Rapport 1/2018. Prosjektet har mottatt midler fra det alminnelige prisreguleringsfondet.

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1 Rapport 1/2018 Prosjektet har mottatt midler fra det alminnelige prisreguleringsfondet.

2 When Should Retailers Accept Slotting Allowances Tommy Staahl Gabrielsen University of Bergen Bjørn Olav Johansen University of Bergen Greg Sha er University of Rochester January 2018 Abstract We consider a model where manufacturers have private information of their products demand potential, retailers have limited shelf space and manufacturers can signal their demand with paying slotting allowances. We analyze the retailer s incentive to demand slotting allowances. Even though asking for slotting allowances would perfectly inform the retailer of the product s demand potential, we show that the retailer sometimes will prefer to be uninformed and insted pick his products based on o ered wholesale prices and expectations of demand potential. We indentify when and why retailers will require slotting allowances and show that our results may explain some of the empirical variation in the use of slotting allowances.

3 The inspiration to create an energy bar occurred during a daylong, 175- mile ride with my buddy Jay. We d been knawing on some other energy bars. Suddenly, despite my hunger, I couldn t take another bite. That s the moment I now call the epiphany. Two years later, after countless hours in Mom s kitchen, Clif Bar became a reality. And the mission to create a better-tasting energy bar was accomplished. 1 Gary, Founder and Owner of Clif Bar What I looked for was a whole new line. In the marketing line, the consumer has a demand, and if it is not being met, that s what I look for. If you walk down the aisle, all you d see in the cookie business was fat, sugar, preservatives, etc. And I said to myself, Listen, if people wanted jam without sugar, they certainly want a cookie without sugar. And simply, that simple realization, and the appearance of that realization, started R.W. Frookies. It was pretty simple. There s fruit and there s cookies. Now there s Frookies. You sweeten it with fruit. 2 Richard, Founder and Owner of R.W. Frookies 1 Introduction There are two products, but room for only one. One claims to be a better tasting energy bar. The other claims to be a healthy cookie. If you are the retailer, which one do you choose? What if a seller is willing to o er you a slotting allowance (i.e., a lump-sum, upfront payment) to help you decide? Should you accept it? If so, why? If not, why not? More generally, does your answer depend on whether the products are already established and merely seeking to upgrade their shelf positioning, or new and seeking to be carried for the rst time? In this paper, we take a fresh look at the use of slotting allowances as a signaling device when manufacturers have private information about their demands. Grocery retailers are constantly making decisions about how to allocate their scarce shelf space. Among other things, they must decide which of their slow-moving products to drop, and which of the new products to add. They must also decide which products to place at eye level, which products to put on display, and which products to place near the checkout. The constant is that there is never a shortage of choices, and the process never ends. Tomorrow, there will be more products to consider, and more decisions to be made. The retailers decisions are not easy and mistakes are inevitable as one would expect when decisions are made under uncertainty. Decisions that looked good ex-ante may turn 1 Found on the package of a chocolate-chip Clif Bar (clifbar.com), purchased at retail. 2 Richard Worth FNN (CNN) interview, July 11, 2012, 1

4 out to be bad ex-post. The products that were added may turn out to be worse than the products that were dropped. Premium space that was given to one product may in retrospect have been more pro tably given to another, and so on. Nowhere are the stakes higher than on grocery items, where pro t margins are thin, shelf space is notoriously scarce, and many more products are available to be stocked than can possibly be carried. Mistakes also hurt the sellers, who may be frustrated by their inability to convince retailers of their products worthiness. Gary, founder and owner of Clif Bar, succeeded. Many others have not. But, who can blame the retailers, who are constantly being told that the product or products being pitched to them taste better than the alternatives (see the above quote from Gary), or will be the next big thing (see the above quote from Richard). The problem is that all sellers have an incentive to make these claims regardless of how con dent they may be, or what their test-market data may be telling them. If one could wave a magic wand and know for certain which products would sell the best, then of course one would want to wave the wand, right? Granted they are not wands, but it is widely believed that slotting allowances, which are lump-sum, upfront payments from a manufacturer or producer (collectively, manufacturer) to a retailer to have a new product carried by the retailer and placed on its shelves can go a long way toward mitigating this problem. 3 A manufacturer who is more con dent about its product s likely success can take advantage of the payments to o er more than a manufacturer who is less con dent, thereby distinguishing itself and providing a valuable signal to the retailer about its product s likely selling potential. Indeed, no one questions that such payments can help the retailers make better informed decisions and mitigate against costly errors. 4 Here is how the FTC (2003) described it in their o cial report on slotting allowances: When a manufacturer believes its product is highly likely to succeed, it will be willing to pay a signi cant slotting fee, knowing that it is likely to recover this expense through pro ts earned from future sales. By contrast, if a manufacturer has signi cant doubts about the likelihood of a product s success, it will not be willing to pay as high a slotting fee. Recognizing this, retailers rationally infer that a new product is more likely to succeed if the manufacturer is willing to pay a higher slotting fee. Based on this rational 3 This is the de nition used by the Federal Trade Commission in FTC (2001) and FTC (2003). Others have used a more expansive de nition, encompassing all upfront, lump-sum payments from manufacturers to retailers. Our results are not sensitive to the precise de nition. The key is that the payments are xed and independent of quantity. In the UK, such payments are referred to as reverse- xed payments because the lump-sum payments go in the reverse direction of what might expect (from sellers to buyers). 4 The signaling explanation for slotting allowances assumes that manufacturers have better information than retailers about the likely success of their products. While this is often the case, it is not always so. 2

5 inference, retailers are more likely to stock products for which higher slotting fees are paid, not only because they receive a higher slotting fee, but also because they expect such products to be more highly valued by consumers... The FTC went on to say that Under signaling theories, slotting allowances can enhance e ciency by helping to ensure that the greater the likelihood that a new product will succeed, the greater the likelihood that it will be stocked by retailers. Signaling is perhaps the most prominent explanation for slotting allowances (certainly it is the most prominent one among the e ciency motives), 5 and would seem to be a win-win for both manufacturers and retailers (and for consumers, who also want the best products carried). The importance of slotting allowances in practice is well established. Since the late 1980 s, they have been the subject of Congressional Hearings and numerous government investigations (both in the U.S. and abroad), and there have been more than eighty academic articles, working papers, and surveys (not to mention countless trade press articles) written about them. 6 They are said to be ubiquitous in grocery retailing, and it has been estimated that, in the U.S. alone, they account for billions of dollars annually. Yet, despite all the scrutiny, there are still a number of anomalies associated with their use. The FTC study cited above has found that slotting allowances are mostly used for new products (as opposed to being used for established products which may, for the rst time, be seeking better shelf positioning). There is also widespread variation in their use. This variation in the incidence of slotting allowances is reported to be along many dimensions. In the same product category, for the same retailer, for example, it is sometimes found that small manufacturers pay slotting fees but large manufacturers do not. Moreover, the frequency of slotting allowances varies widely across product categories, with slotting allowances nearly always being observed in some categories and sectors (e.g., in the refrigerated and frozen food sectors) while seldom being seen in others. There are also di erences in the incidence of slotting allowances across retailers, with some retailers (e.g., Wal-Mart and Costco at the time of the study) refusing to accept them, and other retailers seemingly going out of their way to embrace them. There are even di erences in the incidence of slotting allowances among outlets of the same retailer, with the incidence 5 The signaling explanation for slotting allowances is described on page 1 of the FTC s report, where it is the rst item mentioned. It was also among the rst explanations in the literature (see Kelly 1991). 6 For in-depth survey of the practice, see Sha er (2013), which was commissioned by the UK O ce of Fair Trading. The U.S. Federal Trade Commission conducted its own study of the practice (FTC, 2001, 2003) as did the Canadian Bureau of Competition (2002) and the Norwegian Competition Authority (2005). Slotting fees are mentioned in the Competition Commission s investigation of grocery markets in April 2008, and they are the focus of the UK s Groceries Supply Code of Practice. See also Bloom et al. (2000) and Wilkie et al. (2002) for some insightful surveys regarding the views of practicing managers. 3

6 being higher for stores located in urban areas, and lower for stores located in rural areas. These anomalies are hard to reconcile. Why would any retailer not want to accept slotting allowances? And when retailers do accept them, why do they accept them for some product categories but not for others? Are Wal-Mart and Costco simply better informed than the manufacturers about how well their new products will sell? Are some product categories (e.g. ice cream and TV dinners) systematically more prone to uncertainty about demand than others? Is it the case that for some product categories, signaling how well a new product will sell is typically done through other means (e.g., through wholesale prices only, where the manufacturer announces Yes, my product has a high wholesale price, but you should carry it anyway, because if it were not as good as I say, I would not want to be o ering you such a high price ), as some have argued (see Lariviere and Padmanabhan, 1997). And what about the incidence of slotting allowances di ering across outlets of the same retailer? Is this retailer less well informed at some of its outlets than at others? In this paper, we o er a potential explanation for some of the aforementioned anomalies by challenging the conventional wisdom that retailers necessarily bene t from having manufacturers reveal their private information. In a model with two manufacturers and one retailer, where the manufacturers are vying for a single slot of shelf space, we nd that it is sometimes optimal for the retailer to adopt a policy of not accepting slotting allowances, thereby remaining in the dark when making his shelf space decisions, even if the signaling would have been perfect and allowed him to avoid making costly mistakes. The reason is that accepting slotting allowances often comes with a tradeo. On the one hand, it can lead to better informed decisions per the signaling reasons discussed above (in the model, we bias the results in favor of the retailer accepting slotting allowances by assuming that the manufacturers are perfectly informed about how well their products would sell so that by allowing the manufacturers to signal their information, the retailer will always know with certainty which product is better). On the other hand, it may enable the better manufacturer to capture surplus that would otherwise have gone to the retailer. Understanding when, how, and why this happens is the core contribution of this paper. The idea is that when the manufacturers are allowed to signal their information with slotting allowances, the winning manufacturer only has to o er the retailer the maximum of what the retailer could earn by selling the losing manufacturer s product or sticking with his status quo (and earning his opportunity cost of shelf space), whereas if slotting allowances are not allowed, the manufacturers are subject to the retailer s preconception as to which product is better. 7 With slotting allowances, the winning manufacturer cap- 7 As discussed in the text, there is a small literature that looks at the possibility of a manufacturer 4

7 tures the actual value added of its product. Without slotting allowances, the winning manufacturer captures only the value added that is perceived by the retailer, prior to the resolution of his uncertainty. If the retailer perceives the products to be equally good, competition in wholesale prices ensures that neither manufacturer will earn positive pro t. We can x this idea more concretely by considering the following stylized example. Suppose the retailer believes ex-ante that it could earn an expected pro t of 5 from selling each manufacturer s product (a markup of 1 plus unit sales of 5). However, suppose the truth is that one product is better than the other, and that the better manufacturer s product would in fact generate a pro t of 7 for the retailer, while the other manufacturer s product would only generate a pro t of 3. Then, if the retailer puts his shelf space up for bid by accepting slotting allowances, the winning manufacturer only has to ensure that the retailer would earn a pro t of 3 (plus epsilon) from stocking its product. But if the retailer is able to channel the competition for his patronage into wholesale prices only, such that the better manufacturer has no credible means of signaling, each manufacturer would be forced to o er its product at cost, and the retailer would earn an expected pro t of 5. 8 In this instance, the retailer would be better o not accepting slotting allowances. Note that we could have tipped the decision in the other direction by choosing di erent numbers and incorporating a positive opportunity cost of shelf space (i.e., incorporating a lower bound on what the retailer would be willing to accept if he put his shelf space up for bid). Indeed, our ndings point to the retailer s opportunity cost of shelf space and the variance of the demand potential of the manufacturers products as the key elements that determine whether the retailer would prefer to adopt a policy of accepting slotting allowances, or not. We nd that accepting slotting allowances is more likely to be preferable the higher is the retailer s opportunity cost of shelf space and the greater is the variance in the demand potential. This then gives testable implications for which product categories, and for which types of products, we might expect to observe a higher incidence of slotting allowances. For a company such as Wal-Mart, that has a store wide policy of not accepting slotting allowances, we note that they have chosen not to allow the winning manufacturers to capture the value added of their products, which is consistent with their signaling its type through the use of wholesale price o ers only, but this requires the retailer to know what the potential set of demand curves looks like, and in particular, to recognize when the high-demand rm s wholesale price would be above the vertical intercept of the low-demand rm s demand curve. We avoid this by assuming that the retailer does not have this information, nor would it be practical to implement. 8 By not accepting slotting allowances, the retailer is essentially taking his chances on stocking the better product. He might get lucky, choose the defacto better product, and earn a pro t of 7, or he might get unlucky, choose the weaker of the two products, and only earn a pro t of 3. But notice that even if he turns out to be unlucky, he is still no worse o than what he would have been with slotting allowances. 5

8 oft stated corporate policy of always trying to obtain the lowest possible wholesale prices. In various extensions of the model, we consider how the retailer s decision of whether to accept slotting allowances depends on whether competition for his scarce shelf space typically takes place between two large manufacturers competing for one slot, two small manufacturers competing for one slot, or one large manufacturer and one small manufacturer competing for one slot. Among the settings we consider is the case where the demand potential of the large manufacturer s product has both a higher expected mean and a lower variance than the demand potential of the small manufacturer s product, and the case where it has a lower variance but the same expected mean. These extensions then allow us to consider, among other things, how the incidence of slotting allowances may be expected to vary depending on whether the new products in a given category are dominated by a lot of me-too products, or alternatively by a lot of innovative products. As mentioned previously, there is a vast literature that looks at the competitive e ects of slotting allowances. It does so from a number of di erent angles, both pro-competitive and anti-competitive. 9 The anti-competitive stories primarily have to do with dampening competition among competing retailers (see Sha er, 1991; Foros and Kind, 2008; and Innes and Hamilton, 2006), foreclosing upstream competitors by buying up the available shelf space (see Sha er, 2005), foreclosing downstream competitors by making it too costly for manufacturers to serve them (see Marx and Sha er, 2007), and facilitating tacit collusion at the retail level by making cheating easier to detect (see Piccolo and Miklos-Thal, 2012). The pro-competitive explanations for slotting allowances focus mostly on the signaling story (see Kelly, 1991; Chu, 1992; Lariviere and Padmanabhan, 1997, and Desai, 2000) and its related cousin, screening by the retailer (see Chu and Messenger, 1995; and DeVuyst 2005). 10 There is also some work on the use of slotting allowances as a way of subsidizing demand-enhancing investments by the retailers (see Raju and Zhang, 2004; and Kolay and Sha er, 2016), or keeping wholesale prices high so as to increase incentives for demandenhancing investments by the manufacturers (see Farrell, 2001; and Foros et al, 2009). Lastly, there are competitively-neutral stories that have slotting allowances emerging in equilibrium as part of a bilateral bargaining outcome between a manufacturer and its retailer. These are essentially full information stories, where the slotting allowances arise in equilibrium either for the purpose of obtaining additional distribution (see Sha er, 9 See FTC (2001), FTC (2003), and Sha er (2013), for comprehensive surveys of this literature. 10 Both deal with settings in which the buyers and sellers have di erent information. The di erence between signaling and screening has to do with which party takes the action. Signaling requires that the party with the better information take the action (e.g., signal the product s quality). Screening requires that the lesser informed party takes the action (e.g., o er a menu that is designed to induce self selection). 6

9 1990; and Kuksov and Pazgal, 2007), or for the purpose of extracting surplus away from a third-party (see Marx and Sha er, 2010; and Caprice and von Schlippenbach, 2012). Of this literature, Lariviere and Padmanabhan (1997) and Desai (2000) are the closest to us in the sense that they were the rst to show that the use of slotting allowances for the purpose of signaling demand can be made rigorous, and would be expected to be observed in certain settings. Lariviere and Padmanabhan compare signaling via wholesale prices and slotting allowances, but do not consider the possibility of signaling through demandenhancing advertising. Desai compares and contrasts all three methods of signalling. In both cases, they assume the manufacturer s product is either good or bad. Their main nding is that there tends to be a critical value of the retailer s opportunity cost of shelf space such if the opportunity cost of shelf space is less than this value, the manufacturer will prefer to signal solely through its wholesale price and choice of advertising, if possible. Otherwise, it will signal using slotting allowances. But, if the opportunity cost of shelf space is greater than this value, the manufacturer will signal using all of its instruments. Like us, they identify the retailer s opportunity cost of shelf space as being important. However, we di er from Lariviere and Padmanabhan (1997) and Desai (2000) in important ways. First, we consider the use of slotting allowances from the retailer s perspective. Whereas the manufacturer might prefer to signal through its wholesale price in their models, the retailer always prefers that the signaling take place through slotting allowances. If the retailer could set up the rules of the game as he sees t, as he does in our model, slotting allowances would always be observed independently of the cost of shelf space. Second, their models presume that the retailer knows the shape of the manufacturer s demand curves, and in particular, knows the vertical intercepts of the demand for each product. We do not assume that the retailer knows this. Third, and most importantly, they assume that there is only manufacturer, whose only task is to signal that its product is good. In contrast, we allow for competing manufacturers to engage in signaling. As such, we are rst to identify the importance of enhanced competition as a countervailing reason why retailers may not want to accept slotting allowances even if in doing so demand would be revealed perfectly. This e ect, previously missed, is the key driver of our results. The rest of the paper proceeds as follows. In Section 2, we describe the model and de ne notation. In Section 3, we solve the model assuming both manufacturers products are good. In Section 4, we consider the possibility that one or both products may be bad. In Section 5, we model asymmetry between the manufacturers and consider how this a ects the incidence of slotting allowances. Section 6 concludes the paper. The proofs of the Propositions and Lemmas are contained in the Appendix. Throughout the paper, our focus is on understanding when retailers would be expected to adopt a policy of accepting 7

10 slotting allowances, and when not, and then deriving testable implications as a result. 2 The model Our basic setup is one where two manufacturers face a single retailer. The retailer has limited shelf space and can accept at most one of the manufacturers products in his store. Assuming that the manufacturers have private information about the demands for their products (i.e., how well their products would sell if carried by the retailer), the question we address in this paper is whether, when, and under what conditions will it be pro table for the retailer to adopt a policy of accepting (or not accepting) slotting allowances? 11 We assume for simplicity that the goods are produced at zero marginal cost, and that all consumers who are interested in product i, i = 1, 2, have a willingness to pay of at most v > 0 for a unit of the product. We let q i 0 denote the number of such consumers. We further assume that only manufacturer i knows the actual value of q i at the start of the game. We thus assume that this information is private, and that the rival manufacturer and retailer only know (prior to the retailer s decision of which product to carry) that q i is uniformly distributed with density 1/ [b a] on the support [a, b], where b > a Below we will distinguish between cases where the manufacturers o er simple linear wholesale contracts, and cases where slotting allowances are also o ered. When simple linear wholesale contracts are used, the retailer s total payment for product i is given by T i (x i ) = w i x i, where w i is the per unit wholesale price and x i is the quantity ordered (in equilibrium, x i will either be zero or q i ). When slotting allowances are also o ered, the retailer s total payment for product i is given by T i (x i ) = w i x i S i, where w i and x i are as previously de ned and S i 0 is the slotting fee given by manufacturer i to the retailer. Let the highest and lowest value of q 1, q 2 be denoted by q (1) = max {q 1, q 2 } and q (2) = min {q 1, q 2 }, respectively, and let w (1) and w (2) (and S (1) and S (2) ) denote the corresponding wholesale prices (and slotting fees) of the manufacturers that have these demands (i.e, w (1) and S (1) correspond to the wholesale price and slotting fee of the manufacturer of the product that has the higher demand, and similarly for w (2) and S (2) ). We let π r 0 denote the retailer s pro t, and π i 0 denote manufacturer i s pro t. Furthermore, we let s 0 denote the retailer s opportunity cost of shelf space. This cost is de ned to be what the retailer could earn from the next best use of his available shelf 11 Our assumption is that shelf space is scarce, which is well documented in grocery retailing. 12 Our setup can alternatively be recast as one in manufacturer i has private information about the potential pro tability of its product. Given zero marginal costs, this pro t is given by vq i for product i. 8

11 space if he did not carry either manufacturer s product. It establishes a lower bound on the retailer s expected pro t, and it means, among other things, that if the demand potential of a given manufacturer s product is su ciently low, the retailer will not want to carry the product. As examples, one can think of the retailer s opportunity cost of shelf space as corresponding to the pro t that the retailer can earn from an existing product that he is thinking about replacing, or to the pro t that he can expect to earn if he were to use his shelf space to carry a store brand instead of buying from one of the manufacturers. We formalize the game between the retailer and the manufacturers as follows: 1. The retailer decides whether to adopt a policy of accepting slotting allowances. Accepting slotting allowances means that the retailer will consider contracts that specify a wholesale price and a slotting allowance. Not accepting slotting allowances means the retailer will only consider contracts that specify a wholesale price only. 2. The manufacturers independently choose their contract terms, taking the retailer s decision in stage one as given. We envision a stage-two game of alternating o ers, where rst manufacturer 1 chooses its terms, then manufacturer 2 chooses its terms (after observing manufacturer 1 s terms), then manufacturer 1 gets to revise its terms, and so on, until the manufacturer who is to move decides not to make a better o er. After each new o er, the retailer decides whether to conditionally accept the terms, the condition being that the retailer does not receive a strictly better o er from the rival manufacturer. If the retailer does not receive what it believes to be a strictly better o er, the manufacturer who made the standing o er is declared the winner. The contract phase then ends, and the game proceeds to stage three The retailer accepts at most one of the manufacturers o ers and sets the retail price. At the conclusion of stage three, demand is revealed, payments are made, and all payo s are realized. We will use Perfect Bayesian equilibrium as our solution concept, which means that: (i) at each stage of the game, each player s strategy speci es optimal actions, given her beliefs and the strategies of the other players, and (ii) given the strategy pro le for all players, the beliefs are consistent with Bayes rule whenever possible. That is, the players strategies must be sequentially rational, and their beliefs must be consistent. 13 This game is equivalent to running an English auction (where the manufacturers bid against each other for the retailer s patronage until one of them is no longer willing to continue bidding). It is meant to capture a setting in which a retailer goes and back and forth between the manufacturers, attempting to secure the best deal possible, subject to the constraint that he cannot lie about the o ers he receives. 9

12 3 The case against accepting slotting allowances To illustrate the main tradeo s facing the retailer, and to understand why accepting slotting allowances is not always optimal, we will begin by assuming for now that both products are good in the sense that carrying either one would be an improvement over the retailer s status quo for all realizations of q 1 and q 2 (i.e., each would be pro table for the retailer to carry even in the unlikely event that only a consumers liked the product). Formally, we assume that 0 s va, and note that when both products are good, the problem for the retailer in essence boils down to choosing which one he thinks will be better in the sense of yielding the higher pro t all things considered. 14 The question then arises how should the retailer structure the rules of the game with this task in mind? Should he adopt a policy of not accepting slotting allowances and simply choose whichever manufacturer o ers him the lower wholesale price, or should he allow for o ers that include slotting allowances and see which one gives him the better overall combination of terms? Suppose rst that the retailer adopts a policy of not accepting slotting allowances in stage one. In practice, this might take the form of a store or chain-wide policy of not accepting slotting allowances, as Wal-Mart and Costco allegedly have done, or it might simply re ect the retailer s norms and expectations in a given product category. 15 Either way, the policy forces the manufacturers to compete for the retailer s available shelf space with wholesale price o ers only. With this in mind, the rst thing to notice is that in the continuation game beginning in stage two, the manufacturers ability to signal their products demand potential is e ectively eliminated. The reason is that the low-demand manufacturer can always pro tably mimic the strategy of the high-demand manufacturer. Any attempt by the latter to distinguish itself from the former is therefore bound to fail, which means that in any Perfect Bayesian equilibrium, the equilibrium is not separating. We can formalize this insight as follows: Lemma 1. Only pooling equilibria arise in the game in which the retailer adopts a policy of not accepting slotting allowances. The retailer s updated beliefs about each manufacturer s type (after observing the wholesale prices) will therefore be the same as his prior beliefs. Because the retailer s prior beliefs about each manufacturer s product are symmetric, 14 The reader may wonder why the retailer cannot carry both in this case. The reason is that we have in mind a setting in which shelf space limitations represent a hard constraint in the sense that the opportunity cost of stocking the second product given that the rst one is stocked is prohibitively high (i.e., s > vb). For example, the retailer may only be able to promote one product at a time in its display. 15 FTC (2003) o ers numerous examples of product categories in which slotting allowances play little or no role, and other product categories in which the retailer almost always asks for slotting allowances. 10

13 and because the manufacturers are unable to signal their true demands (there can be no Bayesian updating of the retailer s prior beliefs about the demand potential of the manufacturers products given that all equilibria are pooling), it will be optimal for the retailer in stage three to pick whichever product comes with the lower wholesale price. Knowing this, competition among the manufacturers then ensures that each manufacturer in stage two will o er a wholesale price that is equal to its product s marginal cost, i.e. w 1 = w 2 = 0. As a result, the retailer in stage three can do no better than to pick one of the products at random. His expected pro t in stage three (and thus his expected pro t in stage one from adopting a policy of not accepting slotting allowances) from choosing product i will therefore be equal to v times the expected value of product i s demand, π W r ( ) a + b = (v wi ) E [q i ] = ve[q i ] = v, 2 where we have used the fact that the retailer s pro t-maximizing price in stage three is v. Here, the superscript W denotes the case in which only wholesale prices are permitted. Now suppose that the retailer adopts a policy of accepting slotting allowances. As before, this might take the form of a store or chain-wide policy, or it might simply re ect the retailer s norms and expectations in a particular product category. Either way, it makes a big di erence for the analysis when the retailer accepts slotting allowances because this makes it possible for the manufacturers to signal the demand potential of their products. It is easy to show, for example, that there will always be separating equilibria in this case. We can formalize this insight as follows: Lemma 2. Only separating equilibria arise in the game in which the retailer adopts a policy of accepting slotting allowances, in the sense that the retailer will be able to infer which manufacturer s product is better (and which product is worse) by observing their o ers. Proof: See the appendix. One might think that being able to infer which manufacturer s product is better would always bene t the retailer, but in fact, the opposite holds when both products are known to be good. To see this, note that although overall pro ts would be expected to increase when the retailer accepts slotting allowances (because the better product will always be carried), so too will the manufacturers pro ts. In the absence of slotting allowances, the manufacturers earn zero pro t in equilibrium (because the equilibrium wholesale prices are zero). However, with slotting allowances, the manufacturers pro ts will not necessarily be 11

14 competed down to zero because of the possibility of signaling. Indeed, signaling allows the manufacturer of the better product to earn rents equal to the added value of its product. Whether the retailer will be better o then depends on whether the expected increase in the overall pro ts is greater than or less than the increase in the manufacturers pro ts. To determine which is greater, and thus to determine the expected impact on the retailer s pro t, we need to characterize the equilibrium o ers in stage two. Using Lemma 2, we show in Appendix A that if attention is restricted to contract o ers that would yield non-negative pro t for a manufacturer if its product were carried (hereafter we will assume that this is the case), 16 then not only are all equilibria separating, they are also payo equivalent (i.e., each player earns the same payo in every equilibrium). Moreover, we also show in Appendix A that the better product (i.e., the one that has the greater demand potential) will always be the one carried, and that the manufacturer of this product will leave the retailer with just enough surplus that the retailer does not pick the rival manufacturer s product (in equilibrium, the retailer will be indi erent). It remains only to pin down the losing manufacturer s o er. But this too is straightforward. Under our re nement that rules out contract o ers that would yield non-negative pro t, it is easy to show that the manufacturer that has the lower demand potential will o er the retailer a contract that would yield zero pro t for the manufacturer if its product is carried. 17 It follows that the retailer s expected pro t in stage one from adopting a policy of accepting slotting allowances when both products are good will therefore be given by π S r = E [( ] [ ] v w(1)) q(1) + S(1) = ve q(2) 2 b ( = v 1 q ) i a qi i=1 a b a b a dq i ( b ( = v 1 q ) 1 a b ( q1 b a b a dq q ) ) 2 a q2 b a b a dq 2 = v a a ( 2a + b To see this, note that because the high-demand manufacturer only has to compensate the retailer for what he could earn if he carried the low-demand manufacturer s product, the retailer s expected pro t when both products are good (and he accepts slotting allowances) is equal to his expected pro t from selling the less pro table of the two products. Breaking this expected pro t into its component parts, we have that v b ( a 1 q 2 ) a q2 dq b a b a 2 16 For example, this rules out contract o ers in which the manufacturer s wholesale price is below cost. 17 If the losing manufacturer were to hold out for some positive pro t in the out-of-equilibrium event its product were carried, the winning manufacturer would not have to give as good of terms to the retailer to make her indi erent, which implies that the losing manufacturer would then be able to pro tably deviate. 3 ). 12

15 is the expected pro t the retailer can expect to receive from manufacturer 1 given all possible values for q 2, where for a given q 2, ( ) 1 q 2 a b a is the probability that q1 > q 2 (to ensure that manufacturer 1 will be the winning manufacturer), vq 2 is the payo manufacturer 1 would have to o er the retailer in order to win his patronage, 18 and 1 is b a the density. And similarly for the expected pro t the retailer can expect to receive from manufacturer 2. Summing up these expected pro ts yields the expression for π S r above. Here, the superscript S denotes the case in which the retailer accepts slotting allowances. Comparing the retailer s expected pro t when he does not accept slotting allowances with his expected pro t when he does accept slotting allowances, we can easily see that π W r π S r = v ( ) b a 6 > 0 for all b > a, which implies that the retailer will always be better o adopting a policy of not accepting slotting allowances when both products are good. Proposition 1 When the manufacturers have private information about the demand potential of their products, and the choice is between two good products (i.e., 0 s va), the retailer will always be better o adopting a policy of not accepting slotting allowances. Proposition 1 seemingly contradicts much of the extant literature on the use of slotting allowances as a signaling device, which nds not only that slotting allowances can pro tably be used to signal private information about demand (Kelly, 1991; Chu, 1992; Desai and Srinivasan, 1995; Lariviere and Padmanabhan, 1997 and Desai, 2000), but also that it typically results in a win-win situation. In this literature, the manufacturers of the best products are better o when slotting allowances are used because they can then truthfully signal that their products will have higher demand; the retailers are better o because by carrying the products of the manufacturers that o er the best combination of wholesale prices and slotting allowances, they can avoid making costly stocking mistakes; 19 and consumers are better o because slotting allowances ensure that the best products are indeed carried. To the contrary, we have found that although it is true that slotting allowances can be used to signal a product s demand potential, and although it is true that the retailer would be informed about the best products (the use of slotting allowances ensures that all equilibria are separating), the retailer may nevertheless prefer to remain in the dark and force the manufacturers to compete using linear wholesale prices only. The intuition for this is as follows. For the retailer, there is a trade-o between inducing competition between the manufacturers and having them truthfully reveal their products 18 For example, if w (1) = v, then the retailer can expect to receive a slotting allowance of ve [ q (2) ]. 19 The implicit assumption here is that the manufacturers of the weaker-selling products would not be able to match the higher slotting allowances o ered by the manufacturers of the better-selling products. 13

16 sales potential. On the one hand, allowing the use of slotting allowances ensures that the better product will be stocked, but it is not e cient in extracting rent for the retailer. On the other hand, forcing the manufacturers to compete only on wholesale prices is e cient for rent extraction, because it increases the competition between the manufacturers, but it cannot guarantee that the product with the higher demand will be chosen. When both products are good, Proposition 1 implies that the competitive e ect always dominates. The reason why there is no counterpart to our nding in the previous literature is that the previous literature mainly studies a situation where a retailer faces a single manufacturer that has private information about whether its product is good (in the sense that it would always be pro table for the retailer to introduce) or bad (in the sense that it would never be pro table for the retailer to introduce). In this situation, it is not surprising that the retailer will always want the manufacturer to signal its product s demand potential the retailer would incur a loss if it chose the bad product, and there is no countervailing competitive e ect because the retailer cannot generate competition when there is only one manufacturer. By not allowing for more than one manufacturer with uncertain demand, the previous literature has missed this countervailing e ect. Our nding in Proposition 1 is a negative result in the sense that it speci es a set of circumstances under which we would not expect to observe slotting allowances. Nevertheless, before proceeding in the next section to focus on positive results (i.e., on conditions under which we would expect to observe slotting allowances), it should be noted that this negative result is of interest in its own right because it may shed light on why slotting allowances are typically not observed when retailers are deciding how best to allocate shelf space within their stores (FTC, 2003). 20 It is well known that not all shelf space is created equal. Some spaces within a store are scarcer than other spaces. Yet the evidence from the FTC s study on slotting allowances in the grocery industry suggests that slotting allowance payments typically do not guarantee any particular shelf placement, and that the premium spaces in the store (i.e., the area at eye level, near the cash register, or at the end of the aisles) tend to be auctioned o with the bidding focused instead on which of the manufacturers of the retailer s established products can o er the most attractive promotional deals (quantity discounts, discounts o the list price, etc). This evidence is consistent with what we would predict from Proposition 1. It seems reasonable to assume that the retailer already knows which of his established products 20 An informal argument that is sometimes o ered to explain this phenomenon is that the manufacturers of established products simply have more bargaining power and are thus better able to resist retailer demands for slotting allowances. However, this cannot explain why these same manufacturers do pay slotting allowances to the same retailers when they are trying to obtain shelf space for their new products. 14

17 will sell the best (and thus that he already knows that the products that he is considering for his premium spaces would do better than, for example, some randomly chosen set of products), but he may be uncertain as to which of his top products would bene t the most from the increased visibility. In this case, by reinterpreting q i 0 as the additional quantity that manufacturer i can expect to sell as a result of obtaining the premium space (i.e., over and above what it would expect to sell under the status quo in its current location), our ndings suggest that the retailer should indeed o er to allocate his premium spaces to the manufacturers that o er him the best promotional deals all else equal. That is, the retailer should not adopt a policy of accepting slotting allowances in these cases. 4 The case for accepting slotting allowances In the previous section, the retailer s choice was between two good products. In this section, we extend the model to allow for the possibility that one or both products may be bad. By a bad product, we mean a product that if carried would always earn less pro t for the retailer than his opportunity cost of shelf space, even if he could procure the product at cost. This is an important extension to consider because the FTC study (mentioned above) also found that although slotting allowances are not commonly observed when retailers are deciding where in their stores to place their already established products, they are commonly observed when the retailers are deciding which new products to carry. One of the main characteristics of new products is that they often fail. 21 We incorporate the possibility that one or both products may be bad by assuming now that the retailer s opportunity cost of shelf space lies between va and vb, s [va, vb), which implies that his opportunity cost is less than what he could earn from carrying manufacturer i s product if q i were to realize its maximum sales potential of b, but greater than what he could earn from carrying manufacturer i s product if q i only obtained its lower bound of a. This complicates the model because now the winning manufacturer must not only beat its rival s best o er, it must also ensure that the retailer earns a pro t of at least s va. As in the previous section, our focus is on whether the retailer will be better o adopting a policy of accepting slotting allowances or not accepting slotting allowances. When the retailer adopts a policy of not accepting slotting allowances, the analysis is similar to that in the previous section. In the continuation game that follows, it is still the case that Lemma 1 holds (i.e., there can be no signaling in equilibrium when only wholesale price o ers are allowed whether or not the products may be bad), and thus it 21 The FTC (2003) reports that the failure rate on new products can be as high as 70%. 15

18 is still the case that the second stage o ers will be such that w 1 = w 2 = 0 (for the same reasons as before). The only di erence is that now, in stage three, the retailer will pick one of the two products at random if and only if his expected pro t from doing so exceeds s. Otherwise, he will reject both products and earn his opportunity cost. Given that q i is uniformly distributed between a and b with density 1/ [b a], it follows that the retailer s expected pro t in stage one from adopting a policy of not accepting slotting allowances is π W r { (s) = max s, v ( a + b 2 )}. (1) In contrast, the manufacturers will be able to signal their demand potential when the retailer adopts a policy of accepting slotting allowances. In this case, in the continuation game that follows, all equilibria will be separating (i.e., Lemma 2 will continue to hold for the same reasons as before), and either both products will be rejected (which happens when the retailer perceives that neither product would allow it to earn a pro t of at least s), or the losing manufacturer will o er its product at cost and the winning manufacturer i s o er will be such that the retailer will just be indi erent between carrying product i or going with his next best alternative. 22 Among other things, this means that any manufacturer that o ers the retailer an expected pro t of less than s will not be accepted. And, it means that when we allow for the possibility that one or both products may be bad, and the retailer adopts a policy of accepting slotting allowances, the retailer will earn s in stage three if at least one product is bad, 23 and vq (2) if both products are good. To see what this implies about the retailer s expected pro t in stage one, note that for all s [va, vb], the ex-ante probability that at least one product will be bad is given by 24 Pr(vq 1 < s vq 2 < s) = ( ) 2 ( s/v a s/v a ) s/v a b a b a b a, 22 The retailer s next best alternative to manufacturer i s product will either be the outside option that gives him his opportunity cost of shelf space s (if manufacturer j s product is revealed to be bad), or manufacturer j s product (if, like manufacturer i s product, manufacturer j s product turns out good). 23 If both products are bad, the retailer will realize this from the o ers he receives and go instead with his outside option. If only product j is bad, the retailer will carry manufacturer i s product in equilibrium, but manufacturer i will only need to o er the retailer an expected pro t of s to induce him to do so. ( ) 2 ( ) 24 Here, s/v a b a denotes the probability that both will be bad, and 2 1 s/v a s/v a b a b a denotes the probability that only one will be bad, recognizing that this can be product 1 or 2 with equal probability. 16

19 while the ex-ante probability that both products will be good is given by Pr(vq 1 s vq 2 s) = ( 1 s/v a ) 2. b a It follows that when one or both products may be bad (or good), the retailer s expected pro t in the rst stage from adopting a policy of accepting allowances is given by 25 π S r (s) = Pr(vq i < s vq j < s) s + (2) Pr(vq 1 s vq 2 s) v b {( 1 q ) } j s/v qj dq j, b s/v b s/v j=1,2 where the retailer s expected payo when both products are good (given in the second line in (2)) is the expression for ve[q (2) ] conditional on both products being good. This expression captures the main upside of adopting a policy of accepting slotting allowances (or at least of entertaining the possibility of accepting slotting allowances) as it is always weakly greater than s (strictly greater for all s < vb). Since there is no downside risk in the other cases relative to the status quo (the retailer s payo in these other cases is always s), it follows that an important bene t of accepting slotting allowances is that it allows the retailer to take a chance on both products being good, reaping the bene ts if they are, while ensuring that he can always earn s if one or both turn out to be bad. We can push this insight further, and at the same time express the expected gain to the retailer in a more transparent way, by simplifying (2) and rewriting it as s/v ( ) π S (b s/v) 3 r (s) = s + v 3 (b a) 2, (3) ( ) where s comes from adding Pr(vq 1 s vq 2 )s to the rst line in (2), and v (b s/v) 3 3(b a) 2 comes from subtracting Pr(vq 1 s vq 2 )s from the second line in (2) and simplifying. Recall from (1) that the retailer can also always earn an expected pro t of at least s and sometimes more by forcing the manufacturers to compete through wholesale prices, but the di erence in (1) vis a vis the pro t in (3) is that for all s (va, vb), the retailer only earns more than s if his expected pro t from picking one of the products at random exceeds s. In contrast, the retailer s expected pro t from accepting slotting allowances is always greater than s in this range. This yields our rst main result in this section: if 25 Note that this expression is valid only for values of s [va, vb]. If s < va, then π S r (s) = v (2a + b) /3 (as we showed previously), and if s > vb, then both products are always bad and π W r (s) = π S r (s) = s. 17

20 s [v ( ) a+b 2, vb), the retailer should always adopt a policy of accepting slotting allowances. ) ), there is a tradeo. On the one hand, the retailer In the case of s (va, v ( a+b 2 earns an expected pro t of π W r = v ( a+b 2 the retailer earns an expected pro t of π S r = s + v ) with wholesale prices only. On the other hand, ( (b s/v) 3 3(b a) 2 ) with slotting allowances. It follows that the retailer will prefer slotting allowances only if π S r (s) π W r, or whenever ( ) (b s/v) 3 s + v 3 (b a) 2 ( ) a + b v. (4) 2 As we have seen previously, the tradeo is always resolved in favor of not accepting slotting allowances when s is equal to its lower bound of va (lower bound in this section). But notice that for values of s that are above this level, the left-hand side of (4) is increasing in s, whereas the right-hand side of (4) is independent of s. This implies that the left-hand side will at some point be greater than the right-hand side as s continues to increase throughout its range, and that when this happens, the left-hand side will always continue to be greater. This gives us our second main result in this section: accepting slotting allowances is more likely to be preferred by the retailer the greater is the retailer s opportunity cost of shelf space. More formally, what the monotonicity in s tells us is that there necessarily exists a critical value of s (va, ( a+b 2 )] such that for all values of s that exceed this critical value, the retailer will strictly prefer to accept slotting allowances. Taken together, these results establish the case for accepting slotting allowances. Moreover, they suggest that the retailer s opportunity cost of shelf space will play a critical role in determining whether and when the retailer will want to accept slotting allowances. The model also has implications for when the retailer might want to adopt a policy of accepting slotting allowances as a function of the mean and variance of the demand potential of the manufacturers products. Thus, we can rewrite the inequality in (4) as: s + v (( ) 3 ) q + 3σ s/v 36σ 2 vq, (5) where q = (a+b) denotes the average potential and σ = (b a) 2 12 is the standard deviation. Conducting comparative statics with respect to q, we can see that while both sides of (5) are increasing in q, the right-hand side is increasing faster. This implies that, unlike with increases in s, accepting slotting allowances is less likely to bene t the retailer the higher is q all else equal. With respect to σ, we can see that while the right-hand side of (5) is independent of σ, the left-hand side of (5) is increasing in σ in the relevant range. All else 18

21 equal, this implies that adopting a policy of accepting slotting allowances is more likely to bene t the retailer versus a policy of not accepting slotting allowances the higher is σ. More formally, for a given q, we can establish the relationship between s, σ and the retailer s decision whether to adopt a policy of accepting slotting allowances by letting s (σ) denote the critical value of s that solves π S r (s) = π W r. Our comparative statics imply that s (σ) is decreasing in σ. This can be seen from the plot of s (σ) in Figure 1 below. q = 5 Retailer asks for slotting fees Opportunity cost of shelf space s Retailer asks for wholesale prices Standard deviation of the products sales potential σ Figure 1: The critical s (σ) Figure 1 illustrates the retailer s optimal decision whether to accept slotting allowances 19

22 for a given a and b as a function of s and σ, with σ on the horizontal axis, and s on the vertical axis. As shown in Figure 1, for s su ciently large, the retailer will always be better o adopting a policy of accepting slotting allowances, while for s su ciently small, the retailer will never want to adopt a policy of accepting slotting allowances. For intermediate values of s, the retailer will be better o adopting a policy of accepting slotting allowances if and only if σ is su ciently large. Notice that the threshold of s above which the retailer will always be better o adopting a policy of accepting slotting allowances occurs at s = q (which is obtained by evaluating s (σ) in the limit as σ 0), while the threshold of s below which the retailer will never want to adopt a policy of accepting slotting allowances occurs at s.88q (which is obtained by evaluating s (σ) at the maximum value of σ). 26 We can summarize these results as follows: Proposition 2 When the manufacturers have private information about the demand potential of their products, and the retailer does not know ex-ante whether the individual products are good or bad relative to his opportunity cost of shelf space (i.e., va < s < vb), there exists a critical threshold s = vq such that for all s [s, vb), the retailer will be better o adopting a policy of accepting slotting allowances; there exists a critical threshold s > va such that for all s (va, s], the retailer will be better o adopting a policy of not accepting slotting allowances; and for all s (s, s), the retailer will be better o adopting a policy of accepting slotting allowances if and only if s > s (σ), where s (σ) (s, s) is decreasing in σ. Proposition 2 shows that when the retailer does not know ex-ante whether the individual products he is considering are good or bad, there are two key factors that determine whether he will want to accept slotting allowances: his opportunity cost of shelf space and the variance of the demand potential of the manufacturers products. Of these, the retailer s opportunity cost is more important in the sense that there are settings in which the retailer s decision is independent of the variance of the manufacturers demand potential, whereas the retailer will always want to adopt a policy of accepting slotting allowances if his opportunity cost is high enough. How high it needs to be depends on the variance of the manufacturers demand potential. The greater the variance, the lower is the threshold. Speci cally, we have shown that when the opportunity cost of shelf space is greater than vq, the retailer will always want to accept slotting allowances. This enables the 26 For a given q, the maximum value of σ occurs where b = 2q and a = 0. 20

23 manufacturers to signal their demand potential, and the product with the higher demand potential, assuming it is greater than s/v, will be stocked. On the other hand, when the opportunity cost of shelf space is less than vq, the retailer faces a tradeo. For a low enough opportunity cost, a policy of not accepting slotting allowances will be pro table, whereas if it is high enough (but still below vq) slotting allowances should be accepted. One can best understand the intuition for these results by rst understanding why the retailer may sometimes prefer to remain in the dark the reason is because accepting slotting allowances comes with both an upside and a downside. The upside is that both products may turn out to be better than expected, in which case the retailer bene ts because even the losing manufacturer would then have to o er the retailer better than expected pro ts. The downside is that one or both products may turn out to be bad, in which case the o er by the manufacturer of the better product would be weakly worse (strictly worse if s < vq) for the retailer than what he could have obtained in the absence of slotting allowances. Balancing these two sides determines the retailer s optimal strategy. Notice, however, that as the opportunity cost of shelf space increases, less weight is placed on the downside, making accepting slotting allowances relatively more desirable. Less weight is placed on the downside as s increases because increases in s raise the retailer s oor: if both products turn out to be bad, the retailer can simply say no to both products, earn s, and limit the downside damage, if any, relative to vq. It is as if increases in s provide insurance for the retailer against a bad outcome. At the same time, increases in s have no e ect on the retailer s expected pro t from not accepting slotting allowances whenever this pro t exceeds s. Thus, accepting slotting allowances becomes more and more desirable relative to not accepting them as s increases for all s < vq. For s vq, the retailer s expected pro t from not accepting slotting allowances is xed at s, whereas his expected pro t is always greater than s when he accepts slotting allowances. These ndings, along with our ndings in Proposition 1, may explain why one tends to observe slotting allowances on new products but not on established products, and why, when one does observe slotting allowances on new products, usage is not uniform. In particular, our results have implications for some of the anomalies identi ed in the 2003 FTC sta report cited above. For example, they suggest the following testable implication: Testable implication: All else equal, a higher opportunity cost of shelf space will be associated with a higher incidence of slotting allowances on new product introductions. This nding may explain why the incidence of slotting allowances is often observed to vary across product categories. For instance, the FTC reports that some of the highest incidences of slotting allowances occur for frozen and refrigerated products, where shelf 21

24 space is typically more costly to expand, an observation that can be explained by our result simply because the opportunity cost of shelf space may be higher for these products than for non-frozen and non-refrigerated food items. Our results may also explain why one might observe di erences in the incidence of slotting allowances between di erent outlets of the same retailer. It is well known that stores located in the city center tend to have higher opportunity costs of shelf space than stores of the same retailer that are located in the suburbs, and similarly, convenience stores such as Tesco Express tend to have higher opportunity costs of shelf space than Tesco s main stores and Tesco Extra stores. An implication of our result is that we would expect to see a higher incidence of slotting allowances in the Express stores than, for example, in the Extra stores, and in stores that are located in the city center, than we would elsewhere for the same retailer. Another implication of Proposition 2 has to do with the relationship between the incidence of slotting allowances and the variance in the demand potential of the products: Testable implication: All else equal, as the variance in the demand potential of the manufacturers products increases, so too will the incidence of slotting allowances. The prediction from our result is that categories that consistently have a higher demand variance will tend to have a higher incidence of slotting allowances. This in turn may explain how the incidence of slotting allowances varies across product categories that di er in their mix of large and small manufacturers. On the one hand, in a category that is dominated by a few large, well known manufacturers, the retailer may expect a lower demand variance, which tends to increase the likelihood that he will opt for using simple wholesale prices. Conversely, in a category that is more fragmented and tends to consist of new product introductions from small and lesser known manufacturers, the retailer may expect a higher demand variance, and more often ask for slotting allowances. These predictions are indeed consistent with claims by small manufacturers that they are disproportionately asked to pay slotting allowances relative to their larger counterparts. It should be noted that we are not the rst to o er such testable implications, particularly with respect to why the incidence of slotting allowances would be expected to be increasing in the opportunity cost of shelf space. One informal argument that we have heard that makes a lot of intuitive sense begins with the observation that the higher is the retailer s opportunity cost of shelf space, the more costly it is for the retailer to make a mistake on stocking a new product. Hence, according to this argument, the higher is the retailer s opportunity cost of shelf space, the more important it will be for the retailer to know the demand potential of the manufacturers products, and consequently the more likely it will be that the retailer will demand to be compensated with slotting allowances. 22

25 Another informal argument that we have heard is that the variance in the use of slotting allowances is due to di erences in manufacturers bargaining power. According to this argument, smaller and lesser known producers have weaker bargaining power than larger and more established brand names when it comes to introducing new products. Consequently, smaller manufacturers are required to pay slotting allowances and larger "big name" producers are not (because they are better able to resist the retailers demands). Lastly, an argument that appears in the literature (see Lariviere and Padmanabhan, 1997) to explain why the incidence of slotting allowances would be expected to be increasing in the opportunity cost of shelf space is that manufacturers of good products will nd it more di cult to signal the demand potential of their products when the retailer s opportunity cost of shelf space is high than when it is low. According to this theory, manufacturers prefer to signal the demand potential of their products whenever possible by distorting their wholesale prices upward. And when this is enough to create a separating equilibrium, slotting allowances will not be observed. However, when the retailer s opportunity of cost shelf space is su ciently high, they nd that signaling through wholesale prices alone will not generally be enough to engender a separating equilibrium, and then, and only in these cases, will the manufacturers also resort to using slotting allowances. All of these explanations are insightful, but these explanations, like ours, are incomplete at best. In the case of wishing to avoid costly mistakes as the reason to ask for slotting allowances, the problem is that this argument always hold. There would never be any reason for the retailer not to ask for them when they can serve as a signaling device because having more information is always better for the retailer than not having the information according to this story. This explanation would need to be supplemented with a story such as ours to understand why slotting allowances are sometimes not observed. In the case of the argument that says that the variance in the incidence in slotting allowances is due to some categories having a greater proportion of established manufacturers than others, ultimately, this is an empirical question. Still, it cannot be the whole story because it cannot explain why there would be di erences in the usage of slotting allowances across di erent outlets of the same retailer (e.g., city center versus suburbs), where presumably the manufacturer s relative bargaining power would not be changing. Lastly, in the case of the argument that says that slotting allowances will only be used as a signaling device when attempts to signal through wholesale prices are exhausted, the presumption is that the manufacturers are the ones dictating how and when the retailers will receive slotting allowances, as opposed to the retailers being the ones who can choose their policy. If the retailer had the power to determine its policy in Lariviere and Padmanabhan s model, he would always prefer to receive slotting allowances (because 23

26 their model assumes away upstream competition). In contrast, we have found that, even when wholesale prices cannot be used as a signaling device, the retailer may still not want to accept slotting allowances given that manufacturers are competing for shelf space. 5 Asymmetric manufacturers We have thus far assumed that the manufacturers are symmetric in the sense that both products have the same distribution of demand potential. We now extend the model to allow the manufacturers to be asymmetric. In particular, we have in mind a setting in which a small manufacturer interacts with a large manufacturer. In such settings, small manufacturers often argue that they are disadvantaged relative to large manufacturers, because the retailers are biased in favor of the large manufacturers, all else equal. One way to make sense of this argument, while continuing to assume retailer rationality, is to observe that large manufacturers often have more nancial resources to devote to developing new products than small manufacturers do, and that this observation in and of itself can lead to new products that ex-ante have both a higher expected mean and a lower variance. In other words, a case can be made that large manufacturers may well have objectively better products, all else equal, simply because of their greater resources. In keeping with our demand primitives, the way we model the di erence between small and large rms, given our assumption that large rms typically have greater nancial resources, is to allow one rm to have multiple draws from the support [a, b], while continuing to assume that the other rm has only one draw. An natural interpretation of this is to imagine that the large rm is simultaneously working on several ideas for new products, and that at the end of the day, the rm gets to pick the best of its draws before presenting its case to the retailer. The small manufacturer, on the other hand, does not have the luxury of working on several projects simultaneously, and therefore only has one shot. Note that it may still be the case that the small manufacturer s product turns out to have a higher mean than the best of the large manufacturers products, but of course this will be less likely to hold the more draws the large manufacturer is allowed to take. We let k 1 denote the number of draws the larger manufacturer takes, and we assume for convenience that these draws are independent. The question we now ask is how does this interaction between small and large rms a ect the incidence of slotting allowances. As in Sections 3 and 4, we begin with the case in which the retailer has adopted a policy of not accepting slotting allowances. Without loss of generality, let the large manufacturer be rm 1 and the small manufacturer be rm 2. Both manufacturers draw 24

27 from the same uniform distribution with support [a, b], and the only di erence between the rms is that manufacturer 1 can draw more than once (k 1 times). This means that whereas manufacturer 2 s density function is still f 2 (q) = 1/ (b a), the probability ( density function for manufacturer 1 is now f 1 (q) = k q a k 1. b a b a) To see this, note that manufacturer 1 has k values for q 1 that are equally likely to be highest. Take one of these ) k 1 denotes the probability that all other draws are below q1. values, q 1. Then ( q 1 a b a The expected demand potential of manufacturer 1 when he can make k draws is thus E [q 1 k] = k b a { (q1 ) } k 1 a q 1 dq 1 b a b a = a + kb k + 1, from which it follows immediately that E [q 1 k] > a+b 2 for all k > 1. This is important because it e ectively means that manufacturer 1 will always be able to o er the retailer a better deal than manufacturer 2 can o er, given that signaling is not possible in this case. Keeping this in mind, there are three subcases to consider. Suppose rst that a+b 2 > s v. Then, with wholesale price competition, manufacturer 1 always wins, and in equilibrium it will charge a wholesale price w 1 that is just high enough so that the retailer s expected pro t is equal to his expected pro t from purchasing manufacturer 2 s product at cost: π W r ( ) a + b (s) = (v w1) E [q 1 k] = v. 2 Suppose next that s lies between the expected demand potential of the two manufacturers products, a+b s a+kb. Then, manufacturer 1 will still win the retailer s favor, v 2 v k+1 but now its wholesale price will be such that the retailer s expected pro t is equal to s: π W r (s) = (v w 1) E [q 1 k] = s. Suppose last that s exceeds the expected demand potential of both manufacturers products. Then, both manufacturers products are rejected and the retailer also earns s. Things are more complicated when the retailer accepts slotting allowances, because signaling then becomes possible. To consider this case, note rst that when s a+b, the v 2 retailer necessarily earns s with wholesale prices only. Hence, when s a+b, the retailer v 2 will always be weakly better o adopting a policy of accepting slotting allowances. This follows because he cannot be any worse o by doing that, but he might be better o. Suppose now that the retailer s opportunity cost of shelf space is such that s v < a+b 2. 25

28 Then, the ex-ante probability that at least one of the products will be bad is given by 27 Pr (vq 1 < s vq 2 < s) = s/v a ( s/v a b a b a ( ) ( s/v a + 1 b a ) k ( + 1 s/v a b a ) ) k ( s/v a b a while the ex-ante probability that both products will be good is given by Pr(vq 1 s vq 2 s) = ( 1 s/v a ) ( 1 b a, ( ) ) k s/v a. b a ) ( ) k s/v a b a It follows that the retailer s expected pro t from accepting allowances is given by 28 π S r (s, k) = Pr(vq i < s vq j < s) s + (6) [ {( b ( ) ) k ( ) } q2 s/v q2 Pr(vq 1 s vq 2 s) v 1 dq 2 s/v b s/v b s/v { b ( + k 1 q ) ( ) k 1 ( ) } ] 1 s/v q1 s/v q1 dq 1. s/v b s/v b s/v b s/v The rst line in (6) re ects the fact that the retailer receives its opportunity cost s whenever one or both products turn out to be bad, whereas the second and third lines in (6) re ect the retailer s expected payo (broken down by its expected payo from manufacturer 2 ( rst term inside the square brackets) 29 and its expected payo from manufacturer 1 (second term inside the square brackets) 30 when both products turn out to be good. It is easily veri ed that for k = 1, the expression above collapses to π S r (s) of the 27 The rst term on the right-hand side of the expression denotes the probability that both manufacturers products will be bad, the second term denotes the probability that only manufacturer 1 s product will be bad, and the last term denotes the probability that only manufacturer 2 s product will be bad. 28 Note that this expression is valid only for values of s [va, vb]. If s < va, then π S r (s, k) = v (2a + b) /3 (as we showed previously), and if s > vb, then both products are always bad and π W r (s) = π S r (s) = s. ( ) 29 Here, 1 q1 a b a is the probability that q 2 > q 1 and therefore that manufacturer 2 pays vq 1 and wins. The retailer s expected revenue from manufacturer 2, given all possible values of q 1 is therefore ( ) ( ) k 1 ( ) k 1 1 q1 a q1k q1 a k b a b a b a dq1, where q1 a b a b a is the density function for q1. b s ) kis the probability that q1 > q 2 and therefore that manufacturer 1 pays vq 2 and ( 30 Here, 1 q2 a b a wins. The retailer s expected revenue from manufacturer 1, given all possible values for q 2 is therefore b s ( 1 ( q2 a b a ) k ) q 2 b a dq 2, where 1 b a is the density function for q 2. 26

29 previous section. As an illustration, for k = 2 the pro t expression becomes π S r (s, 2) = s + (3s + 5b 8a) (b s)3 12 (b a) 3 De ne s (k) as the opportunity cost that solves π S r (s, k) = v (a + b) /2. It can be shown that s (k) is a decreasing function of k. This can also be seen by plotting s (k), which we have done in the example in the gure below. q = 15, σ = Opportunity cost of shelf space s Retailer asks for slotting fees s k Retailer asks for wholesale prices Number of draws for manufacturer 1 k Figure 2: The critical s (k) 27

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