No 281. Supply Chain Innovations and Partial Ownership. Matthias Hunold, Shiva Shekhar

Transcription

1 No 281 Supply Chan Innovatons and Partal Ownershp Matthas Hunold, Shva Shekhar February 2018

2 IMPRINT DICE DISCUSSION PAPER Publshed by düsseldorf unversty press (dup) on behalf of Henrch Hene Unverstät Düsseldorf, Faculty of Economcs, Düsseldorf Insttute for Competton Economcs (DICE), Unverstätsstraße 1, Düsseldorf, Germany Edtor: Prof. Dr. Hans Theo Normann Düsseldorf Insttute for Competton Economcs (DICE) Phone: +49(0) , e mal: normann@dce.hhu.de DICE DISCUSSION PAPER All rghts reserved. Düsseldorf, Germany, 2018 ISSN (onlne) ISBN The workng papers publshed n the Seres consttute work n progress crculated to stmulate dscusson and crtcal comments. Vews expressed represent exclusvely the authors own opnons and do not necessarly reflect those of the edtor.

3 Supply Chan Innovatons and Partal Ownershp Matthas Hunold and Shva Shekhar February 2018 Abstract We show that competng downstream frms may rather nvest n ther neffcent nhouse producton than help mprove the technology of the effcent suppler, even f ths s costless. Even worse, a downstream frm can have strong ncentves to decrease the effcency of the suppler n order to mprove ts outsde optons. We demonstrate that non-controllng partal backward ownershp can algn the ncentves of the suppler and ts customers wth respect to supply chan nnovatons. JEL classfcaton: L22, L40 Keywords: knowledge spllover, nnovaton, mnorty shareholdngs, supply chan effcency, vertcal partal ownershp Both authors are at the Düsseldorf Insttute for Competton Economcs (DICE) of the Henrch- Hene-Unverstät (HHU) Düsseldorf, Unverstätsstr. 1, Düsseldorf, Germany; hunold@dce.hhu.de, shekhar@dce.hhu.de. We thank Toker Doganoglu, Paul Hedhues, Ismael Martínez-Martínez, Danel Müller, Hans-Theo Normann, Frank Schlütter, Joel Stebale, Tm Thomes, as well as semnar partcpants at DICE and the Unversty of Würzburg for helpful comments and dscussons.

4 1 Introducton Cooperaton among supplers and ther buyers s essental to mprove supply chans. An mportant element s knowledge sharng as ths can reduce neffcences whch arse due to factors such as the nablty to correctly forecast future demand, low producton technologes and ncompatble qualty control measures. 1 For example, a downstream frm usng an nput mght gan knowledge about how the suppler could produce the nputs more effcently, ether due to ts experence n other markets or own research and development actvtes. 2 The tact nature of some of these supply chan relatons can lead to stuatons where cooperatve actons are non-contractble as ther success s dffcult to verfy n court. For nstance, knowledge sharng mght nvolve exploratory dscussons and collaboratons between the engneers of the customer and ts suppler. 3 In such stuatons, t s crucal that there are ncentves to share knowledge. In ths artcle, we frst show that f supply chan cooperaton s not contractble, t may not take place, even when t s costless and ncreases effcency and ndustry profts. The reason s that the mproved effcency of a suppler can reduce the downstream frm s proft. Ths occurs when the ncreased effcency enables the suppler to serve also competng downstream frms n a better way, for nstance, at lower costs. Even though the ndustry proft may ncrease when effcency s hgher, the downstream frms threat pont when barganng wth the suppler may be worse. Sourcng from an alternatve, less effcent source becomes less attractve when the compettors are at the same tme served wth better or cheaper nputs from the effcent suppler. The ncentves of downstream frms wth respect to supply chan mprovements are thus not algned wth the objectves of ndustry proft maxmzaton. In partcular, we show that downstream frms may rather nvest n mprovng an neffcent alternatve supply source than mprovng the suppler from whch they actually source. Even worse, the downstream frms can have strong ncentves to decrease the effcency of ther suppler. In a second step, we look at nstruments that can help overcome ths neffcency n supply chans. We show that non-controllng partal backward ownershp whch the downstream frms hold of ther suppler, can algn the ncentves wth respect to supply chan cooperaton. The ntuton s that wth partal backward ownershp a downstream frm benefts from a decrease n the costs of ts suppler and thus has ncentves to foster such nnovatons 1 Hartley (2000) and Kwon and Suh (2004) show that nformaton sharng between frms bulds stronger supply chan relatonshps. Lee et al. (1997) suggest that nformaton sharng by downstream frms to upstream frms can mtgate the bullwhp effect. 2 Honda, for example, organzes Kazen (contnuous mprovement) events at supplers facltes. Smlarly, Toyota teaches the supplers ts famed Toyota Producton System. The company has also set up Jshuken, or study group teams, as a way to help the manufacturer and ts supplers learn together how to mprove operatons. Executves and engneers who work for Toyota and ts supplers meet under the drecton of a Toyota sense and go from plant to plant mprovng supplers processes. 3 See Buldng Deep Suppler Relatonshps, Jeffrey Lker and Thomas Y. Cho, Harvard Busness Revew, December 2004 ( last access February 2018). Ths artcle contans the example of Honda of Amerca sendng an engneer to spend a year wth a Cleveland based company, Atlantc Tool and De, where he offered suggestons whch led to marked mprovements on the shop floors. 1

5 f the share s suffcently hgh. In partcular, f each of the n symmetrc downstream frms has a non-controllng backward ownershp share of 1/n, all downstream frms have ncentves to foster nnovatons that reduce the costs of ther common suppler. In addton, no downstream frm has an ncentve to nvest neffcently n an nferor alternatve nput producton technology. 2 Related lterature The startng pont of our analyss s the observaton that a downstream frm may be n a poston to help ts suppler mprove ts effcency. The relevance of ths channel s well documented n the lterature. For nstance, Kotabe et al. (2003) study knowledge exchange n the U.S. and Japanese automotve ndustres and argue that transferrng productve knowledge between a buyer and the suppler s assocated to performance mprovements of the latter. Dyer and Hatch (2004) explan that Toyota encouraged knowledge sharng wth ts supplers. They argue that ths has led to an ncreased effcency of ther own supplers compared to supplers of rval car producers and resulted n a sgnfcant compettve advantage for Toyota. Bönte and Kelbach (2005) nvestgate formal and nformal modes of vertcal R&Dcooperaton among frms n Germany and ther decsons to engage n such cooperaton. They provde evdence that nformal R&D-cooperaton s the most relevant cooperaton mode and fnd that the ablty of frms to protect knowledge s a key determnant of formal and nformal cooperaton. A downstream frm s ncentves to share knowledge that ncreases the effcency of ts suppler has also been studed theoretcally. Hughes and Kao (2001) analyze the ncentves of competng downstream frms to share knowledge wth ther common suppler. They argue that retalers mght be less wllng to share knowledge when the suppler has an own downstream busness, as ths could enjoy a compettve advantage when obtanng the knowledge of ts rvals. Bönte and Wethaus (2007) study the case that knowledge sharng of a downstream frm does not only decrease the suppler s producton costs, but also the producton costs of downstream rvals for a gven nput prce. They conclude that ths drect strengthenng of a rval can prevent knowledge dsspaton. In a complementary artcle, Wethaus (2005) shows that competng frms choose dentcal R&D approaches n order to maxmze knowledge flows between each other. The present artcle s related to two strands of lterature that nvolve partal vertcal ownershp. The frst strand focuses on the compettve effects of partal vertcal ownershp, whereas the second strand focuses on the effects on nvestments n a supply chan, but mostly abstracts from competton. There s a growng lterature that has dentfed varous (ant-) compettve effects of partal vertcal ownershp. One ant-compettve effect s market foreclosure. Baumol and Ordover (1994), Spegel (2013) and Glo et al. (2016) manly consder the effects of controllng an upstream (or downstream) frm va partal ownershp. They emphasze that wth controllng partal acqustons, a frm only nternalzes parts of another frm s profts and losses, 2

6 although t can fully dstort ts strategy to ncrease ts own proft. Therefore, dedcated foreclosure strateges (refusal to supply or bad terms of trade) can be more attractve when compared to full ntegraton. Hunold (2017) has shown that also non-controllng backward ownershp n combnaton wth unform upstream prces can deter competton of downstream frms and decrease consumer surplus. Besdes foreclosure, non-controllng forward ownershp wth lnear tarffs can reduce double margnalzaton and downstream prces, to the beneft of customers (Flath, 1989). Ownershp stakes that downstream frms hold of upstream frms (backward ownershp) tend to have no effect on downstream prces when there s an upstream monopolst (Greenlee and Raskovch, 2006). However, backward ownershp can lead to hgher prces wth both upstream competton and downstream competton n prces as downstream frms nternalze each other s demand through the margn on nput sales (Hunold and Stahl, 2016). 4 To abstract from these prcng effects and focus on cooperaton ncentves, we use downstream quantty competton as a benchmark n the present artcle. Dasgupta and Tao (2000) show that a suppler has more ncentves to make relatonshp specfc nvestments when the customer holds a non-controllng ownershp share of the suppler. The reason s that general nvestments, whch lead to an nput that the suppler can also sell on other markets, become less attractve for the suppler once the customer partcpates n the profts of such alternatve sales of the nput because the suppler s barganng poston s worse n ths case. 5 Smlarly, Cho et al. (2014) consder that an upstream frm can sell exactly one ndvsble unt of nput to one of two dfferent customers, whch do not compete downstream. They assume the customer that values the nput more can make a costly nvestment that ncreases the value for both customers. As they assume that the prce whch ths customer has to pay s the value for the other customer (the resource s auctoned off), the spllover reduces the nvestment ncentves because nvestments then ncrease the prce. Wth partal backward ownershp, the customer pays effectvely less because t gets part of the prce back through the proft partcpaton, whch can agan ncrease the nvestment ncentve. However, partal backward ownershp s not a soluton f the suppler makes take-t-or-leave-t (TIOLI) offers, f each customer can buy a unt of the nput, or f both customers have symmetrc nvestment capabltes. Instead, we consder a settng where a suppler sells nputs do dfferent, and possbly competng, downstream frms and show that partal ownershp can be helpful n all these cases. Besdes supply chan relatons, t s worth mentonng that non-controllng partal ownershp among frms whch are (potental) compettors can also facltate effcency enhancng cooperaton, and n partcular knowledge sharng, albet wth the possble sde effect of reducng product market competton. (Mathews, 2006; Ghosh and Morta, 2017). Allen and Phllps (2000) emprcally study partal ownershp held by corporatons n U.S. 4 In certan stuatons wth asymmetrc nformaton between a manufacturer and ts exclusve customer, non-controllng forward ownershp of the manufacturer n ts customer may also allow them to commt to hgher prces (Focco, 2016). 5 In partcular, the customer s outsde opton opton n case of general nputs s not zero anymore, but postve, whch reduces the gans from trade wth the suppler and thus leads to a more favorable Nashbarganng outcome for the customer. 3

7 frms and dentfy many nstances where downstream frms hold ownershp stakes of upstream frms. They fnd that such partal ownershp combned wth product market relatonshps n R&D-ntensve ndustres s assocated wth mprovements n operatng performance and substantal ncreases n nvestment expendtures by target frms. Ther fndngs are consstent wth our theory that partal backward ownershp facltates cooperaton, and n partcular technology transfer to the target frm. More generally, ther fndngs underlne the mportance of understandng also conceptually the relatonshp between partal ownershp and supply chan cooperaton. 3 Market structure and strategy There are n > 1 symmetrc downstream frms. The producton of one unt of downstream output requres one unt of a homogeneous nput, produced ether by suppler U or nhouse. The margnal cost of suppler U s c U = c > 0, and that of the nhouse producton of each downstream frm s c I = c + c, where c > 0 s the dfference n margnal costs between U and the less effcent nhouse producton. 6 All other producton costs are assumed to be zero. The upstream suppler charges two-part tarffs wth a fxed fee f and a margnal prce w to the n downstream frms ndexed {1,.., n}. 7 We start wth the case where downstream frms produce homogeneous products, compete n quanttes, and where there are no ownershp lnks between the frms. The game has three stages: 1. Each downstream frm decdes whether to nduce an nnovaton at suppler U or ts nhouse supply. If the nnovaton s nduced, the margnal cost of ether suppler U or the nhouse producton decreases by k (0, c) to c U = c k or c I = c + c k, respectvely. 8 The resultng margnal costs become publc knowledge. 2. Suppler U offers secret two-part contracts {f, w } to each downstream frm. Downstream frms ndvdually and smultaneously decde whether to accept or reject the contract offered by U. The acceptance decsons become publc, but not the contract terms. 3. Downstream frms smultaneously buy nput quanttes x U from suppler U, produce x I nput quanttes nhouse, produce output quanttes q and sell them. As regards stage 1, we manly analyze how profts before any nnovaton costs change wth such nnovatons. At ths pont, we abstract away from costs of nnovaton. 6 Ths way of modelng upstream competton s used by, for nstance, Chen (2001), Sandons and Faul- Oller (2006) as well as Hunold and Stahl (2016). One can also thnk of nhouse producton as a compettve frnge supply. A potental dfference only arses f a downstream frm nduces nnovatons at only ts nhouse supply or a frnge that s used also by others, but ths s not essental for our arguments. 7 See Vllas-Boas (2007) and Bonnet and Dubos (2010) for emprcal evdence of non-lnear wholesale tarffs. 8 We assume that c s suffcently large such that c U remans postve. Otherwse, the suppler mght want to produce an nfnte amount of nputs. 4

8 Suppler U s proft s gven by π U = n ( w c ) U x U + f (1) =1 f all downstream frms accept ts contract offer. The downstream prce s a functon of the total output Q = n =1 q and gven by P (Q) wth P < 0. Downstream frm s proft before the fxed fee f n case t accepts the contract of U s gven by π = P (Q) q w x U c I x I. (2) Each downstream frm maxmzes ts proft subject to the constrant x U + x I q, whereby nput purchases are suffcent to satsfy the quantty demanded. Before the downstream frms order and sell quanttes n stage 3, acceptance or rejecton decsons of the wholesale contracts become publc, but the actual supply condtons of the contracts reman secret. A breakdown n negotatons between suppler U and a customer s assumed to be observable but not verfable (n court), and therefore cannot be contracted upon. 9 It seems plausble that n many nstances, an ndustry nsder can fnd out whch upstream frm supples a compettor, whereas t tends to be harder to learn about the exact contract terms. However, one mght wonder whether secret contracts are stll as plausble when downstream frms hold non-controllng ownershp stakes of a suppler. In any case, we show n the extenson secton that one can also obtan our man results when the contract terms are observable, or completely unobservable. We study symmetrc Perfect Bayesan Equlbra n whch downstream frms do not revse ther belefs about the offer made to the other downstream frms when recevng an out-ofequlbrum offer (passve belefs). 10 For what follows, we assume that the proft functons satsfy standard regularty condtons such that the equlbrum s characterzed by frst order condtons and downstream quanttes are strategc substtutes. 11 Denote by π(y, z), the resultng equlbrum flow proft (P (Q) y) q when t s common knowledge that frm has margnal costs of y and all the n 1 other downstream frms have margnal costs of z. Assume that the proft decreases when all costs ncrease unformly from the same level: π(s, s)/ s < 0, and ncreases by a fnte amount when the compettors margnal costs ncrease f there s competton: > π(y, z)/ z > 0. All these assumptons are fulflled for the lnear demand P (Q) = 1 Q. We study prcng, output decson and nnovaton ncentves absent partal ownershp n Secton 4. Afterwards, we ntroduce partal ownershp and study how t affects the market outcome n Secton 5. In Secton 6, we show that ownershp arrangements whch ncrease 9 See Caprce (2006) for a smlar setup. Our results are qualtatvely the same f the contract acceptance s not observable. See Annex B for detals. 10 See Nocke and Rey (2014) as well as Hart and Trole (1990); O Bren and Shaffer (1992); McAfee and Schwartz (1994); Caprce (2006); Rey and Trole (2007); Arya and Mttendorf (2011) for a smlar approach. 11 It s suffcent that profts are strctly concave n own quanttes and the cross dervatves negatve: 2 π /( q q ) < 0 for. 5

9 nnovaton ncentves can be proftable for the ndustry and the nvolved owners. In the above settng, suppler U s assumed able to make take-t-or-leave-t offers to the downstream frms. Ths endows the suppler wth all the barganng power. We show n Secton 6 that our results also hold n cases where barganng power s more balanced. 4 Innovaton wthout partal ownershp 4.1 Market prces and quanttes For the case wthout partal ownershp, we frst derve the output choces and equlbrum contracts whch suppler U charges the downstream frms when the terms of the wholesale contracts reman secret (stages 2 and 3 of the game). Wth passve belefs, upon recevng a contract offer each downstream frm antcpates that ts rvals wll stck to the antcpated equlbrum quantty Q. Moreover, the proft whch suppler U can obtan from the other downstream frms s unaffected by a change n the margnal prce that U charges downstream frm, as ths prce s unobserved by the rvals whch can thus not condton ther output decsons on t. Gven the contracts wth the other downstream frms, suppler U chooses the tarff for downstream frm as f U and were an ntegrated entty. Suppler U can nfluence the quantty choce of downstream frm through w and can adjust the fxed fee f accordngly, and therefore sets w to maxmze (P (q + Q ) c U ) q. Downstream frm exactly maxmzes ths proft f w = c U. Ths s essentally the margnal cost prcng result obtaned for secret contracts and passve belefs when competton s n quanttes, as n Hart and Trole (1990) and Rey and Vergé (2004). Lemma 1. Wthout partal ownershp, suppler U charges tarffs wth margnal prces w equal to margnal costs c U. Proof. See Annex A. Total output equals the output of a Cournot olgopoly wth n frms that all have margnal costs of c U. The flow proft of a downstream frm s thus π(c U, c U ). Suppler U extracts the downstream profts through the fxed fees, but t has to leave each downstream frm the proft that ths frm could earn when producng nhouse. Ths devaton proft equals π(c I, c U ) because the non-devatng downstream frms all have margnal costs c U and (as contract acceptance becomes publc) are aware when settng quanttes n stage 3 that the devatng frm sources nhouse at costs c I. 12 Lemma 2. In equlbrum, all downstream frms accept the wholesale contract {w = c U, f = π(c U, c U ) π(c I, c U )}. Suppler U s proft s π U = n f = n [ π(c U, c U ) π(c I, c U ) ], and a downstream frm s proft s π(c I, c U ). 12 When contract acceptance s unobservable, the devaton proft stll has the features that t decreases n the frnge costs c I and ncreases n the cost c U of suppler U. See Annex B. 6

10 As we show n the extensons, our results do not rely on the assumpton of secret two-part tarffs. Analogous results can be obtaned for observable two-part tarffs and also for the case that the suppler does not sell nputs on a per-unt bass, but can sell to each downstream frm a machne that allows t to produce nputs at margnal costs of c U nstead of c I. Moreover, most results are also obtaned wth lnear tarffs. What matters for our analyss are two thngs. Frst, the proft of the downstream frm conssts (at least partly) of the value of ts outsde opton, that s the proft t can obtan when t produces the nputs nhouse whle the other downstream frms stll source from the effcent suppler U. Second, t s mportant that the ndustry profts ncrease when the margnal costs of the effcent suppler U decrease. 4.2 Innovaton ncentves Let us now turn to the nnovaton ncentves n stage 1. We consder nnovatons that reduce the margnal nput costs. Our leadng example s knowledge that a downstream frm has ganed when usng the nputs n ts producton process. Ths could be knowledge about how the nput can be produced n a more effcent way. Transferrng ths knowledge to the suppler mght nvolve exploratory dscussons and collaboratons of the engneers of the customer and ts suppler, and the causal success of these mght be dffcult to measure. Consequently, such knowledge mght be rather mplct and dffcult to contract upon. Therefore, our man assumpton s that the suppler and customer cannot contract upon the nnovaton. Ths makes the ssue of whether the nnovaton takes place nterestng. For the moment, we analyze the ncentves of one downstream frm, takng as gven that the other downstream frms do not nduce nnovatons. We also assume for smplcty that nducng the nnovaton (for nstance through knowledge transfer) s costless for the downstream frm, as s the nnovaton tself. Ths generalzes to the case that there s a cost, as long as ths s not too large. We generally allow the downstream frm to smultaneously nduce nnovatons at suppler U and nhouse (to exclude ths, one could assume sharply ncreasng ncremental costs of nducng nnovatons). Recall that f downstream frm decdes to transfer knowledge, ths results n a decrease of the margnal cost of suppler U from c U = c to c U = c k. We assume for now that the suppler can serve all downstream frms equally at the lower costs n case of nnovaton. 13 Let us now analyze the ncentve of a downstream frm to share nformaton. Recall from Lemma 2 that the proft of a downstream frm s ts outsde opton proft π(c I, c U ). Ths proft ncreases n the margnal costs c U of the compettors n case they all source from U, whle ths downstream frm produces the nput nhouse at costs of c I. In turn, a decrease of the cost c U decreases the equlbrum proft of a downstream frm. Ths yelds Proposton 1. Wthout backward ownershp, a downstream frm has no ncentve to nduce an nnovaton whch reduces ts suppler s margnal costs c U. A downstream frm has an ncentve to reduce the nhouse producton costs c I. 13 We generalze ths n Subsecton

11 The downstream frm does not obtan any of the benefts from the sharng of cost reducng technology. Even worse, the downstream frm only gets ts outsde opton proft, whch decreases as the margnal prces offered by U to ts downstream rvals fall n response to a decrease n the producton costs c U. Ths yelds Corollary 1. A downstream frm does not nduce nnovatons that reduce the costs of suppler U f the suppler makes take-t-or-leave-t wholesale tarff offers and there are no ownershp lnks among the frms, even f nducng the nnovatons s costless. Note that these results hold both f the suppler can use the nnovaton provded by one downstream equally for reducng the costs of supplyng that downstream frm and ts compettors, or whether the cost reducton for supplyng compettors s smaller (partal spllover). See Subsecton 7.2 for detals. Rent extracton and neffcent nnovatons. It s an nterestng nsght that a downstream frm has ncentves to mprove ts neffcent nhouse producton, but no ncentves to help mprove the effcency of ts suppler. Even worse: The downstream frm has strct ncentves to decrease the effcency of the effcent suppler, whereas t has strct ncentves to mprove the nhouse supply even f t s certan that ths remans the less effcent supply source that wll ultmately not be used for producton. Ths means that technology development could just be a means for a downstream frm to extract rents from ts suppler by mprovng the threat pont n negotatons, wth no effects on ndustry profts and consumer surplus. The technology sharng ncentves of the customer and ts suppler are clearly msalgned n the ndustry. Consder the case that nnovaton s costly and the downstream frm has to choose whether to help nnovate the producton of the effcent suppler or ts (n any case) less neffcent nhouse supply (for example, there mght be only one busy engneer who knows about the nnovaton potental and can ether mplement t here or there). If the nnovaton costs are not too hgh, the downstream frm wll nnovate and reduce the costs of ts nhouse supply. Ths s socally neffcent as t does not reduce the actual producton costs. 14 It does though mprove the frm s outsde opton to sourcng from the effcent suppler and by ths nduces a shft of rents from the suppler to the customer. At the same tme, a socally desrable nnovaton and thus cost reducton n the actual supply chan wll not be undertaken. Ths s a clear neffcency. Contractng upon nnovatons. For reference, assume that the suppler and customer can contract upon the success of the nnovaton, so that the suppler can commt to compensate the downstream frm for actons that lead to lower upstream producton costs. 14 At least as long as the nhouse producton remans less effcent than suppler U. Even f t becomes more effcent, ths remans an sub-optmal nvestment f the alternatve would have been to further reduce the costs of the more effcent suppler U. 8

12 The jont proft of a downstream frm and suppler U s π U + π f = n [ π(c U, c U ) π(c I, c U ) ] + π(c I, c U ) = n π(c U, c U ) (n 1) π(c I, c U ). (3) As π(c U, c U ) decreases n c U and π(c I, c U ) ncrease n c U, the jont proft clearly ncreases as c U decreases. Ths means that t s proftable for suppler U and the downstream frm to wrte an enforceable contract whch rewards the downstream frm wth a transfer t π(c I, c) π(c I, c k) for conductng the cost decreasng nnovaton. 5 Innovaton wth partal backward ownershp We now analyze how the prcng and the ncentves to nduce nnovatons change when there s backward ownershp. Each downstream frm {1, 2..n} may now have a partal noncontrollng ownershp share of suppler U, whch we denote by δ [0, 1). Partal ownershp refers to an ownershp share strctly below one. Backward means that a downstream frm holds shares of an upstream frm. Non-controllng refers to ownershp that does not nvolve control over the target frm s prcng strategy (such as pure fnancal nterests, non-votng shares) and controllng refers to one that does. Unless ndcated otherwse, n the followng analyss ownershp s non-controllng, no matter how large the share s Equlbrum prces and quanttes We frst show that suppler U charges tarffs wth margnal prces equal to margnal costs even wth non-controllng partal backward ownershp. We then characterze the resultng fxed fees and equlbrum profts for the subgame consstng of stages 2 and 3. The total proft of a downstream frm s the sum of the prevous downstream proft and the upstream partcpaton: π f + δ π U. If all downstream frms source from suppler U, the proft of downstream frm equals Π = (P (q BR + Q ) (1 δ )w ) q BR n + δ [(wj c U ) qj + f j ] (1 δ )f, where q BR s the optmal quantty set by frm gven ts nput costs and the antcpated output of the other frms, that s Q = n j qj. Note that for a postve ownershp share δ, frm gets a dscount of δ not only on the upstream margn w c U, but also on the fxed fee f. 15 Ths avods the dscusson concernng the level of shareholdngs at whch control arses, whch depends on corporate law, shareholder agreement and the dstrbuton of ownershp share holdngs n the target frm. j 9

13 Suppler U offers each downstream frm a contract {w, f } that maxmzes ts proft π U = subject to (w c U ) q BR + f + j [(w j c U ) q j + f j ] Π j Π nhouse j j. A downstream frm s antcpated proft when sourcng nhouse s Q DEV Π nhouse = max q [( p(q + Q DEV ) c ) ] I q + δ [(wj c U ) qj DEV + f j ]. Ths s the outsde opton proft of a downstream frm when sourcng nhouse at cost c I. As a breakdown n negotatons s observable, the antcpated quanttes set by frm j are denoted as qj DEV. Ths s the optmal quantty for frm j when the nput costs of frm are c I and antcpatng that everyone else obtans equlbrum prces wk for k. We defne := j qj DEV. Gven the contracts offered to the other downstream frms, t s stll optmal for suppler U to offer a downstream frm a contract wth a margnal prce equal to ts margnal costs c U. As a result, partal backward ownershp does not affect the equlbrum quanttes of the subgame startng n stage 2. Ths mples that partal ownershp δ affects the downstream proft only through the fxed fee. Lemma 3. For any structure of non-controllng backward ownershp shares δ [0, 1), suppler U offers tarffs wth margnal prces equal to margnal costs, w = c U, and serves all downstream frms. The fxed fees are gven by f = [ π(c U, c U ) π(c I, c U ) ] /(1 δ ), and the downstream proft s gven by Proof. See Annex A. π f = π(c I, c U 1 ) 1 δ + π(c U, c U 1 ) δ. (4) 1 δ j 1 δ j j j j 5.2 Innovaton ncentves We now study how partal ownershp affects the nnovaton ncentves. For δ > 0, the equlbrum downstream proft s a weghted sum of the flow proft n case of a devaton, π(c I, c U ), and the actual flow proft on the equlbrum path, π(c U, c U ) see equaton (4). Recall that when c U decreases, the devaton proft π(c I, c U ) decreases, but the actual flow proft π(c U, c U ) ncreases. As δ ncreases, the weght of the devaton proft π(c I, c U ) n a downstream frm s proft decreases, and that of the actual flow proft π(c U, c U ) ncreases. Downstream frm benefts more, or at least suffers less, from a decrease n c U as ts backward ownershp share δ ncreases. Proposton 2. For a suffcently hgh partal ownershp share δ, downstream frm benefts from a decrease n the costs c U of suppler U and thus has ncentves to nduce an nnovaton, at least f ths s costless. 10

14 Proof. The proft of a downstream frm s gven by (4) and ncreases when the margnal costs of suppler U, c U, decrease f the weght attached to the devaton proft π(c I, c U ) s 1 suffcently low. The weght s gven by 1 δ j 1 δ j and s, other thngs equal, hghest for n = 2 and δ j = 0 wth j. In ths case the weght s [1 δ ]. Ths yelds Π = π f = π(c I, c U ) [1 δ ] + π(c U, c U ) [δ ]. As the dervatve π(c I, c U )/ c U s bounded away from and π(c U, c U )/ c U < 0, there exsts a δ [0, 1) such that the margnal proft Π / c U s negatve at ths share and all larger shares. For a dscrete change of c U from c to c k, there, thus, exsts a suffcently large ownershp share δ such that nducng such a decrease n the costs c U s proftable for downstream frm. Proposton 2 shows that t s possble to provde one downstream frm wth the ncentves to reduce the costs of suppler U by means of an approprately szed partal ownershp share. However, t mght be that potentally all downstream frms could nduce such nnovatons. For nstance, each downstream frm could, wth certanty or some probablty, nduce a dfferent nnovaton, such that cost reductons add up. One could also magne that there s complementarty across downstream frms such that each frm needs to have ncentves to cooperate n order to acheve an upstream nnovaton. 16 In ths case t s desrable to algn the ncentves of all downstream frms. The next proposton shows that ths s feasble. Proposton 3. Suppose that each downstream frm has a symmetrc non-controllng backward ownershp share of 1/n. A downstream frm s equlbrum proft s π(c U, c U ) and each downstream frm s wllng to nduce nnovatons that reduce the costs c U of suppler U, whle no downstream frm has an ncentve to reduce the nhouse producton costs c I. Proof. Suppose that all downstream frms have the same ownershp share δ. The proft of a downstream frm stated n (4) reduces to [ ] [ ] π f = π(c I, c U δ ) 1 (n 1) + π(c U, c U δ ) (n 1). 1 δ 1 δ If the term n the frst bracket s zero, only the second summand remans. Ths s the case for δ 1 (n 1) 1 δ = 0 = δ = 1 n. In ths case, the proft of a downstream frm reduces to π(c U, c U ) and clearly ncreases as c U decreases, and s unaffected by c I. 16 Instead, f the downstream frms have perfectly substtutable knowledge (or smlar nputs for upstream nnovaton), t mght be suffcent to ncentvze one downstream n order to acheve an mprovement of suppler U. However, ths leaves potentally neffcent nvestments n nferor supply sources, whch alter the outsde optons and thus terms of trade. 11

15 The ntuton behnd ths result s that by acqurng a large enough partal ownershp n the suppler, the downstream frm becomes the resdual clamant of a proporton of the ndustry proft. Ths algns the ncentves of the downstream frms wth those of suppler U and thus nduces cost reducng technology transfer to the effcent suppler U, and prevents neffcent nvestment n less effcent supply sources. It s remarkable that the stuaton where each of n downstream frms has a share of 1/n, the downstream frms jontly own suppler U, smlar to a jont venture. 17 Note that a share of 1/n perfectly algns the ncentves wth respect to ndustry profts. Stll, accordng to Proposton 2, a smaller share can already be suffcent for downstream profts to ncrease f suppler U becomes more effcent. 6 Proftablty of ownershp acqustons Let us nvestgate whether non-controllng backward ownershp arrangements are proftable, frst for the ndustry as a whole, and then for the owners of two frms whch create a backward ownershp lnk. The total ndustry proft s gven by n π(c U, c U ). The flow proft of a downstream frm (before subtractng the fxed fee) s π(c U, c U ). It s plausble (and we have assumed) that ths proft ncreases f the costs of all downstream frms (that s c U ) decrease by the same amount. For nstance, ths s the case wth lnear demand. Non-controllng backward ownershp only affects the ndustry proft by ncreasng the ncentves of the downstream frms to help decrease the costs c U of the effcent upstream suppler U. 18 In stuatons where the downstream frms can potentally help decrease the cost, t s therefore proftable for the ndustry to have backward ownershp. If the owners of all the frms n the ndustry (or at least those of U and all downstream frms) can effcently arrange ownershp lnks (as wth Coasan barganng), one should expect to backward ownershp n the ndustry. If effcent barganng (and possbly contractng) between all ndustry players s not possble, t s nterestng to study whether backward ownershp arrangements also arse f only decentral ownershp trade s feasble. Let us study the case that there are ntally no ownershp lnks between frms n the ndustry and that each frm s owned by a separate outsde nvestor. Consder that the owners of suppler U and downstream frm negotate blaterally about a sale of a proft partcpaton δ > 0 of U to frm n return for a lump sum transfer to the ntal owner of U. Ths s a proftable trade f the jont proft of U and s hgher n case of ths backward ownershp arrangement. Ther jont proft s π ( c U, c U ) + (n 1) [ π ( c U, c U ) π ( c I, c U )]. (5) Note that ths proft s not a functon of δ as ths s just a redstrbuton of shares from the 17 We abstract here from the queston of corporate control of U, whch s not central to our man arguments but of course mmedate the n downstream together have all proft rghts of U (of course, an outsde nvestor wth no or hardly any proft rghts may stll hold a golden share or have other rghts of control). 18 When downstream frms compete n prce, backward ownershp can further ncrease profts by ncreasng the downstream prces, see Subsecton

16 ntal owner of U to frm. The frst part s the proft obtaned from sales of frm and the second part s the proft whch suppler U obtans of the other n 1 downstream frms (the flow proft mnus the alternatve sourcng proft). The flow proft π ( c U, c U ) ncreases as c U decreases and also π ( c I, c U ) decreases as c U decreases. Ths mples that the total proft of frms U and ncreases as c U decreases. When c U decreases, ths proft ncreases even more than the total ndustry proft because suppler U benefts from decreasng the outsde opton profts π ( c I, c U ) of the other n 1 downstream frms (a redstrbuton effect). Lemma 4. Both the total ndustry as well as the par of one downstream frm and the effcent suppler beneft from non-controllng backward ownershp arrangements whch algn the ncentves of downstream frms wth respect to effcency ncreases of ther suppler. Recall that the blateral proft n (5) s the same as n the reference case n Secton 4 where we dscussed the dffcultes of contractng on actons that foster nnovatons (equaton (3)). In ths perspectve, backward ownershp s an alternatve way to wrte a contract that changes the cooperaton ncentves of a downstream frm. Ths s valuable when drectly contractng upon certan cooperatve actons and ther success s practcally mpossble. 7 Further analyses 7.1 Barganng over wholesale tarffs We have so far assumed that suppler U can make take-t-or-leave-t offers. Ths mples that U has the barganng power to extract the ndustry proft, except for the downstream frms outsde optons. In ths subsecton, we relax ths assumpton and look at the case when the downstream frms have more barganng power and ask the queston: Can downstream barganng power nduce knowledge sharng of downstream frms smlar to partal ownershp? Startng from the case that the downstream frms have no barganng power, we fnd that up to a crtcal level of barganng power, there s no sharng of technology and we get the result of neffcent vertcal nnovaton ncentves as before. For hgher levels of downstream barganng power, the downstream frms have ncentves to reduce the costs of the effcent suppler even wthout vertcal ownershp. Suppose each downstream frm has barganng power of β [0, 1], so that the effcent suppler s barganng power s 1 β. These power shares determne the splt of the addtonal rents from tradng between the partes. We mantan the assumpton of secret wholesale contracts. The equlbrum tarffs solve the correspondng Nash barganng problem max(π (w, w w,f ) f Π nhouse ) β (π U π U,DEV ) (1 β), where gven passve belefs, upon recevng a contract offer each downstream frm antcpates nput costs w of all other downstream frms. The antcpated upstream proft n case of a 13

17 breakdown n negotaton s π U,DEV = [(wj c U ) qj DEV + fj ] j and qj DEV s the quantty ordered by ts rvals n case of breakdown n negotatons wth frm. By the same logc as n the case where suppler U makes take-t-or-leave-t offers, we obtan Lemma 5. Blateral barganng between suppler U and each downstream frm over secret two-part tarffs yelds contracts wth margnal prces that equal margnal costs of U. Proof. See Annex A. Agan, barganng n two-part tarffs results n margnal wholesale prces that maxmze the addtonal blateral surplus of the two negotatng frms. As contracts are secret, the actual margnal wholesale prce does not affect the output choces of the other downstream frms. Hence, the upstream and the downstream frm act lke an ntegrated entty when settng wholesale prces and set the margnal wholesale prce equal to the suppler s margnal costs ndependent of the dstrbuton of barganng power. The assocated fxed fees are gven as f = (1 β) ( π(c U, c U ) π(c I, c U ) ). (6) One can see that the fxed fee decreases as the barganng power β of the downstream frm ncreases. The fxed fees are always weakly postve. The net downstream proft s a weghted sum of the equlbrum flow proft and the outsde opton proft: π f = β π(c U, c U ) + (1 β) π(c I, c U ). (7) If a downstream frm has no barganng power wth respect to the suppler (β = 0), t obtans the outsde opton proft whch decreases as c U falls, as n case of take-t-or-leave-t offers by suppler U analyzed before. Instead, when the downstream frm has all the barganng power (β = 1), t obtans the full flow proft π(c U, c U ). In the latter case, the downstream frm clearly has an ncentve to ncrease the actual flow profts by nducng cost reducng nnovaton at suppler U. As the downstream proft stated n (7) s contnuous n β, we can show the exstence of a β = β, such that for all β > β, t holds that (π f ) > 0. Hence, a downstream frm has c U ncentves to nduce cost reducng nnovaton upstream for large enough barganng power. We summarze the result n Proposton 4. A downstream frm has ncentves to foster upstream nnovaton f t has suffcent barganng power. It s mportant to note that the mere fact that a downstream frm has some level of barganng power (β > 0) does not ensure that a downstream frm has ncentves to foster 14

18 upstream nnovaton. The barganng power needs to be large enough to ncentvze the downstream frms. Hence, there s scope for partal backward ownershp to algn the ncentves as long as the nsuffcent downstream barganng power. It s ntutve to see from the expresson of the net proft n equaton (7) that as the downstream barganng power β rses the downstream frm cares more about the actual flow profts than ts outsde opton. So, the negatve effect from a fall n c U s lower than the postve effect nduced for β large enough. In ths case, the downstream frm has ncentves to nduce cost-reducng nnovaton. In general, barganng power s the ablty of an economc agent to obtan rents from a trade. A proft maxmzng agent therefore does not easly gve up ths power. 19 In vew of non-contractble supply chan cooperaton, such as knowledge sharng, t mght though be benefcal for an upstream frm to endow the downstream frms wth some barganng power n order to nduce non-contractble supply chan nnovatons. The queston s how a frm can commt to far supply terms n the future. One possblty could be long-term framework agreements, but these may not be renegotaton proof. Another soluton s backward ownershp whch smlar to downstream barganng power can algn the ncentves of downstream frms. An obvous advantage of ownershp shares s that they are structural arrangements, whch are n place ndependent of supply contracts. For example, a customer mght dsregard a promse of a suppler to far terms of trade as cheap talk. Instead, ownershp shares are contractual rghts, whch the suppler (or ts ntal owner) can sell to a downstream frm. As ths algns the ncentves wth respect to upstream nnovaton n a credble way, t should also be easer for the (ntal owner of the) suppler to cash part of the addtonal economc value of ths arrangement from the downstream frm through the sales prce of the ownershp stake. 7.2 Lmted nnovaton spllovers to rvals So far, we have assumed that when a downstream frm nduces an nnovaton at ts suppler, ths reduces the margnal producton costs for all downstream frms equally. Suppose we relax ths assumpton and assume that f technology s shared, the rvals can only beneft from a proporton σ [0, 1) of the cost reducton, whereas so far we analyzed the case of σ = 1. It s straghtforward to show that for any σ the wholesale prces (w ) are equal to margnal costs and the proft of a downstream frm wthout backward ownershp s the outsde opton value π(c I, c σk). (8) For σ > 0, the downstream proft decreases n case of an nnovaton absent partal ownershp. For σ = 0, the downstream proft, gven by (8), does not change and a downstream frm s ndfferent between sharng and not sharng the technology wth the upstream suppler. We have shown before that even for the case of σ = 1, a downstream frm s profts decrease the most when t nduces an nnovaton, partal backward ownershp can algn ncentves of the 19 In terms of Nash barganng: adjust β to the own dsadvantage. 15

19 downstream frm wth the ndustry proft and hence nduce cooperaton (Propostons 2 and 3). Consequently, also for any σ [0, 1) t s possble to fnd a level of backward ownershp such that technology sharng s nduced. 7.3 Monopolstc downstream frms If the downstream frms do not compete or do not have the same suppler, an mprovement n the nput costs of the suppler does not harm a downstream frm. If the suppler makes a take-t-or-leave-t offer that sets the downstream frm ndfferent to sourcng from ts best alternatve, the downstream frm s resultng proft s ndependent from the suppler s costs. If the downstream frm has some barganng power, t wll obtan part of the gans from trade wth the suppler. These gans are hgher f the suppler s costs are lower. As a consequence, a downstream frm has ncentves to foster effcency mprovements of ts suppler. Ths dffers from the case of competng downstream frms wth a common suppler, where suffcent barganng power of the downstream frm s necessary to algn ts ncentves (Proposton 4). 7.4 Publc wholesale tarffs Suppose that the supply contracts are publc. In order to maxmze the ndustry proft, an unconstraned monopolst offers observable two-part tarffs to competng downstream frms wth margnal prces above margnal costs. Interestngly, when competng aganst a compettve frnge, t can be optmal for the constraned monopolst to charge margnal wholesale prces below the alternatve sourcng costs c I, even f ths leads to total output above the ndustry proft maxmzng level. The ntuton s that the upstream frm reduces wholesale prces to reduce the outsde opton of the competng downstream frms n order to extract more profts through the fxed fees. We assume that margnal prces cannot be below margnal costs (w c U ) and show that there exsts a level of alternatve sourcng costs c I below whch the corner soluton of settng the margnal prce w equal to c U s optmal for the effcent suppler U, both wthout and wth partal backward ownershp. Ths mples that one can obtan the same results on nnovaton ncentves and partal backward ownershp wth observable wholesale tarffs. To show that the man results can also be obtaned wth publc contracts, we only analyze the case where margnal cost prcng results n ths extenson. We conjecture that one can obtan smlar results also for the case where prces are above margnal costs. For the man results to hold, are postve relatonshp between margnal costs and the resultng sales prces s mportant. It s not necessary that the prces are equal to margnal costs. No partal ownershp. If all downstream frms source from suppler U, the downstream frm sets quanttes that solve the frst order condtons π q = P (Q) q + P (Q) w = 0, {1...n}. 16

20 The soluton to the n frst order condtons gves us equlbrum quanttes and profts for gven margnal nput prces whch we denote by q (w, w ), Q (w, w ) and π (w, w ), where w s the vector of the wholesale prces charged to the frms other than. As the contracts are publc, unlke before, the equlbrum quanttes and profts of each frm depend drectly on all the actual margnal wholesale prces set by suppler U. The outsde opton proft of frm s π (c I, w ). The fxed fees are f = π (w, w ) π (w = c I, w ). The suppler solves max π U = (P (Q ) c U ) Q (w, w ) w, w n π (w = c I, w ) =1 subject to w c U. The followng lemma characterzes the parameter range n whch margnal cost prcng occurs also wth publc contracts. Lemma 6. There exsts a cost level c I = ĉ, such that for all c I < ĉ, the suppler sets wholesale prces equal to margnal costs. The contracts then are the same as n the case of secret contracts. Hence, the downstream frm has no ncentve to nduce an nnovaton whch reduces the margnal costs of the effcent suppler U. Proof. See Annex A. The ntuton s as wth secret contracts. A reducton n costs of the suppler reduces the rval s nput prces and thus worsens the outsde opton of a downstream frm. Partal ownershp. We now show that partal ownershp algns ncentves of the downstream frms wth ndustry surplus also n case of publc wholesale contracts. For expostonal purposes, let us assume that there are two frms (n = 2) whch both have partal ownershp δ = δ of the suppler. Consequently, the proft of frm s 2 (P (q 1 + q 2 ) w ) q + δ [(w j c U ) q j + f j ] f 1, 2. j=1 Let us denote the equlbrum quanttes as (q 1, q 2) and the total quantty n the market as Q = q 1 + q 2. The outsde opton of frm s to source nhouse, whch yelds a proft of Π nhouse = (P (q + q j ) c I ) q + δ[(w j c U ) q j ] + δ f j. Movng on to the contractng stage, the suppler sets (w, f ) for 1, 2. The suppler s problem s to max (w1, f 1 ),(w 2, f 2 ) π U = [(w 1 c U ) q 1 + (w 2 c U ) q 2 + f 1 + f 2 ] subject to π f π (c I, w j ) 1, 2. 17

21 The fxed fees are set such that the partcpaton constrant of the downstream frms are bndng, whch yelds f = π π nhouse (c I,w j ). 20 The suppler s maxmzaton problem becomes 1 δ max π U = (P (Q ) c U ) Q + δ 2 =1 (w c U ) q 2 =1 π nhouse. w 1,w 2 1 δ The followng proposton characterzes the parameter space when the suppler uses margnal cost prcng n wholesale prcng strategy. Proposton 5. For c I < ĉ, the suppler sets wholesale prces equal to margnal costs. For suffcently large partal ownershp shares, the downstream frm s equlbrum proft s π(c U, c U ) and each downstream frm s wllng to nduce nnovatons that reduce the costs c U of suppler U. In ths case, no downstream frm has an ncentve to reduce the nhouse producton costs c I. Proof. See Annex A. For c I < ĉ, the suppler charges margnal prces equal to ts margnal cost. Under ths parameter restrcton, the results are as n the case wth secret contracts. Smlar to the proof of Proposton 3, one can show that for δ = 1, the downstream profts and ndustry profts are 2 algned. Downstream frms are the resdual clamants of a proporton of the ndustry proft and hence would lke to reduce the costs of the ncumbent suppler U. For larger alternatve sourcng costs, we do not provde a formal proof at ths pont, but we conjecture that one can obtan smlar results. 7.5 Lnear upstream prces and partal ownershp So far, we have consdered that suppler U offers two-part tarffs. Let us now look at the case of lnear tarffs, whch means f = 0. For smplcty, suppose that the margnal wholesale prces are observable. As the lnear wholesale prces w are the only source of ncome for suppler U, t clearly has an ncentve to rase them above ts margnal costs c U. Absent partal backward ownershp and f the nhouse supply s suffcently attractve, whch means that the cost dfference c I c U s not too large, t s optmal for U to charge w = c I. Wth nput costs of c I when sourcng from U, the proft of a downstream frm does not depend on whether t sources from U or produces the nputs nhouse. As a consequence, the equlbrum proft equals the outsde opton proft π(c I, c I ). As wth two part tarffs, the proft of a downstream frm does not ncrease as ts suppler s costs (c U ) decrease. 21 Ths means that there s no ncentve for the downstream frm to nvest n the supply relatonshp n a way that reduces the nput costs of suppler U. There s, however, agan an ncentve to reduce the nhouse producton costs c I f a lower nput cost level for all downstream frms leads to hgher profts. 20 Note here that n the term π π nhouse (c I, w j ), the fxed fees f j cancel out. 21 At least as long as the change s not so large that the suppler becomes an unconstraned monopolst. 18