New Product Introduction and Slotting Fees

Transcription

1 New Product Introduction and Slotting Fees Claire Chambolle and Clémence Christin February 6, 016 Abstract The availability of a product in a given store is a form of informational advertising that may go beyond the store itself. We show that each retailer is able to extract a rent in exchange for this informational advertising service, which materializes through the payment of a slotting fee from the producer to the retailer. Therefore, a manufacturer may not find profitable to innovate in order to launch a new and more efficient product. This in turn harms consumers surplus and welfare. Varying the buyer size, we then show that retail concentration may facilitate innovation. KeyWords: Buyer Power, Innovation, Slotting allowances, Informational externality. JEL codes: L13, L4, M37. 1 Introduction Slotting fees are upfront payments from the producer to the retailer that are paid to secure a slot for a new product in retailers shelves. 1 Their amount and frequency have rapidly grown since the mid-1980 s. According to the FTC report on slotting allowances on the We thank Marie-Laure Allain, Stphane Caprice, Laurent Linnemer, Joao Montez, Jorge Padilla, Sylvaine Poret, Patrick Rey, Andrew Rhodes, Jeanine Thal, Christian Wey, participants at EARIE 015, Jornadas di Economia Industrial 015, AFSE 015 as well as participants at LEI lunch seminar and the TSE Food seminar. We gratefully acknowledge support from the Agence Nationale de la Recherche (ANR) and the Deutsche Forschungsgemeinschaft (DFG) for the French-German cooperation project Competition and Bargaining in Vertical Chains. INRA UR1303 ALISS, 65 boulevard de Brandebourg 9405 Ivry-sur-Seine, France; Department of Economics, Ecole Polytechnique, route de Saclay 9118 Palaiseau, France, claire.chambolle@ivry.inra.fr. Normandie Université, UCBN, CREM-UMR CNRS 611, UFR SEGGAT, Esplanade de la Paix, Caen, France, clemence.christin@unicaen.fr 1 As in the FTC study (003), we make a clear distinction between slotting fees (for new products) and pay-to-stay fees (for continuing products) as well as advertising and promotional allowances, or introductory allowances and other per unit discounts. 1

2 U.S market, from 50% to 90% of all new grocery product introductions would trigger the payment of such fees in 000 DATE TO BE CHECKED. The FTC report further mentions that: [... ] slotting allowances for introducing a new product nationwide could range from a little under 1 million to over million, depending on the product category. Retailers have basically justified slotting allowances as a risk-sharing mechanism and a means to screen the most profitable innovations. They also argue that slotting allowances are natural cost shifters to pass on the higher retailing costs that result from the increasing flow of new products from 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 fees. Our starting point is that the demand for a new product depends on the consumers knowledge of its existence. Consumers may be informed through advertising but also more simply 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 form of informational advertising that may go beyond the store itself. Such an informational spillover may for instance be the result of word of mouth communication among consumers across markets. The supply of a new product may thus partly generate its own demand. We show that, by making available the new product, a retailer offers a service to the producer which is paid through a slotting allowance. In turn, this may deter the producer s incentive to launch a new product. However, we point out that the presence of a larger buyer may mitigate this innovation deterrence effect. To do so, we build a simple vertical model with an upstream monopolist and m retailers active on separate markets. We introduce an informational spillover, i.e. we assume that the number of markets where the product is actually sold exerts a positive externality on the demand for a new product: the larger the number of markets where the new product is sold, the larger the demand for this product on each of these markets. To simplify, we compare two symmetric situations: In the first case, the manufacturer launches a new product; then securing one outlet increases demand in all other outlets in which the product is sold. In the second case, the manufacturer sells an old product; then the market is mature and informational spillovers no longer play a role. We then analyze the bargaining between the producer and each of the retailers in these situations. We con- This result is obtained assuming that nationwide introduction would require distribution to 85% of the supermarkets in the U.S., and that 85% of these supermarkets would receive a slotting fee, See FTC (003).

3 sider secret bargaining among each pair following the multilateral bargaining specification of Stole and Zwiebel (1996). 3 We are first able to derive a new source of buyer power: when selling a new product, the manufacturer must compensate each retailer for the positive informational externality of a success of their bargaining on all other markets. Such buyer power increase materializes through the payment of a slotting allowance from the producer to each retailer. As a result, informational spillovers may deter innovation as the producer may earn a smaller profit, i.e. a smaller slice of a bigger pie. Innovation deterrence is then harmful both for consumer surplus and welfare. We then analyze the impact of retail concentration on the launching of new products. To vary the size of retailers, we allow retailers to own outlets on several markets. A larger retailer is a retailer that owns more outlets and is thus present on more markets. Keeping the number of outlets constant, we assume that one retailer owns several outlets, while all other retailers still own only one. The presence of a larger buyer has no impact on the manufacturer s profit when it sells an old product, whereas it increases the manufacturer s profit when it sells a new product. Innovation is here favored by a more concentrated downstream market structure. Our work is first related to the industrial organization and marketing literature on slotting fees. A first strand of the literature highlights diverse potential anticompetitive effects of slotting fees without focusing on new products. Shaffer (1991) shows that when differentiated retailers buy from perfectly competing manufacturers who offer an homogenous good, they obtain a contract with slotting fees in exchange for high wholesale prices that enable to relax retail competition. 4 Shaffer (005) considers a framework in which imperfectly competing retailers can either buy from a dominant firm or a competitive fringe. Because of slotting fees, the dominant firm may obtain scarce shelf space even when it is less efficient than rivals, for it is willing to pay a higher price to protect its rent. Conversely Marx and Shaffer (007) highlight that slotting fees may facilitate retail foreclosure: a powerful retailer can use slotting fees to exclude its weaker rival. However, Miklos-Thal et al (011) show that this result may be reversed allowing for contingent contract. Marx and Shaffer (010) highlight that capturing the rent of manufacturers through 3 As shown by Stole and Zwiebel (1996), this solution concept gives rise to the Shapley value. 4 See also Foros and Kind (008) for an extension of Shaffer (1991) taking into account procurement alliances. 3

4 slotting fees may also push retailers to restrict their shelf space. Slotting fees then reduce the variety of products offered to consumers. Though they relate the existence of such fees to retail buyer power, these articles do not take into account the peculiarities of new product introduction in their analysis. A second strand of the literature partly fills this void. These articles mainly outline that slotting fees are an efficient tool to allocate shelf space when retailers are confronted to the risk associated with new product launching. Slotting fees can be an efficient way for privately informed manufacturers to convey information about the likelihood of success of their new product (e.g. Chu (199), Sullivan (1997)). Larivière and Padmanabhan (1997) show that slotting fees may be used to compensate the retailer for extra costs inherent to the launching of a new product. Foros et al (009) show that when retailers make offers, slotting fees may induce manufacturers to promote the new product through demand-enhancing investments. Slotting fees therefore enable a better coordination within the vertical chain. Yehezkel (014) shows that slotting fees may create incentives for manufacturers to test the quality of their products. This paper is part of this second strand of papers as slotting allowances are paid for the launching of a new product. However, in contrast with this literature which rather emphasizes the efficiency effects of slotting fees, we show that, by deterring the launching of efficient innovations, slotting fees harm consumers and welfare. Our work also builds on the literature on bargaining and buyer size, e.g Inderst and Wey (003,007), Montez (007), Thanassoulis and Smith (01). More specifically the seminal paper by Chipty and Snyder (1999) show that when an upstream manufacturer negotiates simultaneously with separate retailers, a large buyer obtains a larger (respectively smaller) discount whenever the suppliers gross revenue function is concave (resp. convex). In our set-up, although the suppliers gross revenue function is linear, the informational spillover shifts the industry revenue function with respect to the revenue function of an old product. When the industry recevue function for the new product is convex, we find that slotting fees paid for the introduction of a new product to a large retailer are lower. Note that with the simultaneous bargaining framework of Chipty and Snyder (1996), our informational 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 upstream innovation. Inderst and Wey (007), analyze the upstream incentives to innovate 4

5 in a similar framework when production cost is convex and show how the presence of large buyer may strengthen the supplier s incentive to innovate. In contrast Batigalli, Fumagalli and Polo (007) show that a larger buyer power may, by increasing hold-up, reduce the upstream incentives to invest in quality. Chen (014) considers, as we do, a framework in which one of the retailers serves several markets whereas other retailers serve only one. He shows that a large buyer has a larger status-quo profit because it can benefit more from backward integration if the negotiation fails, which hinders the manufacturer s incentive to innovate. In contrast, in our framework, buyer size lowers buyer power and therefore facilitates upstream innovation. Finally, our paper also indirectly relates to the literature on network effects. In our model, informational spillovers create complementarity between retail markets such as in networks. The potential deterrence effect of the innovation may be, at first sight, related to usual result of under-adoption of a single network (see Farrell and Klemperer (006)). However, such result clearly relies on the simultaneity of consumer s adoption decision. In our model, we have adopted a sequential bargaining approach which prevents such effect from happening. Another striking difference with this literature is that we have strategic buyers who have bargaining power instead of a mass of final consumers. In our model, absent downstream bargaining power, an efficient innovation would always be launched. Each buyer is big enough to make the supplier pay for the spillover exerted on other markets and this is the reason why an efficient innovation may be deterred. When considering competition between an entrant who launches a new product and the incumbent firm who offers an old product, only the entrant can benefit from the informational externality effect. In contrast, one key element in network competition is that adopting one network from a consumers means not adopting another and therefore the externalities goes both ways. Section derives the model. Section 3 analyzes the effect of the informational externality on the payment of slotting allowances by comparing 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 more efficient product. Section 5 analyses the robustness of our result when varying the retailers size. Section 6 concludes. 5

6 The Model We consider a framework with N independent and symmetric markets. An upstream firm U may sell a good of quality q through i = {1,..., N} symmetric monopolistic retailers. Production and retailing costs arel normalized to 0. We first assume that each retailer is the owner of a single outlet. 5 We assume that there is a mass of potential consumers on each market, which we normalize to 1. A representative consumer earns utility u(q, x) from consuming a quantity x of a good of quality q. We make the standard assumptions on the utility function, that is u(q, x) 0, u x > 0, u < 0 and u x q > 0. Among the pool of consumers, some may be informed of the existence of a new good, whereas others are not. The representative consumer has a probability ξ(n) of being aware of the existence of the new product, with n {1,, N} the total number of markets on which the product is actually sold. The probability ξ(n) is increasing with respect to n, with ξ(0) 0 and ξ(n) = 1. This reflects the presence of an informational spillover: as more markets sell the new good, there are more informational channels for a given consumer to discover its existence. This informational spillover creates a complementarity link between markets despite the fact that each market is a monopoly. 6 In contrast, we assume that ξ(n) is independent of x i (i {1,, N}), that is the strength of the informational spillover is not affected by the quantity sold on each market. Although a correlation between the quantity sold and the strength of the informational spillover would make sense, it creates additional interactions between markets which we want to rule out in our analysis. On a given market i, the representative consumer maximizes its expected utility ξ(n)u(q, x i ) P x i, which generates the inverse demand function P (q, n, x i ). Our assumptions on the consumer s expected utility translate into the following assumptions on demand for a new product: Assumption 1 P (q, n, x i ) P (q, n 1, x i ) > 0 for all n {1,, N}. Assumption P (q,n,x i) x j = 0 for all n {1,..., N} and all j i. 5 We will allow further a retailer to exploit several outlets. 6 Two consumers do not need to visit the same store to talk with eachother about a new product. 6

7 Therefore, demand on a given market for a new product is at most the demand when all markets are active, that is P (q, N, x i ). If instead a product is old, consumers on all markets i {1,...N} are already aware of its existence and therefore the demand for an old good on every market i is P (q, N, x i ) even if the product is not sold on markets i {n + 1,..., N}. The informational spillover has no role to play as an old product is well known by consumers. 7 We denote by υ n the optimal revenue earned in each outlet i {1,...n} when U sells a new product of quality q through n markets. Conditions on the demand function ensure that the output that maximizes revenue on a given market i is unique. We therefore have: υ n (q) max x i P (q, n, x i )x i. (1) Assumption 1 implies that υ n+1 (q) > υ n (q) (see Appendix A.1): an increase in the number of outlets that actually sell the new good increases the individual profit on each active market. Total industry revenue for a new product with n outlets is defined as follows: Υ n (q) n υ n (q) = nυ n (q). () The optimal revenue earned in outlet i {1,...n} when U sells an old product of quality q through n markets is: max x i P (q, N, x i )x i = υ N (q). (3) Total industry revenue for an old product with n outlets is simply nυ N (q). Although our main assumptions have been presented in a static setting, we will consider a three-period game; periods are denoted by t = 0, 1, and we neglect the discount factor (δ = 1). We assume that the manufacturer can produce an old product of quality q at no cost and can launch a new product of quality q + q at an innovation cost F. This innovation cost is paid only once for all periods. We also assume that the new product is new only in the first period in which it is sold. In other words, if the new product was sold in all markets in period 1, then it becomes an old product in period, i.e. its demand in period is P (q +, N, x i ) even if n < N. 8 7 Note that we assume that only one type of product is sold at a time in a given outlet. One can see this as a capacity constraint on the retailers shelves. For this reason, the quality q has no subscript i. 8 We prove further that in equilibrium, the new product is sold either on N or 0 markets in period 1. 7

8 The timing is as follows. In t = 0, the manufacturer chooses whether or not to innovate; in case it innovates it pays F. 9 Then, in each period t = 1,, the timing of the game is identical. First, the upstream firm bargains simultaneously with each retailer i on a two-part tariff (w it, T it ) where w it is the unit wholesale price and T it a fixed fee for the new (in case of innovation) or the old product (otherwise). 10 on its single outlet. 11 Second, each retailer i maximizes its profit by setting quantities We consider a sequential bargaining à la Stole and Zwiebel (1996). In the sequence of negotiations, the success or failure of any given negotiation is common knowledge. Therefore, each retailer knows how many outlets are open when bargaining with the manufacturer U. Besides, in case of failure of the negotiation between one retailer and U, the failing pair can never negotiate again, and all other pairs renegotiate their contracts from scratch. 1 In this framework, in each period t = 1,, each pair U i uses w it to maximize their joint profit and T it to share it. Assumption ensures that the bilaterally efficient wholesale price is w it = 0 for all i {1,..., N}. Indeed, there is no incentive for a pair to distort the wholesale price, because for a given market structure, the output decision of one retailer does not affect the output decision of the other retailers. 13 The value of T it depends on the firms respective bargaining weights and outside options. Without loss of generality we set the bargaining weights to ( 1, 1 ).14 If the disagreement payoffs of i (resp. U) is d i (resp. d U ), when U bargains with i among n retailers, the optimal fixed fee, T it is given by: υ n (q) T it d i = T it + n j=1,j i T jt d U. (4) 9 This period t = 0 is introduced to facilitate the exposition. Same results would obtain with a twoperiod game in which the manufacturer could innovate in each period before the negotiations take place. 10 In order to reflect actual practices, we assume that long term negotiations over tariffs are not possible. 11 Because we consider local monopolies, we would obtain the same results if retailers set prices. 1 Note that this bargaining framework is equivalent with simultaneous bargaining in which the parties sign contracts which are contingent to the equilibrium market structure, that is, here, the number of active links in equilibrium. 13 For instance, with P (q,n,x i) x j > 0, the producer of the new product would have an incentive to sell its product at a wholesale price lower than the marginal cost in order to increase the quantity bought by each retailer and therefore increase its profits on all other markets. 14 Note that the outcome of the negotiation coincides with the Shapley value. 8

9 3 Slotting allowance for a new product We first determine the equilibrium of the subgame in which the manufacturer launches a new product in t = 0 in section 3.1. Then, we consider in section 3. the other subgame equilibrium in which the manufacturer sells an old product during the two-periods. Finally, we compare both equilibria in section The manufacturer does not innovate in t = 0 In t =, the manufacturer thus bargains with N manufacturers to sell the old product of quality q. In that case, the profit in each outlet is υ N (q) as given by (3). All negotiations are thus independent of one another, and since the manufacturer and each retailer have no outside option in their bargaining (d U = d i = 0), the manufacturer gets half of the profit on each market. As the manufacturer s profit strictly increases with the number of markets served, U bargains in equilibrium with N retailers and therefore in equilibrium obtains a profit Υ N (q)/. When the manufacturer sells an old product, its profit is Υ N (q)/, and the profit of each retailer i is Υ N (q)/(n). Solving backward the period 1, results are similar to period, and the manufacturer obtains a profit Υ N (q)/. We denote Π n t (q) the equilibrium profit of the manufacturer in period t when dealing with n firms and selling an old product of quality q. We obtain the following lemma: Lemma 1 When the manufacturer offers an old product over the two periods, its equilibrium profit is Π N t (q) = ΥN (q) for t = 1,. Proof. Straightforward. 3. The manufacturer innovates in t = 0 If now the manufacturer has paid F in t = 0, it bargains to sell the new product in t = 1,. We solve again the game backward. Assume that the new product was effectively sold in N markets in t = 1 15, then, in t =, the new product generates a profit υ N (q + ) on each market i since the informational spillover has already played its role in period 1. Again all negotiations are independent 15 We prove further that if the new product is sold in the first period, it is always sold by all N retailers. 9

10 of one another. However, an important difference remains as compared to the previous case of an old product. In case of a breakdown in one pair s negotiation, the producer is still able to bargain over the old product with the retailer and therefore each of them (U and i) obtains the same disagreement payoff d i = d U = ΥN (q) N. As by assumption q + q, υ N (q + ) υ N (q), and therefore any negotiation between the manufacturer and a retailer over the new product succeeds, and υ N (q + ) is shared according to equation (4). The optimal fixed fee is thus given by: υ N (q + ) T i ΥN (q) N = T i ΥN (q) N As the term ΥN (q) N is on both sides, it cancels out. In the period equilibrium, N retailers sell the new product and pay the same tariff denoted ˆT N = ΥN (q + ) N. Denoting the equilibrium profit of the manufacturer in period by ˆΠ N (q+ ), we obtain: ˆΠN (q + ) = Υ N (q + )/. We now go backward to solve the negotiation in period 1. In this period, due to the informational spillover, negotiations are no longer independent of one another. When U bargains with n {1,..., N} retailers, the outside option of U with retailer i amounts to the profit it would earn if it were negotiating with all n 1 retailers except for i plus the profit obtained from bargaining over the old product on market i. The same reasoning can be applied when U bargains with n 1 retailers, etc. Note that in equilibrium, each retailer considers itself as marginal in its bargaining with the manufacturer, and therefore all n retailers pay the same tariff to U, which we denote ˆT n 1 if n markets are open. We define the upstream equilibrium profit in period 1 as: ˆΠ n 1 (q + ) n ˆT n 1. (5) We first consider the case in which U bargains with only one retailer. In this case, both disagreement payoffs are d i = d U = ΥN (q) N : U can still bargain with the retailer to sell the old product. Equation (4) can be rewritten as follows: υ 1 (q + ) ˆT 1 1 ΥN (q) N = ˆT 1 1 ΥN (q) N (6) There are now two cases to consider. Case (1) If υ 1 (q + ) > ΥN (q) N : the negotiation succeeds as it is possible to find a 10

11 mutually profitable agreement and the equilibrium tariff is thus given by: U obtains a profit ˆΠ 1 1 (q+ ) = ˆT 1 1. ˆT 1 1 = Υ1 (q + ). (7) Case () If υ 1 (q + ) ΥN (q) N : the negotiation breaks and the manufacturer and the retailer negotiate for the sale of the old product. U obtains a profit ˆΠ 1 1 (q+ ) = ΥN (q) N. Let us now proceed with the complete bargaining in cases (1) and (). In case (1), Υ N (q) N υ 1 (q + ) > ΥN (q) N and therefore it is immediate that i 1, we have υi (q + ) > and therefore all the negotiations from the first will succeed in equilibrium. If U now bargains with two symmetric retailers, the outside option of U with i = 1, is given by d U = ˆT ΥN (q) N, whereas the outside option of each retailer is d i = ΥN (q) N. From equation (4), and since retailers are symmetric, we obtain: Υ (q + ) ˆT 1 ΥN (q) N = ˆT 1 ˆT 1 1 ΥN (q) N 3 ˆT 1 = Υ (q + ) In period 1, the total profit of U when facing two retailers is: + ˆT 1 1 ˆT 1 = Υ (q + ) + Υ 1 (q + ). 6 ˆΠ 1(q + ) = ˆT 1 = 1 3 ( Υ (q + ) + Υ 1 (q + ) ). From this point on, we determine a recurrence relation to obtain ˆΠ n 1 (q+ ) for any n 1. When υ 1 (q + ) > ΥN (q) N, the manufacturer always bargains in equilibrium with N retailers and realizes a profit: ˆΠ N 1 (q + ) = 1 N + 1 The details of the recurrence are provided in Appendix A.. Υ i (q + ). (8) In case (), υ 1 (q + ) ΥN (q) N, i.e. the first negotiation fails. To determine the equilibrium profit in that case, first assume that negotiations succeed if and only if the producer bargains at least with ˆn retailers. Therefore the cut-off level ˆn is such that the following condition is satisfied: Υˆn 1 (q + ) ˆn 1 ΥN (q) Υˆn N < (q + ) ˆn (9) 11

12 Note that there always exists a cut-off level ˆn [1, N] since Υ N (q + ) > Υ N (q) and Υ 0 (q + ) = 0. Solving the negotiations for all n ˆn, we determine by recurrence the equilibrium profit depending on the value of ˆn [0, N]. manufacturer bargains with N retailers in equilibrium and obtain a profit: When υ 1 (q + ) ΠN (q) N, the ˆΠ N 1 (q +, q, ˆn) = 1 N + 1 Υ i (q + ) + i=ˆn ˆn(ˆn 1) Υ N (q) N + 1 N (10) Details of the recurrence are provided in Appendix A.3. It is interesting to note that the profit of the manufacturer in case (1) is the limit of the profit of the manufacturer in case () for ˆn = 1. Thefore, we can summarize the equilibrium profit of the manufacturer on the two period-game in the following lemma: Lemma In case the manufacturer innovates in t = 0, its profit in the subsequent periods are: ˆΠN 1 (q +, q, ˆn) = 1 N N+1 i=ˆn Υi (q + ) + ˆn(ˆn 1) Υ N (q) N+1 N where ˆn [1, N[ is defined by (9) and ˆΠ N (q+ ) = ΥN (q + ). Note that ˆΠ N 1 (q+, q, ˆn) is decreasing with respect to ˆn (See Appendix A.7) 3.3 New vs. old product Comparing the manufacturer s profit in the two cases, we now obtain the following proposition: Proposition 1 When selling an old product, the manufacturer obtains the same profit from the retailer in each period t = 1,. When launching a new product, the manufacturer ( obtains a smaller profit in the first period than in the second ˆΠN (q + ) ˆΠ ) N 1 (q+, q, ˆn) > 0 each retailer is able to extract a slotting fee for the informational spillover it creates on all other markets. Proof. From Appendix A.1 we know that Assumption 1 implies that υ i (q + ) < υ N (q + ), i. Therefore: i=ˆn Υ i (q + ) < ΥN (q + ) N i=ˆn i = (N(N + 1) ˆn(ˆn 1))ΥN (q + ) N 1

13 Besides, we know that Υ N (q) < Υ N (q + ), and therefore we obtain: ˆΠ N 1 (q, q +, ˆn) = 1 N + 1 Υ i (q + ) + i=ˆn ˆn(ˆn 1) Υ N (q) N + 1 N < (N(N + 1) ˆn(ˆn 1))ΥN (q + ) N(N + 1) = ΥN (q + ) = ˆΠ N (q + ). + ˆn(ˆn 1) Υ N (q + ) N + 1 N The rent the retailer is able to capture in the first period from the manufacturer who launches the new product results from a renegotiation effect. Note first that since in equilibrium, N retailers sell the new product in period 1, the joint industry profit is the same in both periods, and equal to Υ N (q + ). The sharing of this profit, however, is affected in period 1 by the information spillover. In period 1, for any number of open markets n, negotiations are symmetric as each retailer considers itself as marginal in its negotiation with the manufacturer. For all n, in case of a breakdown in the negotiation with one retailer, the profit realized on each remaining market is strictly lower than in case of success, as there is less spillover, i.e. the demand is lower with n 1 markets open than with n. Because of our renegotiation setting, this is common knowledge to all players, therefore each retailer is able to extract some rent from its marginal extra-contribution (the spillover) to total industry profit. For instance, assume N = and the negotiation with retailer 1 already took place and succeeded. When bargaining in period 1, in case of a breakdown outside options are d U = υ1 (q + )+υ (q), as retailer sells the old product and retailer 1 sells the new, and d = υ (q). In contrast, in period, outside options are d U = υ (q + )+υ (q) and d = υ (q). As the outside option of the manufacturer is strictly lower in period and the outside option of the retailer is unchanged, the share of the joint profit that the manufacturer is able to extract is lower in period 1. Assume now that N = 3. The equilibrium profit of the manufacturer obtained when N = is nothing else than its outside option in the negotiation with the marginal retailer when N = 3. Therefore, applying the same reasoning as above, the equilibrium profit of the manufacturer is strictly lower than Υ3 (q + ), i.e. the profit it would earn with an old product. This cumulative lag in the status-quo profit of the manufacturer remains and 13

14 keeps degrading the equilibrium manufacturer s profit for all 3 < n N. Note that in a simultaneous bargaining setting à la Chipty and Snyder (1999), as a breakdown would not change the equilibrium tariffs paid by all remaining retailers to the manufacturer, the marginal retailer would not be able to extract a rent from the spillover. 16 As a consequence of the spillover and renegotiation effects, each retailer pays a lower fixed fee to the manufacturer in period 1 than in period. Conversely, the manufacturer has to pay slotting fees to each retailer to introduce a new product. Note here that, in contrast to Shaffer (1991), slotting fees do not materialize through negative fixed fees in equilibrium. In our approach slotting fees and standard franchise fees are mixed, and result in equilibrium in a payment from the retailer to the manufacturer. 17 slotting fees are only paid upfront, that is in period 1. However, Let us now partly relax Assumption 1 by assuming that the informational spillover entirely disappears once the manufacturer has reached N 1 markets in period 1. Indeed, it seems reasonable to assume that a new product only needs to be present in a large enough share (lower than 100%) of the market to reach all its potential consumers. Though there is no extra-contribution of the marginal retailer when bargaining for a new product (as the spillover effects disappears), retailers still obtain slotting fees from the manufacturer. Indeed, the status-quo profit of the manufacturer that results from negotiations with N 1 retailers is still lower in period 1 than in period. Therefore in its negotiation, the manufacturer still obtains a profit lower than ΥN (q + ). 18 Our result is thus robust to such a variation in the spillover effect (the same reasoning applies whenever the spillover stops after the opening of n markets). 4 Innovation deterrence We now solve stage t = 0. The manufacturer chooses to innovate if and only if the net benefit it yields (as compared to selling an old product) exceeds the cost of innovation, 16 In eq. (4), if the bargaining is simultaneous, d i = ΥN (q) and N du = P j i Tj + ΥN (q), and therefore N T i = υn (q + ). 17 In contrast with Marx and Shaffer (007) and Miklos-Thal et al (011), we do not distinguish formally the franchise fee as paid when a positive quantity of good is ordered from a slotting fee paid also if the quantity ordered is zero. 18 From eq (4), in period 1, given symmetry among retailers and that d i = υn (q) and d U = υn (q) ˆΠ N 1 ˆΠ N (q + ), we have (N + 1) ˆT 1 N = υ N (q + ) + 1 (q + ). Taking into account that υ N (q + ) = υ N 1 (q + ), as N 1 long as ˆΠ 1 (q + ) < ΥN 1 (q + ), that is as long as some spillover exists, we have ˆT N 1 < υn (q + ). 14

15 that is: ˆΠ N 1 (q +, q, ˆn) + ˆΠ N (q + ) (Π N 1 (q) + Π N (q)) F, We thus obtain the following proposition Proposition Due slotting fees, efficient innovations are deterred for any fixed cost of innovation F such that: F [ ˆΠN 1 (q +, q, ˆn) + ˆΠ N (q + ) Υ N (q), Υ N (q + ) Υ N (q)]. We can show that regardless of the value of ˆn, when dealing with N retailers, we always have ˆΠ N (q+ ) > ˆΠ N 1 (q+, q, ˆn) > ΥN (q). Therefore, absent innovation costs, it is always profitable for the producer to introduce the new product when it can use the old product as a threat point in its bargaining with the retailers: without innovation cost, an efficient innovation is always launched in equilibrium. The insight is that, by using the old product as a threat point, the manufacturer is by definition able to extract at least the profit it would get by selling the old product. Note that, the larger the quality gap between old and new products, the less restrictive this condition. hold-up effect arises. Moreover, for F [ Υ N (q + ) Υ N (q), (Υ N (q + ) Υ N (q)) ], a standard Indeed, since the manufacturer has to leave half of the rent of innovation to retailers while incurring all the cost, it naturally under-invests. Besides this effect, slotting fees reinforce the innovation deterrence. Proposition shows that the need for the manufacturer to compensate each buyer for the informational externality deters the introduction of some efficient innovations on the market. This damages consumer surplus, because efficient innovation would increase the quality of the product offered to consumers. It also damages the industry profit, as higher quality leads to larger industry profit: although the manufacturer prefers selling the old product, the loss inflicted to the retailers is clearly larger than the gain for the manufacturer. Such deterrence effect of slotting fees paid for the introduction of new products was pointed out by the FTC in its 003 report on Slotting allowances: roughly 10 percent of ice cream products fail to earn enough revenue in their first year to cover their slotting fees. 15

16 Let us now consider a variation in spillover intensity. In our framework, this corresponds to a change in the funciton ξ(.). If the spillover decreases, that is the spillover is now ξ(n) ξ(n) for all n {1,..., N} and there exists n such that ξ(n) > ξ(n), information across markets through the sales in retailers outlets has a smaller role to play to boost demand. Among all potential consumers on a given market, fewer can be captured through word of mouth and/or more consumers are prompt to purchase a new product as soon as it appears in their store. As a result, the gap between the profit without spillover (υ N (q + )) and the profit on each market when n < N markets are open (υ n (q + )) weakly decreases. 19 We obtain the following corollary: Corollary 3 A decrease (resp. increase) in the informational spillover weakly reduces (resp. reinforces) the amount of slotting fees paid by the manufacturer for the new product introduction. It weakly softens (resp. reinforces) the innovation deterrence effect. Proof. When the information spillover decreases, from eq (), Υ n (q + ) weakly increases for all n [1, N 1] and n N 1 such that Υ n (q + ) strictly increases. Recall that the profit of the manufacturer is: ˆΠ N 1 (q +, q, ˆn) = 1 N + 1 Υ i (q + ) + i=ˆn ˆn(ˆn 1) Υ N (q) N + 1 N Then, there are three cases: First, if the change in spillover only affects v n (q + ) for n < ˆn and ˆn is unchanged, there is no effect of this change on the manufacturer s profit. Indeed, the term 1 N+1 N i=ˆn Υi (q + ) is not affected as it only depends on v n (q + ) for n ˆn. The second term is by definition independent of the spillover. Second, if the change in spillover only affects v n (q + ) for n < ˆn and ˆn decreases as a result of the decrease in spillover, the profit of the manufacturer increases. Indeed, assume that only Υˆn 1 changes and is now equal to Υˆn 1, so that the new threshold 19 Note that we restrict our attention to monotonic variations in the spillover intensity in the sense that the difference υ N (q + ) υ n (q + ) weakly decreases when the spillover decreases for all n [1, N 1] and strictly decreases for at least one n [1, N 1]. 16

17 is ˆn 1. Then, the new profit of the manufacturer is: 1 N + 1 i=ˆn Υ i (q + ) + Υˆn 1 (q + ) N + 1 We compare this to its former profit, that is: 1 N + 1 i=ˆn + (ˆn 1)(ˆn )ΥN (q). N(N + 1) Υ i (q + ) + ˆn(ˆn 1)ΥN (q). N(N + 1) The difference between these two profits is given by: ( 1 Υˆn 1 (q + ) ˆn 1 ) N + 1 N ΥN (q). Because we now have Υˆn 1 (q + ) ˆn 1 > ΥN (q) N, this term is positive. Finally, if there exists n ˆn such that the decrease in spillover affects v n (q + ), it is immediate that the profit of the manufacturer increases, as 1 N+1 N i=ˆn Υi (q + ) increases. Consider now that the manufacturer can affect the informational spillover intensity. He could do so for instance by launching an advertising campaign to inform consumers about its new product and therefore increase ξ(n). This advertising campaign would result in a decrease in spillover intensity, and each retailer would then contibute less to the diffusion of the information about the product, and thus be able to extract lower slotting fees. The manufacturer then faces a trade-off between the ex-ante advertising cost and the ex-post reduction in slotting fees. We therefore obtain the following corollary: Corollary 4 Manufacturers may have an incentive to advertise their new products in order to reduce the amount of slotting fees paid to the retailers. This result is well illustrated by the findings of the Food Marketing Institute in 003 which claims that Manufacturers that perform thorough market research and support new products with strong advertising campaign often do not pay allowance. 0 0 FMI, Slotting Allowances in the Supermarket Industry, section 6, p3. 17

18 5 A new product is launched by an entrant Assume now that the new product of quality q + is launched by a potential entrant, denoted E, while the incumbent manufacturer, denoted I, sells the old product that yields total profit Υ N (q). Note that here the innovation stage t = 0 boils down to an entry decision stage by E. When threatened by the entry of a rival, the incumbent may now wish to offer exclusive dealing agreements to (part of) the retailers to deter entry. Such pay-to-stay fees are however generally forbidden (TBC). In what follows, we first analyze in section 5.1 the decision to enter when pay-to-stay fees are not allowed, and compare innovation deterrence in the two cases in which innovation is made by I and E. In section 5., we then allow I to offer pay-to-stay fees to (part of) the retailers and analyze how such possibility affects innovation deterrence. 5.1 No pay-to-stay fee Assume first that pay-to-stay fees are forbidden. We solve the game backward. Consider first period t =. If E has entered in t = 0, then we prove further that the product is sold in N markets in t = 1. Therefore, as by assumption q + q, υ N (q + ) υ N (q), and any negotiation between the manufacturer and a retailer over the new product succeeds, and negotiations are independent of one another. Then, the equilibrium tariff T n t by the following equation (4) : is determined υ n (q + ) T n ΥN (q) N = T n T n = 1 ( ) Υ n (q + ) ΥN (q). (11) n We denote Π n t = n T t n the profit of the entrant who bargains with n retailers at period t. Therefore, we obtain Π ( ) N (q+, q) = 1 Υ N (q + ) ΥN (q). In case of entry, the incumbent obtains 0 whereas absent entry, it obtains Π N Υ(q) (q) =. We now solve period t = 1. Consider first that all negotiations but one have failed with E. The disagreement payoff of E is 0, whereas the disagreement payoff of the retailer is ΥN (q) N. From equation (4), the optimal fixed fee denoted T 1 1 is thus given by: Υ 1 (q + ) T 1 1 ΥN (q) N = T 1 1 T 1 1 = 1 ( ) Υ 1 (q + ) ΥN (q). (1) N It is immediate that T 1 1 is smaller than the tariff ˆT 1 1 earned by an incumbent firm selling 18

19 a new product, since the entrant has no status-quo in its bargaining with each retailer. This negotiation does not occur if Υ 1 (q + ) ΥN (q) N. Therefore, as in the previous case, there exists a cut-off value ñ that represents a minimum number of negotiations that must take place in order to succeed. Here, the cut-off value is defined by: Υñ 1 (q + ) ñ 1 ΥN (q) N < Υñ(q + ) ñ It is lower than ñ < ˆn: the entrant needs access to less retailers than the incumbent to successfully launch the new product. By recurrence, we determine the profit made by E in period 1 with n > ñ retailers : ( n Π n 1 (q +, q, ñ) = 1 Υ i (q + ) n + 1 i=ñ n(n + 1) ñ(ñ 1) ) Υ N (q) N (13) As N firms bargain with E in equilibrium, E obtains Π N 1 (q+, q, ñ). Without innovation cost, the entrant would always find it profitable to enter and launch the new product, as in the previous case. We summarize our results in the following lemma: Proposition 3 If pay-to-stay fees are forbidden, due to slotting fees efficient innovations by the entrant are deterred for any innovation cost such that: [ ] F Π N 1 (q +, q, ñ) + Π N (q + ), Υ N (q + ) ΥN (q) Due to the Arrow replacement effect, a new entrant always has higher incentives to launch a new product than an incumbent manufacturer. Proof. See Appendix A.4. Two forces are in balance to explain that it is easier for the entrant than for an incumbent to launch a new product. On the one hand, the lower bound Π N 1 (q+, q, ñ) is always lower to ˆΠ N 1 (q+, q, ˆn). Indeed, despite the fact that ñ < ˆn, the entrant has a lower status-quo than the incumbent in its first negotiation (0 v. Υ N (q)/). Therefore, it gets a lower share of the joint profit in this first negotiation. This affects all subsequent negotiations and tends to reduce the profit of the entrant as compared to the profit of the incumbent: the hold-up effect is stronger for the entrant than for the incumbent. 19

20 On the other hand, while the entrant launches the new product as soon as it yields a positive profit, the incumbent must ensure that it yields a larger profit than Υ N (q)/, the profit it would earn with the old product. This corresponds to the Arrow replacement effect (Arrow, 196), which reduces the net gain of launching a new product for the incumbent. This second effect always dominates. Note that the upper bound Υ N (q + ) ΥN (q) is larger than the upper bound in the incumbent case Υ N (q + ) Υ N (q). Again, this is because the replacement effect overwhelms the hold-up effect. 5. Pay-to-stay fees We now assume that the incumbent may offer pay-to-stay fees to the retailers. Stage t = 0 is now made of two successive stages which we denote (i) and (ii). In stage (i) the incumbent may offer an exclusive dealing agreement to each retailer in exchange for a lumpsum payment ( i.e. offer a pay-to-stay fee). Without loss of generality, we assume that the exclusivity agreement prevails over t = {1, }. These agreements may be discriminatory. In stage (ii) again, a new entrant selling a new product of quality q + > q chooses to enter or not at cost F. Assume first that in stage (i) f > ñ retailers are free, i.e. they have refused the incumbent contract. Next, assume that in stage (ii) E entered. Then, in stages t = 1,, the f free retailers may bargain with E. In this bargaining, each of the free retailers has a status-quo profit equal to ΥN (q) N. Let now solve the period t = of this subgame. Since f > ñ retailers are free, we consider the case where E enters. According to the previous section, we know that E thus succeeds in its bargaining with all f retailers in equilibrium in t = 1. As N n retailers where selling the product of the incumbent, the spillover has not entirely played its role. In the second period, though, there is no more spillover among the n free retailers: the joint profit on each of the f free outlets is υ f (q + ). In period, I obtains a profit (N f) ΥN (q) N (minus the pay-to-stay fees), each tied retailer earns ΥN N the profits of the entrant Π f (q+, q, ñ). We denote π n t (plus the pay-to-stay fee), and the profit of a single retailer which deals with the entrant when n retailers sell the new product in period t. Here, each retailer obtains π f (q+, q) = 1 f (Υf (q + ) + ΥN (q) ). We now solve period t = 1. Again, since by assumption f > ñ, E enters and succeeds 0

21 in its bargaining with all f retailers in equilibrium in t = 1. As among the f retailers, the spillover effect arises, the profit of the entrant in the first period is Π f 1 (q+, q, ñ) defined by equation (13). In equilibrium, the profit of a free retailer is π f 1 (q+, q, ñ) = Υf (q + ) Π f 1 (q+,q,ñ) f The profit of I and the tied retailers are the same as in t =. In Stage 0, E enters in stage (ii) if and only if it expects a positive profit, i.e. when F < Π f 1 (q+, q, ñ) + Π f (q+, q). In that case the profit of I over the two periods is (N f) ΥN (q) N. In Stage (i), the incumbent chooses between two types of strategies: either to accomodate or to blockade entry. Assume first that I offers a pay-to-stay fee to N ñ or less retailers. In that case, regardless of the number of tied retailers, E enters and sells to all f ñ free retailers. In each period t = 1,, the profit of each retailer that buys from E is necessarily larger than its status-quo profit, ΥN (q) N. Then, each pay-to-stay fee would have to be larger than ΥN (q) N for any exclusivity contract for t = 1, to be accepted by a retailer. However, I earns at most (N f) ΥN (q) N. I therefore cannot profitably lock-in less that N ñ retailers. Second, assume that I offers a pay-to-stay fee to strictly more than N ñ retailers. In that case, if all retailers accept, entry is blockaded and I earns ΥN (q). It is then optimal for I to offer pay-to-stay fees to exactly N ñ + 1 retailers. Each retailer is ready to accept a pay-to-stay fee, denoted φ, if its profit with I is then at least equal to the profit he would obtain in refusing the exclusive dealing agreement and successfully negotiating with E after entry. This condition can be written as follows: Υ N (q) N + φ πn 1 (q +, q, ñ) + π N (q +, q, ñ). (14) The incumbent chooses φ in order to bind the above constraint. As in case of entry, the incumbent has no profit, it is ready to pay such a fee to each of the (N ñ + 1) retailers whenever it obtains a larger profit in blockading entry, that is if: Υ N (q) (N ñ + 1)φ. (15) This condition can then be written as follows: Υ N (q) > N ñ + 1 N ( π N ñ (q +, q, ñ) + π N (q +, q) ). (16) We obtain the following proposition: 1

22 Proposition 4 With pay-to-stay fees, entry can be blockaded by the incumbent even without innovation cost. It is all the easier to blockade entry that the threshold ñ is larger. In particular, it is impossible for the incumbent to blockade the entrant if ñ = 1 as long as q + > q. Entry is more likely to be blockaded as the difference in quality between the old and new products decreases. Proof. TBC Compared to the previous cases, pay-to-stay fees facilitate innovation deterrence. Entry is blockaded without innovation cost, but only because, due to pay-to-stay fees, less than m retailers remain free to bargain with the entrant. The condition for entry to be blockaded when m = M is very likely to hold, as Assumption 1 implies that ΠM 1 (q + ) M 1 < ΥN (q + ) M. Entry could only occur if the informational spillover was extremely strong and concentrated on the last retailer. In particular, if we consider that the informational spillover is constant or decreasing, the incumbent always blockades entry when m = M. The strategy of the incumbent in this framework corresponds to the divide-andconquer strategy highlighted in the literature on naked exclusion. In particular, Segal and Whinston (000) focus on a framework in which an incumbent producer sells its good to several buyers. Because of cost economies of scale, a potential rival can only enter if it can deal with a sufficiently large number of buyers (say m). Then, when buyers can coordinate and the joint profit is large enough, the incumbent may profitably deter entry by offering exclusive dealing agreements to a large enough subset of buyers. Our condition (15) precisely corresponds to this argument. 1 In our framework, however, the advantage of the incumbent results from the informational externality, which similarly ensures that the optimal profit is convex with the number of firms. Note also that, in contrast with the literature, it is essential that retailers have a positive bargaining power. Indeed, the need to secure at least m retailers to launch its product would not exist absent any retailer s bargaining power. Besides, in our framework, it is possible to exclude the potential entrant even if it bears no cost to launch the new product. 1 Note also that the result of Rasmusen et al. (1991) holds in our framework. That is, if retailers cannot coordinate over accepting or refusing the incumbent s offer, there exists an equilibrium in which the incumbent can profitably deter entry by offering any pay-to-stay fee between 0 and Π N /M to each retailer.