ECOLE POLYTECHNIQUE. Retail structure and product variety. Marie-Laure Allain Patrick Waelbroeck. hal , version 1-6 Feb 2008.

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1 ECOLE POLYTECHNIQUE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Retail struture and produt variety Marie-Laure Allain Patrik Waelbroek January 2006 Cahier n LABORATOIRE D'ECONOMETRIE 1rue Desartes F Paris (33) mailto:lyza.raon@shs.poly.polytehnique.fr

2 Retail struture and produt variety Marie-Laure Allain 1 Patrik Waelbroek 2 January 2006 Cahier n Résumé: Abstrat: Mots lés : Nous examinons l'impat de la struture horizontale et vertiale d'un marhé sur les initations à l'innovation et sur la variété des produits. Nous onsidérons le marhé d'un bien homogène où un produteur peut innover pour étendre sa gamme de produits en réant un nouveau produit substitut. Le oût de lanement du nouveau produit est fixe, et réparti entre les ativités de prodution et de distribution. Nous montrons qu'une haîne intégrée vertialement offre une plus grande variété de produits qu'une haîne de monopoles. Si le oût de lanement du nouveau produit est réparti équitablement entre les deux seteurs, ou supporté essentiellement par l'amont, une onurrene imparfaite dans le seteur aval ne restaure que partiellement les initations à innover de la struture vertiale. En revanhe, si e oût est supporté prinipalement par le seteur aval, la onurrene en aval peut amener plus d'innovation que dans une struture vertialement intégrée. We examine the impat of horizontal and vertial market struture on innovation and produt variety. We onsider a market for a homogeneous good where it is possible to innovate to launh a new substitute produt. The ost of launhing the new produt is fixed and spread between the manufaturing and the retail industries. We show that a vertially intergrated firm offers a wider variety of produts than a hain of monopolies. If the ost of launhing a new produt is equally shared among the vertial struture or mostly supported by upstream firms, retail ompetition partially restores the inentives to innovate of the vertial struture. Yet when the ost of launhing a new produt is mostly supported by the retail setor, downstream ompetition even leads to more innovation than vertial integration. Conurrene, Distribution, Relation vertiale, Variété des produits Key Words : Competition, Retailing, Vertial struture, Produt variety Classifiation JEL: L13, L22, L40 1 Laboratoire d Eonométrie, CNRS et Eole polytehnique. 2 ENST Paris.

3 Retail struture and produt variety Marie-Laure Allain and Patrik Waelbroek Abstrat In this paper, we examine the impat of horizontal and vertial market struture on innovation and produt variety. We onsider a market for a homogeneous good where it is possible to innovate to launh a new substitute produt. The ost of launhing the new produt is fixed and spread between the manufaturing and the retail industries. We show that a vertially intergrated firm offers a wider variety of produts than a hain of monopolies. If the ost of launhing a new produt is equally shared among the vertial struture or mostly supported by upstream firms, retail ompetition partially restores the inentives to innovate of the vertial struture. Yet when the ost of launhing a new produt is mostly supported by the retail setor, downstream ompetition even leads to more innovation than vertial integration. 1 Introdution The market struture of the retail setor is an important poliy issue in most developed ountries. Sine the seventies, the emergene of new store formats and the development of large and inreasingly international retail hains, through diversifiation and external growth, have onsiderably modified the retail landsape. The inreasing onentration of the retail industry has resulted in an oligopolisti struture in most European ountries: the 5 main retail hains ontrol about 65% of the food sales in the UK, 80% in Frane, 65% in Germany, 56% in Spain and up to 98.5% in Norway. Large mergers among retail groups have ourred in the nineties. The 2000 merger between Carrefour and Promodès has given birth to the seond largest CNRS, Laboratoire d Eonométrie de l Eole Polytehnique (1 rue Desartes Paris, Frane, marie-laure.allain@polytehnique.fr) and London Business Shool. ENST (Rue Barrault, Paris, waelbroe@enst.fr). 1

4 worldwide retail group with sales above 70 billions euro. In 1999, the Amerian giant Wal Mart aquired the British supermarket hain ASDA, but the same year, the European Commission set restritive onditions to the merger of the German retailers REWE and Meinl. The Commission even prohibited merger of the Finnish groups Kesko and Tuko in This trend towards inreasing retail onentration leads to inreased buying power from the retailers, and thus indues a shift in the balane of power between retailers and their suppliers, whih has generated many onflits. The retail industry may be ompared to the bottlenek of an hourglass, ontrolling the links between numerous manufaturers of onsumer goods and their onsumers. Publi authorities have debated over the last years issues related to the bargaining power between produers and retailers in order to assess the eonomi onsequenes of inreasing retail onentration (see, for instane, the green book on vertial restraints published by the European ommission in 1997 or the offiial report by the British Offie of Fair Trading of 1999). Broadly speaking, arguments against large retailers relate to the fat that a marked disequilibrium in the bargaining power between suppliers and retailers an be detrimental to the survival of small produers and espeially to the variety of produts available to the onsumers. Both retailers and suppliers onsider the breadth of the produt line as a ruial point in the bargaining proess. On the one hand, produers implement innovation strategies that segment the market in order to disriminate between different types of onsumers. They thus tend to extend their produt lines. On the other hand, retailers fear brand proliferation as it inreases osts assoiated with inventory ontrol and involves inreasing marketing and promotion expenses. As a onsequene, retailers often impose ontrats that limit the number of produts available on the shelves. Hene the eonomi inentives to produe and distribute a new variety differ aording to the side of the vertial relation. While produers expet their new produts to inrease demand by building new nihes, retailers fear market segmentation that inreases distribution osts (Marvel and Pek, 2000). Upstream and downstream firms goals an thus diverge and harsh ommerial bargaining talks reflet these divergenes. In order to understand the eonomi fores behind the onflit, we analyze the inentives to supply variety in a vertially related industry between innovating produers, retailers and onsumers. We determine the effet of the vertial relation on soial welfare by studying the inentives to inrease produt variety aording to the ompetitiveness of the downstream setor. We fous on two main points: the size of the innovation, i.e. its novelty, and the fixed osts of launhing the new produt, split 2

5 up into prodution and retail osts related to inventory ontrol and promotion. We study a vertial relation between a monopolist produer and a retail setor, whih is suessively monopolisti and oligopolisti. The produers develop a new produt (that we will also refer to as "innovation") that is ostly to develop and that generates distribution osts. We analyze how the way these fixed osts are shared between produers and retailers influene the inentives to offer a new variety. It is diffiult to assess the osts assoiated with the launhing of a new produt. Deloitte and Touhe (1990) estimate that this ost is on average $222 per item and per store for a produer. The ost an be broken down as follows: 18% omes from researh and development, 66% from marketing expenses, and 16% in slotting allowanes that an reah $36.4 per item and per store. For a retailer, osts related to assessing the market potential of a produt, hanging the information proessing system and inventory ontrol are smaller (about $13.5 per item and per store). However, these osts do not inlude the opportunity ost related to shelf spae oupied by the produt line that ould have been granted to another produt, nor the marketing efforts that are required to sell the new produt, nor the ost of deleting another item from the atalogue that an reah, aording to the same study, $11 per item per store. Of ourse, these estimates must be taken with aution sine these osts greatly vary aording to the nature of the new produt. From an empirial perspetive, the diffiulty to orretly measure these osts and the strategi dimension of the issue ertainly explain why there are few studies on this topi. A reent survey of German food produers (Weiss and Wittkopp, 2005) highlights a negative relationship between the bargaining power of large retailers and the introdution of new produts. However, this effet is redued by the market power of produers. While there is a huge literature on the eonomi analysis of vertial relationships on the one hand, and on innovation and inentives to innovate on the other hand, there has been little work on the inentives to innovate in a vertially separated industry. Yet most of the onsumers goods are sold through a vertial hannel, and the produers have to deal with retailers to sell their produts. Lariviere and Padmanabhan (1997) analyze slotting allowanes paid by produers to distribute their produts through retail hannels. In a hain of monopolies, they show that a produerwhoisbetterinformedondemandonditionsthantheretaileransethigh wholesale pries in order to signal a high expeted demand. The produer thus pays a slotting allowane that inreases with the fixed distribution ost supported by the retailer. However, their analysis takes the innovation deision as given and does not 3

6 take ompetition between retailers into aount. Broas (2002) is loser to our analysis, but she deals with a proess innovation and not a produt innovation on the one hand, and on the other hand, the vertial struture that links the researh unit to the produers does not inlude a retailer. Her artile analyses the effet of ompetition and vertial integration between produers and the researh units on the inentives to innovate. Researh units liense their proess innovation that an be more or less substitutable. The effiieny of a vertial integration between researh units and produers depends on the substitutability and the size of the innovation. We assume on the ontrary that R&D ativities are arried out in-house. Produt variety in a ompetitive and vertially strutured setting also involves bargaining issues. Inderst and Shaffer (2003) analyze the effet of a horizontal merger between non-ompeting retailers (assuming for instane that they are operating on two distint geographial areas) on the variety offered to onsumers. They show that after the merger and in order to improve their bargaining power with the produers, retailers might have to remove some produts from the shelves: making their produt lines more uniform would enable them to get better bargaining terms with their suppliers. In this ase, an inrease in the bargaining of the retailers leads to a derease in produt variety. However, rather than looking at produt line simplifiation, we address the question of launhing new produts when it inurs speifi osts. Our artile ontributes to the literature on three points. First, we show that a vertially integrated struture better internalizes the fixed osts of R&D and marketing than a hain of separated monopolies and offer a larger variety of produts. This first result rests on a lassial redution of the ineffiieny related to the double margin that limits produt innovation. Next, we show that a situation in whih retailers are ompeting gives more inentives to improve the produt line than a hain of monopolies, mainly by reduing vertial ineffiienies. Finally, we show that ompetition between retailers an surprisingly lead to more produt innovation than a vertially integrated struture when the ost of launhing the new produt is mainly borne by the upstream firm. This result stems from the fat that the produer might strategially redue ompetition between retailers by harging them retail pries that fore them to speialize. In this ase, one of the retailers speializes in the new produt, while the other only sell the old produt. By reduing ompetition in suh way, this situation allows the produer to redue the osts assoiated with the new produt, where a vertially integrated struture would not have innovated. In addition, we 4

7 show that this inrease in produt variety is welfare-enhaning. The remainder of the artile is organized as follows. First, we study the deision of a produer who sells his produts through a vertially separated hain of monopolies in Setion 2. Next, we analyze in setion 3 a situation where the same produer faes two retailers who ompete for his produts. The last setion onludes the artile. 2 The model We onsider a vertial relation between a produer P and her retailer D. We assume that the produer is unable to set up shop and sell independently. She initially produes a good A at a onstant marginal ost A that we normalise to zero without loss of generality. The produer an invest a fixed ost Ω to innovate and then produes also a substitute good B with a onstant marginal ost B = A =0. Produts A and B are horizontally differentiated: we onsider here produt innovation as a mean to improve produt variety, not produt quality. Inverse demand is linear and translates onsumers taste for variety, with P I theunitprieofgoodi, and q I the quantity of good I on the market ({I,J} = {A, B}): P I (q I,q J )= q I q J Parameter, that we assume to be in [0,1[, measures the substitution between the two goods. The retailer distributes the produt A without ost. However if he deides to introdue the new produt on the final market, he has to inur a fixed ost of marketing and inventory ontrol, noted F. The retailer also faes a onstant marginal ost of distribution independent of the type of produt that is distributed, whih we normalise to zero. The exogenous parameters of the models are:, Ω, F. We ompare the produer s inentives to invest the fixed ost of innovation Ω in two different ases: when the produer and the retailer are vertially integrated and when they are separated. 2.1 The benhmark ase: vertially integrated monopoly We first onsider as a benhmark a situation in whih the produer and the distributor are vertially integrated. The integrated unit only innovates and sells both produts if it is profitable to do so. If the vertially integrated struture does not innovate, it sells only A in quantity q A = 1, andwithprofit ΠVI 2 A = 1. As introduing the 4 5

8 new produt involves a fixed ost, the struture that innovates has to hoose whether to ontinue selling produt A in addition to produt B or not (selling only B is a dominated strategy, as it would lead to a maximum profit ofπ VI B = ΠVI A Ω F ). If on the ontrary the vertially integrated struture hooses to distribute both produts, the profit-maximizing quantities are then q A = q B = 1, and the profit ΠIV 2(1+) A+B = 1 F Ω. 2(1+) The vertially integrated monopoly thus innovates and sells both produts if and only if it leads to higher profits than without innovation, whih is equivalent to the following ondition: F + Ω 1 4(1 + ) Thus the new produt is profitable to market as long as the total fixed ost of produing and retailing the new good are not above a threshold level that dereases with the substituability between produts: as tends to 1 and produts beome more substitutable, the firm is less likely to introdue the new produt as its profits beome smaller. In a vertially integrated struture, this lassial annibalisation effet is driving innovation deisions. 2.2 Produt variety in a vertially separated hain We now study how the innovation deisions of a vertially separated industry depend on how the total fixed ost is shared between the produer and the retailer. When the produer and the retailer are vertially separated, the innovation deisions are taken sequentially. Formally, the produer and the retailers play the following game: in the first stage, the produer deides whether to inrease her produt line and aordingly spends the fixed ost Ω. Then she sets the two wholesale pries w A and w B,eahin 1 [0, 1]. In the seond stage, the retailer deides whih goods to sell to the onsumers (and whether to pay the fixed ost F ) and whih quantities q A and q B to order. The last stage is onsumption in the downstream market. We are looking for the subgame perfet equilibria of this game. Vertial separation, induing a double margin externality, modifies the inentives to innovate for the produer. 1 Any wholesale prie above 1 would lead to a zero demand, and would thus not be rational, so that we an make this assumption without loss of generality. 6

9 2.2.1 Downstream listing and priing strategy In the seond stage, the retailer hooses his listing strategy given the wholesale pries harged by the produer. If, on the one hand, he deides to distribute the old produt only, he orders the optimal quantity q A = w A and gets a profit Π D = (w A) 2 while 2 4 the produer gets Π P = w A(w A ), possibly less the fixed ost Ω. If, on the other hand, 2 the retailer deides to distribute produt B only, provided that the upstream firm has innovated, he has nevertheless to pay the fixed ost F. He then maximizes his profit byorderingthequantityq B = w B and makes a profit ofπ D 2 B = (w B) 2 F. 4 Finally, if the retailer hooses to distribute both produts, he orders quantities q I = Max{0, w I (w J ) } (with {I,J} = {A, B}). 2( 2 ) Given the wholesale pries w A and w B, the retailer determines his listing strategy by omparing his profits with or without the new produt. Regardless of w A and w B, the retailer always prefers to distribute both goods instead of only produt B: the strategy of selling the new produt only is dominated by the strategy of selling both produts. In addition, if w B 1 + w A, the retailer would make losses if he sold both produts, in whih ase he prefers to save on the fixed ost F and sell produt A only. In the other ases, the optimal listing strategy depends on the fixed ost F. Finally, the retailer distributes the new produt only if the fixed ost F of marketing is smaller than a threshold level that dereases with the wholesale prie w B : F (1 w A) 2 +( w B ) 2 2(1 w A )(1 w B ) 4(1 2 ) (1 w A) 2 4 The following figure illustrates the listing hoie of the retailer in the (w B,F) plane for a given value of w A. (1) 7

10 F (1 (1 wa)) 2 4(1 ) 2 A only A+B +w A 1 w B Upstream strategy Figure 1: listing strategies of the retailer In the first stage, the produer deides whether to innovate and sets the wholesale pries antiipating the outome of the seond stage. If she does not innovate, she sets a wholesale prie of w A = 1 that orresponds to a maximal profit 2 ofπp A = 1.Ifonthe 8 ontrary she innovates, she has to make sure that the retailer will list the new produt as she would make at most Π P B = 1 Ω otherwise. She then sets the two wholesale 8 pries in order to maximize her profit under the onstraint (1), whih guarantees that the retailer will list both produts. The only interior solution is wa = wb = 1 2 as long as F. For higher values of the fixed ost of distributing the new 16(1+) produt, the produer has to adopt a limit-priing strategy that indues the retailer to sell both produts. The orner solution is to set a prie ew A = 1 for the old 2 produt and ew B = p 4F (1 2 2 ) for the new one. Finally, the omparison of the expeted profits in eah ase determines the optimal strategy of the produer in the first stage (see appendix 1 for the details). Figure 2 ompares the resulting equilibria with the orresponding solution under the vertially integrated struture. The neessary ondition under whih a hain of monopolies innovates is more binding than the orresponding ondition for a vertially integrated struture.. 8

11 F 4(1 + ) 8(1 + ) A+B lim A only 16(1 + ) A+B A only 8(1 + ) 4(1 + ) Figure 2 : Comparison of innovation strategies Thegreyareaindiatesthevaluesoffixed osts for whih a separated hain of monopolies would not innovate even though an integrated firm would. Proposition 1 Vertial separation in a hain of monopolies an redue produt variety. In other words, an integrated struture has better inentives to distribute a new produt than a separated struture. This results from the double margin externality: the standard issue of oordination in a non-integrated vertial relation generates a new form of ineffiieny by reduing the profitability of the new produt. Notie that in this simple ase, a two-part tariff assoiated to a tying ontrat, or a two-part tariff with a fixed fee independent of the range of produts sold by the retailer, would be suffiient to restore the inentives: when innovation inreases total profits, the upstream firm an set wholesale pries equal to the marginal osts (here, zero) and get the whole profit 2 through the fixed fee. However, if the two goods have to be pried singly, with two-part tariffs w A,F A and w B,F B, the upstream produer is not able to get all the profit anymorebeauseshehastoleavearenttotheretailer in order to have him selling the two goods. The produer has to give the retailer Ω 2 This point relies on the assumption that the produer has all bargaining power, and is only to enable a omparison with the lassial prinipal-agent literature on double margin. Of ourse, this assumption would be unrealisti in most industries, inluding the musi setor. 9

12 an inentive to list both produts rather than only one of them, whih requires the following inentives onstraints to be satisfied, where Π I D isthevariablepartofthe retailer s profit (exluding the payment of the fixed osts) : Π A+B D F A F B Π A D F A and Π A+B D F A F B Π B D F B, whih implies that 2Π A+B D Π A D ΠB D F A + F B. Yet Π A+B D < Π A D + ΠB D beause the produts are substitutes. Thus F A + F B < Π A+B D : finally, even if the produer an delegate the optimal hoies to the retailers by setting variable pries to her marginal osts of prodution, she annot get the whole profit of the vertial struture through the fixed part F A + F B. Furthermore, it is interesting to observe that the inentives to distribute the new produt are more sensitive to the fixed ost of prodution Ω than to the fixed ost of distribution F. Indeed, when the latter is high, the produer an adapt her wholesale prie by setting a limit prie that leads the retailer to distribute both produts. On the ontrary, when the fixed ost of prodution is high, the retailer annot ommit to share the ost spent by its vertial supplier who unilaterally deides not to introdue the new variety. 3 Competition in the retail industry We have seen in the first part that vertial separation of the ativities of prodution and distribution an redue produt variety. However, it is well known that downstream ompetition redues double margin problems: we address here the question of how retail ompetition an affet produt variety, when variety brings about fixed osts at both levels. We thus analyze the effet of imperfet ompetition between two retailers on the inentives of an upstream firm to introdue a new variety. We look now at the following situation: two retailers D 1 and D 2 sell produer P s prodution to the onsumers. The 3-stage game is as follows. In the first stage the produer deides whether to innovate or not and sets the wholesale pries. In the seond stage, the retailers simultaneously deide whether to invest the fixed ost to be able to sell the new produt. This ost is sunk. In a third stage, as the outome of the investment deisions are made publi, the retailers simultaneously order the quantities of the two goods they are going to put on their shelves, and the pries on the final market are determined by the onsumer inverse demand. Retail ompetition is thus à la Cournot. The fixed ost F is sunk and represents a ommitment 3 of the retailers on their listing 3 In a previous version of this artile, we solved the game without this ommitment effet of the sunk ost, onsidering that stages 2 and 3 were simultaneous. This led to more equilibria: for a 10

13 hoies: if a retailer does not pay F intheseondstage,hewillnotbeabletosell the new produt in stage 3. We solve this game for subgame perfet equilibria. 3.1 Downstream quantity ompetition In this setion we determine the equilibrium outome of downstream ompetition, given wholesale pries (w A,w B ) and the investment deisions of the seond stage. We assume that wholesale pries are smaller than 1, a neessary ondition for produts to be profitable to market. At the third stage of the game, retailers are already ommitted to their listing strategies, and there are three different subgames to analyze (plus the symmetri ones): either both retailers have invested the sunk ost F, or one only, or none of them No retailer has invested In this first subsetion, only one good is distributed: A. Downstream ompetition is thus a simple monoprodut Cournot game. There exists a unique equilibrium where the two retailers sell the same quantity of the old produt A: q 1 A = q 2 A = w A 3.Both retailers make profit Π D A = (w A) Both retailers have paid the fixed ost In this onfiguration, eah retailer hooses two quantities (possibly setting them to zero). Solving the Cournot game leads to the following strategies aording to the values of the wholesale pries (tehnial details are given in the Appendix). If the wholesale prie of good B is too high, only good A is distributed. On the ontrary, for small values of w B, only the new good is distributed. Finally, there exists an equilibrium in whih both goods oexist on the shelves for intermediary values of w B. In addition, the set of values of w B for whih both produts are distributed shrinks with, the degree of substitutability of the two produts: the lower bound on w B below whih the retailers only distribute B inreases with, while the upper bound above whih the retailers only sell the old good dereases with. Indeed, for high values of, produts are highly substitutable and ompete for shelf spae, in whih ase the retailers prefer to only distribute the most profitablegood. Wealsoshow given onfiguration of retail osts, several equilibria existed. However, our results were qualitatively similar. 11

14 that the same set of values of w B shrinks with w A. However, now, both the upper and the lower bounds of the interval shift to the right as w A inreases. This shift translates the fat that the profitability of A dereases with w A regardless of whether produt B is also distributed or not. We should also point out that in this subgame, none of the asymmetri market onfigurations arises at equilibrium, although they were aprioripossible Asymmetri onfiguration: one retailer only has paid the sunk ost In this subgame, one of the retailers an only sell produt A. We refer to this retailer as retailer 2. The other retailer hooses his listing strategy. We ompletely solve the downstream Cournot subgame in the Appendix. There are 4 onfigurations to analyze aording to the values of w B. Only good A is distributed if the wholesale prie of B is too high, and this threshold is idential to the one found in the previous subsetion. For values of w B slightly below this threshold, both goods are distributed by the retailer who has invested the fixed ost of marketing the new produt. For even smaller values of w B, this retailer only distributes good B while his ompetitor is onstrained to sell only good A. Finally, for very small values of w B, the retailer who did not spend the fixed ost to distribute the new good must exit the market, leaving his ompetitor in a monopoly situation in the market for good B. Notie that in that ase, retailer 1 still leaves good A out of the shelves to avoid annibalization of the sales of good B. As in the previous subsetion, the set of values of w B for whih the new produt is distributed shifts to the right as w A inreases and the size of the interval dereases as parameter inreases. It is interesting to observe that asymmetri equilibria with downstream speialization are due to the ommitment value of the sunk ost F. Indeed, in a Cournot game without this ommitment effet, the retailers do not have inentives to speialize: a retailer who did not pay the fixed ost ould always deviate from the equilibrium strategy by reduing the quantities of A on the shelves and by offering a small but positive quantity of B. When the fixed ost F is sunk, the retailer who has paid it knows that, at the last stage of the game, his ompetitor an not sell good B. Under this assumption, for small values of w B, distributing good A will only annibalize sales from good B and this retailer prefers to leave his ompetitor in a monopoly position on the market for good A, while enjoying a monopoly position on the market for good B. We an now analyze the investment deisions of the retailers at the seond stage 12

15 of the game. 3.2 Investment deisions This stage of the game is only played if the produer has developed the new produt. Retailers have to hoose whether to invest the fixed ost or not in order to distribute the new produt. They take wholesale pries w A and w B as given and antiipate downstream market outomes. There are five market onfigurations in this subgame. In the symmetri equilibria eah retailer only sells the new good, or only the old one, or both. In the first asymmetri onfiguration, eah retailer speializes in only one good. In the seond asymmetri ase, one retailer only sells the old good and his ompetitor sells both goods. The following figure summarizes these onfigurations, whih are detailed in appendix 2. F F, non F (B) F, non F (B,A) non F, non F (A,A) F, F (B,B) F, non F (AB,A) F, F (AB,AB) (1 w A ) (1 w 2 A ) 2 (2 + )(1 wa) 3 1 A (1 w ) Figure 3 : downstream subgame equilibria with ompetition w B For given values of the wholesale pries, equilibria in whih good B is sold disappear as the fixed ost of marketing the new produt inreases. Moreover, the higher the value of w B the lower the profits generated by sales of B. These results onfirm 13

16 the intuition that for low values of the wholesale pries and of the fixed osts, both retailers invest to distribute good B, while for high values of F and w B,thetotalost of distributing the new produt is too high and both retailers symmetrially hoose to stik to the old produt. The ommitment value of the sunk ost F has an interesting impliation: for intermediate values of F, retailers adopt a speialization strategy that is haraterized by the fat that only one retailer invests in the distribution of the new good (possibly together with produt A) and the other retailer only distributes the old produt. 3.3 Innovation deision In the first stage of the game, the produer deides whether to introdue the new variety and determines the wholesale pries. She antiipates the strategies of the retailers in stage 2 and sets her produt lines and the wholesale pries in order to maximize her profits. The subgame perfet equilibrium outomes are detailed in Appendix A4 where we also ompare profits of the different players with those obtained in the hain of monopolies. The main results are summarized in proposition 2. Proposition 2 A produer faing a ompetitive downstream market innovates more often than if she faed a single retailer. Proof :seeappendixa4. More preisely, when the fixed osts of introduing the new variety are suh that the hain of monopolies innovates, a produer who faes a ompetitive downstream market also innovates. However, there are parameter onfigurations in whih the hain of monopolies does not innovate whereas the downstream ompetition leads to innovation. This situation ours in two areas where one of the fixed osts is large and the other is small (see Figure 4). In the first area, the total ost of introduing the new variety is mainly supported by the produer. h When i the downstream fixed ost is relatively small ( F and Ω, ), a hain of monopolies does 36(1+) 8(1+) 6(1+) not introdue the new produt, while downstream ompetition allows the produer to harge wholesale pries that are below the unonstrained optimum (w A = w B =1/2). Donwstream ompetition inreases the quantities of both goods sold by the produer who an then bear a larger fixedostofinnovationthanwhenshefaesasingle retailer. For larger values of F, the produer redues the wholesale prie of the new produt to give inentives to the retailer to distribute it. This limit-priing strategy 14

17 is profitable aslongasthefixed ost is not too large and as retailers keep distributing the new produt, i.e. until F =. In the area being disussed, the ompetitive 16(1+) downstream market has a higher innovation rate mainly beause ompetition redues thedoublemarginexternalities,whih makesthenewprodutmoreprofitable to introduefortheproduer. For intermediate values of the fixed osts, downstream ompetition does not lead to more produt introdution than the hain of monopolies: the area in whih the new produt is marketed is the same under the two strutures. Indeed, ompetition between retailers redues profits and make it harder to support the fixed osts. As a matter of fat, in this area, only one retailer distributes the new produt, while both retailers keep distributing the old produt. The quantity of good B sold under this onfiguration is the same as in the vertially separated monopoly ase; the profits generated by sales of good B are also idential. It would be too ostly for the produer to harge wholesale pries that give more inentives to the retailers to distribute the new produt, as the produer also faes a fixed ost of innovating. Thus, the produer faing a ompetitive downstream market has the same innovation inentives as when he only faes a single retailer. On the ontrary, as the fixed distribution ost inreases even more and the share of the total ost supported by the produer shrinks, downstream ompetition leads to anewareawheretheompetitivestrutureinnovatesmorethanthehainofmonopolies. This area only exists when the produts A and B are rather lose substitutes (for 1/2). In this ase, for F in the interval [ 2, F ] where F,produt (1+) B is distributed when Ω is relatively small. This area is larger under downstream ompetitionthaninthehainofmonopolies. Indeed,thefixed ost of innovating of the produer being small, she an afford a lower wholesale prie w B that leads one of the retailers to distribute the new good. This produt line extension inreases total demand. In this area, the ommitment value of the fixed ost F analyzed in the seond stage of the game leads the retailers to speialize: eah retailer sells only one of the goods and has a monopoly position on its market. This market onfiguration leads to a paradoxial outome. When the fixed ost F is large, retailers speialize in the distribution of only one good, whih inreases the profitability of the new produt but limits ompetition between retailers. It is worth stressing that the strategy of speialization is only feasible when both produts are relatively lose substitutes, i.e. when produts are ompeting for shelf spae. This implies that the retailer who hooses to distribute the new produt gives up the old produt to avoid annibalization. 15

18 To summarize, downstream ompetition inreases the rate of innovation through two mehanisms: a lassial mehanism related to a redution in the vertial externality and a strategi mehanism related to the speialization of the retailers, whih is onditioned by the ommitment value of the fixed ost of marketing the new produt. We an now ompare the inentives to innovate when retailers are ompeting to the inentives of a vertially integrated struture. Proposition 3 If the two goods are poor substitutes ( 1/2), aproduerselling her produts through a ompetitive downstream setor introdues less variety than a vertially integrated monopoly; If the two goods are lose substitutes ( 1/2), a ompetitive retail industry innovates less than a vertially integrated monopoly exept when the share of the total fixed ost of introduing the new variety supported by the produer is small (F >>Ω). Proof: see appendix A.5. We illustrate Proposition 2 and 3 in the following figure in the (Ω,F) plane (for 1/2). F 4(1 + ) F Zone d innovation : Chaîne de monopoles et onurrene aval Conurrene aval 16(1 + ) 36(1 + ) 8(1 + ) 6(1 + ) 4(1 + ) Ω Figure 4 : omparison of equilibrium innovation strategies Even if downstream firms are ompeting, the vertial externality related to the double margin remains and lowers the inentives to innovate of the produer. This 16

19 effet dominates when the distribution ost (F ) is low. In this ase, the vertially separated struture innovates less than a vertially integrated monopoly. However, an opposite vertial effet appears when the new produt is less profitable to market(i.e. when F is large ompared to Ω) and is a lose substitute to the old produt (i.e. is large). Now, the upstream firms soften downstream ompetition by setting wholesale pries so as to enfore an asymmetri retail market in whih one firm distributes the old produt and another firm distributes the new produt. Hene, speialized firms do not diretly ompete for the new produt. This market environment an sustain innovation when a vertially integrated firm would not innovate. Proposition 3 has several impliations. First, from an empirial perspetive, the strategy of the upstream firm of relaxing the ompetitive pressure in the downstream market is observed for a new produt that is ostly to distribute and that strongly substitutes to the older produt. In this ase, even if retailers speialize, downstream ompetition is relatively strong (at the seond stage of the game). Seondly, ompetition authorities do not generally frown upon vertial mergers beause of the vertial externality. In our model, a vertial integration an have a negative effet on innovation strategies if the innovation is ostly to market but relatively heap to produe (inremental innovation), whereas a vertially integrated struture innovates more when the innovation is ostly to produe but not too ostly to market (radial innovation). Finally, total surplus (net of the fixed osts) is defined as W (Q A,Q B ; ) =Q A + Q B 1 2 (Q2 A + Q 2 B) Q A Q B. It is easy to show that the total welfare at equilibrium, W () =W (Q A(),Q B()), is dereasing in for 0 <<1 in eah produt onfiguration. Moreover, for almost eah equilibrium listing strategy, total surplus is higher under vertial integration, followed by downstream ompetition and then vertially separated monopolies. In the ase in whih a ompetitive retail setor distributes the new produt but the vertially integrated struture does not, total surplus is higher when there is innovation: ompetition inreases soial surplus by inreasing the variety offered to onsumers, when the ost of launhing the new produt is mainly supported by the upstream firm, and when the new produt is a lose substitute to the old one. 17

20 4 Conlusion We have explained how a market s vertial and ompetitive strutures influenes endogenous produt variety hoies, when the launhing of a new produt involves fixed osts of distribution as well as fixed osts of prodution. We have highlighted several mehanisms -both horizontal and vertial- behind this influene. First of all, the profit-utting effet of double marginalization redues the inentives to invest in the launhing of a new produt. In a hain of monopolies, vertial integration thus favours the adoption of a new produt that inreases the sope and the variety of produts distributed to onsumers with heterogeneous tastes. Thus, vertial separation of the prodution and the distribution ativities may generate onflits of interest between the vertially related firms, whih translates into a lower innovation effort and leads to too few produts distributed to the onsumers. To restore the vertial effiieny, two-part tariffs with a franhise fee independant of the range of produts distributed, or sophistiated ontrats inluding full-line foring lauses would be neessary. Downstream ompetition may however soften the vertial ineffiienies. When we analyze a more omplex framework with a produer launhing a new produt and two ompeting retailers, the effet of ompetition on the inentives to inrease produt variety depends on the degree of novelty of the new produt, and also from the alloation of the fixed osts between upstream and downstream firms. If manufaturing and retail ativities are vertially separated, then downstream ompetition leads to more variety than does retail onentration. In addition, vertial separation with downstream ompetition may lead to more or less innovation than vertial integration, depending again on the alloation of fixed osts and on the degree of produt substitution. When the retail osts are less than the manufaturing osts of launhing the new produt, retail ompetition, by reduing downstream profits, lessens the retailer s ability to invest in the fixed ost, and thus hinders the development of the new produt. In that ase, a vertially integrated firm would launh the new produt more often than an upstream monopoly faing two ompeting retailers. On the ontrary, when the new produt is more ostly to sell than to manufature, a vertially separated struture with downstream ompetition may innovate more than a vertially integrated monopolist beause retailers are ready to sell the new produt even with high osts in order to segment the downstream market. In terms of poliy impliations, our model stresses the neessity to preserve ompetition at the retail level to support innovation. 18

21 5 Referenes Allain, ML and C. Chambolle (2003) Eonomie de la distribution, Repères, La Déouverte. Boone, J. (2001), Intensity of ompetition and the inentive to innovate, International Journal of Industrial Organization, 19, 5, Broas, I. (2003), Vertial Integration and Inentives to Innovate, International Journal of Industrial Organization, 21 (4), Bonanno, G. and J. Vikers (1988) Vertial separation, The Journal of Industrial Eonomis, Vol. 36 N 3, Deloitte and Touhe (1990) Managing the Proess of Introduing and Deleting Produts in the Groery and Drug Industry, Washington DC, Groery Manufaturers of Ameria. Desiraju (2001) New produt introdution, slotting allowanes and retailer disretion, Journal of Retailing, Dobson Consulting (1999) Buyer Power and its Impat on Competition in the Food Retail Distribution Setor of the European Union, report for the European Commission, Brussels. Inderst, R. and G. Shaffer (2003) Retail Mergers, Buyer Power and Produt Variety, forthoming Eonomi Journal. Larivière, M. and V. Padmanabhan (1997) Slotting allowanes and new produt introdutions, Marketing Siene, 16(2), Marvel, H. P. and J. Pek (2000) Vertial Control, Retail Inventories and Produt Variety, Working Paper n.00-09, Ohio State University. Motta, M. (2004) Competition Poliy : Theory and Pratie, Cambridge University Press. Rey, P. (1997) Impat des aords vertiaux entre produteurs et distributeurs, Revue Française d Eonomie, Vol. 12, N. 2, Rey, P. and J. Tirole (1986) The Logi of Vertial Restraints, Amerian Eonomi Review, Vol.76N 5, pp Spengler, J. J. (1950) Vertial Integration and Antitrust Poliy, Journal of Politial Eonomy, 58, Tirole, J. (1988) The Theory of Industrial Organization, MIT Press. Weiss, C. and A. Wittkopp (2005) Retailer onentration and produt innovation in food manufaturing, European Review of Agriultural Eonomis, 32-2,

22 A Appendix A.1 Equilibrium in the hain of monopolies Retailer s strategy If only produt A is available, the retailer orders q A = w A, 2 gets profit Π D = (w A) 2,and the produer s profit isπ P = w A(w A ). 4 2 If the retailer lists both produts, his maximum profit is: Π A+B = (w A) 2 +(w B ) 2 2(w A )(w B ) F and is attained for the following quantities ({I,J} = {A, B}) 4( 2 ) : q A+B I = Max{0, 1 w I (1 w J ) } 2(1 2 ) Produer s strategy The omparison of her antiipated profits gives the produer s optimal strategy in the first stage: -if F and Ω, she innovates, sets the optimal wholesale pries 16(1+) 8(1+) wa = wb = 1 and gets the interior optimal profit 2 ΠP A+B = 1 q Ω. 4(1+) -if F and Ω F ( ) 2F, she innovates, sets the optimal wholesale 16(1+) 1+ prie wa = 1 and the limit-prie ew 2 B = p 4F (1 2 2 ), and gets profit Π e P A+B = 16F F ( + 2 ) Ω q -if Ω or F and Ω F ( ) 2F, she does not innovate, sets 8(1+) 16(1+) 1+ w A = 1, and gets profit 2 ΠP A = 1. 8 A.2 Downstream ompetition : third stage of the game If both retailers have paid the fixed ost F, downstream Cournot equilibrium are as follows, for given values of the wholesale pries : -ifw B 1 (1 w A ), only A is sold. -if(1 w A ) w B 1 (1 w A )/, eah retailer sells both goods. -if(1 w A )/ w B, only B is sold. If only one retailer, say 1, has paid the fixed ost F, downstream Cournot equilibrium are as follows : -ifw B 1 (1 w A ), only A is sold by both retailers. -if(1 w A ) w B 1 (w A)(2+ 2 ), retailer 1 sells both goods in quantities 3 qa 1 = (2+2 )(w A ) 3(w B ), q 1 6( 2 ) B = w B (w A ) and his ompetitor sells only good A in 2( 2 ) quantity qa 2 = w A. 3 20

23 -if (w A)(2+ 2 ) w 3 B 1 2(w A), the retailers speialise in a narrower range of produts: retailer 1 sells only B and his ompetitor only A. -if2(1 w A )/ w B, there exists a unique equilibrium where the retailer who did not invest the fixed ost exits the market (or sells a zero quantity of good A) while the other one enjoys a monopoly situation over the two goods, but hooses not to sell good A in order to avoid annibalisation of his sales of good B. Then he hooses to sell the monopoly quantity of the new produt: qb, 1M = w B. 2 A.3 Retailers investment strategies In the seond stage, in the subgame where the produer has innovated, and given the wholesale pries w A and w B : A.3.1 if w B 1 (1 w A ), In that ase, the wholesale prie of new produt is so high that even if a retailer pays the fixed ost F, he annot sell the new produt with profit, whatever his ompetitor s strategy might be. Thus both retailers deline to invest in the fixed ost, and in the following stage A will be the only produt available. A.3.2 If 1 (w A)(2+ 2 ) 3 w B 1 (1 w A ), Antiipating the third stage outomes, the seond stage hoies an be summarised in the following normal form game, where F denotes the hoie of paying the fixed ost and non F the other strategy : F non F F Π D AB,AB, Π D AB,AB Π 1 AB,A, Π 2 AB,A non F Π 2 AB,A, Π 1 AB,A (w A ) 2, (w A) Comparing these profits gives the following subgame equilibria : if F ((w A) (w B )) 2, both retailers pay F andsellbothgoodsinthethird 9( 2 ) stage; if ((w A) (w B )) 2 F ((w A) (w B )) 2, only one retailer invests F to sell both 9( 2 ) 4( 2 ) goods, and his ompetitor sells only A; if F ((w A) (w B )) 2, both retailers give up the selling of the new produt: none 4( 2 ) pays F, and both sell A. 21

24 A.3.3 If 1 w A w B 1 (w A)(2+ 2 ) 3 In that ase the normal form game is as follows : F non F F Π D AB,AB, Π D AB,AB Π 1 B,A, Π 2 B,A non F Π 2 B,A, Π1 B,A (w A ) 2, (w A) Comparing these profits gives the following subgame equilibria : if F (w A) 2 2(w A )(w B )+(w B ) 2 (2(w A) (w B )) 2, both retailers pay F and 9( 2 ) (4 2 ) 2 sell both produts; if (w A) 2 2(w A )(w B )+(w B ) 2 (2(w A) (w B )) 2 F ((w A) 2(w B )) 2 9( 2 ) (4 2 ) 2 (4 2 ) 2 (w A ) 2, only one retailer invests F to sell only B, and his ompetitor sells only A; 9 if F ((w A) 2(w B )) 2 (w A) 2, no retailer pays F, both sell only produt A. (4 2 ) 2 9 A.3.4 If 1 2 2w A w B 1 w A This zone may exist only if w A 1. In that ase the normal form game is as follows : F non F F Π D B,B, Π D B,B Π 1 B,A, Π 2 B,A non F Π 2 B,A, Π 1 B,A (w A ) 2, (w A) Comparing these profits gives the following subgame equilibria : if F (w B) 2 (2(w A) (w B )) 2, both retailers pay F and sell only B; 9 (4 2 ) 2 if (w B) 2 (2(w A) (w B )) 2 F ((w A) 2(w B )) 2 (w A) 2, only one retailer 9 (4 2 ) 2 (4 2 ) 2 9 pays F to sell only B, his ompetitor sells only A; if F ((w A) 2(w B )) 2 (w A) 2, no retailer pays F,bothsellonlyA. (4 2 ) 2 9 A.3.5 If w B 1 2 2w A This zone may exist only if w A 1. In that ase the normal form game is as 2 follows : F F non F (w B ) 2 F, (w B) F (w B) 2 non F 0, (w B) 2 4 F 4 F, 0 (w A ) 2, (w A)

25 Comparing these profits gives the following subgame equilibria : if F (w B) 2 (w A) 2, no retailer pays F,bothsellonlyA; 4 9 if (w B) 2 F (w B) 2 (w A) 2, only one retailer pays F, his ompetitor exits the market. The monopolist retailer sells only produt B; if F (w B) 2 both retailers pay F and sell only B. 9 A.4 Upstream hoie: proof of proposition 2 In the first stage, the produer innovates if the profit she gets by selling the new produt is higher than Π P AA = 1, the profit she gets with produt A only. If she 6 innovates, her profit depends on the quantities sold by the retailers in stage 3. We summarize here the produer s optimal hoies in equilibrium. (i) If F, she innovates if and only if Ω, and both retailers sell both 36(1+) 6(1+) goods in the interior optimum. For suh values of F, the hain of monopolies would innovate only if Ω : downstream ompetition leads here to more innovation 8(1+) than a hain of monopolies would offer. (ii) If F, the produer has to use a limit-priing strategy 36(1+) 16(1+) in order to indue the two retailers to qsell both goods eah q in equilibrium. The F () F () produer innovates if and only if Ω 2 6F, with 2 6F for (1+) F [, ]. For suh values of F, the hain of monopolies would innovate 144(1+) 16(1+) only if Ω : downstream ompetition leads here again to more innovation than 8(1+) a hain of monopolies would offer. (iii) If F, the produer sets the wholesale pries in order to indue one 16(1+) of the retailers to list the new produt, the other retailer selling only the old one. In that ase, if 1/2, the produer hooses a limit-priing strategy, denoted ^AB, A, suh that one only of the two retailers invests F and sells both goods, the other sellingq only good A. This strategy brings about more profit than no innovation for F () Ω 2F, whih orresponds exatly to the frontier of innovation in the 1+ hain of monopolies ase. On the ontrary if 1/2, this strategy is no more possible for F 2, and the 36 2 best the produer an do is then to set pries induing the retailers to speialize, one of them paying F to sell only the new produt B, and the other selling only A without investing. This strategy always dominates 4 the absene of innovation for fixed osts 4 Notie that this partiular priing strategy is not neessary the optimal one, but it is enough to show that the optimal strategy will lead to innovation in this zone. 23