Understanding Retail Assortments In Competitive Markets 1

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1 Understanding Retail Assortments In Competitive Markets 1 Kanishka Misra 2 Kellogg School of Management June 26, I wish to thank my advisors Eric Anderson, Karsten Hansen, Igal Handel Aviv Nevo, and Vincent Nijs. I thank Robert Blattberg for his advise. I thank IRI for providing the data in this study. Correspondence can be directed to Kanishka Misa, Kellogg School of Management, 2001 Sheridan Road, Evanston, IL 60208, [email protected]. 2 Kanishka Misra is a Ph.D. candidate at Kellogg School of Management.

2 Abstract Assortment planning, where a retailer decides which products to place on their store shelves, is one of the most fundamental decisions in retailing. Retail assortments are important drivers in consumers shopping decisions. With the ever increasing number of products available to retailers, category managers face a complex decision to select the right assortment for their categories. These assortment decisions are impacted by local consumer preferences, competition and costs. Under these conditions, a retailer s optimization problem is mathematically daunting and empirically challenging. In this paper we address the analytical and empirical challenges of modeling retailers assortment decisions. The analytical model shows that the optimal retail assortment can be described by ranking products based on a combination of demand and cost parameters. The advantage of this representation is that it can be used to study retail categories with a large number of available products. In the empirical study, we use these analytical results to model supermarket assortment decisions across 10 categories and 34 local markets. Our estimates suggest that the differences in assortment decisions across categories are driven by the size of products in the category and whether or not they require refrigeration. We show that competition between retail stores can result in an increase in assortment size and a decrease in retail prices. Using the empirical estimates, we can advise retailers on the optimal assortment and prices with a change in category size. We estimate that the optimal assortment with a 25% reduction in category size results in only a 3% reduction in category profits. Understanding retailer assortment decisions is also important for manufacturers to increase distribution for their products. We find wholesale price discounts can increase a manufacturer s distribution, particularly with retailers who have large allocated spaces for a category. We show that the introduction of manufacturer tying contracts can have a large negative impact on retailers profits and small manufacturers distribution.

3 1 Introduction Assortment planning, where retailers decides which products to place on their store shelves, is one of the most fundamental decisions in retailing. Consumers view the assortment as an important category management service output that drives their decisions on where to shop (Kok and Fisher [2007]). Consistent with this view, in a recent meta analysis, Pan and Zinkhan [2006] reviewed 14 papers all concluding that assortments are an important driver for consumers purchase decisions. A recent survey by Nielsen found that store assortment is the second most important factor driving consumers decisions (Nielsen, Dec 17, 2007). Moreover, category managers believe that their assortments are important competitive tools that allow them to differentiate. Understanding the mechanics behind assortment decisions is important for retailers, manufacturers and policy makers alike. Over the last few decades there has been an sharp increase in the number of products sold in retail stores, from 14k in 1980 to 49k in 1999 (Food Marketing Institute [2004]). With this increase in available products, retail category managers face a complex decision when selecting the right assortment for their categories. These assortment decisions are impacted by local consumer preferences, competition and costs. Given the large number of available options, the optimization problem is mathematically daunting and empirically challenging. Researchers often consider simplifications to the problem to make it more tractable, for example, considering only a small number of products in a subcategory (Draganska et al. [2007]) or relying on heuristics that the retailer can use (Kok and Fisher [2007]). In this paper we develop a different approach to address the analytical and empirical challenges of modeling retailers assortment decisions. In the analytical model, we consider the two decisions made by a retail store category manager: category assortment and retail prices. We show that the optimal retail assortment can be described by ranking the products based on a combination of demand and cost parameters. The advantage of this representation is that it can be used to study a large number of options in the retailer s consideration set. This provides a realistic view of managerial decision making, and there is evidence in the literature that retailers do indeed use a form of rank ordering to make their assortment decisions (Esbjerg et al. [2004]). When considering the empirical analysis, we take the view that data are generated from a market equilibrium (Bresnahan [1987]) where demand is based on consumer purchase decisions and supply is based on retailers pricing and assortment decisions. Therefore in each market and category we simultaneously model the demand and supply processes. A key advantage of the derived analytical result is that it allows us to consider the retailer s assortment decision as a sorting problem. This allows us to include information about products not in the assortment when modeling demand and supply parameters. For example, the fact that a store in an affluent neighborhood does not store value products informs us that consumer preferences for value products are low in this area. Our empirical study models supermarket assortment decisions across 10 categories and 34 local markets across the United States. Studying multiple categories allows us to make generalizations about retailers assortment decisions. In our model we introduce a fixed cost of introducing a product on the retail shelf. This fixed cost represents a minimum threshold profit that an introduced product must add to the category profits. Our estimates suggest that the differences in fixed costs across categories are driven by the size of products in the 1

4 category and whether or not they require refrigeration. In our framework we empirically estimate the three main drivers of local retail store assortments: demand, costs, and competition. This allows us to consider the impact of changes in any of these characteristics on retailer assortment decisions. With our analytical framework and econometric estimates we can quantify the effect of changes in assortment sizes on demand or profits (Broniarczyk et al. [1998], Boatwright and Nunes [2001]). When considering changes to the size of the assortment, we describe which UPCs a retailer should store and the prices the retailer should charge. In our data, we estimate that a 25% reduction in total assortment size results in about a 3% reduction in total profits. This suggests that retailers might strategically reduce their assortments with a small impact on category profits if the additional shelf space created can be used to carry additional categories. This methodology can be a powerful tool that retailers can use to make assortments decisions across multiple categories. Our model considers competition between retailers in their assortment and pricing decisions. We model this as a full information pure strategy Nash Equilibrium where each retailer plays a best response to competitors actions. Theoretically the effect of competition on assortments is ambiguous, therefore we will study this problem empirically. We estimate that, in our data, competition between retailers can lead to an increase in the total number of UPCs available to consumers as well as the predicted decrease in prices. Moreover, the magnitude of this effect depends on the space allocated to the category in retail stores. This can be an important result for policy makers, as mergers can have two negative influences on consumer welfare: higher prices and smaller selection. In this study, we model marginal costs for retailers. These costs are largely made up of wholesale prices charged by manufacturers. This allows us to consider the effect of changes in manufacturers decisions on the distribution of their products in retail stores. Consider wholesale price discounts; these reduce costs (and increase profits) for retailers and therefore can impact assortment decisions. We show that such discounts are most effective with retailers who have allocated large amounts of shelf space to a category. On the other hand retailers with limited space allocated for a category might not change their assortment decisions even with large wholesale discounts. Another tactic that manufacturers can use to increase distribution is to introduce tying contracts, where retailers must store all or none of the UPCs they offer. We estimate that these contracts negatively impact retailers and small manufacturers. We find that these contracts are most damaging in the case of retailers with limited category space. Retailers can lose a majority of their profits because they offer restricted assortments and small manufacturers have minimal distribution. An important finding from our empirical estimation is that not accounting for retail assortment decisions results in substantially different demand and supply estimates. This difference is particularly noticeable for the price estimate in the demand system, where without modeling assortment decisions, one would estimate that consumers are less price elastic. This in turn would cause a researcher to infer that retail margins are higher, in some cases greater than 100%. We believe that this provides evidence that researchers should consider assortment decisions when modeling retail demand and supply. To ground our model in managerial practice, we worked with a large retail chain to understand their decision making process and believe this is consistent across retailers. Assortments are based on decisions made at different levels of the organization space (Kok 2

5 and Fisher [2007]). First, a retail chain headquarters (national or regional) decides which products to store in its warehouse. More explicitly, here a category buyer negotiates with manufacturers and decides which products to store in the retail warehouse. Second, an individual store category manager, decides which products to store on the store shelf. These decisions are important, as each retail store faces a different localized market, characterized by (a) demand depending on the preferences in its neighborhood, (b) costs of space and (c) competition (Rigby and Vishwanath [2006]). As an example, consider the Cookies category. Jewel Osco stores in a higher income neighborhood in Chicago stock more biscotti and macaroons, while Jewel Osco stores in a low income neighborhood stock more value products. In this paper, we consider decisions made by a local retail store category manager who observes the products stored in the chain s warehouse and decides which of these products to sell and the price to charge. In our application, we use a unique dataset that allows us to consider local assortment decisions for retail stores. Our data have two unique features that allow us to study this problem empirically. First, we observe detailed attribute information for each UPC in each category. The advantage of these attributes is that we can distinguish one UPC from another and therefore make inferences based on which UPCs are sold. Without this detailed information a researcher would incorrectly infer that assortment decisions are based on random shocks (Richards and Hamilton [2006]). For example consider the Cookie example studied above: without detailed attribute information about the base of the cookie we could not distinguish biscotti and macaroons from other cookies. Without observable products characteristics to distinguish assortment decisions across stores, these differences would be treated as random shocks. Second, we observe a set of retail stores for each retail chain, this allows us to consider local warehouse decisions made by the chains. Without these data, a researcher would incorrectly assume that every store could offer any UPC from any manufacturer. 2 Related literature This paper builds on two main classes of literature: estimation of demand with endogenous product choices and pricing (e.g. Draganska et al. [2007]), and the retail assortment marketing and operations literature (e.g., Kok et al. [2006] and McAlister and Pessemier [1982]). We extend the endogenous product choice literature by introducing an approach that does not require solving the combinatorial assortment problem. To the operations literature we extend the analytical results for optimal assortments and add a structural view to the empirical modeling. These advances allow us to model the current assortment decisions made by retailers and consider how these are affected by changes in market conditions. There has been a recent increase in the area of endogenous product choices in competitive markets in the marketing and industrial organization literature. Early papers in this area by Mazzeo [2002] and Seim [2006] studied endogenous product choice decisions by firms entering markets. For example, Mazzeo [2002] considers the decisions of hotel chains to enter markets and choose the quality level. In marketing, this literature considers the entry decisions of retailers in markets (Zhu and Singh [2007]). The paper closest to our model is Draganska et al. [2007], where the authors consider 3

6 models with endogenous product assortments and pricing. In this paper, the authors study the endogenous decisions of ice cream manufacturers to sell different varieties of vanilla ice cream in different markets. To see the importance of this model, notice that literature on estimating demand and supply (e.g, Berry et al. [1995] and Nevo [2001]), looks at the demand from products sold and the prices of products in the market. Any change in product offering is considered to be exogenous (Nevo [2001]) and therefore explicitly uncorrelated with demand and supply. Considering endogenous assortment decisions essentially relaxes this assumption by modeling the decisions of firms to select certain products to sell in their stores. A drawback of the model proposed in Draganska et al. [2007] is that they need to evaluate every possible assortment to estimate their model. In some categories with 600 UPCs to choose from this leads to evaluations which is infeasible to solve. In addition, Draganska et al. [2007] make two assumptions that we do not in our model. First, unlike much of the discrete choice literature (Berry [1994]), they assume there are no unobserved (to the researcher) demand shocks and second, they assume retailers do not have full information about their competitors. We show that with a logit demand system that is similar to Draganska et al. [2007] but with including unobserved demand shocks, we can derive analytical optimal assortment results. We then use these results to estimate retailer assortment decisions in categories where retailers have large consideration sets. Another branch of this literature considers product lines and firm pricing decisions (e.g., Draganska and Jain [2005], Richards and Hamilton [2006]). In this literature, it is assumed that consumers have some utility for product lines as a function of the number of products in the product line. In our paper, we assume consumer preferences for each individual UPC. We therefore derive a preference for product lines that is not based only on the number of UPCs but also on which UPCs are included in the assortment. We can extend this literature due to on a key advantage of our data which contains detailed attribute information for each UPC. This allows us to consider each UPC as a different entity with a different set of attributes. Notice that while most of the multi-product firm choice literature has considered decisions made by manufacturers, we look at decisions made by retailers. While the problems are conceptually similar, considering a retailer as the decision maker allows us to simplify our model in two key ways. First, the set of available products for a retailer is restricted to the set of products available in the warehouse, whereas a manufacturer could produce a new product that is not currently available. Therefore, as researchers, we have more information about the consideration set for the retailer. Second, manufacturers face fixed costs to produce a good and this cost is heterogeneous across products. On the other hand, a retailer does not face an explicit cost for adding a UPC on the store shelf, and if there is a stocking cost it is homogeneous across products in a category. This difference allows us to simplify the optimization function (as compared to Draganska et al. [2007]) and allows us to derive our analytical result. The operations management literature considers the retail assortment problem coupled with an inventory problem, that is, they consider the number units of each UPC a retailer should stock (see Kok et al. [2006] for survey of the operations literature). The theoretical literature in the operations management, started with VanRyzin and Mahajan [1999], where the interest was in modeling the supply side of the retailing industry. VanRyzin and Mahajan [1999] consider a logit demand system, with exogenous pricing. The main result of this paper 4

7 is that a retailer will add SKUs in the order of expected contribution (i.e., add highest selling SKU first, 2nd highest selling SKU next, and so on) untill it is not profitable to add any more SKUs. The advantage of this result is that a retailer need not calculate the profitability of all combinations of the the SKUs to find the optimal assortment, instead the problem can be solved by a simple ranking. Maddah and Bish [2007] extend the VanRyzin and Mahajan [1999] model to include a joint decision of assortment and pricing. They find the main result, that optimal assortments can be found by ranking the SKUs, holds if the marginal costs are non-increasing (i.e., the most popular product does not cost more that the least popular product). In particular, in a setting where the marginal costs are constant, they find that ranking heuristic can be used by monopolistic retailers. This result can be a bit problematic as the main component of the retailer s marginal cost is the manufacturer s wholesale price. In most economic settings the manufacturer would charge a higher wholesale price for more popular products which would not satisfy the condition in their result. We extend the results of these papers and show that we can derive a different condition that depends on value and costs and that simplifies the optimal assortment problem. Additionally, we extend this framework to account for oligopoly markets. Another class of papers in the operations literature (e.g, Kok and Fisher [2007], Cachon and Kok [2006]) takes a more algorithmic approach to this problem to solve for optimal assortments. They view this problem from the point of view of a grocery retailer who wants to maximize profits and faces a shelf space constraint (with facings). They view this problem as a knapsack problem and use a greedy algorithm to solve for the optimal assortment. In this model they assume demand (and price) is exogenous to the assortment decision. The advantage of model specification is that they can consider more complex demand systems for more robust study of consumer preferences. With this algorithm they find with all else equal, products with higher margins (or demand) have higher facings. In an empirical application, Kok and Fisher [2007] apply their model to Albert Heijn, BV, a large supermarket chain in the Netherlands, and report that optimal assortment allocation would have increased profits by 50%. While this paper offers a more complete operation research solution to the problem, it abstracts away from the economics of the problem. Adding two economic features to the model, namely, pricing decision and retail competition would make this approach less computationally feasible. Overall the operations research literature considers the retail assortment problem as one where the retailer chooses UPCs while considering inventory decisions and modeling the probability of stock-outs. In our paper we model retailer pricing and assortment decisions in competitive markets simultaneously with demand for the category. While the theory is structured similarly, there is an important conceptual difference in the empirical outlook. The empirical operations literature estimates demand and then optimizes the retail assortment decisions. But in this paper we follow the Industrial Organization view (Bresnahan [1987]), where we believe the data we observe are from equilibrium decisions made by retailers. Therefore, when modeling demand, we explicitly account for the endogenous price and assortment. Importantly we find that, without considering endogenous assortment decisions, a researcher would infer incorrect demand estimates. This suggests that the operations research approach will optimize the assortment decision with biased inputs. The product assortment literature in marketing focuses on consumers responses to product assortments. In a recent meta analysis, Pan and Zinkhan [2006] report that all 14 5

8 studies that have measured store patronage report that assortment selection increases the propensity of a consumer to visit the store. These studies suggest that assortment decisions can have significant implications for overall retail store patronage. When considering assortments, researchers consider the variety offered by this assortment. This idea of retail variety started with Baumol and Ide [1956] and the marketing literature has emphasized the variety of assortments (see McAlister and Pessemier [1982] for a review) are important in consumer decision making. In empirical applications, researchers (Hoch et al. [1999], Hoch et al. [2002]) measure the variety in an assortment using the (psychological) distance between items in the assortment. In addition to attribute based variety, these papers also show that the organization of the store shelf does indeed affect the perception of variety in an assortment. In our data we do not observe shelf allocation and therefore are restricted to attribute based variety. We view the assortment variety as an important metric, specifically as it influences demand for all products. In our paper we account for variety in our demand system to understand underling consumer preference. We feel this notion of variety is very important and for this reason we explicitly model the specific UPCs and just not the number of UPCs a retailer stores. The marketing literature has argued that larger assortments might not be optimal for retailers. The experimental literature (e.g., McAlister and Pessemier [1982], Chernev [2003], Chernev [2006]) argues that giving too many choices might reduce consumers purchases as this makes purchase decision harder. There is some evidence from an on-line grocery retailer described in Boatwright and Nunes [2001], where the researchers show that the overall category purchases increased with smaller assortments. Additionally Sloot et al. [2006] show that 25% experimental reductions in assortment sizes did not result in a significant long term decrease in demand. In our paper, we focus only on the first order effect of retail assortments and do not model the behavioral process that might lead to difficulty in choice from large assortments. We do believe this is an area for further empirical research. Another field of research dealing with assortments in the marketing literature is cross categories consumer purchase decisions (e.g., Andrews and Currim [2002], Chung and Rao [2002], Arentze et al. [2005], Song and Chintagunta [2007]). Their papers consider consumer purchase behavior when purchasing from multiple categories or on multiple purpose shopping trips. They consider the purchase decision of a customer driven by the categories of products at retail stores. In our paper we study each category in isolation for three main reasons: first, assortment decisions are most often taken by individual category managers given shelf space restrictions, second, our data include a sample of categories on different store shelves, and third, we are restricted to store level aggregate purchase data for each category so cross category purchases are not observed. The remainder of the paper is structured as follows: in section 3 we discuss the analytical model and empirical specification, in section 4 we describe the data used in the paper. Section 5 covers the results of the model, in section 6 we describe the counterfactual analysis, and section 7 concludes. 6

9 3 Model In this section we will describe the assumed decision making process used by the retailer, and the analytical results we can derive from this to simplify the empirical analysis. In this paper we use a Bayesian econometric setup to estimate the model. The details of the empirical estimation will be shown at the end of this section. Our model is formulated from the perspective of a grocery category manager for a large retail store. In every decision cycle, the manager observes the products that are stored in the chain s warehouse. The manager observes the marginal costs for each product in the category, this can be thought of at the wholesale price charged by the manufacturer plus any additional economic cost associated with selling the product. Additionally the manager is given a constrained space in the store where she can store only a certain number of products. Given these inputs, the manager has two sets of decisions: first she must decide which products to sell in her store, and second she must decide the prices to charge. We will start with a model for a monopolistic retailer and then extend this to allow for retail competition. In economic terms, the retailer manager s problem for any time period t, can be written as max max π j (Θ t, C t, P t ) (1) Θ t Ω t P t j Θ t subject to Θ t n t where Ω t represents all available products in time period t, Θ t is the chosen subset of products for the retailer, C t represents the cost of selling the products and P t represents the selected price for each product in the assortment. The profit depends on the profit for each product sold, which is represented by π j. n t represents the space constraint for the retailer. Notice here we have assumed the space constraint for the retailer is a constraint on the number of different products sold. In a retail setting this is normally a constraint on the number of facings available for the category. However, since we do not observe data on facings we need to make a simplifying assumption here. Under this formulation we assume that retailers first decide which products to store and then allocate shelf space to these products. Consistent with the empirical pricing research in economics and marketing (e.g., Nevo [2001]) we will assume that the cost function in linear, or marginal cost is constant. This assumption is consistent with wholesale prices not varying with the number of units purchased, as is the case in retail. So, we write the profit function for product j as follows π j (Θ t, C t, P t ) = M t (p j,t c j,t )s j,t (Θ t, P t ) For a given time period t: m t is the size of the available market, p j,t and c j,t are the price and marginal cost for product j, and s j,t (Θ t, P t ) represents the share captured by product j when the retailer stores Θ t products and charges a price P t. So, the retailers problem can 7

10 be considered as max max M t (p j,t c j,t )s j,t (Θ t, P t ) (2) Θ t Ω t P t j Θ t subject to Θ t n t This is a complex problem for the retailer as we have the retailer selecting both the optimal assortment and the optimal prices. The optimal assortment problem is a difficult combinatorial problem where the retailer selects a subset of products from a large available set. Although the optimal pricing problem is one that has been studied extensively, this remains a complex problem, as the optimal price for all products needs to be found simultaneously. Prior research has suggested algorithmic solutions to this problem. These require finding all possible subsets of the choice set (power set) and then calculating the optimal price in each case. To see the complexity of this, consider a case where we only have three available products in Ω t say, x, y, z. Now we would need to calculate the optimal profits for each set in P(S) = {φ, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. In general the number of calculations is 2 Ωt. Therefore while these methods are feasible in cases with a small number of available options, they become less so as the number of available options in large. In most grocery retail categories, there are between 60 and 600 options, this would require an infeasible 1.15e18 to 4.15e180 calculation. To overcome these problems, in this paper we provide a simpler analytical solution by making specific assumptions about the nature of demand in the market. In particular, we assume a logit demand function, which has been used extensively in the literature. In the appendix we show that our results extend to nested-logit demand systems 1. The optimal assortment will allow retailers to follow a simple algorithm for ranking a product and then decide on the optimal assortment based on this ranking. In the next few subsections we will define specific parametric assumptions to describe the nature of the industry and then derive our main analytical results. 3.1 Demand model We will assume a logit demand system in this paper (an extension to a nested logit demand system is available in the appendix). We assume that each consumer in a given market will have the following utility function u i,j,t = αx j,t βp j,t + ξ j,t + ɛ i,j,t where i represents consumers, j represents product and t represents the time period. X j,t represents the product characteristics for product j. α represents consumers preferences for the product characteristics. p j,t is the price charged by the consumer at time t and β represents the marginal utility of money. There are random utility shocks (ξ j,t ) that impact all customers in the market; these demand shocks are observed by the all agents, though unobserved by the researcher (Berry [1994]). ɛ i,j,t represents the idiosyncratic fit, per the 1 Please contact the author for the technical appendix at [email protected] 8

11 logit assumption these are assumed to be from an i.i.d. type I extreme value distribution. Additionally consumers have a utility u i,0,t = ɛ i,0,t that represents their utility from selecting out of the market. In the model presented here, heterogeneity of consumer decisions are based on unobserved idiosyncratic demand shocks (logit error term). This is a simplifying assumption and is made to focus our attention on understanding the local assortment decisions of retailers. However, note that to study local assortments we must allow demand preference for local markets to be different. We will discuss this further in the empirical model section. In this demand system, consumers select the product that maximizes their utility. Or, the decision for a consumer in time t is given by d i,t = arg max j [0,Θ t] u i,j,t With the logit assumption we can write this as a probabilistic choice, as below (d i,t = j) = (u i,j,t > u i, j,t ) = e αx j,t βp j,t +ξ j,t 1 + k Θ t e αx k,t βp k,t +ξ k,t where j refers to all products other than j. Prior IO models (Berry [1994], Nevo [2001]) simplify this by defining this define δ j,t αx j,t + ξ j,t. Therefore we can write the model as (d i,t = j) = e δ j,t βp j,t 1 + k Θ t e δ k,t βp k,t Integrating over customers and taking logs we get the following well established (Berry [1994]) relationship from our demand model: log(s j,t ) log(s 0,t ) = δ j,t βp j,t (3) This is a relationship that can be taken to the data as we observe aggregate shares in our data. 3.2 Supply model In this paper, there are two parts to the supply model: assortments and pricing. In this section we will discuss both of these and derive the analytical results to construct an empirical model for studying. We will start with considering the retailer pricing problem and then continue on to studying the retailer assortment problem. In this section, we first look at a monopoly setting and then extend it to allow for competition between retailers Retailer pricing We begin with the simplified model where the retailer has decided the products in the assortments (Θ t ) and is deciding the optimal price. The retailer will solve the problem of 9

12 the form max P t j Θ t M t (p j,t c j,t )s j,t (Θ t, P t ) (4) This is a well-studied problem and the solution from the first order condition for all j must satisfy s j,t (Θ t, P t ) + (p j,t c j,t ) s j,t(.) p j,t + k j (p k,t c k,t ) s k,t(.) p j,t = 0 A result from prior research (Anderson de Palma 1992 and Nevo and Rossi [2008]) simplifies this equation further to describe the optimal price as ( ) ( ) 1 1 p j,t c j,t = β 1 (5) k Θ t s k,t (Θ t, P t ) For the interested reader we have re-derived this result in the appendix of this paper. Interestingly, with this relationship the optimal price involves charging a constant margin across all products in the retailers assortment; this is because the right hand side of equation 5 does not involve any terms specific to j. Therefore we can define m(θ t ) as the optimal markup given the assortment Θ t. This simplification helps reduce the complexity of the modeling, as now the optimal pricing is reduced to a one dimensional parameter. However, we need to expand this expression further as we currently have the price on both the left and right hand sides of equation 5 (note that price is in the share calculation). Claim 1. The optimal markup in this setting can be simplified as below: log(βm(θ t ) 1) + (βm(θ t )) = log( k Θ t e δ k,t βc k,t ) (6) Proof. From equation 5, we have ( ) ( ) 1 1 m(θ t ) = β 1 k Θ t s k,t (Θ t, P t ) ( ) 1 + l Θ βm(θ t ) = t e δ k,t βm(θ t) βc k,t 1 ( ) l Θ βm(θ t ) = 1 + t e δ k,t βc k,t e βm(θt) e βm(θt) (βm(θ t ) 1) = l Θ t e δ k,t βc k,t βm(θ t ) + log(βm(θ t ) 1) = log( l Θ t e δ k,t βc k,t ) This relationship will prove useful when we consider the assortment selection section of the supply model. 10

13 Next, we consider the optimal profits of an assortment Θ t given retailers use the optimal pricing described above. Claim 2. The optimal profit can we written as: max P t j Θ t M t (p j,t c j,t )s j,t (Θ t, P t ) = M t (m(θ t ) 1 β ) (7) Proof. max P j Θ t M t (p j,t c j,t )s j (Θ t, P t ) = j Θ t M t (m(θ t ))s j,t (Θ t ) = M t (m(θ t )) j Θ t s j,t (Θ t ) 1 1 = M t β 1 s j,t (Θ t ) j Θ t s j,t (Θ t ) j Θ t = M t 1 β = M t 1 β = M t 1 β = M t 1 β j Θ t e δj,t β(cj,t+m(θt)) j Θ t e δ j,t βc j,t e βm(θt) e βm(θ) (βm(θ) 1) e βm(θ) βm(θ) 1 1 = M t (m(θ) 1 β ) This derivation uses equation 5 going from line 2 to line 3 and uses equation 6 when going from line 3 to line 4. Summarizing this subsection of the paper, we have simplified the pricing problem by reducing it (from equation 4) to the following max P t j Θ t M t (p j,t c j,t )s j,t (Θ t, P t ) = M t (m(θ t ) 1 β ) With m(θ t ) satisfying the following relationship, log(βm(θ t ) 1) + (βm(θ t )) = log( k Θ t e δ k,t βc k,t ) 11

14 3.2.2 Assortment decision In our supply problem we assume the retailer solves the following problem: max M t max (p j,t c j,t )s(θ t, P t ) Θ t Ω t P t j Θ t subject to Θ t n t Claim 3. The capacity constraint will always be satisfied Proof. The above is true in general for any demand system that (1) assumes no products has a zero probability of purchase and (2) assumes the share of any product (including the outside option) does not increase if we add a new product to the assortment. This second condition is added to ensure we do not have a consumer leaving the market as the number of products increase. Assume that the optimal assortment Θ t has fewer than n t products. Consider adding a product l (l Ω t and l / Θ t ). Now add product l to the assortment now adding a new product and setting the price for product l to be c l,t + max j Θt (p j,t c j,t ) + ɛ, with ɛ > 0. Therefore the profit margin of product l is higher than any other product in the market. Under assumption 1, no product is a strictly dominated, so the share of product l is strictly positive (non-zero). Now, there are two forms of substitution that might happen with the introduction of product l. First, consumers may switch from purchasing a product in Θ t to purchasing product l. This substitution is strictly profitable for the firm, as the profit margin for product l is higher than for any other product in Θ t. Second, consumers may switch from not purchasing to purchasing product l, this is clearly profitable for the firm. Therefore Θ t could not have been the optimal assortment. The two conditions required are clearly true for the logit model. With the idiosyncratic error term with infinite support (under the type-1 extreme value distribution), the probability of purchase of any product in always non zero. And second, clearly the introduction of a new product can only reduce the share of other products in the market. Notice that these two conditions are satisfied by almost all of the standard demand models (e.g., probit). With this result we can add a Lagrange multiplier (called F t ), given the constraint Θ t n t is satisfied. Therefore we can rewrite the retailer s problem as; max max [M t (p j,t c j,t )s j,t (Θ t, P t ) F t ] Θ t Ω t P t j Θ t where F t is the shadow price of adding a product (or the fixed cost of space). As this is a Lagrange multiplier, we must have F t > 0. From an economic perspective, the marginal benefit of adding a product to the assortment must be at least F t. 12

15 Substituting in the results from the pricing section earlier, this problem simplifies to: max Θ t Ω t M t (m(θ t ) 1 β ) F t with log(βm(θ t ) 1) + (βm(θ t )) = log( k Θ t e δ k,t βc k,t ) The advantage of the above representation is that this equation only considers the maximization over the space of Θ t. Moreover, Θ t only enters though m(θ t ), therefore to simplify this further we need to understand the properties of m(θ t ). Claim 4. The equation log(βm(θ t ) 1) + (βm(θ t )) = log( k Θ t e δ k,t βc k,t ) is invertible (in m(.)). Moreover, the solution is strictly increases with log( k Θ eδ k β(c k ) ). Proof. Define a function f(m) log(βm 1) + (βm) defined from ( 1, ) to R. β We will show this in three steps: first we will show that the inverse exists, second we will show the inverse is well-behaved and third we will show the inverse is unique. To observe the existence of the inverse, notice that As m 1, we must have f(m). This is because log(βm 1) and βm β is finite (tends to 1). m, we must have f. Here both βm and log(βm 1). Though the former tends to faster. Taken together, these suggests that there exists an inverse function g(.) such that f(m) = k g(k) = m. In more formal terms, we need to ensure that for every finite k, the function f(.) has a finite inverse. To prove this, consider the function h(m) f(m) k. We need to show that a unique finite m with h(m) = 0, moreover this is true finite k and β. To show this, first define A = 1 β [1+min(ek 3, 1)]. So we have h(a) = log(βa 1)+βA k = log(min(e k 3, 1)) min(e k 3, 1) k log(e k 3 ) k = 1 < 0. Therefore h(a) < 0. Second, define B = 1 (1 + max(1, k)). So we have h(b) = log(βb 1) + βb k = β log(max(1, k)) max(1, k) k log(1) k k = 1 > 0. Thus, h(b) > 0. The function h(.) is clearly continuous; therefore, by the implicit function theorem we have the required inversion. To complete the proof we need to show uniqueness. First, consider the fact that f = m β + β > 0 as the function is defined for m > 1. Therefore the function f(.) is strictly βm 1 β increasing in m; thus h(.) is strictly increasing in m. For allm < A, by construction we must have h(m) < 0 as h(a) < 0 and m < A, h(m) < h(a). Similarly, for all m > B, by construction we must have h(m) > 0. Therefore we cannot have h(m) = 0 for any m / [A, B] Finally, since h(.) is increasing in the interval [A, B] we must have there only one solution. 13

16 Moreover since f(.) is strictly increasing we must have the inverse g(.) is strictly increasing. This proves this claim that there is a unique m(.) that satisfies equation 6 and moreover the higher the value of log( k Θ eδ k βc k) the higher the m(.) that satisfies this equation. To extend this result further, notice that the profit for an assortment are an increasing function of m(.). By the claim above we must have that these profits are an increasing function of k Θ t e δ k,t βc k,t (notice we remove the log as it is a strictly increasing function). This leads us to our next claim to get the optimal assortment Claim 5. When deciding the optimal assortment, the retailer can rank product based on their δ k,t βc k,t and pick the top n t products to include in the market. Proof. The importance of the previous claim is that we can now know that the solution to the problem max Θ t Ω t M t (m(θ t ) 1 β ) Subject to Θ t n t is the same as the solution to the problem max e δ k,t βc k,t Θ t Ω t k Θ t Subject to Θ t n t as profits are a strictly increasing function of k Θ t e δ k,t βc k,t. Now, suppose that picking the n t products with the highest δ k,t βc k,t was not the optimal solution. It must be the case that j Θ t and l / Θ t with δ l,t βc l,t > δ j,t βc j,t. However, we have k Θ t,k j eδ k,t βc k,t + e δ l,t βc l,t > k Θ t,k j eδ k,t βc k,t + e δ j,t βc j,t which contradicts the optimality of Θ t. = k Θ t e δ k,t βc k,t This solves the normative problem for a monopolistic retailer and we will extend this problem to include competition. In relation to prior literature, this result is most similar to that of Maddah and Bish [2007]. Their main result using the notation of this paper is that products can be ranked using δ.,t if the c.,t have the (weakly) reverse ranking. Thus they get the rank ordering works only if products with higher δ.,t have (weakly) lower c.,t. The result derived in our paper clearly satisfies this condition as a special case. 14

17 3.2.3 Extension from monopoly to oligopoly We consider a full information simultaneous move oligopoly model where in an pure strategy Nash equilibrium each firm plays a best response to the other firms assortment decision and pricing decisions. The retailers problem (best response) can now be written as the solution to max M t max (p j,t c j,t )s j,t (Θ t, P t, Θ t, Pt ) Θ t Ω t P t j Θ t subject to Θ t n t where Θ t refers to the assortment decisions of all other retailers and Pt refers to the pricing decisions of all other retailers in the market. In this section we will update the claims from the monopoly model and show that similar claims hold in an oligopoly setting. First, for the pricing model, notice that the optimal margin for the retailer does still satisfy p j,t c j,t = ( 1 β ) ( ) 1 1 k Θ t s k,t (Θ t, P t, Θ t, Pt ) The only difference between the monopoly and oligopoly pricing problem is that the share calculation now also depends on products offered by competitive firms as well. Similar to the monopoly case we can rewrite this the optimal markup to satisfy the following: log(βm(θ t, Θ t, Pt ) 1) + (βm(θ t, Θ t, Pt )) = log( e δ k,t βc k,t ) log(1 + e δ k,t βp k,t ) k Θ t (8) This equation differs from the the monopoly case in two important ways. First, the markup (m(.)) now is written as a best response to the competitors actions and therefore depends on the assortment and pricing decisions of the competitors. Second, the right hand side of equation 8 has an additional term that captures the effect of the competition. Notice, the difference between the first and second term on the right hand side of this equation: the first only depends on the cost c where as the second depends on the price p. This is important because we are solving for a best response and not an equilibrium here, therefore we can have the other firms decisions (prices and assortments) on the right hand side of the equation. Importantly, we can use the result in claim 4, as there is no difference between the left hand side of the equation above in the monopoly or oligopoly cases. However, we need to reprove the claim for optimal profits with a given assortments below. Claim 6. In competitive markets, we claim that the retailer s profit conditional on assortment is given by: max P t k Θ t j Θ t M t (p j,t c j,t )s j,t (Θ t, P t, Θ t, P t ) = M t (m(θ t, Θ t, P t ) 1 β ) 15

18 Proof. max M t (p j,t c j,t )s j (Θ t, P t, Θ t, Pt ) P t j Θ t = M t (m(θ t, Θ t, Pt ))s j,t (Θ t, Θ t, Pt ) j Θ t ( 1 = M t β = M t 1 β = M t 1 β = M t (m(θ t, Θ t, P t )) j Θ t s j,t (Θ t, Θ t, P t ) 1 1 = M t β 1 j Θ t s j,t (Θ t, Θ t, Pt s j,t (Θ t, Θ t, Pt ) ) j Θ t j Θ t e δ j,t β(c j,t +m(θ t,θ t,p t )) 1 + k Θ t ( j Θ t e δ j,t βc j,t e βm(θt,θ t,p t ) e δ k,t βp k,t ) ( ( j Θ t e δ j,t βc j,t 1 + k Θ e δ k,t βp k,t t ) k Θ t ) ( 1 e δ k,t βp k,t e βm(θt,θ t,p t ) 1 e βm(θ,θ t,p t ) (βm(θ, Θ t, Pt ) 1) = M t β e βm(θ,θ t,p t ) 1 βm(θ, Θ t, Pt ) 1 = M t β 1 = M t (m(θ, Θ t, P t ) 1 β ) ) ) This claim is important as it shows that the best response (profit) function for the retailer is strictly increasing in m(θ t, Θ t, Pt ). Therefore exactly as in the case of the monopoly model (claim 5), we must have the optimal assortment is defined by selecting the n t products with the highest δ j,t βc j,t. Notice that the competition effects assortment decision of the retailer in the following way: the space allocated to each category will depend on the level of competition. In an full information simultaneous move game we consider this to a reasonable prediction for a pure strategy equilibrium, as we would expect two identical firms in such a game to have identical assortments 2. However, if this were a sequential game, we would not expect this to be a stable equilibrium. To describe the Nash Equilibrium in our counterfactual settings, we consider the best response curves for each player in the market and consider explicitly where these best response curves intersect. 3.3 Empirical specification In this section we will describe the methodology for the empirical analysis that translates this analytical model into one that can be estimated with data. In this paper we set up a 2 Note that in our empirical setting we consider grocery stores from large retail chains 16

19 hierarchical Bayesian model. In our estimation we will estimate separate coefficients for each market and time period, this include demand and supply coefficients. As mentioned before this is important as we want to capture local market conditions that drive retail assortment decisions. In the remainder of this section every parameter is market specific. The hierarchy allows us to integrate these local parameters. Detail of the Gibbs sampler are given in the appendix of this paper. 3.4 Local market In this paper we need to construct an estimator that allows for local market variation from from market/quarter to another. As stated in the introduction, localization is important, especially given the restrictions from our logit demand system. Here we introduce an additional index m, to represent a market. A market in defined as a local physical market with multiple stores in a specific quarter. The remainder of this section specifies demand, marginal cost and assortment models consistent with the analytical derivations so far Demand As described earlier, we will consider only a logit demand model in this paper. Here we will assume that the consumers have a utility of the form u i,j,m = α m X j,m β m p j,m + ξ j,m + ɛ i,j,m where X j,m is the demand characteristics, these include all product attribute information. p j,m is the price charged by the retailer. In addition to the common assumptions we will assume that the random shocks ξ j,m are distributed from the Normal distribution with mean 0 and variance σ ξm. This assumption is exactly similar to the ones made in papers that consider other structural Bayesian approaches to modeling demand (e.g., Yang et al. [2003], Jiang et al. [2007]). This however, is unlike the Berry et al. [1995] and Berry [1994] assumptions, where the researchers assume only that there are some variables Z, that are uncorrelated with the demand shocks (ξ). However, Jiang et al. [2007] show that the normal assumption is not restrictive and estimate this demand system correctly. To estimate demand with aggregate data we will use the following equation (for all products j Θ m, this includes all retailers) Marginal cost log(s j,m ) log(s 0,m ) = α m X j,m β m p j,m + ξ j,m (9) The optimal markup for all product in Θ m,r (assortment for an assortment for any one retailer) in our model is given by ( ) ( ) 1 1 p j,m,r c j,m,r = 1 k Θ m,r s k,m,r (Θ m,r, Θ m, r, P m, r ) β m 17

20 Alternatively this can be written as ( 1 c j,m,r = p j,m,r β m ) ( ) 1 1 k Θ m,r s k,m,r (Θ m,r, Θ m, r, P m, r ) We parametrize marginal cost such that ( 1 c j,m,r = γ m Z j,m + ν j,m = p j,m,r β m ) ( ) 1 1 k Θ m,r s k,m,r (Θ m,r, Θ m, r, P m, r ) (10) where the Z j,m variables are possible marginal cost shifters, here we include all product attributes in this equation. γ m describes how these impact marginal cost. The ν j,m term is a cost shock for product j in market m. We assume ν j,m N(0, σ νm ); this parametrization allows us to estimate the effect of marginal cost shifters. Also the simultaneous modeling of equation 9 and 10 allows us control for endogenous prices. While many industrial organization and marketing papers control for endogenous prices using an instrumental variable regression in equation 9, the simultaneous modeling of demand and supply is a more direct method and has been used in early industrial organization papers (Bresnahan [1987]) Assortments In this paper we have shown that the optimal assortment for a retailer consists of selecting the n m,r products with the highest δ j,m,r βc j,m,r. Therefore we must have the following relationship for all products in the choice set Ω m,r : min δ j,m,r β m c j,m,r > max δ k,m,r β m c k,m,r (11) j Θ t k / Θ t where δ j,m,r = α m X j,m,r + ξ j,m,r. Notice that in equation 9 conditional on β m we can point identify δ j,m,r, for all j Θ m,r directly from the data (without any error). Similarly in equation 10, conditional on β m we can point identify c j,m,r, for all j Θ m,r directly from the data. Therefore conditional on β m we can treat the left hand side of equation 11 as data. Our restriction for all products k not in the market is therefore summarized by δ k,m,r βc k,m,r < min j Θ t δ j,m,r βc j,m,r αx k,m,r + ξ k,m,r β m γ m Z k,m,r β m ν k,m,r < min j Θ m,r δ j,m,r β m c j,m,r ξ k,m,r β m ν k,m,r < ( min j Θ m,r δ j,m,r βc j,m,r ) α m X k,m,r + β m γ m Z k,m,r (12) Now notice that equation 12 can be written as a CDF as we know the joint distribution of ξ k,m,r β m ν k,m,r is N(0, σ ξm + βmσ 2 νm ). Therefore conditional on model parameters we write down the likelihood of those products that are not in the market. To estimate F m,r we assume that the last product added to the assortment satisfies the profit constraint exactly. In other words, the marginal profit of adding the last product is exactly equal to the F m,r. Thus, the marginal profit of adding the last product is min j Θm,r M m,r [m(θ m,r, Θ m, r, P m, r ) m(θ m,r j, Θ m, r, P m, r )] where Θ m,r j refers to 18

21 the set of product Θ m,r without the product j. Notice that our estimation procedure guarantees that for all k / Θ m,r, the marginal profit of adding product k to the assortment Θ m,r is less that F m,r. Also note that we estimate a F m,r coefficient for every store in every market. The advantage of the Bayesian setup here is that as we traverse the posterior distribution of the demand and supply parameters, with our gibbs sampler, we can trace out the entire posterior distribution for F m,r. Details of the Gibbs sampler used for the estimation are available in the appendix of this paper. The key parameterization in the Bayesian analysis is to consider two model parameters δ and c to be augmented parameters (Tanner and Wong [1987]). The advantage here is that only need to consider the selection model when drawing β m. Also notice that with this simplification the selection model here is similar to a Bayesian probit model (Rossi et al. [2005]). Finally, to estimate this model we impose a hierarchical structure across all markets for the parameters as follow: α m N(ᾱ, Σ α ) (13) log(β m ) N( β, σ β ) (14) γ m N( γ, Σ γ ) (15) F m,r N( F m + F t, σ F ) (16) Notice that in the β shrinkage model, we force the distribution to be log normal, this is done to enforce that beta (the price coefficient) is always positive (notice that in the utility we assume the term to be β times Price). Additionally we add fixed effects for markets and quarters in the fixed cost hierarchy to understand the variation in the fixed costs across geographical markets and time period. 4 Data The data used for this project are IRI movement data across 6 cities for 10 categories. The data include store level movement data, including price and units sold of every UPC each week. The key advantage of these data are that we have detailed attribute descriptions for each UPC in each category. Therefore, for each UPC we observe, detailed product attribute information that allows us to distinguish one UPCs from another. For example, in the canned tuna category, for each UPC we observe the brand, size, type of tuna, cut, packaging, form, color, and the storage liquid (water versus purified water versus oil). These detailed attributes allow us to specify a detailed demand system for consumer preference over these attributes. Additionally we can better understand the supply side of the market by better estimating variation in marginal cost across these parameters. Without these data many UPCs would be indistinguishable, and therefore difficult for the researcher to understand why some UPCs are offered and others arenot. These detailed attribute variables are mainly incomplete for private label brands and therefore in this analysis we limit our focus to national brand only. In the data we observe a sample of 368 stores in 6 different markets, the markets are: Illinois (around Chicago), Massachusetts (around Boston), Washington (around Seattle), 19

22 California (north and south), Georgia (around Atlanta), and Colorado (around Denver) 3. In each of these markets we observe the weekly store data for each store in the largest grocery chains in the area. We observe these data for 56 weeks from 31st January 2006 till 25th February We will discuss these markets in further detail when defining our local markets. We observe a wide range of categories: analgesics, canned tuna, coffee, cookies, frozen dinners, ice cream, orange juice (refrigerated), mustard, paper towels and toothpaste. A nice feature of this set of categories is that we observe both shelf-stable categories (e.g., analgesics, tuna, coffee), and refrigerated categories (e.g., orange juice, frozen dinners). In addition, we observe both categories that take up relatively less shelf space (e.g., tuna, mustard) and those that take up more (e.g., paper towels). In the remainder of this section we will discuss our assumptions for making local markets to study local market competition and then describe each of the categories we study in this paper. 4.1 Local markets As discussed in the introduction, retail assortments are formed based on two levels of decisionmaking. First, the headquarters of the chain decides on the products to store in the warehouse and second, the individual retailers decide on the products to store on the store shelves. Our objective here is to study the second of these decisions. However, since we don t observe the warehouse decision directly we assume the warehouse decision is the union of all products sold at any of the chain s stores. For example, we assume that the products in Jewel Osco s warehouse in Chicago is a union of all products sold in the 18 local Jewel Osco stores. The assumptions here are: (1) the warehouse will not store a product not sold in any store, and (2) our sample of stores is wide enough to capture all the variation in the stores. To defend the second of these assumptions, our sample of stores from a chain are a random selection of stores from all local neighborhoods (e.g., the 18 Jewel Osco stores we observe in Chicago cover 5 counties and span 80 miles from North to South and 40 miles from Each to West). We believe that, given this variation, we can approximate the products stored in local warehouses for large chains. Restricting our attention to large chains leads us to study the following chains in each of our geographic areas: Chicagoland area: Jewel Osco and Dominick s Finer Foods Washington State: Albertsons, Safeway, Quality Food Center, and Fred Meyer Massachusetts: Stop & Shop, Shaws & Star, and Hannaford Colorado: Safeway, Albertsons, and King Sooper Inc. Georgia: Publix Supermarket, and Kroger California: Safeway and Albertsons 3 In our data we also observe data for Texas, however were unable to match the address of stores for this market and therefore drop Texas from our analysis 20

23 In this paper we study local market competition between grocery stores in large retail chains. To this end we needed to define local markets where local retail stores compete. We mapped all our 368 stores using a mapping software called Mappoint (registered trademark). We then created local markets using the US census tract information for competitive retail stores that were close to one another (within 12/15 minutes driving time) and were not separated by a national highway or geographical factors (e.g., rivers, mountains, etc.). The latter two observations are used to ensure that we make conservative definitions of local markets: for example, even if two grocery stores are a 12/15 minutes drive, if they are separated by a bridge consumers are unlikely to cross the bridge for groceries, therefore we do not consider this to be a local market. Based on these definition we find 34 local markets in all (6 in Illinois, 6 in Washington, 6 in Massachusetts, 4 in Colorado, 5 in Georgia, and 7 in California). Examples of local markets are shown in the appendix. Due to our conservative definition of local markets, 31 of our local markets are duopoly markets and 3 markets (in California) are three-firm markets. To determine the market size, we look at the total population in the the census tracts around the stores in the market. This results in areas with radii of about 2.0 miles for stores in the city (where census tracts are smaller) and about 5.0 to 6.0 miles for stores in the suburbs (where census tracts are larger). We use the total population in each of these local markets times the average consumption of each category to define market size for our later analysis. Note that we use a conservative definition of local markets for two main reasons. First, we only observe a sample of stores; therefore if we observe a Jewel Osco in Chicago without a Dominick s nearby, this could be because there is not a Dominick s or there is one and it is not in our sample. In most cases we determined it was the latter; therefore, viewing the Jewel Osco store as a monopolist would create a natural bias. Second, in cases were we do observe a Dominick s near a Jewel Osco, we clearly observe the entire set of competitors and therefore can define competition cleanly. We recognize that each retail chain might make these decisions at different time-periods though we need to define a uniform time period for all stores. Most stores make their assortment decisions every quarter. Since we observe one year of data, for purposes of the analysis, we divide it into 4 quarters. We also need to define when a product is sold. Again, to be conservative with this definition, we define a product as sold only if we observe multiple weeks of sales for the UPC in a quarter. We run two forms of robustness checks to ensure that this does not affect our results: first, we consider different definitions of quarters, and second we consider different definitions of products sold. In both cases we do not find similar results for these situations to the ones presented in this paper. 4.2 Categories In this subsection we will describe the 10 categories in this analysis and provide some descriptive statistics for these categories. A key advantage of these data is that we observe detailed product attribute information for each UPC. This allows us to construct a detailed attribute based demand system. However, in our data, the attribute descriptions are incomplete for private label products, and we restrict our attention to only non-private label (national) brands. The reason we choose 10 categories is to create generalizable results across these categories 21

24 to understand the differences in retailer decisions across categories. Table 1 below provides a summary of the total number of UPCs offered in the warehouse and the number chosen by stores. The numbers in the table represent averages across markets and quarters. As we can see there is quite a bit of variation in the number of choices in these categories, from 35 to 625 products. Notice, across the board that the size of the assortment for the retailers is quite large. In analgesics, retailers on average sell 87 distinct UPCs and in toothpaste they sell on average 153 distinct UPCs. Clearly models that consider all combinations to estimate optimal assortments will not be able to model these decisions. [Table 1 about here.] In the next few subsections we will describe the key attributes of each category in more detail. These attributes are important, as they provide information during the econometric estimation Analgesics In the analgesics category we consider all products that are classified as Internal Analgesics and consider only the UPCs that come in pills. The second restriction is to ensure the UPCs are comparable (pills versus syrups are not directly comparable). In all we have 348 unique UPCs in this category. The main differentiator in this category is the active ingredient of the pills, the four most popular active ingredients are Ibuprofen (brand name Advil), Acetaminophen (brand name Tylenol), Aspirin, and Naproxen Sodium (brand name Aleve). Description statistics for the product attributes are provided in Table 2 below. On average, the UPCs have about 63 individual pills. Only 16% have fewer than 10 pills and about 30% of the category has above 100 pills. 90% of the UPCs are unflavoured. Of the remaining the most common flavors are sweet, orange, grape, vanilla, and cherry. In this category there are three main forms of products: tablets, caplets, and gelcaps. These cover more than 90% of the market. Most pills can be sold in plastic bottles; the other main alternative is boxes. About 50% of the UPCs are classified as extra strength, about 32% are low strength. Only about 5% of pills are indicated for children; examples of these are junior Tylenol or children s Mortin. Our information about the active ingredient dosage is in ranges: most UPCs have between 200mg and 400mg doses. About 88% of UPCs are swallowed, other UPCs are dissolved, chewable or rectal. Most UPC claim efficacy for between 4 to 6 hours, 22% claim more that 6 hours, and 18% claim less than 4 hours. About 39% of the UPCs in the category are coated pills. We include fixed effects for active ingredient, manufacturer and brand. The reason we can identify these is: (1) not all products with a specific active ingredient are branded (e.g., not all Ibuprofen is Advil) and (2) manufacturers make more than one brand in this category. [Table 2 about here.] On average, a warehouse stores about 134 UPCs (ranging from 53 to 177) of these 348 UPCs in any quarter. A store selects on average about 87 UPCs (ranging from 36 to 139). Therefore on average a store selects 66% (ranging from 25% to 94%) of the available choices to store and sell. In the analysis, we observe 119 combinations of local markets and 22

25 quarters, each treated as an independent market. The total number of market and product combinations considered are 33,406. Price and share in this market are derived as price per pill and share of pills. Therefore the total market size is derived from assuming an average number of 5 pills consumed by each member of the population. In addition we add feature and display information, in this market most feature advertisements are classified as A or B and most displays are minor displays Canned Tuna We define the Canned Tuna category as all products defined by IRI as Canned Tuna 4. In all we have 182 unique UPCs in this category. Three main manufacturers, Bumble Bee, Chicken of the Sea, and Del Monte account for over 65% of the UPCs in the category. UPCs in this category differ by the size of the can, The median size is 6 oz and the range of sizes varies from 3 oz to 24 oz. Some Tuna is flavored (e.g., lemon, roasted garlic), though the large majority (90%) of UPCs are classified as regular. A majority of UPCs are sold in cans, though other forms of packaging include vaccum pouches, foil pouches, and plastic wrapped cardboard. The demand effects of flavor and packaging are unclear, though we would expect that flavoring and non-can packaging increase marginal costs. The actual meat is either classified as tuna or Albacore. Per Wikipedia 5, Albacore is prized food that can be found in tropical and temperate oceans, and the Mediterranean Sea. Albacore is the only type of tuna that can be classfied as white meat tuna in the United States. Based on this description we expect that Albacore is preceived as being of higher quality. Thus we expect that Albacore has a positive demand effect on consumer preferences and a higher marginal cost. Tuna can be cut in one of three main ways, chunky, solid, and steak 6, In our data most UPCs are classified as chunky. We expect tuna classified as steak to have higher demand and cost, In turn, we expect that chunky tuna to have a lower cost. For canned tuna, the meat can be stored in regular water, purified water (spring or distilled) or oil (could be vegetable or olive oil). We find that 63% of UPCs are stored in regular water. We expect that storing in purified water and oil does increase costs. The last attribute we have is he color of the tuna, which is either light or white. About 52% are classfied as light. Based on industry reports, we expect that light tuna has a lower demand and costs than white tuna. [Table 3 about here.] On average, a warehouse stores about 65 UPCs (ranging from 37 to 106) of these 182 UPCs in any quarter. A store selects on average about 52 UPCs (ranging from 27 to 86). Therefore on average a store selects 81% (ranging from 56% to 98%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent markets. The total number of market and product combinations considered are 16,352. Intrestingly we observe about the same number of UPCs sold during 4 When defining the canned tuna category we do not consider other canned sea food 5 The Wikipedia definition of Albacore can be found on 6 Other cuts include spreadable, fillet, and flaked 23

26 Lent and other quarters therefore we expect to find that the fixed cost of storing tuna is higher during Lent (as clearly the demand is higher during these periods) Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived from assuming an average 8oz volume consumed by the population. In addition we add feature and display information, In this market most feature advertisements are classified as A or B and most displays are minor displays Coffee The coffee category is defined quite broadly here; it includes coffee powder (instant or ground), coffee beans, and coffee substitutes. We include all products because these are all normally stored on the same shelf in the coffee aisle. The descriptive statistics for the key attributes in the coffee category are shown in Table 4 below. First notice the very high number of UPCs (1,366) in this category. Coffee is an unusual category due to the number of regional players in local markets. For example, if these 1,366 UPCs, there are only 600 available in Massachusetts (the most of any region). In fact, of these UPCs, 708 are available in only one region and only 132 are available in all regions. The 132 UPCs available in all regions are the large national brands (e.g., Maxwell, Folgers, Starbucks/Seattle, Nestle Taster s Choice). A few example of local manufacturers are Nicholas A. Papanicholas Coffee Co. in Chicago, Comfort Foods Inc. and Dunkin Donuts in Massachusetts, Barnies Coffee and Tea Co. 7 in Georgia, Caffe Trieste Superb Coffee in California, Silver Canyon Coffee based in Colorado, and Caffe Appassionato Coffee Co. located in Seattle, Washington. The coffee category has distinct high end and low end brands, the high end brands include Starbucks and the Seattle coffee company and the low end brands include some of the local regional players in the market. The average size of a UPC in our data is 12oz, though the sizes greatly from 0.4oz to 80oz. One of the main differentiators in our attributes is flavor. This can either be defined by the added flavor (e.g., hazelnut) or the region the coffee comes from. We expect positive demand effects for Colombian (a region known for its coffee) and espresso coffee and a negative demand effect for flavored coffee as these are normally from lower quality beans. We expect negative cost effects for regional (due to regional competition), flavored, and blended coffee (due to poorer quality beans). There are many packaging materials used for coffee. The most popular is cans, others include paper bags, foil bags, and glass jars. Our variable for caffeine stated indicated brands that are not sold as reduced caffeine or low or no caffeine. Under this definition a large majority of brands are classified as caffeinated. Only a very small percentage of UPCs (9%) are classified as organic. One expect that consumers do prefer organic products though they also cost more on the marginal cost side. About 49% of coffee UPCs are classified as ground coffee; the remaining include whole bean, instant and coffee subsitutes. The last of these only form a very small share of the UPCs in the market. Finally, observe that the big national brands and manufacturers only form a small share of the UPCs in this industry. [Table 4 about here.] 7 Barnies Coffee and Tea Co. is officially listed in Florida, though in the markets we consider we only observe sales in Georgia. Note they also have one retail outlet outside Florida, in Atlanta 24

27 On average, a warehouse stores about 301 UPCs (ranging from 212 to 392) of these 1,366 UPCs in any quarter. A store selects on average about 190 UPCs (ranging from 103 to 297). Therefore, on average, a store selects 63% (ranging from 36% to 86%) of the available choices to store and sell. In this analysis we observe 119 combinations of markets and quarters, each we treat as independent market. The total number of market and product combinations considered are 75,172. Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived from assuming an average 8oz volume consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B, and most displays are minor displays Mustard The mustard category is defined as a subcategory of the condiments category. We limit analysis to this subset of the category as our demand model does not account for consumers making multiple purchases or any bundling within a category, as is likely in the broad condiments category. The descriptive statistics for the key attributes are in Table 5 below. In our data we observe 322 mustard UPCs. Most brands have national distribution though there are some brands which are regional. For example, Chicago stores sell Ditka s Mustard, Massachusetts stores sell Olde Cape Cod. The median size of a UPC here is 9oz, with the largest UPC at 128oz and the smallest at 1oz. The main flavors in mustard are Honey (15% of UPCs), and Dijon (12% of UPCs). We expect the honey and dijon flavors to have a positive demand effect. A majority of the UPCs are sold in glass containers; other packages include squeeze bottles and jars. Given the mass-production of the two most popular units, glass and squeeze bottles we expect them to have lower costs. Mustard UPCs are mainly used by spreading, pouring or squeezing, other forms include diping. The largest manufacturer in this industry is Beaverton Foods Inc., who make the brands Beaver, Inglehoffer, and Old Spice. This is not a concentrated industry where the top eight manufacturers here only account for 111 of the 322 UPCs (34%) offered. [Table 5 about here.] On average, a warehouse stores about 74 UPCs (ranging from 38 to 131) of these 322 UPCs in any quarter. A store selects on average about 48 UPCs (ranging from 17 to 107). Therefore on average a store selects 66% (ranging from 18% to 94%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent. The total number of market and product combinations considered are 18,622. Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived by assuming an average 3oz volume consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B and most displays are minor displays Frozen Dinners The frozen dinner category is defined as the dinner subcategory of the frozen entrees category. The analysis is limited to frozen dinners for the following two reasons: (1) because 25

28 the items in the remainder of the category (e.g., frozen burrito and frozen breakfast) are not as comparable. 2) consumers may select multiple items in the category, for example, consumer may purchase dinner and burritos. Such multi product purchasing is not captured in our demand system. The descriptive statistics of the key attributes are in Table 6 below. In our data we observe 332 UPC of frozen dinners. The median size of a UPC here is 17oz, with the largest UPC at 64oz and the smallest at 4.4oz. Here we have classified the contents as either meats (pork or beef), chicken, or other. The other are either vegetarian or fish. A majority of the UPCs are sold in plastic containers or vacuum packed, other packaging includes cardboard and foil. We expect that vacuum packed UPCs will have higher demand (as they preserve the product better) and higher costs. These dinners are with sauce or cheese added which are captured in our attributes. Finally UPCs can come pre-cooked or require some cooking by the consumer. We expect that pre-cooking will be greater in demand. The largest manufacturers in this category are Hormel Foods, Smithfield Foods Inc, Tyson Foods Inc, Perdue Farms Inc., and Harry s Fresh Foods. In this category we don t have detailed information about cut or style of cooking for each UPC. [Table 6 about here.] On average, a warehouse stores about 58 UPCs (ranging from 27 to 88) of these 332 UPCs in any quarter. A store selects on average about 47 UPCs (ranging from 19 to 78). Therefore on average a store selects 80% (ranging from 50% to 100%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent. The total number of market and product combinations considered are 14,376. Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived by assuming an average 5oz volume consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B and most displays are minor displays Ice Cream The ice cream category is one where our attribute data is the most limited. This is because ice creams UPCs are classified mainly by flavor. The descriptive statistics of the key attributes are provided in Table 7 below. In our data, we observe 886 UPCs of ice creams. Most of these are from national manufacturers. The median size of a UPC here is 3.5 pt. (pints), with the largest UPC for 10 pt. and the smallest for pt. The most sold flavors of ice cream are vanilla and chocolate, these account for 40% of the UPCs. Other flavors have been classified as assorted (multiple flavors), fruit, and all other (this includes mint, cookie etc.). An innovative new design for UPC storage in this category is sqround (square and round) packaging. In our data this is used for 31% of the UPCs. 13% of the UPCs are classified as low sugar, and 21% of the UPCs are classified as low fat. The direction in which these affect demand is unclear. The largest brands in this category are Breyer, Ben and Jerry s, Haagen-Dazs and Dreyers Edys. The first two are distributed by Unilever and the latter two are distributed by Dreyers. [Table 7 about here.] 26

29 On average a warehouse stores about 253 UPCs (range is from 181 to 365) of these 886 UPCs in any quarter. A store selects on average about 199 UPCs (range is 113 to 307). Therefore on average a store selects 79% (range is from 40% to 97%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent. The total number of market and product combinations considered are 63,347. Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived from assuming an average 64oz volume consumed by the population. In addition we add feature and display information, in this market most feature advertisements are classified as A or B, and most displays are minor displays Orange Juice The orange juice category includes only refrigerated orange juice. This limited category definition (rather than all fruit juices) ensures we only consider real substitutes, and that consumers make only one purchase from the category. The descriptive statistics of the key attributes is in Table 8 below. There are 126 unique UPCs in our data. The median size of a UPC is 64oz and the range is between 8oz and 128oz. Refrigerated orange juice UPCs are sold in bottles, jugs and cartons, with the latter being the most popular. The three main attributes that distinguish UPCs are: first, whether or not the UPC is made from concentrate, second whether or not artificial sugar is added, and third whether or not additives are added (for example, extra calcium). We expect that not from concentrate and natural sugar have positive demand increases and negative cost affects. The main manufacturers in this industry are Tropicana, Minute Maid and Florida, who account for about 58% of the UPCs in this market. [Table 8 about here.] On average, a warehouse stores about 53 UPCs (ranging from 34 to 61) of these 126 UPCs in any quarter. A store selects, on average, about 48 UPCs (ranging from 33 to 59). Therefore, on average, a store selects 92% (ranging from 63% to 100%) of the available choices to store and sell. We notice that the average percentage of warehouse stored items sold is the highest in this category, however we observe only 7% of retailers stocking all warehouse UPCs. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent. The total number of market and product combinations considered are 13,142. Price and share in this market are derived as price per 16oz and share of volume. Therefore the total market size is derived by assuming an average 50x16oz (about 1 64oz carton per household per week) consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B and most displays are minor displays Paper Towels The paper towel category is different from the other categories studied here as it considers larger sized UPCs that take more shelf space than the others. There are 147 unique UPCs in our data, details are given in table 9 below. 27

30 We split the UPCs for paper towels into three roughly equal sizes and labeled them small, medium and large. The measure for units in a UPC is based on the total length of paper sold, a value of 1 is about 1 roll of between strips 8 of paper towels. The median size in our dataset is about 2 rolls of 90 strips. The two attributes that we expect to have positive demand effects are extra absorption (about 35% of UPCs) and extra strength (about 26% of UPCs). Paper towels are either white or have some form of print. We find that about 49% of UPCs are white in color. The size of sheets in papertowel UPCs is either regular, large or Upick. In the Upick UPCs, there are no predefined sheets and the consumers can tare the paper towels depending on their need. The three main manufacturers in this industry are P & G (Bounty), Kimberly Clarke Co. (Scott and Kleenex Viva), and Georgia-Pacific Co. (Brawny and Sparkle). This is a very concentrated industry, where these three manufacturers account for 89% of the UPCs in this category. [Table 9 about here.] On average, a warehouse stores about 36 UPCs (ranging from 18 to 68) of these 147 UPCs in any quarter. A store selects, on average, about 27 UPCs (ranging 11 to 54). Therefore, on average, a store selects 78% (ranging from 32% to 96%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each treated as independent. The total number of market and product combinations considered is 8,879. Price and share in this market are derived by price per unit (about 1 roll of between strips) and share of volume. Therefore the total market size is derived by assuming an average 1 roll consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B and most displays are minor displays Toothpaste The toothpaste category is also a broadly defined category in our data. The category includes children s and toddler s toothpaste. Unlike the other categories studied here, there are very few regional manufacturers in this market. The details for this category are described in table 10 below. There is a great variety in sizes of toothpaste UPCs in our data from the travel kits to the large toothpastes. To capture this variation, we assign UPCs as tiny, small, medium and large. The median size of a UPC is 6oz, with the largest UPC at 42oz and the smallest at 0.75oz. The most popular additive in the UPCs is Fluoride. We also classify UPS with multiple additives separately. Our expectation is that consumers prefer multiple additives. Mint is the most popular flavor for toothpaste. Most toothpaste UPCs are sold in tubes, of the remaining 7% are sold in bottles. Toothpaste UPCs are marketed as whitening, tartar protection, or both. About 9% of our UPCs are listed as adult only and about 8% are listed as children only, the remaining UPCs can be used by the entire family. The top manufacturers in this market are P & G (Crest and Oral-b), Colgate Pamolive, Church & Dwight Co. Inc. (Close Up, Mentadent and Arm & Hammer), J. & J. (Reach and Rembrandt) and Tom s of Maine Inc.. Additionally we seprate out the Gerber brand as they make unique products for toddlers in this market. 8 In the paper towel category the size of strips varies across UPCs 28

31 [Table 10 about here.] On average, a warehouse stores about 217 UPCs (ranging from 115 to 355) of these 664 UPCs in any quarter. A store selects, on average, about 153 UPCs (ranging from 61 to 265). Therefore, on average, a store selects 71% (ranging from 30% to 93%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each we treat as independent. The total number of market and product combinations considered are 54,299. Price and share in this market are derived by price per 16oz and share of volume. The total market size is derived by assuming an average 2oz volume consumed by the population. In addition we add feature and display information, in this market most feature advertisements are classified as A or B, and most displays are minor displays Cookies The final category we consider is cookies. The attributes for the UPCs in this category are shown in Table 11 below. First notice that this category has more than double the number of UPCs in any other category in our data. There are 2,620 unique cookie UPCs in our data. The median size for a cookie UPC is about 9.1 ounces which equates to between 24 and 26 standard sized cookies. The package sizes have a large range in our data, from 0.7oz (about two standard sized cookies or one large cookie) to 64oz (about 172 standard sized cookies). The most popular flavor for cookies is chocolate followed by vanilla. Cookie UPCs are commonly in boxes (31% of UPCs), bags (20% of UPCs) or trays (17% of UPCs). Other forms of packaging include plastic wrap, cups and buckets. In terms of demand and costs, based on industry reports, we expect the demand of boxes as containers to be the highest. And we expect boxes and tin cans to be the most expensive, and bags to be the least expensive. Cookies are of three main kinds: either classified as regular cookies (73%) or sandwich cookies (11%) or sugar wafer cookies (6%). Most cookies are round in shape (50%). Other shapes include square, assorted, alphabet, flower, and animal. The most popular forms of cookies are patties, pieces and bars. About 12% of our UPCs are seasonal cookies. These include Christmas, Thanksgiving, Halloween, and Passover cookies. Cookies can have different bases. The most common are unflavored or flavored bases. Others inlcude chocolate chip, shortcake, oatmeal, macaroon and biscotti. We expect that shortcakes, oatmeal, and biscotti have the highest positive demand affects, and the highest costs. The cookie category is not concentrated, the top manufacturer, Alteria, produce only 9% of the category UPCs. The high end manufacturers here are Alteria, Archway, Kellogg, Campbell and Lofthouse and we expect these to have a positive demand effect. The value manufacturer here is McKee which we expect this to have a negative average demand effect. [Table 11 about here.] On average, a warehouse stores about 626 UPCs (ranging from 430 to 861) of these 2,620 UPCs in any quarter. A store selects, on average, about 373 UPCs (ranging from 197 to 565). Therefore, on average, a store selects 60% (ranging from 37% to 78%) of the available choices to store and sell. In the analysis we observe 119 combinations of markets and quarters, each 29

32 treated as independent. The total number of market and product combinations considered are 156,470. Price and share in this market are derived as price per 16oz and share of volume. The total market size is derived from assuming an average 16oz volume consumed by the population. In addition we add feature and display information. In this market most feature advertisements are classified as A or B, and most displays are minor displays. 4.3 Assortment summaries In this paper, we assume that retailers make retail assortment decisions every quarter (13-14 weeks), more over that these decisions are made at the individual store level. To support some of these assumptions, we provide some summary statistics below to show that assortment decisions are indeed made by stores and not chains and that these decisions do vary over time. Table 12 below shows the variation of assortment decisions within stores in the same chain. For this we consider two categories, analgesics and coffee 9, and show the number of common UPCs sold in these stores. This table can be read as follows, the 9 in the second row represent the fact that of all the UPCs sold in all Dominick s Finer Food (DFF) stores in quarter 1, 9 are sold in only 1 of the 6 stores in competitive markets. In this table we can see that while 51 UPCs are sold in all 6 stores, there are 61 UPCs 10 are not sold in all 6 stores, therefore 54% 11 are not sold in 5 DFF stores. Across the board we find that more that 50% of UPCs are not sold in all stores. This supports the belief that stores make individual decisions. [Table 12 about here.] To consider a more specific example to see the difference in stores in a chain, we consider the case of biscotti UPCs in the cookies category. In our 6 markets in Chicago, 4 are suburban markets, one north side of the city (Lincoln Park) and the final one is on the south side of the city. This first five of these markets are in affluent neighborhoods, the median household income in three suburban neighborhoods and the north Chicago neighborhood is between $60,000 and $74,999, and is between $75,000 and $99,999 in the other suburban neighborhood. In contract, the south side market has a much lower median household income, it is between $25,000 and $29,999. We find that the Jewel Osco stores in the affluent markets store 62% of the biscotti UPCs in the warehouse, whereas the south side Jewel Osco store only sells 19% of these UPCs. We find the same trend in other speciality cookies. For example, the affluent neighborhood stores store 37% of the macaroon cookies, while the south side store sells only 14% of these UPCs. On the flip side, the store on the south side of Chicago stores more cookies (80% of offered UPCs) from McKee Food Corporation, a company known for its value 12, while the stores in affluent neighbourhoods store only 24% of these UPCs. 9 The trend displayed by both these categories holds for all categories in our data is calculated as 9 sold in 1 store + 11 sold in 2 stores + 8 sold in 3 stores + 12 sold in 4 stores + 21 sold in 5 stores 11 54% is calculated as 61/(61+51) 12 McKee Food Corporation is the only manufacturer that claimed value as its brand promise on the website 30

33 To show that retail stores do make this decision differently in every quarter, consider Table 13 below/ This table shows the total number of unique UPCs sold in each retail store for four chains in our data, in the analgesics category 13. To read this table consider the first row. It shows that in the first Jewel Osco store, there are a total of 150 analgesics UPCs sold across all quarters, of these 55% (or 82 UPCs) are sold in all four quarters, while the remaining UPCs 45% (or 68 UPCs) are not sold in at least one quarter. Based on this table we infer that on average about 61% of retail store decisions do not vary across quarter, this ranges from 40% to 77% in individual stores. [Table 13 about here.] Note that this percentage does vary by category, one category in which we were surprised to see less variation is canned tuna. Canned tuna does have an increase in demand during the Lent months (in Quarter 1 of our data), however the number of UPCs stored by retailers does not vary too much across time. The percentage of of UPCs common in all quarters for a store in this category is as high as 88% (for one Jewel Osco store in Chicago). 5 Empirical results In this section we will first present the estimates from all 10 categories, we will then summarize these estimates and key learnings. 5.1 Analgesics Table 14 below shows the mean posterior estimates of the demand and supply model in the analgesics category. The demand model shows the following effects. Customers have a nonlinear preference for the number of pills in a UPC, that is, customers prefer small UPCs with fewer than 10 pills and large UPCs with more than 100 pills. Customers prefer for caplets, followed by gelcaps, and then tablets. Plastic and box containers are most preferred; note here the other alternatives here are envelopes and blister packs. Regular strength pills are most preferred, a reason consumers may not like extra strength pills is that consumers also have a preference for pills without caffeine. Additionally we find that consumers prefer pills that last for more than six hours. The fixed effects for active ingredient, manufacturer and brand reveal that consumers most prefer the manufacturer producing the pill. We also find that displays and feature advertising does increase demand for the products. On the supply side we find that smaller UPCs are more costly (per pill), and plastic and box containers are more expensive. Our estimate of the price elasticity in this category is a higher than we expected. The average elasticity is estimated as -1.63, this results in high expected profit margins for the retailer (about 77%). We believe this is high for this industry, where the expected margins are between 30% and 50%. We will review this for each category. [Table 14 about here.] 13 While results are shown only for the analgesics category, all other categories follow a similar trend 31

34 Table 15 below shows the mean posterior estimates for the fixed costs by market and by quarter. We find that the fixed costs are quite low in this category, about $1.93 to $3.41. In order to interpret these numbers, consider the fact that the lowest selling UPCs in the markets sell for an average $4.3 of revenue per quarter. For example, in a Dominick s Finer Foods store in Chicago the lowest selling UPC is a two pill aspirin peg card manufactured by Lil Necessities. This pack normally sells for $0.75 and in each quarter sells only about 5 to 6 units. The fixed cost estimate is the marginal category profit increased by including this UPC in the assortment. Therefore this is different from the actual revenue of the UPC in two important ways. First, we consider profit to the retailer rather than revenue. Second, had this UPC not been sold by the retailer, some customers might have switched to other brands in the assortment (rather than switching out of the market). To understand the estimate, we can compare it to industry standards. The fully loaded cost 14 per retailer square foot is reported to be between $7.5 and $13 per square foot per month 15. Using some back of the envelope calculation, our lowest selling UPCs normally take about 2 inches by 3 inches by 0.1 inches per UPC. In the Dominick s store these UPCs are stacked on top of each other and take about 2 inches by 5 inches of store facing space, therefore we would estimate the cost per square foot to be about 12 times our fixed cost estimate (divided by 3 to convent the number from a quarter to a month) that would result in between $7.73 and $13.64 per square foot per month, which is in line with the industry standards for retail space. [Table 15 about here.] In our fixed cost calculation we only consider the fixed cost of the last UPC added. An alternative to this is to consider the marginal profit for each UPC in the assortment. We consider this alternative in the counterfactual section of the results. 5.2 Canned Tuna Table 16 below shows the mean posterior estimates for demand and supply parameters in the tuna category. In general consumers prefer small UPCs to large UPCs. However, the preferences across sizes is non-linear the total onces of tuna. On the cost side, smaller UPCs are more expensive than larger UPCs, this is also non-linear in total ounces. We find that flavored tuna is preferred to regular tuna and is estimated to be cheaper for the retailer. Similarly, tuna sold in cans has on average a negative effect and is estimated to be significantly cheaper for retailers. Albacore is believed to be a better variety of tuna and consistent with this we find that it has higher demand and costs. We find that tuna cut as steak has a higher demand and also costs more. Interestingly we find that tuna stored in purified water or oil (versus in water) does not have a higher demand effect though do cost more than tuna in normal water. We find positive demand effect for the major manufacturers and positive demand effects for display and feature advertising (expect for C features). We also find that display and feature advertising is normally associated with lower costs, suggesting that these might be partially financed by manufacturers. 14 This may be an accounting cost rather than an economic cost 15 Fixed cost numbers are estimated on many websites such as and much inventory per squa 32

35 We find the average price elasticity in this category is -3.31, which results in an average profit margin of 36% for the retailer. This estimate is consistent with margins in retailing. [Table 16 about here.] The fixed costs estimates are displayed in Table 17 below, which shows that the fixed costs are between $2.50 and $6.10 for the last UPC added. Another back of the envelope calculation suggests that the smallest UPC (normally a 4 oz can) takes up about 3 inches by 3 inches by 1 inch of retail space. Assuming that the inventory of such UPCS are stacked one on top of the other. We estimate that a square foot of retail shelf space can hold 12 such stacks and therefore the fixed cost per square foot per month is between $7.50 and $18.30, which is consistent with retailing estimates for retail space. Additionally, we find that the fixed costs are higher in quarter 1, which is during Lent. This is because demand is higher during Lent though we do not find a large increase in total number of UPCs stored. 5.3 Coffee [Table 17 about here.] Table 18 details the posterior demand and cost estimates for the coffee subcategory. We find that consumers have a preference for smaller pack sizes, though preferences are non linear in total quantity. The costs follows a more clear monotonic pattern, where smaller pack sizes are more expensive than larger pack sizes. We find that consumers have a preference for regular, espresso and Colombian roast, while flavors have a small effect on costs. We find consumers have a negative preference for coffee sold in a can, but it costs the retailer less. Organic coffee is interesting as consumers have a negative preference for organic coffee and it costs more for the retailer. The brand and manufacturer dummies, suggest that consumer preferences are brand based rather than manufacturer based in this industry. Finally, the display and feature ads increase demand and are supported by manufacturer this can be seen by the lower costs associated with displays and features. We find the average price elasticity in this category is This results in an implied profit margin for the retailers of about 41%. Once againm this is roughly the normal profit margin in retail. [Table 18 about here.] The fixed cost estimates for the coffee category are displayed in Table 19 below. These estimates suggest that even though the coffee category has a much higher assortment size, as compared to analgesics and tuna the fixed costs are similar. We find the fixed cost are lower in the first quarter this suggest that retailers had a lower minimum threshold to store products in the first quarter of our data. [Table 19 about here.] 33

36 5.4 Mustard The demand and marginal cost estimates in the mustard category are shown in Table 20 below. These estimates show that consumers do have a preference for smaller sizes, which are more expensive for the retailer. Consumers prefer the regular and Dijon flavors, and prefer sweet mustard. While spreadable, pourable, and squeezable mustard are the most sold varieties, the most preferred in our data are the others which include dippable. These are believed to be of higher quality. Consistent with this, spreadable, pourable, and squeezable mustard are cheaper for the retailer. We observe consumers do have preferences for specific manufacturers, with the largest preferences being for Unilever and Altra. As in other categories we find that features and displays have a positive effect on demand. The price elasticity for this category is estimated as and the estimated average margin in this category is 50%. Once again this is in the expected margin range in retail. [Table 20 about here.] Table 21 below show that the fixed costs estimates in this category are similar to those in coffee, tuna and analgesics. This is as we expected, as the sizes of the UPCs across these categories are quite similar. 5.5 Frozen Dinners [Table 21 about here.] Table 22 below shows the demand and marginal cost estimates in the frozen dinner category. As in other categories we observe, customers prefer smaller units though retailers pay a higher price for these UPCs. With regard to the products attributes we observe, that customers do not prefer items with cheese added and pre cooked items, but they do prefer seasonal items. We also see that customers have a preference for UPCs manufactured by Perdue, Tyson and Hormel. We find that displays and features do have a positive effect on demand. The average estimated price elasticity in this category is This results in an average implied mark up of about 56%. This is a little high side for retail, though it is possible that markups are higher in specialized categories like frozen dinners. [Table 22 about here.] Turning to the fixed costs, in Table 23 we see that the fixed costs estimated for the frozen dinner category are significantly higher than those of shelf stable categories. This is an intuitive result as we would expect the cost of frozen food real estate in a retail store to be higher than that for the other store space. Here we find that these costs are about 5 times higher for the freezer than the shelf. [Table 23 about here.] 34

37 5.6 Ice Cream As we mentioned in the data section, ice creams are one category where we observe limited attribute information. The demand and costs estimates in Table 24 suggest that customers do not have a preference for smaller units, though these do cost more for the retailer. Also we find that vanilla is the most preferred category and fruit flavored ice creams are the least favored. Interestingly we find that the sqround containers do not increase demand though these do indeed cost more. We find negative effects of low sugar and fat free. Ben and Jerry s and Haagen-Dazs are the two most favored brands. Also we do find that display and features do increase in demand. We find the average price elasticity is and the implied markup in this market is 39%. Both of these are very consistent with standard retailing beliefs. [Table 24 about here.] The fixed costs estimates for ice cream are shown in Table 25 below. Interestingly, the fixed cost estimates for ice cream are much lower that than for those for frozen dinners. We found this quite surprising as both categories are normally stored in the same aisle. To check this is a feature of our data and the model imposed on the data. We consider the raw revenue numbers from the lowest selling ice cream UPC in each market and find that the average lowest selling UPC only sells on average $9.60 per quarter. With a 39% margin we therefore expect then profit from the lowest selling UPC to be about $3.75. Now some of this is not incremental to the market and therefore we expect the fixed cost number to be less than %3.75. Our fixed cost estiamtes are consistent with this rational. Therefore it appears that retailers use different cost metrics to evaluate ice cream and frozen dinner categories. One possibility is that ice cream is seen as a loss leader to drive consumer store visits. 5.7 Orange Juice [Table 25 about here.] The demand and marginal cost estimates from the orange juice category are shown in Table 26 below. Here we observe that customers do have preferences for the key attribute that defines premium orange juice, there are (1) the UPC is made with fresh or not for concentrated orange juice. (2) the UPC does not have sugar added. Additives (e.g, added calcium) do not influences demand. In general, Tropicana is the most preferred brand. We find that displays do increase demand, though do not get significant results for feature advertisements. We find the average price elasticity in this category is and the average margin is estimated to be 78%. This markup percentage is a bit higher than we expected. [Table 26 about here.] The fixed costs in the orange juice category are shown in Table 27 below. Consistent with our expectations, these are higher than the shelf stable categories. This is because the orange juice category require refrigeration. This provides additional evidence that the retailers consider different fixed costs for refrigerated and shelf stable categories. [Table 27 about here.] 35

38 5.8 Paper Towels The demand and supply estimates for the paper towel category are shown in Table 28 below. As in other categories, consumers do have a preference for smaller UPC, though trend is non-linear in UPC size. Retailer costs are monotonically decreasing in sizes. Customers have a preference for plain white paper, which we estimate also costs the retailer more. We find both mega size paper and Upick (where the consumers can pick the size of each sheet) increase demand. The Upick UPCS are also associated with lower costs. Extra strength UPCs have a higher cost and are more preferred by customers. We find the three main manufacturers in this industry do have higher demand and charge higher prices. Finally, we find that displays and feature advertisements increase demands and are associated with lower costs. We find that price is quite elastic in this category with an average elasticity of about This results in profit margins of about 32% on average. These results are consistent with much of the retailing literature. [Table 28 about here.] The Table below (table 29) contains the estimated fixed costs for the paper towel category. These estimates and much higher than the estimates for all the other shelf-stable categories. This is to be expected due to the larger UPC sizes in this category. This provides evidence that retailers do indeed consider the size of UPCs when allocating retail space across categories. 5.9 Toothpaste [Table 29 about here.] The demand and marginal cost estimates for the Toothpaste category are shown in Table 30 below. These estimates indicate that consumers do have a higher utility for smaller toothpaste sizes, particularly the travel sizes. However these smaller packages do tend to cost more as well. We estimate that added fluoride has negative demand while multiple additives have positive demand and cost. One reason for this result could be that fluoride is considered a standard in this industry and all UPCs are expected to have this addition as a minimum requirement. We find that mint flavored UPCs have a positive demand and cost effect. Consistent with our expectations, we estimate that the UPCs with more indications (whitening and tartar) have higher costs than UPCs with only the tartar indication. We estimate that white colored toothpaste has the highest demand effects and also the highest cost. We estimate toothpaste UPCs that serve only adults or children have a negative demand effect. In terms of manufacturers, we find that Gerber, who make toddler toothpastes, charges a significantly higher wholesale price. As in other categories, we find that display and feature ads have positive demand effects and are associated with some trade dollars from the manufacturer. In this category we estimate the average PE is -1.92; this is a bit lower that we expected and results in about 68% expected margins for the retailer. [Table 30 about here.] 36

39 The fixed cost estimates for the toothpaste category are displayed in table 31 below. These estimates suggest that the average fixed costs for toothpaste are about $2.50 on average. Again the lowest profit UPC in the toothpaste category tends to be the small travel toothpaste. A back of the envelope calculation for this category does suggest that the cost of retail space is about $10 per square foot per month (assuming the dimensions of this UPC are about 3 inches by 2 inches by 1 inch and they are stored one above the other). This estimate is consistent with trade reports for retail space Cookies [Table 31 about here.] The demand and supply estimates for the cookies category are shown in Table 32 below. Consistent with the other categories we, find that consumers prefer smaller units, and on the cost side we find that larger UPCs are less expensive per unit. We estimate that boxes of cookies have the highest demand and are the most expensive for retailers. Also we find that bags of cookies are the least preferred packaging. We find customers have the greatest preference for cookies and sandwich cookies, and the least for sugar wafers. In terms of shapes, we find that the standard geometric shapes (round, square) are preferred less than other shapes of cookies like alphabets. Interestingly, we do not find an increase in demand for seasonal cookies, though we do find an increase in the cost for these cookies. As expected, the most preferred bases for cookies are shortcakes, oatmeal and biscotti. Also, there are positive demand effects for the higher quality manufacturers and negative ones for the lower quality manufacturers. Note that the estimates for Manufacturer Rab are unstable due to a lack of observations for this manufacturer. Finally, as in all other categories, we find that displays and feature ads are effective and are partially sponsored by manufacturers. We find the average price elasticity for this category is -2.82, which results in an average markup of about 45% for this category. This markup is inline with retail industry expectations of about 30% to 50%. [Table 32 about here.] Table 33 below contains the fixed cost estimates for the cookies category. These results suggest that the cookie category does have the smallest fixed cost of any category studied in this paper, the average fixed cost estimated as $1.30. We argue that this is consistent with our expectation, as the lowest selling UPCs are normally the small UPCs (about 2oz packets). These UPCs are normally of the two cookies in a plastic wrapper variety and occupy little self space, and are often stored in racks on the retail floor. [Table 33 about here.] 5.11 Importance of local markets In the results section for each category we have shown only the mean posterior estimates of the overall distribution. One advantage of our methodology is that we have posterior estimates for each market and each quarter. For an example of these preference, consider 37

40 the example from the data section, where we had observed that for five markets in the Chicagoland area are located in high income neighborhood and the sixth market was in a low income one. We notice that the Jewel Osco store in the less affluent neighborhood sell fewer UPCs of biscotti in the cookies category. We hypothesized that this was due to the inherent preferences for biscotti in this market. Consistent with this hypothesis we estimate the preference for biscotti in a suburban neighborhood is 1.48, while the estimate for the store in the low income area is On the flip side we noticed that the less affluent store stored more products from the value manufacturer McKee. In our estimates the mean demand preference for this manufacturer in the less affluent market is 0.62, while the mean preference for McKee in the other five markets is -3.16, -1.27, -3.12, -3.36, and respectively. These data and estimate provide some intuition for the fact that local demand preferences play an important role in a retailer s assortment selection. The advantage of considering local markets in our analysis is that we capture the local demand preferences, costs and competition differently. When we consider our counterfactual results in the next section we will use these local market estimates to see the impact of changes in markets. From a managerial point of view this allows us to give advice to retailers and manufacturers at the local retail store level Importance of modeling assortment decisions We estimated our model for three categories without accounting for the assortment decisions made by retailers. In this model we model logit demand, and account for endogenous pricing by simultaneously modeling marginal cost. The only divergence from the complete model is that we do not consider any information from the assortment decisions in our estimation. The three categories where we run our analysis are: paper towels, ice cream and analgesics. For paper towels, without considering assortment decisions, the average price elasticity estimated as This is about half of the estimated elasticity in the full model. This estimate implies the profit margins for a retailer in the paper towel category are about 68% which is almost three times that of the full model. Therefore we believe our full model does provide better estimates of price elasticity and retail markups. In addition to the price estimate, not considering assortments does impact the other demand and supply estimates. For the ice cream category we find find a similar result, where the price elasticity is estimated as -1.36, as opposed to with the full model. The model without consider assortments to be endogenous results in an estimated profit margin of 76%, which is almost double that of the full model. Again we believe the estimates of the full model are more appropriate in this case. The third category we choose is a category where our full model estimated a low price elasticity and high margin: analgesics. A restricted model estimates the price elasticity With the estimated price elasticity less than -1, the estimated profit margins are greater than 100%. Here theestimated profit margins are about 140% implying that retailers are subsidized to sell products. This seems very unlikely and the estimates from the full model are clearly more appropriate in this case. To understand the managerial impact of not modeling assortment decisions in this setting we consider the decisions retailers would make with the biased estimates. Here we would recommend that retailers in general should (1) increase prices, as consumers are not as sensi- 38

41 tive to changes in price, and (2) store larger assortments, as customers will buy their favorite product independent of price, therefore availability is important. Given the magnitude of the difference between the estimates we believe that modeling assortment decisions is very important to accurately capture consumer preferences. We also believe that assortment decisions could be one reason that researchers have noticed high price elasticities (low absolute value) in store data in the past. As a boundary condition we note that there are situations when modeling assortments would be inappropriate. First, with weekly demand models, the assortment model is misspecified, as assortment decisions are not taken weekly. Second, in models with city or RTA level aggregated data, here we are aggregating decisions across stores and therefore cannot specify an assortment model correctly Summary across categories Table 34 provides a summary of the average store level fixed cost estimates across the 10 categories we study. We notice that for seven of the categories, we observe small estimated fixed costs. Six of these categories, namely Tuna, Coffee, Analgesics, Toothpaste, Mustard, and Cookies, are shelf-stable categories with small package sizes. In particular, the UPCs that represent the lowest selling UPCs are small package sizes. We find that the shelf-stable category with larger package sizes (paper towels) and refrigerated categories (orange juice and frozen dinner) have higher fixed costs. These are higher by an order of magnitude of about 6. This is an intuitive finding, as larger UPCs take up more store shelf space and refrigerated shelf-space is more expensive. The only category that does not follow this intuition is ice cream. We expected ice cream to have a higher fixed costs 16. One reason could be that the retailers views ice cream as a loss leader to drive store traffic, and therefore are willing to over-stock ice cream, as it has positive externalities to other categories. Additionally in this table we include the average assortment size, and estimated price elasticity. We observe that neither of these two columns describes the differences in fixed costs across categories. Consider frozen dinners and mustard, they both have similar assortment sizes and price elasticity, and yet have vastly different fixed costs. Similarly, Orange juice and Analgesics have similar estimated elasticity and yet highly different fixed cost estimates. [Table 34 about here.] Another view of the cross-category effects is to consider the correlation of the fixed cost 17 for a store across the 10 categories. Here we find that, in general, the correlations are positive and significant, suggesting there is some underlying store characteristic that impacts all categories. This could be the size of the store that impacts all categories. Interestingly we find that ice cream, coffee, and tuna, are correlated with the most other categories. This could suggests that the assortment sizes for these 3 categories are driven more by store size than the other categories. Also, cookies and analgesics are least correlated with other categories. We believe this is driven by the fact that there is less variation in assortment costs across stores in these categories. 16 Notice that in the ice cream results section, we confirmed that this is an attribute of the data and not of the model imposed on the data 17 The fixed cost for a store is the average across the quarters 39

42 5.14 Summary of the estimates [Table 35 about here.] Overall, the estimates of our models across all 10 categories show the following key results. First, with regard to the demand and supply parameters, we believe our model does provide believable estimates, suggesting that we are correctly capturing the key features of these categories. We stress this because the demand and supply are the key inputs to the assortment problem. Second, we find that estimated price elasticity and profit margins are consistent with what is observed in the retailing industry. For seven of our ten estimated categories, we find that price markups are around the 30% to 50% range. Moreover we find that incorrectly estimating demand, without explicitly accounting for assortment decisions, tends to bias price elasticity upwards (less negative). This leads to very high price markups, which can be greater than 100% in some categories. Third, when looking at retailer assortment decisions we show with back of the envelope calculations, that our fixed cost estimates are close to the estimates of retailing monthly rents for space. This suggests that retailers keep adding products to the category untill the last product justifies the space needed to store the product. In our counterfactual analysis we will consider the effect of reducing the assortment sizes on retailer profits. Fourth, across all categories, we find that fixed costs depend on two main category characteristics: the size of products in the category, and refrigeration requirements. Our estimates suggest that six categories (Tuna, Analgesics, Mustard, Coffee, Cookies, and Toothpaste) with similar shelf-stable UPCs sizes have similar estimated fixed costs. We find that the paper towels category with larger shelf-stable UPCs have higher fixed costs. And so do the categories (orange juice and frozen dinners) that require refrigeration. The only category where we would have expected higher fixed costs is ice cream, though we show that our estimates are driven by the raw data. In the next section we will discuss how we can use these estimates to make suggestions for improving retail assortment decisions. 6 Counterfactual predictions 6.1 Changing current assortments The analytical model described in this paper allows us to construct optimal assortments to provide normative prediction for retailers. In this section we will show an example of the use of this model for managerial decision making. Here we consider the decision for the Tuna category manager at a Jewel Osco store in Chicago. The category manager currently stores 63 UPCs of tuna on the store shelf and wants to understand the impact of changing this decision on category sales. To analyze this situation we define the marginal profit of each assortment size as follows. The marginal profit of an assortment of size n is the total profit from the optimal n UPC assortment with optimal pricing minus the total profit from the optimal assortment (with reoptimizing prices) of size n 1. In general there are are three effects that we consider 40

43 when calculating this: first, the customers who now purchase from the category with the expanded assortment, second, the customers who change their purchase decision, and third, the ability of retailers to change prices with large assortments. Notice that by definition in our setup the marginal profit number is always positive. The figure below (Figure 1) shows the marginal profit for each UPC added in this category. Here we include two lines: the first line (in blue) is the raw data for total revenue from each UPC (sorted from 1 to 63), and the second line (in green) is the estimated marginal profit for each UPC added to the assortment. In this chart we notice that the marginal profit curve is always below the actual revenue, this is by definition as profit accounts for costs. Observe that the marginal profit curve is more concentrated than the revenue curve, in that the first 30% (10 UPCs) can generate 78% of the total profit, while it only acounts for 66% of the revenue. To understand this result, remember that if the retailer sold only 10 UPCs, they can reopimize the price to charge for these UPCs. This optimal price will be lower than the current price charged by the retailer and so will result in more demand. Notice that the marginal profit curve has a long tail, where 42 of the 63 UPCs have a marginal profit of less than $100 per quarter. A retailer can use this chart to understand the effect of changes in their assortment on expected profits. In particular, if the retailer takes the view that a UPC must have at least $50 in marginal revenue to be included in the assortment, we can advice which UPCs should be kept and estimate the impact on profit. In this case we observe that the retailer will store 29 UPCs (46%) and can expect to capture 88% of total the profits from the category. A question often raised in marketing is understanding the impact of UPC reductions. Here, consider a situation where the category manager wants to understand the effect of reducing the tuna assortment size by 25%. We find that with reoptimizing the prices for the assortment, a reduced assortment can capture 97% of the total category revenue. Overall this does suggest that if a retailer has additional (more profitable) requirements for this store space, she could reduce some UPCs in the tuna category. This result is consistent with the long term 18 assortment reduction impact on revenue that Sloot et al. [2006] find in an experimental setting. We feel this formulation can be used as a tool to guide retail assortment decisions for retailers in changing environments. [Figure 1 about here.] To show the importance of the counterfactual prediction, we consider the situation where the retailer just uses the total profit for a given product (rather than the total revenue shown in Figure 1). Here we consider the total profit to be the profit of each UPC given the current assortment. Conceptually, there are two key differences between using the marginal profit and actual profit: first the actual profits does not consider the number of sold units that not incremental to the category and second the actual profit does not include the ability for the retailer to change price. Consider a simple example where the current assortment included 2 products A and B, priced at $4 and $5. Currently we find 100 consumers purchase A and 50 consumers purchase B. Now if B were not in the assortment, some of these 50 consumers 18 We compare our results to the long term impact as our results study the steady state equilibrium outcome of the market after a change in assortment size 41

44 would purchase A instead (first effect described above) and the retailer would reduce the price for A to get more customers to purchase A (second effect described above). The effect of not considering price changes is apparent when assortment sizes are small, Figure B plots the marginal profit and the actual profit. Here we observe the actual profit underestimates (by as much at 30%) the true marginal profit of UPCs. While Figure 3 shows that for the last few UPCs added to the assortment, the effect of not considering subsitution is that the actual profit overestimates the true marginal profit by about 25%. [Figure 2 about here.] [Figure 3 about here.] To check the robustness of the effect of reducing assortment sizes across category, we consider the paper towel category for the Dominick s Finer Food store in a Chicago market. The marginal profit curve for this category is shown in Figure 4 below. This chart shows that the marginal profit curve appears more gradual for the paper towel category versus the tuna category. However consistent with the previous result, here we estimate that reducing the assortment from 28 UPCs to 21 UPCs (a 75% reduction), will result in only a 3% loss of total revenue. This change would imply a fixed cost of $150 per quarter for a product to be included in the assortment. 6.2 Importance of competition [Figure 4 about here.] To study the importance of competition in this industry we consider the following thought experiment. We examine a retail market with two competing retailers and then construct a counterfactual setting where both these retailers are optimizing jointly (as a monopolist). The difference between these two situations allows us to understand the importance of competition on assortment and pricing decisions. For this analysis, we consider two retail stores in a market in Washington. The chosen stores are the Quality Food Center and Fred Meyer. We consider a case where both stores have the same fixed cost. A uniform fixed cost allows us to isolate the effect of competition from effect pf different fixed costs. We look at three different levels of fixed costs to understand the importance of competition: First we consider a low fixed cost of $5, then a medium fixed cost of $50 and finally a high fixed cost of $150. We consider the Coffee category as an example category. In this market, the Quality Food Center can select their Coffee assortment from 275 UPCs available in the warehouse and Fred Meyer can select from 276 UPCs available in their warehouse. To isolate the effect of competition we do not change the consideration sets for the stores in our conterfactual simulation. In the case of duopoly decisions, we find the competitive Nash equilibrium from the intersection of best response curves (in assortment and prices). Table 36 shows the results for this simulation. [Table 36 about here.] 42

45 Consider the case of $50 fixed costs, in a competitive setting Quality Food Center and Fred Meyer will hold 122 and 111 UPCs respectively in their assortments. Further the two stores will charge markups of $5.17 and $6.06 respectively. We find that if these two stores were maximizing profits jointly we would find that the two stores will hold 97 and 108 UPCs respectively and will charge a markup of $6.74. This represents a 25 UPC reduction from the assortment in the Quality Food Center store and a 3 UPC reduction in the Fred Meyer store. Note that the UPCs stored in the joint optimization case are also stored in the individual store model. The intuition for this result is that the monopolist will charge a higher price when optimizing across the two stores, though now small UPCs in the Quality Food Center store will not have enough demand (therefore profit) to justify the shelf space. Also that reducing the price on these UPCs will lead some customers to switch from higher margin product to lower margin product and therefore will lead to a reduction in total profits. Consider the effect at the different levels of fixed costs for the two stores. At a low fixed cost ($5) we see only a effect change in the assortment decisions for the two stores. In particular, we find that only two fewer UPCs are sold in the Quality Food Center store in a setting without competition. The intuition here is that at a low fixed cost, the demand threshold for storing a product is low and therefore even with higher prices most UPCs meet this low value. At a high fixed cost ($150) we can see that there is a smaller effect of competition on assortment decisions (as compared to when the fixed cost is $50). This is due to the fact that the smaller the assortment, the more assortment decisions depend on demand. Further we find that at very high fixed costs ($1,000) we simulate that competition does not change assortment decisions. Interestingly, this suggests that the effect of competition on the number of available options is non-monotonic in fixed costs (or allocatable space). On the other hand, considering markups, we notice that the larger the fixed cost the smaller the markup increase without competition. This simulation also has implications for the study of mergers in the retail industry. We show a merger can reduce the total number of choices available to customers and increase the prices for these products. Both these events reduce consumer welfare for the market. Therefore this analysis suggests that when studying mergers between competing firms, researchers should consider not only consider price implications but also assortment implications. 6.3 Changing manufacturer prices In our setup we explicitly model the marginal costs for a retailer. These costs are mainly made up of a manufacturer s wholesale prices. The question we ask in this exercise is: how do changes in wholesale prices effect retailers assortment decisions? To study this we consider the toothpaste category in an Albertson s store in San Francisco. As before, we consider the changes in assortment decisions at various levels of fixed costs (or space constraints). Here we consider Colgate-Pamolive as the focal manufacturer, for whom we vary wholesale prices. We will report our results here in two tables: the first shows the case in which the retailer has space cost and can increase the total number of UPCs stored in the category as long as they justify the cost; the second is where the the retailer has a fixed space and needs to pick UPCs to fill this space. The difference between these two cases is that, in the first, an additional UPC can be added to the assortment if it provides sufficient profit, whereas in the second we effectively increase the threshold for adding products to the assortment. 43

46 The results of the first simulation are shown in Table 37 below. This table should be read as follows: the rows represent the different levels of fixed costs for the store, and columns represent the wholesale price discounts. For each combination of the fixed costs and discounts, the numbers in the cells are (a) the total number of UPCs Colgate UPCs stored and (b) the total number of other manufacturer UPCs stored in the store. Moving across the columns in a row shows us the effect of wholesale price discounts at each fixed cost level. Here we observe that if the fixed costs are very low (50c), then Colgate can increase their distribution in the store by offering wholesale price discounts. As a matter of fact, a 40% discount increases distribution by 43%. Interestingly most of this increase comes from category expansion and not from subsitution. However, we do notice some subsitution: for example, in the 40% Colgate discounts, we observe that the retailer does remove one competitor UPC from the assortment. From the second and third rows of this table we notice that under higher fixed costs we get the same effects though we observe fewer Colgate UPCs added to the assortment. Even at $100 fixed costs, with large wholesale discounts, the retailer does include more Colgate UPCs in the assortment without subsituting other manufacturers UPCs. However at $150 fixed costs, even with a 40% discount, the retailer does not include any additional Colgate UPCs to the assortment. This is because at this cost level, the UPCs in the assortment are selected based on their consumer demand. In summary, this analysis suggests that with a fixed cost of space, wholesale discounts have the largest impact on distribution in large retail stores (where the fixed cost is low) and the smallest impact in small retail stores (where the fixed cost is high). Additionally most of the increase in distribution is from category expansion rather than subsitution of other manufacturers. [Table 37 about here.] In the second analysis, we consider the total number of UPCs that the retailer can store to be constant (at current) across fixed cost groups. The results from this analysis are presented in table 38 below. To clarify the distinction of this analysis from the previous analysis, under the current pricing with $0.50 fixed cost we observe that the retailer stores 186 UPCs. We keep this size fixed when studying the effects of reducing wholesale prices. The major difference in this analysis is in the first row, where we estimate that the retailer will now substitute non-colgate UPCs to add Colgate UPCs when offered wholesale discounts. This shows that with fixed retail space, wholesale prices can have on a large impact assortment decisions in stores with large category space allocated. 6.4 Manufacturer demands [Table 38 about here.] A question in retailing is understanding the effect of manufacturers tying contracts. A tying contract is one where a manufacturer makes an offer to the retailer to store some group of UPCs or no UPCs at all. For example, Dannon could offer retailers to store a set of flavors of yogurt in their stores. To study the implications of such contracts we take an extreme version of the contract and study the optimal retailer decisions. In this case we assume that 44

47 all manufacturers offer contracts where the retailer must store all UPCs offered or none of the UPCs offered by that manufacturer. Our purpose in this section is to understand the implications of these contracts for retailers, manufacturers and policy makers. Here we look at a Dominick s Finner Food (DFF) store in Chicago and study the analgesics category. We choose the analgesics category, as there are only a few manufacturers in this category. To create the optimal assortments with tying contracts we need to consider the full combinatorial problem and cannot use the simplification derived in this paper. The DFF warehouse holds products from Bayer, GlaxoSmithKline, Insight, Johnson and Johnson, Little Drug Store, Little Necessities, Novartis, Polymedica, Upsher-Smith, and Wyeth Labs. We will study the effect of tying contract at 3 levels of fixed cost: low ($10), high ($75), and very high ($150). The results of this simulation are shown in Table 39 below. This table has the results of the simulation at each of the three different fixed cost levels. The results include the optimal assortment decision in the presence or absence of tying contracts. Considering the low fixed cost ($10), we see that the retailer will just store additional products in their assortments. In this case, tying contracts lead the retailers to be over assorted. The intuition behind this is that the cost of space is lower than the missed opportunity of not selling a specific UPC. This has a small effect on retailer profits, we estimate only about 3% lowers profits. This helps all manufacturers as all have their UPCs stored on the shelf. With a high fixed cost ($75), a retailer will now only store products of the largest retailers, here Bayer and Wyeth (and GSK with only three UPCs). In this assortment, the retailer carries the top selling products (these are manufacturered by Bayer and Wyeth), however tying contracts force her to also carry all other products offered by these manufacturer. Optimally (without tying contract) the retailer would store some products from the larger manufacturers and some from the smaller manufacturers. This has a large effect on retailer profits, the expected retailer profit are reduced by 53% with tying contract. Therefore tying contracts in this setting affect retailers and small manufacturers adversly. This effect is further magnified with very high fixed costs ($150), where in the presence of tying contracts the retailer will only store Wyeth UPCs. Note that in this market Wyeth (Aleeve) manufacturers the top two UPCs in the store. In this case, the retailer s profits are heavily impacted (reduced about 77%) as the retailer can no longer satisfy consumer demand for other brands (e.g. Advil). Small manufacturers in this setting do not get any retail distribution for their products. [Table 39 about here.] In summary, tying contracts can have one of two effects on retail assortments. First, if fixed storage costs are low, (high category space) then tying contracts cause a retailer to over-assort. Specifically, they store low selling UPCs of all manufacturers just to satisfy these contracts. In this setting, the affect on a retailer s profits is small. Second, when the fixed storage costs are high (or category space is limited), tying contracts cause the retailer to only store products from large manufacturers. Therefore a retailer does not satisfy consumer demand for smaller manufacturers products. We find this can lead to big profit losses for the retailer. In addition these contracts hurt small manufacturers as they do not get distribution in retail stores. 45

48 7 Summary and conclusions In this paper we consider the assortment decisions made by retailer category managers. The paper presents an analytical framework that derives optimal assortment decisions. The key analytical result is that UPCs can be ranked based on a combination of demand, price sensitivity and marginal cost. Based on this analytical result we derive an empirical methodology that allows us to study local retail assortment decisions. In the empirical analysus, we study assortment decisions for retailers across 119 competitive markets and 10 categories. Studying the assortment problem across multiple categories allows us to make generalizations about retailers assortment decisions. In our model we estimate a fixed cost of introducing a product on the retail shelf. This fixed cost represents a minimum threshold profit that an introduced product must add to category profits. The estimated fixed costs in categories with small UPCs are about $2 per to $5 UPC per quarter. Back of the envelope calculations suggest this amounts to about $7 to $20 per square foot of retail space. This estimate is consistent with trade reports for monthly costs of retail space. This suggests that retailers store products in the assortment untill the profits they add to the category cover the cost of storage. We find that the category with larger UPCs, paper towels, does have higher fixed costs. And refrigerated categories, frozen dinners and orange juice, have higher fixed costs. Both these trends are intuitive as they suggest that the cost of retail space is tied to the size of the UPC and the refrigeration requirements for the category. With our analytical model we can predict the impact of changes in assortment sizes on category profits. In particular, we describe which UPCs a retailer should store and the prices the retailer should charge for smaller assortments. In our data, we estimate that a 25% reduction in total assortment size results in about a 3% reduction in total profits. The prediction that a 25% assortment reduction does have a large impact on long run profits is consistent with experimental studies from Sloot et al. [2006]. More boardly, the methodology used in this paper can be a powerful tool that retailers can use to decide their assortments across multiple categories. Our model considers competition between retailers in their assortment and pricing decisions. We estimate that competition between retailers can lead to an increase in the total number of UPCs available to consumers and a decrease in prices. Moreover, the effect of competition depends on the space allocated to the category in the retail stores. The effect of competition on assortment decisions varies non-monotonically with space allocated to the category. This can be an important result for policy makers as mergers can have two negative influences on consumer welfare: increase prices and reduce selection. Understanding retailer assortment decisions is also important for manufacturers in order to increase distribution for their products. Consider wholesale price discounts for a manufacturer; these reduce costs (and increase profits) for a retailer and therefore can impact assortment decisions. We show that such discounts are most effective with retailers who have large spaces allocated to a category. On the other hand retailers with limited space might not change their assortment decisions even with large wholesale discounts. The intuition behind this result is, for retailers with limited space assortment decisions are based on demand. Another tactic that manufacturers can use to increase distribution is to introduce tying contracts, where retailers must store all or none of the UPCs offered. We estimate that these contracts negatively impact both retailers and small manufacturers. We find that these 46

49 contracts are most damaging when considering retailers with limited category space. These retailers can lose a majority of their profits because they offer restricted assortments. They are also damaging to small manufacturers who have minimal distribution for their products. Consider the example of the analgesics category, with tying contracts a retailer with limited shelf space will not store Advil and Tylenol and therefore will lose consumer demand from these products and manufacturers of these products will not get retail distribution. An important finding from our empirical estimation is that we show that not accounting for retail assortment decisions will bias demand and supply estimates. This bias is particularly noticeable for the price estimate in the demand system, where we observe that price elasticity is biased upward (or smaller negative numbers) without modeling assortment decisions. This in turn would cause a researcher to infer retail margins are biased upwards, is some cases more than 100%. In this paper we take a simplified view of consumer demand, where we assume a consumer has a utility for each UPC in each category. There are two refinements to this model that we could consider, first, we could include some cost of making a decision from the assortment in the consumers utility function. There is evidence from the behavioral literature (e.g., Chernev [2003]) that consumers do find it harder to make decisions when faced with large assortments. Adding this term would imply that total category demand is not increasing (with fixed prices) in assortment size. Second, we could consider category shoppers (Cachon and Kok [2006]), where consumers make the store decision based on multiple product categories. Understanding cross category assortments would allow us to consider the optimal use of retail store space for a retailer. Our current demand system models competition between similar retail or grocery stores. Another possible advancement of this research is to consider a case where a retailers are in different price tiers. Here we could consider competition between grocery stores, big box retailers (w.g, Walmart) and specialty retailers (e.g., Wholefoods). The key difference in a model for this set up is that consumers utility from purchasing in these stores should have different formations. Another area for further research is considering the dynamics of assortment decisions. Here a retailer could be uncertain of demand for a product and might place the product on the product shelf to learn about unobservable consumer preferences. 47

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53 A Optimal pricing Claim 7. The optimal pricing in the logit is derived as p j,t c j,t = 1 β 1 1 k Θ t s k,t (Θ t, P t ) (17) Proof. Remember the first order conditions provided the following This simplifies as follows s j,t + (p j,t c j,t ) s j,t + (p k,t c k,t ) s k,t = 0 p j,t p j,t k j s j + (p j,t c j,t )( βs j,t (1 s j,t )) + k j (p k,t c k,t )(βs j,t s k,t ) = 0 s j (p j,t c j,t )βs j,t + (p j,t c j,t )(βs j,t s j,t ) + k j (p k,t c k,t )(βs j,t s k,t ) = 0 s j (p j,t c j,t )βs j,t + k (p k,t c k,t )(βs j,t s k,t ) = 0 1 (p j,t c j,t )β + k (p k,t c k,t )(βs k,t ) = 0 (p j,t c j,t )β = 1 + β k (p k,t c k,t )s k,t Now since there is no dependence of j on the RHS of the above equation, and the above equation is true for all j then we must have that p j,t c j,t = p k,t c k,t for all j, k. Therefore we must have (p j,t c j,t )β(1 k s k,t ) = 1 (p j,t c j,t ) = ( 1 β )( 1 1 k s ) k,t B Gibbs sampler In this estimation we will consider two augmented parameters, for each product in the consideration set, they are δ j,t and c j,t For all products in the assortment can do the following: Calculate base markup is given by ( ) ( ) 1 1 m(θ t ) = β 1 l Θ t s l,t 51

54 Calculate the costs c j,t = p j,t m(θ t ) Calculate the δ j,t δ j,t = log(s j,t ) log(s 0,t ) + βp j,t Calculate the counter factual markup (m(θ t j)) by inverting the relation log(βm(θ t j) 1) + (βm(θ t j)) = log( e δ k,t βc k,t ) log(1 + e δ k,t βp k,t ) k Θ t k Θ t This in turn allows us to calculate the minimum profit of each added product (F) Posterior draws: draw β Prior, α, γ, δ k ( k / Θ t ), σ ξ, c k,t ( k / Θ t ) Method: Metropolis Prior given by log(β) N ( β, A 1 ) Likelihood for products in the market given by two equations, first from demand we have Second, from marginal cost we have P (δ j,t = log(s j,t ) log(s 0,t ) + βp j,t δ j,t N(X j,t α, σ 2 ξ) P (c j,t = p j,t m(θ t )) c j,t N(µZ j,t, σ 2 µ) Additionally we know have information from the inclusion equations for products in/out of the assortment. k / Θ t δ k,t β c k,t < min j Θ t δ j,t β c j,t This acts like a CDF as we know δ k,t β c k,t N(X j,t α βµz j,t, σ 2 ξ + β2 σ 2 µ) Note that here we also estimate delta j,t ( k / Θ t ) and c j,t ( k / Θ t ) draw δ k,t, c k,t ( k / Θ t ) (α, β), σ ξ, σ µ, δ j,t, c j,t This is like drawing the latent utility in a probit model (see Tanner and Wong [1987] and Rossi et al. [2005]) Method: Giibs 52

55 Prior given by δ k,t N(X j,t α, σ 2 ξ ), c k,t N(γZ j,t, σ 2 µ) The posterior draw is based on fact that δ k,t β c k,t < min j Θ t δ j,t β c j,t draw γ, σ 2 µ c.,t Method: Gibbs - linear regression (see Rossi et al. [2005]) draw α, σ 2 ξ δ.,t Method: Gibbs - linear regression (see Rossi et al. [2005]) Once we have estimated the parameters for each market we estimate the hierarchical parameters (see Rossi et al. [2005]) 53

56 Figure 1: Chart represents the marginal profit and the total (current) revenue for each of the 63 UPCs currently stored in the Tuna category at a Jewel Osco store 54

57 Figure 2: Marginal profit for each product added in Tuna category in Jewel Osco Chicago first 9 UPCs 55

58 Figure 3: Marginal profit for each product added in Tuna category in Jewel Osco Chicago last 12 UPCs 56

59 Figure 4: Chart represents the marginal profit for each of the 28 UPCs currently stored in the Paper towel category at a DFF (Chicago) store 57

60 Attribute Products sold Products available Analgesics Canned Tuna Mustard Ice Cream Orange Juice Paper Towels Frozen Dinner Cookies Toothpaste Coffee Table 1: Products offered in each category 58

61 Attribute Mean Median Maximum Minimum Number of pills < 10 pills > 100 pills Regular flavor Tablets Caplets Gelcap Plastic container Box container Low strength Extra strength Children s indication No caffeine mg to 400mg dose More that 400mg dose Not swallowed Less than 4 hours More than 6 hours Acetaminophen Ibuprofen Aspirin Naproxen Sodium Coated J&J manufacturer Bayer manufacturer Novartis manufacturer Wyeth manufacturer Tylenol Bayer Advil Excedrin Aleve Table 2: Descriptive statistics for the 348 UPCs in the Analgesics Category. 59

62 Attribute Mean Median Maximum Minimum Less than 4 Oz Oz to 8 Oz Oz to 8 Oz Oz to 10 Oz Oz to 16 Oz Size (16 Ounces) Regular Can Albacore Cut chunky Cut Steak In pure water In oil Color light Bumble Bee manuf Chicken of the sea manuf Del Monte manuf Table 3: Descriptive statistics for the 182 UPCs in the Canned Tuna Category. 60

63 Attribute Mean Median Maximum Minimum Low end High end < 4 oz oz to 8 oz oz to 10 oz oz to 12 oz oz to 16 oz oz to 35 oz Units (16 Oz) Regular flavor Chocolate flavor Espresso flavor Blended French roast Added flavor Colombian roast Regional coffee Carried in Can Caffeine stated Organic Coff substitute Decafinated Instant coffee Instant decafinated Whole bean Manuf P & G Manuf Altria Manuf Saralee Manuf Gryphon Manuf Nestle Brand Maxwell Brand Starbucks/Seattle Brand Folgers Brand Hills Brand Tasters choice Table 4: Descriptive statistics for the 1366 UPCs in the Coffee Category. 61

64 Attribute Mean Median Maximum Minimum Small Large Units (16oz) Regular Honey flavored Dijon flavored Carry in glass Carry in squeeze Hot Sweet Spreadable Pourable Squeezable Manuf Beaver Manuf Heinz Manuf Reckitt Manuf Conagra Manuf Plochman Manuf Hunts Manuf Unilever Manuf Altra Table 5: Descriptive statistics for the 322 UPCs in the Mustard Category. 62

65 Attribute Mean Median Maximum Minimum Small Large Units Chicken Meat (beef or pork) Carry vacuum packed Carry plastic Sauce added Cheese added Pre cooked Seasonal Manuf Hormel Manuf Smith Manuf Harry Manuf Perdue Manuf Tyson Table 6: Descriptive statistics for the 332 UPCs in the Frozen Dinners Category. 63

66 Attribute Mean Median Maximum Minimum Small Units (Pt) Flavor Chocolate Flavor Vanilla Flavor Assorted Flavor Fruit Carry Sqround Sugar low Fat Free or low fat Brand Breyer Brand Benjerry Brand Haagendaz Brand Dreyers Edys Table 7: Descriptive statistics for the 886 UPCs in the Ice Cream Category. 64

67 Attribute Mean Median Maximum Minimum Units Carry Bottle Carry Jug Not from concentrate No sugar Additives added Brand Tropicana Brand Minmaid Brand Florida Table 8: Descriptive statistics for the 126 UPCs in the Orange Juice Category. 65

68 Attribute Mean Median Maximum Minimum Small Large Units Absorb extra Color white Size Mega Size Upick Strength extra Manuf P & G Manuf Kimberly Manuf Georgia Table 9: Descriptive statistics for the 147 UPCs in the Paper Towel Category. 66

69 Attribute Mean Median Maximum Minimum Tiny or Travel Small Large Units (16oz) Added Fluoride Added Multiple Flavor mint Type Gel Container Bottle Form Tartar protection Form White and Tartar protection Color white Color multicolored Adult only Child Manuf P & G Manuf Colgate Manuf Church Manuf GSK Manuf Tom Maine Manuf J & J Brand Gerber Table 10: Descriptive statistics for the 664 UPCs in the Toothpaste Category. 67

70 Attribute Mean Median Maximum Minimum Volume (16Oz) Chocolate Vanilla Assorted Carry Box Carry Bag Carry Tin Carry Tray Cookie Sandwich Cookie Sugar Wafer Shape Round Shape Square Shape Assorted Form Patty Form Piece Form Bar Seasonal Base Unflavored Base Flavored Base Choc. Chip Base Shortcake Base Oatmeal Base Macaroon Base Biscotti Manuf Altria Manuf Archway Manuf Kellogg Manuf Campbell Manuf Lofthouse Manuf Pepsico Manuf Voortman Manuf Mckee Manuf Rab Manuf Hershey Table 11: Descriptive statistics for the 2,620 UPCs in the Cookies Category. 68

71 Number of Quarter stores Q1 Q2 Q3 Q4 Analgesics category DFF, Chicago (6 stores) Total % not in all 54% 51% 56% 46% Alberstons, Seattle(4 stores) NA NA Total % not in all 80% 75% 71% 69% Shop and shop, MA (5 stores) Total % not in all 69% 70% 61% 67% Coffee category Jewel Osco, Chicago (6 stores) Total % not in all 47% 57% 53% 49% Table 12: Variation in assortment across stores within a chain. Numbers represent the number of common products sold, therefore the 6 in the first row of the data represents the fact that 6 UPCs held in any DFF store in Chicago in quarter 1 are not sold in any of the 6 stores we consider. The 9 in the second row, 69 represents the fact that 9 UPCs are sold in only one of the DFF stores

72 Number of % of UPCs Store UPCs sold Same in all quarters Different across quarter Analgesics category Jewel Osco, Chicago Store % 45% Store % 40% Store % 27% Store % 27% Store % 34% Store % 36% DFF, Chicago Store % 35% Store % 47% Store % 41% Store % 38% Store % 37% Store % 60% Alberstons, Seattle Store % 57% Store % 33% Store % 40% Store % 43% Shop and shop, MA Store % 23% Store % 32% Store % 43% Store % 30% Store % 38% Table 13: Variation in assortment across quarters within a chain 70

73 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant < 10 pills > 100 pills Number of pills Regular flavor Tablets Caplets Gelcap Plastic container Box container Low strength Extra strength Children s indication No caffeine mg to 400mg dose More that 400mg dose Not swallowed Less than 4 hours More than 6 hours Acetaminophen Ibuprofen Aspirin Naproxen Sodium Coated J&J manufacturer Bayer manufacturer Novartis manufacturer Wyeth manufacturer Tylenol Bayer Advil Excedrin Aleve Weeks on display Feature B or C Feature A or A Table 14: Demand and marginal cost estimates for Analgesics 71

74 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 15: Fixed cost estimates for Analgesics 72

75 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Less than 4 Oz Oz to 8 Oz Oz to 8 Oz Oz to 10 Oz Oz to 16 Oz Ounces Regular Can Albacore Cut chunky Cut Steak In pure water In oil Color light Bumble Bee manuf Chicken of the sea manuf Del Monte manuf Minor display Major display C feature B feature A, A+ feature Table 16: Demand and marginal cost estimates for Canned Tuna 73

76 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 17: Fixed cost estimates for Canned Tuna 74

77 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Low end High end < 4 oz oz to 8 oz oz to 10 oz oz to 12 oz oz to 16 oz oz to 35 oz Units (16 Oz) Regular flavor Chocolate flavor Espresso flavor Blended French roast Added flavor Colombian roast Regonal coffee Carried in Can Caffine stated Organic Coff subsitute Decafinated Instant coffee Instant decafinated Whole bean Manuf P & G Manuf Altria Manuf Saralee Manuf Gryphon Manuf Nestle Brand Maxwell Brand Starbucks/seattle Brand Folgers Brand Hills Brand Tasters choice Minor display Major display B, C feature A, A+ feature Table 18: Demand and marginal cost estimates for Coffee 75

78 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 19: Fixed cost estimates for Coffee 76

79 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Small Large Units Regular Honey flavored Dijon flavored Carry in glass Carry in squeeze Hot Sweet Spreadable Pourable Squeezable Manuf Beaver Manuf Heinz Manuf Reckitt Manuf Conagra Manuf Plochman Manuf Hunts Manuf Unilever Manuf Altra Minor display Major display B, C feature A, A+ feature Table 20: Demand and marginal cost estimates for Mustard 77

80 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 21: Fixed cost estimates for Mustard 78

81 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Small Large Units Chicken Meat (beef or pork) Carry vaccum packed Carry plastic Sauce added Cheese added Pre cooked Seasonal Manuf Hormel Manuf Smith Manuf Harry Manuf Perdue Manuf Tyson Minor display Major display B, C feature A, A+ feature Table 22: Demand and marginal cost estimates for Frozen Dinners 79

82 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 23: Fixed cost estimates for Frozen Dinner 80

83 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Small Units Flavor Chocolate Flavor Vanilla Flavor Assorted Flavor Fruit Carry Sqround Sugar low Fat Free or low fat Brand breyer Brand Benjerry Brand Haagendaz Any display B, C feature A, A+ feature Table 24: Demand and marginal cost estimates for Ice Cream 81

84 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 25: Fixed cost estimates for Ice Cream 82

85 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Units Carry Bottle Carry Jug Not from concentrate No sugar Additives added Brand Tropicana Brand Minmaid Brand Florida Minor display Major display B, C feature A, A+ feature Table 26: Demand and marginal cost estimates for Orange Juice 83

86 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 27: Fixed cost estimates for Orange Juice 84

87 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Small Large Units Absorb extra Color white Size Mega Size Upick Strength extra Manuf P & G Manuf Kimberly Manuf Georgia Minor display Major display B, C feature A, A+ feature Table 28: Demand and marginal cost estimates for Paper Towels 85

88 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 29: Fixed cost estimates for Paper Towels 86

89 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Tiny or Travel Small Large Units Added Fluoride Added Multiple Flavor mint Type Gel Container Bottle Form Tartar protection Form White and Tartar protection Color white Color multicolored Adult only Chlidrens Manuf P & G Manuf Colgate Manuf Church Manuf GSK Manuf Tom Maine Manuf J & J Brand Gerber Display B, C feature A, A+ feature Table 30: Demand and marginal cost estimates for Toothpaste 87

90 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 31: Fixed cost estimates for Toothpaste 88

91 Demand estimates Marginal cost estimates Attribute Estimate 95% credibility Estimate 95% credibility log(price) Constant Volume Chocolate Vanilla Assorted Carry Box Carry Bag Carry Tin Carry Tray Cookie Sandwich Cookie Sugar Waffer Shape Round Shape Square Shape Assorted Form Patty Form Piece Form Bar Seasonal Base Unflavored Base Flavored Base Choc. Chip Base Shortcake Base Oatmeal Base Macaroon Base Biscotti Manuf Altria Manuf Archway Manuf Kellogg Manuf Campbell Manuf Lofthouse Manuf Pepsico Manuf Voortman Manuf Mckee Manuf Rab Manuf Hershey Minor display Major display B or C Feature A or A+ feature Table 32: Demand and marginal cost estimates for Cookies 89

92 Attribute Estimate 95% credibility region Chicago markets Washington markets Massachusetts markets California markets Colorado markets Georgia markets Quarter Quarter Quarter Table 33: Fixed cost estimates for Toothpaste 90

93 Category Storage Fixed cost Assortment Size Price Elasticity Orange Juice Refrigerated $ Paper towels Shelf (large UPC) $ Frozen Dinner Refrigerated $ Tuna Shelf (small UPC) $ Coffee Shelf (small UPC) $ Ice cream Refrigerated $ Analgesics Shelf (small UPC) $ Toothpaste Shelf (small UPC) $ Mustard Shelf (small UPC) $ Cookies Shelf (small UPC) $ Table 34: Summary of assortment estimates, numbers represent the average across stores and quarters 91

94 Ice Orange Tooth- Paper Must- Analg- Category Cream Coffee Tuna Dinner juice paste towels ard Cookie esics Ice cream 1.00* 0.36* 0.37* 0.34* 0.29* 0.26* 0.36* 0.34* Coffee 0.36* 1.00* 0.40* 0.37* * 0.24* Tuna 0.37* 0.40* 1.00* 0.48* 0.39* * 0.25* Frozen 0.34* 0.37* 0.48* 1.00* * * Orange Juice 0.29* * * * * Toothpaste 0.26* 0.28* * * * 0.13 Paper towels 0.36* 0.24* 0.30* * * Mustard 0.34* * 0.42* * Cookies * * 0.17 Analgesics * * Table 35: Correlations of fixed costs 92

95 Fixed Duopoly Monopoly Cost Variable Store 1 Store 2 Store 1 Store 2 $5 Number of UPCs sold Markup $5.23 $6.10 $6.91 $50 Number of UPCs sold Markup $5.17 $6.06 $6.74 $150 Number of UPCs sold Markup $4.97 $5.93 $6.37 $1,000 Number of UPCs sold Markup $4.54 $5.62 $5.68 Table 36: Understanding the effect of competition on assortment decisions in coffee 93

96 Fixed Colgate wholesale discounts Cost UPCs by Current 10% 25% 40% $0.50 Colgate Other manuf $8.00 Colgate Other manuf $30.00 Colgate Other manuf $ Colgate Other manuf $ Colgate Other manuf Table 37: Understanding the effect of wholesale discounts, with cost constraint and no space constraint, table contains the number of UPCs stored 94

97 Fixed Colgate wholesale discounts Cost UPCs by Current 10% 25% 40% $0.50 Colgate Other manuf $8.00 Colgate Other manuf $30.00 Colgate Other manuf $ Colgate Other manuf $ Colgate Other manuf Table 38: Understanding the effect of wholesale discounts, with cost constraint and with space constraint, table contains the number of UPCs stored 95

98 UPC Fixed cost $10 Fixed cost $75 Fixed cost $150 Manufacturer offered Optimal tying Optimal tying Optimal tying Bayer 28 82% 43% 25% Glaxo Smith-Kline 3 100% 33% 33% Insight 2 Johnson and Johnson 43 72% 35% 14% Little drug store 1 Little necessities 2 Novartis 22 77% 41% 9% Polymedica 1 100% 0% 0% Upsher-Smith 1 Wyeth Labs 15 53% 53% 20% Total UPCs Total profits $9,904 $9,637 $5,828 $2,731 $3,668 $842 % of optimal profits 97% 47% 23% Table 39: Understanding the effect of tying contracts 96