New Product Introduction and Slotting Allowances

Transcription

1 New Product Introduction and Slotting Allowances Claire Chabolle and Cléence Christin July 20, 205 Abstract The availability of a product in a given store is a for of inforational advertising that ay go beyond the store itself. We show that each retailer is able to extract a rent in exchange for this inforational advertising service, which aterializes through the payent of a slotting allowance fro the producer to the retailer. Therefore, a anufacturer ay not find profitable to innovate in order to launch a new and ore efficient product. This in turn hars consuers surplus and welfare. Varying the buyer size, we then show that retail concentration ay facilitate innovation. KeyWords: Buyer Power, Innovation, Slotting allowances, Inforational externality. JEL codes: L3, L42, M37. Introduction Slotting allowances are upfront payents fro the producer to the retailer that are paid to secure a slot for a new product in retailers shelves. Their aount and frequency have rapidly grown since the id-980 s. According to the FTC report on slotting allowances on the U.S arket, fro 50% to 90% of all new grocery product introductions would trigger the payent of such fees in 2000 DATE TO BE CHECKED. The FTC report further entions that: [... ] slotting allowances for introducing a new product nationwide could range fro a little under illion to over 2 illion, depending on the product category. INRA UR303 ALISS, 65 boulevard de Brandebourg Ivry-sur-Seine, France; Departent of Econoics, Ecole Polytechnique, route de Saclay 928 Palaiseau, France, claire.chabolle@ivry.inra.fr. Norandie Université, UCBN, CREM-UMR CNRS 62, 9 Rue Claude Bloch, 4032 Caen, France, cleence.christin@unicaen.fr This result is obtained assuing that nationwide introduction would require distribution to 85% of the superarkets in the U.S., and that 85% of these superarkets would receive a slotting fee, See FTC (2003).

2 Retailers have basically justified slotting allowances as a risk-sharing echanis and a eans to screen the ost profitable innovations. They also argue that slotting allowances are natural cost shifters to pass on the higher retailing costs that result fro the increasing flow of new products fro suppliers. In contrast, producers often see slotting allowances as rent extracted by increasingly powerful retailers. This paper provides a new rationale for the use of slotting allowances. Our starting point is that the deand for a new product depends on the consuers knowledge of its existence. Consuers ay be infored through advertising but also ore siply by the availability of the new product on retailers shelves. In this regard, the presence of a new product in a given store is a for of inforational advertising that ay go beyond the store itself. Such an inforational spillover ay for instance be the result of word of outh counication aong consuers across arkets. The supply of a new product ay thus partly generate its own deand. We show that, by aking available the new product, a retailer offers a service to the producer which is paid through a slotting allowance. In turn, this ay deter the producer s incentive to launch a new product. However, we point out that the presence of a larger buyer ay itigate this innovation deterrence effect. To do so, we build a siple vertical odel with an upstrea onopolist and retailers active on separate arkets. We introduce an inforational spillover, i.e. we assue that the nuber of arkets where the product is actually sold exerts a positive externality on the deand for a new product: the larger the nuber of arkets where the new product is sold, the larger the deand for this product on each of these arkets. To siplify, we copare two syetric situations: In the first case, the anufacturer launches a new product; then securing one outlet increases deand in all other outlets in which the product is sold. In the second case, the anufacturer sells an old product; then the arket is ature and inforational spillovers no longer play a role. We then analyze the bargaining between the producer and each of the retailers in these situations. We consider secret bargaining aong each pair following the ultilateral bargaining specification of Stole and Zwiebel (996). 2 We are first able to derive a new source of buyer power: when selling a new product, the anufacturer ust copensate each retailer for the positive inforational externality of a success of their bargaining on all other arkets. Such buyer power increase aterializes 2 As shown by Stole and Zwiebel (996), this solution concept coincides with the Shapley value. 2

3 through the payent of a slotting allowance fro the producer to each retailer. As a result, inforational spillovers ay deter innovation as the producer ay earn a saller profit, i.e. a saller slice of a bigger pie. Innovation deterrence is then harful both for consuer surplus and welfare. We then analyze the ipact of retail concentration on the launching of new products. To vary the size of retailers, we allow retailers to own outlets on several arkets. A larger retailer is a retailer that owns ore outlets and is thus present on ore arkets. Keeping the nuber of outlets constant, we assue that one retailer owns several outlets, while all other retailers still own only one. The presence of a larger buyer has no ipact on the anufacturer s profit when it sells an old product, whereas it increases the anufacturer s profit when it sells a new product. Innovation is here favored by a ore concentrated downstrea arket structure. Our work is first related to the literature on buyer power and slotting fees. The industrial organization literature has first highlighted that slotting fees could have anticopetitive effects on retail copetition (e.g Shaffer, 99; O Brien and Shaffer, 992). Others papers have shown that slotting fees could help retailers in deciding how to allocate scarce shelf space (Marx and Shaffer, 200; and Shaffer, 2005). Although they relate the existence of such fees to retail buyer power, these papers do not take into account the peculiarities of new product introductions in their analysis. This void is partly filled by the arketing literature, which analyzes the use of slotting allowances as a eans to ensure an allocation of the risk inherent to a new product launching (see e.g. Sullivan, 997; Larivière and Padanabhan, 997; Rao and Mahi, 2003). We provide here a copleentary rationale for the payent of slotting allowances to retailers in exchange for the introduction of a new product, based on the existence of a positive inforational externality. Our work also builds on the literature on bargaining and buyer size, e.g Inderst and Wey (2003,2007), Montez (2007), Thanassoulis and Sith (202). More specifically the seinal paper by Chipty and Snyder (999) show that when an upstrea anufacturer negotiates siultaneously with separate retailers, a large buyer obtains a larger (respectively saller) discount whenever the suppliers gross revenue function is concave (resp. convex). In our set-up, although the suppliers gross revenue function is linear, the inforational externality creates a convexity of the industry revenue function, and thanks to our sequential bargaining setting, slotting fees paid for the introduction of a new product 3

4 to a large retailer are lower. Note that with the siultaneous bargaining fraework of Chipty and Snyder (996), our inforational externality would not alter the sharing of profits between the producer and retailers. This paper also relates to the industrial organization literature on buyer power and upstrea innovation. Inderst and Wey (2007), analyze the upstrea incentives to innovate in a siilar fraework when production cost is convex and show how the presence of large buyer ay strengthen the supplier s incentive to innovate. In contrast Batigalli, Fuagalli and Polo (2007) show that a larger buyer power ay, by increasing hold-up, reduce the upstrea incentives to invest in quality. Chen (204) considers, as we do, a fraework in which one of the retailers serves several arkets whereas other retailers serve only one. He shows that a large buyer has a larger status-quo profit because it can benefit ore fro backward integration if the negotiation fails, which hinders the anufacturer s incentive to innovate. In contrast, in our fraework, buyer size lowers buyer power and therefore facilitates upstrea innovation. Finally, our paper also indirectly relates to the literature on network effects. In our odel, inforational spillovers create copleentarity between retail arkets such as in networks. In particular, Richard and Hailton (202) derive a odel to take into account network effects in ulti-product retail arkets. In their odel, network effects coe fro copleentarity aong products in a given consuer basket. We depart fro their analysis in studying network effects between arkets rather than between products in the sae arket. Section 2 derives the odel. Section 3 analyzes the effect of the inforational externality on the payent of slotting allowances by coparing the bargaining between a producer and several retailers when launching a new product or when selling an old product. Section 4 study the incentive of producer to launch a new ore efficient product. Section 5 analyses the robustness of our result when varying the retailers size. Section 6 concludes. 2 The odel We consider a fraework in which an upstrea fir U ay sell a good through M outlets owned by i M retailers R i : one retailer ay own several outlets. U has a constant 4

5 arginal cost of production denoted c. Each outlet s arket is a local onopoly, which iplies that there also exist M arkets. As we focus on new products, we assue that selling the good through ore outlets increases deand on each individual arket, for instance by increasing the eans through which a consuer on any arket ay get inforation on the existence of the new product. This creates a link between arkets despite the fact that each arket is a onopoly. The inverse deand function on each individual arket j (j {,...M}) is thus of the for P j (q j, ), with the nuber of outlets (or arkets) where the good is actually sold and P j q j < 0. We ake the following specific assuptions on the deand function. Assuption P j γ > 0. Assuption 2 γ q j = 0. Assuption 3 γ > 2 γ. We denote by Π j through arkets, that is: the optial revenue earned in outlet j when U sells the product Π j = arg ax q j (P j (q j, ) c)q j. We denote the industry revenue with outlets: Π = Π j. An iediate consequence of Assuption is that Π Π > Π for all >. Indeed, if we consider standard local onopolies, we have Π Π = Π, that is, each additional outlet brings the sae additional profit to the whole industry. In our fraework, opening an additional outlet also increases profits at all the other outlets because of the positive inforational effect. An iediate consequence of Assuption 2 is that even if one retailer owns k > outlets when arkets are open, the optial revenue on each arket is independent of k. We therefore avoid a size effect through quantities. Assuption 3 iplies that Π Π j > Π Π j for any > and j [, ], and that Π 0 = 0: The industry revenue is convex with respect to. Assuption 5

6 3 also iplies that Π k is decreasing with the inforational externality. Indeed, as Π 0 and Π are both independent of the externality, for a given k, although Π k increases in k, the function Π k is strictly decreasing in γ and therefore the industry profit is ore convex when the externality increases. 3 The tiing of the gae is as follows. First, the upstrea fir bargains siultaneously with each retailer R i on a two-part tariff (T i, w i ), with T i the fixed fee and w i the unit wholesale price. Second, each retailer axiizes its profit by setting quantities on each outlet it owns. 4 We consider the sae bargaining fraework as Stole and Zwiebel (996). We assue secret contracting with passive beliefs. The success or failure of a given negotiation, however, is coon knowledge. Therefore, each retailer knows how any outlets are open when setting its quantities. Besides, in case of failure of the negotiation between R i and U, the failing pair can never negotiate again, and all other pairs renegotiate their contracts fro scratch. In this fraework, each pair U R i uses w i to axiize their joint profit and T i to share the profit. Assuption 2 ensures that the bilaterally efficient wholesale price is w i = c. Indeed, there is no incentive for a pair to distort the wholesale price, because for a given arket structure, the output decision of one retailer does not affect the output decisions of the other retailers. The value of T i depends on the firs respective bargaining powers and outside option. We denote by λ the bargaining power of U (and ( λ) the bargaining power of R i ) in each negotiation. The outside option of R i is 0. For now, we denote by Π sq the status quo of U in the negotiation. The optial fixed fee, T i, in the negotiation with retailer i is given by: λ(π i T i ) = ( λ)(t i + T h Π sq ). () h i Henceforth, for siplicity, we assue that λ = /2. In section 3, we assue that there are retailers, i.e. each retailer owns a single outlet on a local arket. In that siple fraework, we analyse the role of the inforational externality on the bargaining between the producer and each of the retailers and analyze its role on innovation. Then, in section 5 we vary the size of one retailer who owns several 3 See Appendix A. for details. 4 Note that because we consider local onopolies, we would obtain the sae results if retailers set prices. 6

7 outlets, and analyze the role of buyer size on the sharing of profits in the vertical chain and innovation. 3 Slotting allowance for a new product We focus on the general fraework specified above, and assue that each retailer owns a single outlet (i.e. there are retailers outlets and arkets). We copare two cases. We first deterine the equilibriu when the anufacturer sells a new product, as specified above. Then we copare this case with a benchark in which the anufacturer sells an old product. 3. New product Assue first that the anufacturer launches a new product. We deterine the fixed fee that results fro the negotiation for any nuber of outlets. When U bargains with retailers, the outside option of U with R i aounts to the profit it would earn if it were negotiating with all retailers except for R i. The sae reasoning can be applied when U bargains with retailers, etc. The su of the fixed fees deterined for a given nuber k of retailers thus gives the outside option of U when bargaining with k + retailers. We thus first consider the case in which U bargains with only one retailer. In that case, both outside options are 0: U has no alternative outlet and R has no alternative supplier. Fro equation (), the optial fixed fee denoted ˆT is thus given by: ˆT = Π 2. (2) This also corresponds to the total profit of U when facing only one retailer, which we denote ˆΠ U = ˆT. If U now bargains with two syetric retailers, the outside option of U with R i is given by ˆT. Fro equation (), and since retailers are syetric, we obtain: Π 2 i ˆT i = 2 ˆT i ˆT 3 ˆT i = Π 2 i + ˆT ˆT i = 6 ( Π 2 + Π ). 7

8 The total profit of U when facing two retailers is therefore ˆΠ 2 U = 3 ( Π 2 + Π ). Fro this point on, we deterine a recurrence relation to obtain the for of ˆΠ U any >. We thus obtain the following lea. for Lea When the anufacturer introduces a new product, retailers sell the product in equilibriu, and the profit of the anufacturer is given by: ˆΠ U = + Π i. Proof. Assue that the profit of U with retailers is given by: i= ˆΠ U = With retailers, fro equation (), the bargaining process between U and R i yields: i= Π i. Π i ˆT = ˆT Π U ( + ) ˆT = Π i ˆT = ( + ) + i= ˆΠ U = ˆT = + ˆΠ U Π i Π i. i= = Π + i= Π i Note however that the profit of the anufacturer strictly increases with the nuber of downstrea firs. Indeed, for all j [, ] we have: ˆΠ j U 3.2 New vs. old product ˆΠ j U = j j(j + ) (jπj i= Π i ) > 0 (3) We now deterine the anufacturer s incentives to sell a new product rather than an old product. We define an old product as a product for which the deand on each arket j 8

9 is D j (P j, ). Indeed, the inforational spillover has already played its role: all potential consuers are aware of the existence of the product, and therefore the deand on each arket is axiu and independent of the nuber of retailers that actually sell the product. To fix ideas, we first consider that the only difference between the new and old products is that the new product is unknown to the consuers. In particular, there is no real innovation as both products have the sae arginal production cost c. We obtain the following lea. Lea 2 When the anufacturer sells an old product, its profit is Π /2, and the profit of each retailer is Π /(2). Proof. As there is no externality aong arkets, each arket is a local onopoly in which the profit is Π /. All negotiations are thus independent fro one another, and therefore the anufacturer gets half of the profit on each arket. Coparing the anufacturer s profit in the two cases, we obtain the following lea. Lea 3 Without innovation the anufacturer is always better off selling an old product than a new product. Proof. It is iediate that Π > Π i for any i <. Therefore, since /2 > /( + ) for all >, it is always true that Π 2 > ˆΠ U. With a new product, each retailer has ore buyer power because of the inforational spillover, and can therefore extract a rent in exchange for the positive externality of a success in their bargaining on all other arkets. Indeed, in any given negotiation, each retailer considers itself as the arginal buyer, as it anticipates that the supplier will bargain with all other retailers. When U sells an old product, the profit function of the industry is a linear function of the nuber of buyers. In contrast, under Assuption 3, when U sells a new product, the profit function of the industry is convex with respect to the nuber of buyers, due to the inforational externality. Therefore, in the bargaining between one retailer and U, the arginal contribution to the industry profit of the retailer is larger in the case of a new product than in the case of an old product. Since the industry profit in equilibriu (i.e. when retailers sell the product) is the sae in both cases, the profit of U is always lower when selling a new product than when selling an old product. 9

10 A siilar result ay be found in the literature on bargaining with externalities (see e.g. Chipty and Snyder, 999; Inderst and Wey, 2007 and Thanassoulis and Sith, 202). Our fraework differs fro this literature in that we consider an externality on deand and not on supply (for instance through the shape of the cost function). DISCUTER l HYPOTHESE 3 si on relche la convexit...si convexe jusqu ce que la deabde rejoigne la droite pur k M alors on peut dire que les fires ne payent pas de slotting allowance. En revanche si S shaped function, et qu il reste un effet jusqu au dernier arch, alors, c est robuste. 4 Buyer power and innovation deterrence We now assue that the new product is ore efficient than the old product. That is, we consider a process innovation such that the production cost of the new product is now c, and the cost difference between the new and old product is c = c c > 0. 5 To clarify, we denote in this case Π (c) the joint profit of the industry when an old product is sold, and ˆΠ U (c ) the profit of the anufacturer when the new product is sold. We therefore obtain the following proposition. Proposition There exists a unique threshold δ such that introducing the new product is profitable for the anufacturer if and only if c > δ, i.e. if the cost reduction due to innovation is sufficient. Innovation deterrence directly daages consuer surplus and social welfare Proof. It is iediate that Π (c) 2 ˆΠ U (c ) is decreasing with respect to c since we have Π / c < 0. Proposition shows that the need for the anufacturer to copensate each buyer for the inforational externality deters the introduction of soe efficient innovations on the arket. This directly daages consuer surplus, because efficient innovation reduces the arginal production cost and therefore final prices. It also daages the industry profit, as higher efficiency leads to higher industry profit. We thus find that although the anufacturer prefers selling the old product, the loss inflicted to the retailers is clearly larger than the gain for the anufacturer. 5 Equivalently, we could assue that the new product has better quality. 0

11 ˆΠ U. We also derive the role of the inforational externality on the anufacturer s profit Corollary 4 An increase in the inforational externality γ reinforces the deterrence of efficient innovations. As entioned in the coents regarding assuption 3, for a given k, Π k decreases with γ. Therefore ˆΠ U naturally decreases as the inforational externality increases. In the extree case where there is no externality, i.e. γ = 0, it is clear that the profit on each arket is the sae and therefore Π k = kπ /. Rewriting the anufacturer s profit in that polar case, we have : ˆΠ U = + i= ( Π i = Π ) i = Π ( + ) = Π i= Therefore the profit obtained through the launching of a new product is equal to that obtained through the sale of an old product. As a consequence, without an externality an efficient innovation would always be successfully launched. 5 Size effect In order to account for a size effect, we assue that the large retailer owns outlets,..., k, and each reaining retailer owns only one of the ( k) reaining outlets. Allowing for the presence of a larger retailer enables to account for the effect of downstrea concentration on the sharing of industry profit and on innovation. 5. Effect of buyer size on profits We denote by Π U (k, x) the profit of a anufacturer that faces a large retailer with k outlets and x = k sall retailers (with one outlet each). Bargaining progras (and therefore tariffs) are now asyetric. We denote by T k the tariff negotiated between the anufacturer and a retailer who owns k outlets when outlets are open. Note that because of the syetry between outlets, we always have Π j = Π /, and therefore, a retailer that owns k stores has a revenue kπ /. The equilibriu tariffs derive fro the following bargaining progras.

12 In case of a failure with the large fir, U bargains with x syetric sall firs, and its outside option is thus given by: Π SQ = x + Π i. In case of a failure with a sall fir, U bargains with x syetric sall firs and one large fir of size k, and therefore its outside option is given by: i= Π U (k, x ) The two bargaining progras thus yield: We obtain the following lea: k Π T k = T k + xt x + Π i (4) Π T = T k + xt Π U (k, x ) (5) Lea 4 When the anufacturer introduces a new product and faces one large retailer with k outlets and x sall retailers (with one outlet each), it earns a profit: Π U (k, x) = (x + )(x + 2) x (x j)π +j + i= (x j + )Π x+k j Proof. The full proof is available in Appendix A.2. We give here a sketch of the proof for k = 2 and = 3. Retailers never have a status-quo in their bargaining. In contrast, the anufacturer has a status-quo ˆT given by equation (2) when negotiating with the large retailer as in case of a breakdown, it is negotiating only with one reaining sall retailer. When negotiating with the sall retailer, in case of a breakdown, the anufacturer faces only the large retailer. It is straightforward that both the anufacturer and the large retailer would have no status-quo in their bargaining and each would therefore obtain Π 2 /2. Following, the bargaining progra with the large retailer is: 2Π 3 3 T 3 2 = T T 3 Π 2 2T T 3 = 2Π3 3 + Π 2. 2

13 The bargaining progra with the sall retailer is: Π 3 3 T 3 = T T 3 Π2 2 T T 3 = Π3 3 + Π2 2. Solving the equation syste, we obtain the following tariffs and corresponding upstrea profit: T 3 2 = 6 (2Π Π 2 + 2Π 3 ), T 3 = 6 (2Π2 Π ), Π U (2, ) = T T 3 = 6 (Π + Π 2 ) + Π3 3 = 3 2 3(3 ) 2 i= Π i + Π3 3. We now derive the coparative statics of equations (5) and (4) with respect to k, holding and other tariffs constant. Consider first equation (5). Assue for now that the large retailer is of size 2. We copare the gain fro the relationship of U with this large retailer to the gain that would arise fro independent bargaining with two sall retailers. We know fro Assuption 3 that the increental value of the relationship with an infraarginal retailer is always lower than the increental value of the relationship with the arginal retailer. Therefore, the profit that U extracts fro the large retailer (coposed of the arginal retailer and the infraarginal retailer) is strictly larger than the profit it extracts fro two sall retailers (each being a arginal retailer). As k increases, the sae reasoning applies. As the nuber of infraarginal retailers increases, the profit of the anufacturer increases even ore. As a consequence, all things being equal, Tk is increasing with respect to k. Consider now equation (4). Clearly an increase in k has no ipact on the gain fro the relationship of U with the sall retailer, since in both cases the bargaining concerns the arginal retailer. We now account for the interaction between the two types of negotiations. Fro equations (5) and (4), tariffs are strategic substitutes. Therefore, the negotiation with any retailer affects the equilibriu tariff paid by all other retailers. 6 Interestingly, this ay 6 This strategic substitutability derives fro the sequential bargaining fraework we adopt. By contrast, tariffs would be independent with the siultaneous bargaining fraework considered for instance by Chipty and Snyder (999) and Inderst and Wey (2007). 3

14 give rise to waterbed effect, in that the equilibriu tariff of the large retailer and that of a sall retailer ay vary in opposite direction with respect to k. Eventually, we find that the tariff of the large retailer always increases with respect to k, whereas the tariff of a sall retailer ay decrease with respect to k. We now copare the profit of U when it faces sall syetric retailers, that is ˆΠ U, and its profit when it faces ( k) sall retailers and one large retailer of size k, that is Π U (k, x). We define (k, x) Π U (k, x) Π U (k, x + ) > 0. (k, x) represents the effect of an increase in size of the large retailer on the anufacturer s profit. We obtain the following proposition. Proposition 2 For any nuber of open arkets, when the anufacturer is dealing with one large retailer (that owns k outlets) and x = k sall retailers, (k, x) > 0: The profit of the anufacturer increases with retail concentration. Proof. See Appendix A Effect of buyer size on innovation We copare profits realized by the anufacturer either through the sale of an old product or through the introduction of a new product in the presence of a large buyer. The structure of the retail arket has no incidence on the anufacturer s profit in the case of the sale of an old product: The anufacturer and the large retailer who owns k outlets siply share equally the increental value of their relationships, which aounts to kπ /. In contrast, and as entioned in the previous section, the presence of a larger buyer has an incidence on the anufacturer s profit who introduces a new product. We have shown in Proposition 2 that the anufacturer s profit was larger when confronted to a large buyer rather than only single-outlet retailers. Assue again that the new product has a arginal cost equal to c whereas the old product has a constant arginal cost c > c. We denote by Π U (k, x, c ) the profit of the anufacturer when introducing the ore efficient product when there is a large retailer of size k. We now obtain the following proposition. Proposition 3 The threshold δ(k) above which introducing the new product is profitable for the anufacturer is decreasing with respect to k. The inforational externality deters 4

15 the introduction of ore efficient products on the arket, but to a lesser extent as retail concentration increases. Proof. The threshold δ(k) above which the ore efficient product is launched is iplicitly defined by the following equation: Π (c) 2 Π U (k, k, c ) = 0. Fro Proposition 2, Π (c) 2 Π U (k, k, c ), and hence δ(k), is decreasing with respect to k. In the polar case in which all outlets are in the hands of a single retailer, we show that Π U (, 0) tends towards (Π (0)/2), and therefore it is clear that Π (0) > Π (c) and thus an efficient innovation is always launched. Corollary 5 Single-outlet retailers ay have an incentive to erge when doing so enables the anufacturer to launch a ore efficient product. Assue that in a preliinary stage, retailers can decide whether or not to erge. It is iediate that, absent innovation, there is no incentive to erge. Indeed, as retailers are active on independent arkets, there is no externality to internalize through erger. When the new product is innovative enough, a erger between two retailers has two contradictory effects on the profit of the erged firs. On the one hand, the joint profit increases as a result of innovation. On the other hand, as entioned above, a larger buyer obtains a saller share of this increased joint profit, due to the inforational externality. Balancing these two effects, it ay be profitable for firs to erge so as to induce innovation, and hence earn a saller share of a larger pie. However, the erger always benefits the outsiders ore than the insiders. If the following inequality is satisfied, then the retailer have an incentive to erge for a lower k than the upstrea fir: k(2 + x)π U (k, x, c ) (x + k)xπ U (k, x, c ) < Π (c ). (6) Consider the following expression of Π U (k, x): Π U (k, x, c ) = Π (x+)(x+k) + x i= Πi + Π U (k, x )(x + )x (x + )(x + 2) 5

16 We can rewrite this equation as follows: (x + )(x + 2)Π U (k, x, c ) Π U (k, x, c )(x + )x = Π (c )(x + )(x + k) (x + 2)Π U (k, x, c ) xπ U (k, x, c ) = Π (c )(x + k) (x + 2)Π U (k, x, c ) xπ U (k, x, c ) = Π (c ) + x + We thus have the following expression of Π (c ): Π (c ) = (x + 2)Π U (k, x, c ) xπ U (k, x, c ) + x + x = x (x j)π j + (x + j)π j k + i= Π i + Π i (c ) x + i= Π i (c ) i= Π i (c ) i= Π j + ( k)π 6

17 References Chipty, T. and Snyder, C.M., 999, The Role of fir size in bilateral bargaining: a study of the cable television industry, Reveiw of Econoics and Statistics, 8, Chen, Z Supplier Innovation in the Presence of Buyer Power, CARLETON ECONOMIC PAPERS Departent of Econoics. Econoides, N., 996, The Econoics of networks, International Journal of Industrial Organization, 4, Federal Trade Coission, 2003, The Use of Slotting Allowances in the Retail Grocery Industry: Selected Case Studies in Five Product Categories, Washington, DC. Available at Horn, H. and Wolinsky, A., 988, Bilateral onopolies and incentives for erger, RAND Journal of Econoics, 9, Inderst, R. and C. Wey, 2007, Buyer Power and Supplier Incentives, European Econoic Review, 5(3), O Brien, D. P., and G. Shaffer (992), Vertical Control with Bilateral Contracts, The RAND Journal of Econoics, 4(2): Larivière Martin A. and V. Padanabhan, 997, Allowances and New Product Introductions, Marketing Science, 6:2, Marx,. L. M. and Shaffer, G. 200, Slotting Allowances and Scarce Shelf Space, Journal of Econoics & Manageent Strategy, 9: Rao, A. R., and H. Mahi, 2003, The price of launching a new product: Epirical evidence on factors affecting the relative agnitude of slotting allowances, Marketing Science, 22(2), Richard, T. and Hailton S.F., 202, Network externalities in superarket retailing, European Review of Agricultural Econoics, -22. Shaffer, Greg. 99, Slotting Allowances and and Retail Price Maintenance: A Coparison of Facilitating Practices, RAND Journal of Econoics, 22 (), Shaffer, Greg., 2005, Slotting Allowances and Optial Product Variety, The B.E. Journal of Econoic Analysis & Policy. Volue 5, Issue Sith, H. and J. Thanassoulis, 202, Upstrea uncertainty and countervailing power, International Journal of Industrial Organization, 30,

18 Snyder, C.M., 998, Why do larger buyers pay lower prices? Intense supplier copetition, Econoics Letters, 58, Stole, L.A. and Zwiebel, J., 996, Intra-fir bargaining under non-binding contracts, Review of Econoic Studies, 63, Sullivan, Mary W., 997, Slotting Allowances and the Market for New Products, Journal of Law Econoics, 40 (2),

19 A Appendix A. Assuption 3 In this appendix we show that Assuption 3 is a sufficient condition to ensure that the industry revenue Π is convex with respect to. Given that all arkets are syetric, the industry revenue is given by: Π = Π j = Π. Therefore, the first and second derivatives of the industry revenue are respectively: Π = Π + Π, 2 Π 2 = Π Π. It follows that the industry revenue is convex if and only if: 2 Π 2 > 2 Π. (7) We now write this expression as a function of, γ and γ. Let us first find the first derivative of Π with respect to : Fro the envelope theore, we obtain: Π ( = P + P q ) q + q q P (q, ). Π = P q. We now deterine the second derivative of Π with respect to : 2 Π ( 2 2 = P P q ) q + P q q. 9

20 Fro Assuption 2, we obtain: Denoting the first order condition as follows: 2 Π 2 = 2 P 2 q + P q. (8) ϕ(q, ) = P (q, ) + q P (q q, ) = 0, we use the iplicit functions theore to deterine an expression of q : with: q = ϕ/ ϕ/ q, ϕ = P q q + P = P, ϕ = 2 P q + 2 P. q q q 2 We can therefore write equation (8) as follows: 2 Π 2 = 2 P 2 q 2 P q 2 ( P )2 q + 2 P. q Noticing that fro the second order condition we have 2 P q q P q < 0, it is clear that: 2 P q 2 ( P )2 q + 2 P q > 0. We can now write expression (7) as a function of the derivatives of the inverse deand function. The industry revenue is thus convex if and only if: 2 P 2 q 2 P q 2 ( P )2 q + 2 P q > 2 P q. Finally, using the notation γ = P, we obtain the following condition for the industry 20

21 revenue to be convex: ( γ + 2γ ) q > γ 2 P q q P q Assuption 3 is therefore a sufficient condition so that the above inequality is satisfied. A.2 Proof of lea 4 The profit of U when it faces 2 retailers, one large, which owns k = 2 outlets and one sall (x = ) is given by: Π U (2, ) = T T 3 = 6 (Π + Π 2 ) + Π3 3 = 3 2 3(3 ) This can be written as follows: 2 i= Π i + Π3 3. Π U (k, x) = x (x + )(x + 2) ( (x j)π +j + (x j + )Π x+k j ) where k = 2 and x =. Assue that this result is true with one large buyer of size k and x = k sall retailers, we deterine the profit of U with one large buyer of size k and x = k outlets. The bargaining progras are given by equations (4) and (5). We solve the equation syste by subtracting (4)fro 2 x(5), which yields: T (k, x) = Π (2 k) x+ x Πj + 2Π U (k, x ) x + 2 (9) Subtracting (4) fro (5), we also obtain: T k = Π (k ) + T + x + Π i Π U (k, x ) i= We therefore obtain an expression for the profit of U. Π U (k, x) = T k + xt = Π (k ) + (x + )T + x + Π i Π U (k, x ) i= 2

22 Replacing T by its value given by (9) and siplifying, we obtain: Π U (k, x) = Π (x+)(x+k) + x i= Πi + Π U (k, x )(x + )x (x + )(x + 2) (0) As x + k =, we therefore siplify the equation above and replacing Π U (k, x ) = x(x+) ( x 2 (x j)π+j + x (x j)πx +k j ), we obtain that: Π U (k, x) = Π U (k, x) = Π (x + 2) + x i= Πi + x 2 x (x + )(x + 2) ( (x j)π +j + (x j)π+j + x (x j)πx +k j (x+)(x+2) (x j + )Π x+k j ) We therefore obtain a recurrence relation for the profit of U. Equilibriu tariffs are given by: T k (k, x) = 2 + x [ xπu (k, x ) + T (k, x) = A.3 Proof of Lea?? Π j + (k x( k)) Π ] () 2 + x [2ΠU (k, x ) Π j + (2 k) Π x + ] (2) We want to show that T (k, x) is decreasing with respect to k, that is T T (k, x) < 0. We have the following expression: T (k, x) = 2Π U (k, x ) 2 + x x + Π j + (2 k) Π (k +, x ) which, fro the expression of Π U (k, x) given in Proposition (??) we can write as follows: T (k, x) = = x x(x + ) 2 + x x + x 2 x (x j)π +j + (x j)π x +k j x + 2 x x (x j)π +j + (x j)π x +k j Π j x Π j + (2 k) Π + (2 k) Π 22

23 Fro this we derive an expression of T (k +, x ): T (k +, x ) = = 2 + x x x + x x 2 x In order to properly copare the two expressions, we rewrite T T (k, x) = = T (k, x) = T (k, x) = x 3 x 2 x (x 2 j)π +j + (x j)π x+k j x 3 x x (x 2 j)π +j + (x j)π x+k j 2 x 2 (x j)π +j x x + x 2 x 2 (x 2 j)π +j x x + x Π j + (2 k) Π 2 x 3 (x 2 j)π +j x x + x ] +(2 k) Π + x x x + ] (2 k)π x + 2 (k, x) as follows: x (x j)π x +k j Π j Π j Π j + ( k) Π + ( k) Π + (2 k) Π x 2 x x Π +j + (x j)π x +k j + x x (x j)π x+k j + Π j + 2 x 3 x x (x 2 j)π +j + (x j)π x+k j + Π j + x We now deterine the difference between the two profits, which we denote T : Π x+k j Π x+k j Π x +k j Π j Π j T = T = ( ) 2 + x x(x ) 2 x x 2 (x j)π j + (x j)π x+k j x Π j + x(x + 2) x x x ( Π j + Π x+k j + ( k) x + ) Π (2 k) x(x + 2) x x 2 x (x j)π j + (x j)π x+k j x Π j + Π j + x x(x )(x + 2) x x x Π j + Π x+k j Π x(x + 2) x + 2 Π j 23

24 T = = = 2 x 2 x (x j)π j + (x j)π x+k j + x x(x )(x + 2) 2 x Π j + Π x+k j Π x(x + 2) x x 2 x (x j)π j + (x j)π x+k j + x x(x )(x + 2) 2 x 2 Π j + Π x+k j Π x(x + 2) x x 2 x (x j)π j + (x j)π x+k j ( + x)(2 + x) x(x ) 2 x 2 Π j + Π x+k j x + 2 x x(x + 2) Πx x Π x Π Π j + Πx x + 2 We now focus on the following expression, which is positive if and only if T with respect to k: is increasing T = 2 x 2 x x (x j)π j + (x j)π x+k j 2 Π j + Π x+k j + Π x Π x x x 2 ( ) = 3(x j) x ( ) 3(x j) 2 Π j + x x Π x+k j (2Π x + Π k) + Π x Π x 2 ( = 3j ) x ( ) Π j 3(j ) + 2 Π x+k j (2Π x + Π k) + Π x Π x x A.4 Proof of Proposition 2 We prove that for any (k, x), we have (k, x) = Π U (k, x) Π U (k, x + ) > 0. Fro 0, we write that : Π U (k, x + ) = Π (x + 2) + x+ i= Πi + Π U (k, x)(x + )(x + 2) (x + 2)(x + 3) (3) Fro our recurrence relation given in lea (4), we also have: Π U (k, x) = x (x + )(x + 2) ( x+ (x j)π +j + (x j + 2)Π x+k j ) (4) 24

25 and therefore we can replace (4) in (3) to obtain : x Π U (k, x+) = (x + 2)(x + 3) ( x+ x+ (x j)π +j + (x j +2)Π x+k j + Π j )+ Πx+k x + 3 And therefore we obtain: (5) (k, x) = x (x + )(x + 2) ( (x j)π +j + (x j + )Π x+k j ) x (x + 2)(x + 3) ( x+ x+ (x j)π +j + (x j + 2)Π x+k j + Π j ) Πx+k x + 3 Siplifying the above expression, we have : (k, x) = A (x + )(x + 2)(x + 3) x A = 2 (x j)π +j + (x + )(Π x+k = = x (x 2j )Π +j + (x+)/2 x+ Π j ) + (x 2j + )Π x+k j (x + )Π k (x 2j + )Π x+k j + (x + )(Π x+k Π k Π x+ ) (x 2j + )[(Π x+k j Π x j+ ) (Π k +j Π j )]. Assuption 3 ensures that the above expression is always positive. 25