrated entty wll wthdraw from the upstream competton t nether buys the nput from other upstream frms nor sells t to other downstream frms. Some researchers have rased concerns about commtment power n Salnger s settng, but the ssue s not serous n ths analyss because frms compete on quantty rather than prce (Hart and Trole, 990). 6

7 procured at cost c rather than the market prce t. In the downstream competton, therefore, a vertcally ntegrated frm chooses q v to maxmze π v (α Q c)q v,whch leads to the frst-order condton α q v Q = c. SnceQ = vq v + dq d (usng symmetry), the frst-order condton can be rewrtten as: α (v +)q v dq d = c. Lkewse, the frst-order condton for an ndependent downstream frm s α q d Q = t, or α (d +)q d vq v = t. These two equatons lead to q v = α (d +)c + dt d + v + and q d = α (v +)t + vc. d + v + The demand for the nput for ndependent upstream frms s therefore d[α + vc (v +)t] Q dq d =, d + v + or t = α + vc v + d + v + d(v +) Q, where Q dq d uq u s the total quanttes produced by the ndependent upstream or downstream hfrms. Facng ths derved demand, an upstream frm wll choose q u to maxmze π u α+vc v+ d+v+ d(v+) Q c q u. The Cournot equlbrum s then gven by Consequently, q d = and Q = q u = d(α c) (u +)(d + v +). u(α c) (u +)(d + v +), q [d +(u +)(v +)](α c) v = (u +)(v +)(d + v +), [(u +)(v +)(d + v) d](α c). (u +)(v +)(d + v +) It s clear that all profts are proportonal to (α c) 2, so we can normalze α c wthout losng any generalty. The profts of the three types of the frm are then: π v (v, u, d) = π u (v, u, d) = π d (v, u, d) = [d +(u +)(v +)] 2 (u +) 2 (v +) 2 (d + v +) 2, d (u +) 2 (v +)(d + v +), and u 2 (u +) 2 (d + v +) 2. Schrader and Martn (998) provde further arguments n support of Salnger s concluson. 7

8 Now move back to stage one. There are sx possble market confguratons as lsted n Table. Frms payoffs can be calculated usng the formulas derved above. For example, n S {A, B;, 2}, v =0, u =2, d =2. As specfed earler, each merged entty dvdes the merger surplus/defct equally between the two partners. Table : Payoffs nthesxconfguratons 9 Confguraton π A π B π π 2 Total profts S {A, B;, 2} S 2 {AB;2} S 3 {A,B2} S 4 {B; A, 2} S 5 {AB;, 2} S 6 {A, B;2} Proposton. Only S and S 3 are stable. Proof: S s stable. There are three possble devatons, but none of them are proftable: A + B s unproftable when and 2 merge; +2s unproftable when A and B merge; and A +s unproftable when B and 2 merge. S 2 s not stable because A + s a proftable devaton: If B and 2 merge, A + wll leave A ndfferent but strctly better off; fb and 2 reman ndependent, both A and are strctly better off. S 3 s stable. There are three possble devatons (excludng symmetrc ones), but none s proftable: Breakng up B2 s unproftable when A and reman merged; A + B s unproftable when and 2 merge; +2s unproftable when A and B merge. S 4 s not stable because B +2 s a proftable devaton (whether A and separate or reman merged). S 5 s not stable because +2 s a proftable devaton (whether A and B separate or reman merged). S 6 s not stable because A + B s a proftable devaton (whether and 2 separate or reman merged). Q.E.D. Proposton says that the four frms ether reman ndependent or carry out two vertcal mergers. To understand ths concluson, t s useful to summarze the payoffs n Table nto the followng three rankngs. R : An exogenous merger, one fxng the confguraton among the remanng two frms, s always proftable. Ths s because a merger nternalzes ether the horzontal externalty (due to horzontal competton) or the vertcal externalty (due to double markup), whch benefts the mergng frms. 9 For ease of comparson, the fractons of the payoffs are multpled by, 000 andturnedntonumercal values. 8

9 R2 : A merger always hurts other frms and consequently a breakup always benefts other frms. By elmnatng double markup, a vertcal merger makes the merged entty more aggressve n the downstream competton, whch hurts other frms. A horzontal merger between duopolsts wll hurt the other ndustry by reducng quanttes suppled or demanded. R3 : S Pareto domnates S 3, whch n turn domnates S 2. Frms face horzontal externalty n S 3 and therefore tend to produce too much from the vewpont of ther jont profts. They face vertcal externalty n S 2 and tend to produce too lttle. Both externaltes are present n S, but ther opposte effects mtgate each other, so S domnates both S 2 and S 3. The horzontal externalty n S 3 s moderate because the downstream competton (Cournot rather than Bertrand) s mld, whle the vertcal externalty n S 2 s severe because t leads to successve monopoly, so S 3 domnates S 2. These three proft ranks help us understand the ntuton. Frst, t cannot be stable to have only one merger because the remanng two ndependent frms wll be better off mergng. They gan f the orgnally merged frm remans merged (R ), and wll gan even more f the merged frm breaks up (R2 ). Second, havng two horzontal mergers s unstable, as an upstream frm and a downstream frm would rather merge vertcally. Such a devaton s proftable f the other two frms also merge vertcally (R3 ), and s even more proftable f the other two frms do not merge (R2 ). That leaves two confguratons: all frms reman ndependent (S )orcarryouttwo vertcal mergers (S 3 ). Both are stable. Consder frst the no-merger case. An exogenous merger would have been proftable (R ). However, f the other two frms also merge, the partcpants n the frst merger would be worse off (R3 ). Therefore, no devaton (n the form of a merger) wll be carred out n S. Now consder two vertcal mergers. It s unproftable to ether break up (f the other merged frm remans merged R )or swtch to a horzontal merger (f the other two frms also merge horzontally R3 ). 2.3 Dscusson Four conclusons can be drawn from Proposton. Frst, mergers occur n waves. Proposton shows that t s stable to have two vertcal merged frms (S 3 ), and t s unstable to have a sngle merger (S 4, S 5,andS 6 ). Therefore, whenever a merger occurs, t must be accompaned by another. A sngle merger hurts the other two frms, whch wll then fnd t proftable to merge regardless of what the frst par does (dssolves or remans merged). Sothedrvngforceformergerstoclustersthenegatvempactofamerger on other frms. 0 0 The negatve mpact has also been emphaszed by Nlssen and Sorgard (998) and Frdolfsson and Stennek (2005). Ths result contrasts wth Qu and Zhou s (2007) dscovery that a postve mpact may also account for merger waves. 9

10 Second, t s also stable to have no merger (S ): all four frms may reman ndependent even though any ndvdual merger would have been proftable. When a gven merger s sad to be proftable, the confguraton among the remanng two frmssmplctly assumed to be fxed,.e., they reman ndependent. If those two frms also merge, however, the frst par wll be hurt. Concerns about a second merger s negatve mpact therefore prevent the frst one from takng place. Thrd, a merger wave may take place wthout any fundamental change n the underlyng condtons. Proposton predcts two stable confguratons: The frms may reman n S (or 4I, meanng four ndependent frms, for a more nformatve notaton) or they may carry out two vertcal mergers, endng up wth S 3 (or 2V). A change of the market structure from 4I to 2V duly endogenzes the vertcal merger wave. Because the two structures are stable under the same condtons, shftng from 4I to 2V does not requre any change n the economc fundamentals such as demand or technology. The trgger may be somethng trval or totally unrelated: mood, expectaton, rumor, etc. Although 4I and 2V are both stable, they are not on an equal footng. Swtchng from 4I to 2V s possble or even lkely because f, for whatever reason, a par of frms expect the other par to merge, they wll prepare to follow sut. The reverse process of jumpngfrom2vto4i,advestturewave,smoredffcult. If for some reason a par breaks up, t s n the best nterest of the second par not to follow. Ths asymmetry between the two stable confguratons may explan why n real lfe merger waves are much more common than dvestture waves. Fourth, a merger wave may be vertcal or horzontal dependng on the tradeoff between the vertcal and horzontal externaltes. In ths 2 2 settngamergerwavemay consst of two vertcal mergers (2V) or two horzontal mergers (S 2 or 2H), referred to respectvely as vertcal and horzontal merger waves. A frm chooses a vertcal or horzontal merger takng nto account possble reactons by the remanng frms, so ultmately t s a choce between 2V and 2H. As mentoned earler, 2V elmnates double markup but ntensfes horzontal competton; 2H does the opposte. In the present settng, the damage of double markup s greater than that of horzontal competton, so the frms end up makng two vertcal mergers. In other settngs, however, the comparson may be reversed and horzontal mergers may emerge n equlbrum. If, for example, the competton s à la Bertrand rather than Cournot, a merger wave could be horzontal. 3 Generalzaton The conclusons dscussed so far are derved from a hghly stylzed model wth symmetrc 2 2 frms, constant margnal costs, homogeneous products, lnear demand and Cournot competton. To what extent do they hold under more general assumptons? In ths sec- 0

11 ton we wll nvestgate fve varatons of the baselne model by relaxng ts assumptons, oneatatme, sothatproductsaredfferentated, the competton s n prce rather than quantty, the margnal cost s ncreasng, or the demand s non-lnear. Snce the baselne model s a specal case of some of the varaton models, we are able to put the conclusons n perspectve and understand better ther reason, condtons and mplcatons. In partcular, we wll dscuss the condtons for a merger wave to be vertcal or horzontal, and dentfy a second trgger of merger waves. 3. Product dfferentaton Suppose that the fnal products are dfferentated (though the nputs are stll homogeneous) so that the demand for frm s product s p = α q βq j,where, j {, 2} wth 6= j, andβ [0, ] represents the degree of product dfferentaton. Further, assume that each ndustry may compete on ether quantty or prce. Ths gves rse to the followng three combnatons: Cournot competton n both ndustres (Cournot-Cournot); upstream Cournot competton and downstream Bertrand competton (Cournot-Bertrand); and Bertrand competton n both ndustres (Bertrand-Bertrand). All other aspects of the model reman the same as n the baselne model. For each of the three cases, a payoff table smlar to Table can be constructed (an example s shown n the appendx), where each payoff s a functon of β only. 2 Proposton 2. () In the Cournot-Cournot case, S s stable for β>0.29 and S 3 s stable for any β. (2) In the Cournot-Bertrand case, S s stable for 0.22 <β<0.8, S 2 s stable for β>0.66, ands 3 s stable for β<0.66. (3) In the Bertrand-Bertrand case, S 3 s stable for β<0.66 and S 2 s stable for any β. Proof : See the appendx. As Proposton 2 suggests, a sngle merger (S 4, S 5 and S 6 )canneverbestable.the reason has been dscussed n the baselne model and wll be further elaborated later. The remanng three confguratons, no-merger (S ) and horzontal and vertcal merger waves (S 2 and S 3 ), can all be stable under certan condtons. A general pattern s that as competton ntensfes (movng from Cournot to Bertrand), horzontal mergers become more lkely, whle vertcal mergers and no-merger become less lkely. The equlbrum results shown n Table 2 exemplfy the mplcatons of Proposton 3. The parameter range ndcates the condton for a partcular confguraton to be stable, Furthermore, a 3 3 casesanalyzedntheappendx. 2 Agan, α c can be normalzed wthout losng any generalty.

12 and the parenthess below ndcates the proftable devaton that makes the confguraton unstable when the condton s volated. For example, n the Cournot-Cournot case, S s stable for β>0.29. If β<0.29, S becomes unstable because A + B s a proftable devaton. Table 2: Results of Propostons 2 and 3 Cases S (4I ) S 2 (2H ) S 3 (2V ) Cournot-Cournot β>0.29 Never (A + B) (A +) Always Cournot-Bertrand 0.22 <β<0.80 β>0.66 β<0.66 (A + B) (+2) (A +) (A + B) Bertrand-Bertrand Never β<0.66 Always (A + B) (A + B) Increasng mc γ<2 γ>2 γ<2 (+2) (A +) (+2) General demand Always σ> σ (A +) (A + B) Cournot-Cournot The settng s the same as the baselne model except that the fnal products are dfferentated, so the baselne model s a specal case wth β =. Greaterdfferenta- ton between the fnal products weakens the downstream competton. If products are suffcently dfferentated (β s small), the downstream horzontal externalty s greatly weakened. 4I s no longer stable because there s no need to use vertcal externalty to mtgate the horzontal externalty. In the baselne model, 2V domnates 2H because downstream horzontal competton s less damagng than double markup. Product dfferentaton further reduces the damage of horzontal competton, so 2V s always stable whle 2H s never stable for any β. Cournot-Bertrand When downstream frms compete on prce rather than quantty, downstream competton s ntensfed. 4I s stable only f the products are modestly dfferentated (ntermedate β). When products are hghly dfferentated the downstream competton s too weak; when products are close substtutes the downstream competton s too strong. 4I s unstable n ether case. As explaned earler, product dfferentaton favors 2V over 2H, so 2V contnues to be stable when products are suffcently dfferentated (small β). Conversely, when products are close substtutes (large β), ferce competton n the downstream ndustry rases both the benefts of horzontal mergers and the drawbacks of vertcal mergers, so 2H becomes stable. Bertrand-Bertrand 2

13 The upstream frms also compete on prce now, so upstream competton s ntensfed. In fact t s ntensfed to the greatest extent as nputs are homogeneous. 4I s never stable because upstream frms earn zero profts n the 4I stuaton and they wll always attempt to merge. As n the prevous case, 2V s stable when the products are suffcently dfferentated. 2H s stable for any β because the upstream horzontal competton s too strong Cost and demand Let us now move back to the settng wth a homogeneous fnal product and Cournot competton n both ndustres. In the baselne model, the cost of nput producton and the demand for the fnal product are both lnear: C(q) =cq and p = α Q. Onthecost sde, the model can be generalzed to allow ncreasng margnal cost (mc): C(q) =γq 2 wth γ 0. Note that the baselne model s a specal case of ncreasng mc wth γ =0. 4 On the demand sde, t can also become more general n the form of p = α Q σ wth α>0 and σ>0. Agan the baselne model s a specal case wth σ =. Note a pecular property of ths general demand functon: Its concavty, defned as p00 (Q)Q p 0 (Q), s constant.5 Proposton 3. () In the ncreasng margnal cost case wth C(q) =γq 2, S and S 3 are stable for γ<2, and S 2 s stable for γ>2. (2) In the general demand case wth p = α Q σ, S s stable for any σ, S 2 s stable for σ>, ands 3 s stable when σ. Proof : See the appendx. The results of Proposton 3 have already been summarzed n Table 2. Agan, a sngle merger (S 4, S 5 and S 6 ) s never stable. Increasng margnal cost Producng the nputs at ncreasng margnal cost wll reduce the upstream competton. 6 When the mc curve s steep (γ s large), 4I s unstable because an upstream merger wll not rase the nput prce by much and therefore wll do lttle damage to the 3 Startng from 2H, f an upstream and a downstream frm devate to form a vertcal merger, one scenaro they may face s that the other two frmsdonotmerge.theupstreamfrm s proft sharenthe merger wll then be very low because t s calculated based on the stuaton where the merger does not take place, n whch case ts proft wll be zero due to upstream prce competton. 4 In the baselne model the exact value of c s nconsequental, as all profts are proportonal to (α c) 2 and consequently α c has been normalzed wthout any loss of generalty. We may as well thnk that c =0. 5 p In fact, 00 (Q)Q = σ. Ths functon has been used by Greenhut and Ohta (976) and other p 0 (Q) scholars of merger ncentves and/or vertcally related ndustres. 6 In terms of olgopoly behavor, product homogenety wth ncreasng margnal costs s mathematcally equvalent to product dfferentaton wth constant margnal cost (Vves, 999). In a sense, the ncreasng margnal cost consdered here ntroduces dfferentaton to the nputs. 3

14 downstream frms. As a result, the downstream frms wll fnd t proftable to merge. An ncreasng margnal cost favors 2H over 2V. The beneft of a vertcal merger comes from output expanson due to the elmnaton of double markup. When the margnal cost of the nput ncreases wth quantty, expanson s ncreasngly costly, so the benefts of vertcal mergers decrease. When the mc curve s flat (γ s small), such a decrease s small, so 2V contnues to domnate 2H, meanng that 2V s stable whle 2H s not. General demand An ncrease n the concavty of demand lessens the severty of the double markup problem. 7 As wll be argued below, 4I s always threatened by horzontal mergers rather than vertcal ones. But demand concavty affects manly double markup, whch s present n both the 4I and 2H confguratons, so 2H s never a real threat and consequently 4I s stable for any value of the demand s concavty. When the demand s convex (σ <) the double markup problem s very severe, so frms merge vertcally to avod the damage, leadng to 2V. Conversely, when the demand s concave (σ >) doublemarkupslessof a problem. Avodng horzontal competton becomes the major concern, so 2H s stable. 3.3 Dscusson As was seen wth the baselne model, the stablty of a confguraton depends crucally on the relatve ntensty of double markup and horzontal competton n the two ndustres. Each of the fve varaton models ntroduces a parameter that affects one of the three ntenstes. Compared to the baselne model, dfferentaton of the fnal products (Cournot-Cournot) weakens the downstream competton; Bertrand competton downstream (Cournot-Bertrand) ntensfes the downstream competton; Bertrand competton upstream (Bertrand-Bertrand) ntensfes the upstream competton. Increasng margnal cost for nput producton weakens the upstream competton, whereas greater demand concavty lessens the severty of double markup. The equlbrum outcomes of the fve varaton models are presented graphcally n Fgure, where the bullet pont represents the baselne model s result as a specal case Mergng n waves In all cases wth any parameter values, there s always a stable confguraton nvolvng two mergers, ether horzontal or vertcal, whle a sngle merger (S 4, S 5 and S 6 )snever stable. So mergers always come n waves. The drvng force s stll the two proftablty 7 A sngle-level monopolst facng constant margnal cost c and demand p = α Q σ wll choose α c σ quantty Q =. In successve monopoly wth the same cost and demand, the quanty chosen +σ α c σ wll be Q 2 = <Q (+σ). As a measure of the severty of double markup, Q 2 Q 2 ( + σ) σ declnes wth σ, ndcatngthatdoublemarkupslessofaproblemwhenσ ncreases. Bascally, when σ s larger, the demand for nput s closer to the demand for the fnal product. 4

15 Fgure : Stable confguratons n the fve varaton models rankngs seen n the baselne model. An exogenous merger between any two frms s always proftable (R ), and a merger always hurts other frms (R2 ). Below we explan why they stll hold n general. Once they are establshed, our game rule mmedately mples that confguratons wth only sngle merger can never be stable. Consder frst the confguraton wth only a vertcal merger (S 4 ). The merged frm becomes more compettve n the downstream competton, so the merger hurts the other two frms. Fxng the frst merger, a merger between the remanng two frmssproftable because t nternalzes the vertcal externalty generated by double markup. Next consder the confguraton wth only an upstream horzontal merger (S 5 ). Ths merger rases the nput prce and thereby hurts downstream frms. Fxng the upstream merger, the downstream frms can merge from duopoly to monopoly, whch should always be proftable. But the complcaton s the presence of the upstream ndustry. In partcular, upstream frms may try to share the beneft of the downstream merger by rasng the nput prce, whch wll reduce the proftablty of the downstream merger. However, t can be verfed that n all the models we have consdered so far, a downstream merger never changes the equlbrum nput prce. 8 As a result, a downstream 8 In the baselne model, for example, the equlbrum nput prce s t = c + α c, whch does not (u+)(v+) 5

16 merger contnues to be proftable despte the upstream ndustry s response. Fnally consder the confguraton wth only a downstream horzontal merger (S 6 ). Ths merger reduces the quantty of nputs demanded wthout changng the nput prce, so t hurts upstream frms. Fxng the downstream merger, the upstream frms may merge from duopoly nto a monopoly, whch agan should always be proftable. And agan the complcaton s the presence of a vertcally related ndustry downstream. However, the demand that upstream frms face s derved from the downstream competton. As long as the downstream confguraton s fxed, that demand does not change. An upstream merger contnues then to be proftable despte the downstream ndustry s response The stablty of not mergng In all cases except Bertrand-Bertrand competton, t s stable under certan condtons for all frms to reman ndependent (4I). Frms n 4I may devate nto ether a horzontal or a vertcal merger, but what really matters s how the devators expect to do n a stuaton where the other two frms also merge. That s, the alternatve to 4I s essentally a merger wave resultng n ether 2H or 2V. The stablty of 4I depends on the four frms total profts and ther dstrbuton among them. In terms of total profts, 4I tends to outperform both 2H and 2V. In all cases except Bertrand-Bertrand competton, 2V elmnates double markup but retans horzontal competton, so the frms over-produce from the vewpont of ther jont profts, a horzontal externalty. By contrast, 2H removes horzontal competton but retans double markups, so the frms under-produce, whch can be vewed as a vertcal externalty. 4I has both externaltes, but snce the two externaltes move n opposte drectons, one mtgates the other and the frms total profts tend to ncrease. The dstrbuton of the total proft also matters for the stablty of 4I. For a devatng vertcal merger n 4I to be proftable, the mergng par wll have to earn more. Because the two vertcal pars are symmetrcal, the four frms total profts must therefore be hgher n 2V than n 4I, whch s unlkely. By contrast, 4I can easly be dsrupted by a horzontal merger; such a devaton need only beneft one horzontal par, not both. So the stablty of 4I s always threatened by a horzontal merger, not a vertcal one. Whether or not the threat wll materalze depends on the relatve ntensty of horzontal competton n the upstream and downstream ndustres. If the two compettons depend on d. Softheresadownstreammerger(.e.,d decreases by ), the equlbrum nput prce wll not change. A downstream merger rotates the demand for nputs clockwse around the ntercept. Ths rotaton has two opposte effects on t: For any gven t, the quantty demanded s smaller, so t tends to drop. At the same tme, the demand becomes less elastc, so t tendstorse. Inthecaseoflnear demand for the fnal product, the two forces exactly cancel each other so the equlbrum nput prce wll be ndependent of the number of downstream frms. For non-lnear demand, Greenhut and Ohta (976) and Zss (2005) have shown the same nvarance as long as the demand has constant concavty, whch s satsfed by the general demand adopted here. 6

17 are more or less balanced, 4I can be stable. For example, n the Bertrand-Bertrand stuaton, the upstream competton s very strong, so 4I s never stable at any β. In the Cournot-Bertrand stuaton, the competton s balanced only for moderate dfferentaton n the fnal products Vertcal and horzontal merger waves In all cases and wth any parameter values there s always a stable confguraton nvolvng two mergers, ether horzontal (2H) or vertcal (2V). Furthermore, except wth Bertrand- Bertrand competton, the two structures are mutually exclusve: When 2H s stable, 2V s unstable, and vce versa. For 2H, the threat to stablty comes manly from a vertcal merger. Gven the assumptons, the devatng frms are manly concerned about the stuaton n whch the other two frms also merge vertcally, so the alternatve market structure to 2H s bascally 2V. Smlarly, the alternatve to 2V s 2H. Therefore, 2H and 2V wll be essentally the only market structures that the frms consder when they ponder a merger or devaton. At any gven set of parameter values, ether 2H domnates 2V (for a horzontal par) or 2V domnates 2H (for both vertcal pars), so one and only one of the two confguratons s stable. Whch s stable depends crucally on how the total profts dstrbute among the four frms, whch n turn depends on the relatve ntensty of upstream and downstream competton. Because frms wthn an ndustry are assumed symmetrc, the two vertcal pars are symmetrc whle the two horzontal pars are not. For 2H to be stable, 2H needs to domnate 2V for only one horzontal par, ether upstream or downstream. By contrast, for 2V to be stable, 2V has to domnate 2H for all four frms. When competton n both ndustres s balanced, 2V tends to be stable. When an ndustry s competton s greatly ntensfed or weakened, 2H tends to be stable. For example, prce (rather than quantty) competton or closer substtutablty between fnal products wll lead to a horzontal merger wave. Greatly weakened competton n the upstream ndustry, due to ncreasng margnal costs of nput producton, wll have a smlar effect, because downstream competton s now relatvely ntensfed and frms there would lke to merge horzontally. These results demonstrate that changes of competton n one ndustry may nduce mergers n a vertcally related ndustry. To summarze, both 4I and 2V are dsrupted by 2H, whle 2H s dsrupted by 2V. 4I tends to outperform both 2H and 2V n terms of the four frms total profts. Between 2H and 2V, the comparson of total profts depends on the tradeoff between double markup and downstream horzontal competton. For example, when the demand for the fnal products s convex, double markup s a severe problem, so 2V prevals. When the downstream competton s Bertrand and the fnal products are close substtutes, the downstream competton s ntense, so frms merge horzontally. These predctons 7

18 are straghtforward. More nterestng and somewhat surprsng s the role of the relatve ntensty of competton n the two ndustres. When the ntenstes are balanced, both 4I and 2V tend to be stable. When the competton n one ndustry s greatly ntensfed or weakened, 2H tends to be stable Causes of merger waves A model of endogenous merger waves must explan not only why a merger wave takes place, but also why t dd not take place earler. In other words, the structure before and after the wave must both be stable. As Fgure ndcates, n all fve cases at any parameter value, there are at most two stable confguratons and at least one. For some ranges of the parameters there s a unque stable confguraton, whch nvarably contans two mergers, ether 2V or 2H. If the parameter falls nto that range, the mergers should take place mmedately, so the only explanaton for why they dd not take place earler s that the parameter was outsde the range, where t was stable for all frms to reman ndependent. Such a change of parameter value can be nterpreted as an economc shock. For example, n the Cournot-Cournot stuaton, 2V s the unque equlbrum for β<0.29, and 4I s an equlbrum (though not unque) for β>0.29. Ifβ drops from a value greater than 0.29 to a value below t, the ndustry wll undergo a wave of vertcal mergers. So an ncrease n the dfferentaton of the fnal products (due to, say, more nvestment n R&D or advertsng) may trgger a vertcal merger wave. Lkewse, a more convex demand curve may also trgger a vertcal merger wave. Smlarly, a horzontal merger wave may be trggered by greater substtutablty between the fnal products (Cournot-Bertrand), steeper margnal cost n nput producton, or greater concavty of demand. For some other ranges of the parameters there are exactly two stable structures, and n most cases one s 4I and the other s ether 2V or 2H. When that s the case, t s possble for a merger wave to take place wthout any change n the underlyng economc condtons, as the baselne model shows. For example, a vertcal merger wave s possble when the products are close substtutes (Cournot-Cournot), when margnal cost rses slowly, or when the demand s convex. A horzontal merger wave can occur when product dfferentaton s moderate (Cournot-Bertrand) or the demand s concave. So both tangble and ntangble causes may trgger a merger wave. 9 A tangble trgger s an economc shock that changes busness condtons. An ntangble trgger mght be a rumor or a sudden change n expectatons or mood whch shfts the market structure between two stable confguratons wthout any change n the underlyng economc 9 In a study of horzontal mergers, Toxvaerd (2008) found no merger as the unque equlbrum at one end of the fundamentals spectrum, multple mergers at the other end, and both structures as multple equlbra for ntermedate values of the fundamentals. The two types of trggers are therefore mpled by Toxvaerd s result. 8

19 condtons. The equlbrum may also swtch between 2H and 2V. In a sense ths s also a merger wave, although t nvolves more restructurng because frms have to dsntegrate and then re-ntegrate. Both tangble and ntangble trggers also can be found for such merger waves. For example, wth Bertrand-Bertrand competton the economy may swtch from 2V to 2H, the pattern of structural changes observed n the semconductor ndustry. Such a wave of vertcal dsntegraton followed by horzontal ntegraton can have an ntangble trgger when the products are poor substtutes, or a tangble trgger when the fnal products become closer substtutes. 4 Conclusons We have studed endogenous merger waves n vertcally related ndustres where frms can engage n both vertcal and horzontal mergers. Whether, why and how a merger wave takes place has been shown to depend on the balance between vertcal and horzontal externaltes and the balance between upstream and downstream competton. A merger wave may happen wth or wthout any fundamental change n the underlyng economc condtons. Ths research has generated many emprcally testable predctons relatng merger waves to condtons such as product dfferentaton, cost structure, and demand concavty. The smplest possble settng wth two upstream and two downstream frms was studed. In ths smple settng an exogenous merger always benefts the mergng frms and hurts non-mergng frms. These effects conform to common understandng of what a merger means, partcularly for vertcally related ndustres, and they hold regardless of whether frms compete on prce or quantty. The drawback of ths smple settng s that horzontal and vertcal merger waves cannot co-exst. 20 In fact they are mutually exclusve and always generate a tradeoff. Mergng from duopoly nto a monopoly s also specal, so t s mportant to go beyond the 2 2 settng. Presented n the appendx, an analyss of the 3 3 settng shows that there are two equlbra, one n whch all frms reman ndependent and the other n whch three vertcal mergers take place. Smlar patterns have been found n the 3 4, 4 3 and4 4 settngs (not shown). Merger decsons n ths model are made smultaneously. A sequental game would 20 Interestng ndustry dynamcs nvolvng both horzontal and vertcal mergers can be seen n the vertcally related ron ore mnng and steelmakng ndustres. In November 2007, the world s two largest ron ore producers, BHP Bllton and Ro Tnto, announced a plan for a horzontal merger. Concerned that the concentraton of the ron ore market would rase ron ore prces and jeopardze the downstream steel ndustry, one of Ro Tnto s bggest customers, Chnese state-owned Alumnum Corporaton of Chna (Chnalco), launched a preemptve move n February 2009 to purchase 4.9% of Ro Tnto s shares. Such a (partal) vertcal merger was apparently meant to preempt a horzontal merger n the upstream ndustry. 9

20 have the advantage of generatng strategc ncentves for mergers and may therefore yeld other explanatons for merger waves (Qu and Zhou, 2007). But the dsadvantage s that the equlbrum wll be senstve to the order of moves and other detals of the game, 2 whch a researcher has no compellng reason or suffcent nformaton to specfy exogenously. So ths study has adopted a smultaneous game and an equlbrum concept borrowed from one-to-one matchng games wth externaltes. Ths has enabled us to capture the essental nterdependence of merger ncentves wthout havng to specfy the detals. It may therefore prove useful n studyng other merger-related ssues. The merger surplus was calculated assumng a fxed confguraton among remanng frms, whch seems to contradct the dea that frms consder all possble confguratons when contemplatng a merger. However, f confguratons are allowed to vary n calculatng proft sharng, the profts wll be ll-defned because there are multple confguratons. The assumpton of arm s length transacton may seem problematc when an ndustry has only one frm, but what s really needed s double markup and the property that vertcal transactons depend on the market structure n both ndustres. Such assumptons are relevant n many stuatons. An alternatve to arm s length transactons may be two-part tarff. The Bertrand-Bertrand assumpton removes double markup and may therefore havealreadycapturedwhatwllhappenwhenatwo-parttarff s used between upstream and downstream frms. Ths has been a frst step n studyng endogenous merger waves n vertcally related ndustres. Many nterestng extensons reman to be explored, such as asymmetrc frms, dynamc game rules, and more sophstcated settngs and sharng rules. 5 Appendx Procedures for provng propostons 2 and 3 The calculaton and proofs are tedous. Here we provde only the procedures. In each case, we construct a payoff table smlar to Table. Each payoff wll be a functon contanng a sngle parameter (t turns out that α c can be normalzed to wthout any loss of generalty). For example, n the Cournot-Cournot case the followng payoff table results. Other tables are avalable from the correspondng author on request. Table 3: Payoffs n the Cournot-Cournot case 2 For example, Colangelo s (995) sequental game leads to very dfferent predctons about the equlbrum market structure dependng on the dentty of the frst acquston target, whch s exogenously gven. 20