Understanding Retail Assortments In Competitive
Markets1
Kanishka Misra2
Kellogg School of Management
June 26, 2008
1I
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.
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.
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
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
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
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 2600 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
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
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
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
X
max max
πj (Θt , Ct , Pt )
(1)
Θt ⊆Ωt
Pt
j∈Θt
subject to
|Θt | ≤ nt
where Ωt represents all available products in time period t, Θt is the chosen subset of products
for the retailer, Ct represents the cost of selling the products and Pt represents the selected
price for each product in the assortment. The profit depends on the profit for each product
sold, which is represented by πj . nt 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
πj (Θt , Ct , Pt ) = Mt (pj,t − cj,t )sj,t (Θt , Pt )
For a given time period t: mt is the size of the available market, pj,t and cj,t are the price
and marginal cost for product j, and sj,t (Θt , Pt ) represents the share captured by product j
when the retailer stores Θt products and charges a price Pt . So, the retailers problem can
7
be considered as
max max
Θt ⊆Ωt
Pt
X
Mt (pj,t − cj,t )sj,t (Θt , Pt )
(2)
j∈Θt
subject to
|Θt | ≤ nt
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 Ωt 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 systems1 . 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
ui,j,t = αXj,t − βpj,t + ξj,t + i,j,t
where i represents consumers, j represents product and t represents the time period. Xj,t
represents the product characteristics for product j. α represents consumers preferences
for the product characteristics. pj,t is the price charged by the consumer at time t and β
represents the marginal utility of money. There are random utility shocks (ξj,t ) that impact
all customers in the market; these demand shocks are observed by the all agents, though
unobserved by the researcher (Berry [1994]). i,j,t represents the idiosyncratic fit, per the
1
Please contact the author for the technical appendix at [email protected]
8
logit assumption these are assumed to be from an i.i.d. type I extreme value distribution.
Additionally consumers have a utility ui,0,t = 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
di,t = arg max ui,j,t
j∈[0,Θt ]
With the logit assumption we can write this as a probabilistic choice, as below
℘(di,t = j) = ℘(ui,j,t > ui,−j,t ) =
eαXj,t −βpj,t +ξj,t
P
1 + k∈Θt eαXk,t −βpk,t +ξk,t
where −j refers to all products other than j.
Prior IO models (Berry [1994], Nevo [2001]) simplify this by defining this define δj,t ≡
αXj,t + ξj,t . Therefore we can write the model as
℘(di,t = j) =
eδj,t −βpj,t
P
1 + k∈Θt eδk,t −βpk,t
Integrating over customers and taking logs we get the following well established (Berry
[1994]) relationship from our demand model:
log(sj,t ) − log(s0,t ) = δj,t − βPj,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.
3.2.1
Retailer pricing
We begin with the simplified model where the retailer has decided the products in the
assortments (Θt ) and is deciding the optimal price. The retailer will solve the problem of
9
the form
max
Pt
X
Mt (pj,t − cj,t )sj,t (Θt , Pt )
(4)
j∈Θt
This is a well-studied problem and the solution from the first order condition for all j must
satisfy
∂sj,t (.) X
∂sk,t (.)
sj,t (Θt , Pt ) + (pj,t − cj,t )
+
=0
(pk,t − ck,t )
∂pj,t
∂pj,t
k6=j
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
(5)
pj,t − cj,t =
β
1 − k∈Θt sk,t (Θt , Pt )
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(Θt ) as the optimal
markup given the assortment Θt . 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:
X
eδk,t −βck,t )
log(βm(Θt ) − 1) + (βm(Θt )) = log(
k∈Θt
(6)
Proof. From equation 5, we have
1
1
P
m(Θt ) =
β
1 − k∈Θt sk,t (Θt , Pt )
!
P
1 + l∈Θt eδk,t −βm(Θt )−βck,t
⇒ βm(Θt ) =
1
!
P
δk,t −βck,t
l∈Θt e
⇒ βm(Θt ) = 1 +
eβm(Θt )
X
⇒ eβm(Θt ) (βm(Θt ) − 1) =
eδk,t −βck,t
l∈Θt
⇒ βm(Θt ) + log(βm(Θt ) − 1) = log(
X
eδk,t −βck,t )
l∈Θt
This relationship will prove useful when we consider the assortment selection section of
the supply model.
10
Next, we consider the optimal profits of an assortment Θt given retailers use the optimal
pricing described above.
Claim 2. The optimal profit can we written as:
max
Pt
X
Mt (pj,t − cj,t )sj,t (Θt , Pt ) = Mt (m(Θt ) −
j∈Θt
1
)
β
(7)
Proof.
max
P
X
Mt (pj,t − cj,t )sj (Θt , Pt ) =
j∈Θt
X
Mt (m(Θt ))sj,t (Θt )
j∈Θt
= Mt (m(Θt ))
X
sj,t (Θt )
j∈Θt
X
1
1
P
sj,t (Θt )
β 1 − j∈Θt sj,t (Θt ) j∈Θ
t
1 X δj,t −β(cj,t +m(Θt ))
Mt
e
β j∈Θ
t
P
1 j∈Θt eδj,t −βcj,t
Mt
β
eβm(Θt )
1 eβm(Θ) (βm(Θ) − 1)
Mt
β
eβm(Θ)
1 βm(Θ) − 1
Mt
β
1
1
Mt (m(Θ) − )
β
= Mt
=
=
=
=
=
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
Pt
X
Mt (pj,t − cj,t )sj,t (Θt , Pt ) = Mt (m(Θt ) −
j∈Θt
1
)
β
With m(Θt ) satisfying the following relationship,
X
log(βm(Θt ) − 1) + (βm(Θt )) = log(
11
k∈Θt
eδk,t −βck,t )
3.2.2
Assortment decision
In our supply problem we assume the retailer solves the following problem:
X
(pj,t − cj,t )s(Θt , Pt )
max Mt max
Θt ⊆Ωt
Pt
j∈Θt
subject to
|Θt | ≤ nt
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 Θt has fewer than nt products. Consider adding
a product l (l ∈ Ωt and l ∈
/ Θt ). Now add product l to the assortment now adding a new
product and setting the price for product l to be cl,t + maxj∈Θt (pj,t − cj,t ) + , with > 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 Θt
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 Θt . Second, consumers may
switch from not purchasing to purchasing product l, this is clearly profitable for the firm.
Therefore Θt 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 Ft ), given the constraint |Θt | ≤
nt is satisfied. Therefore we can rewrite the retailer’s problem as;
X
max max
[Mt (pj,t − cj,t )sj,t (Θt , Pt ) − Ft ]
Θt ⊆Ωt
Pt
j∈Θt
where Ft is the shadow price of adding a product (or the fixed cost of space). As this is
a Lagrange multiplier, we must have Ft > 0. From an economic perspective, the marginal
benefit of adding a product to the assortment must be at least Ft .
12
Substituting in the results from the pricing section earlier, this problem simplifies to:
max Mt (m(Θt ) −
Θt ⊆Ωt
1
) − Ft
β
with
X
log(βm(Θt ) − 1) + (βm(Θt )) = log(
k∈Θt
eδk,t −βck,t )
The advantage of the above representation is that this equation only considers the maximization over the space of Θt . Moreover, Θt only enters though m(Θt ), therefore to simplify
this further we need to understand the properties of m(Θt ).
Claim 4. The equation
X
log(βm(Θt ) − 1) + (βm(Θt )) = log(
k∈Θt
eδk,t −βck,t )
P
is invertible (in m(.)). Moreover, the solution is strictly increases with log( k∈Θ eδk −β(ck ) ).
Proof. Define a function f (m) ≡ log(βm − 1) + (βm) defined from ( β1 , ∞) to R.
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 → β1 , we must have f (m) → −∞. This is because log(βm − 1) → −∞ and βm
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 = β1 [1 + min(ek−3 , 1)]. So we have h(A) = log(βA − 1) + βA −
k = log(min(ek−3 , 1)) + 1 + min(ek−3 , 1) − k ≤ log(ek−3 ) + 1 + 1 − k = −1 < 0. Therefore
h(A) < 0.
Second, define B = β1 (1 + max(1, k)). So we have h(B) = log(βB − 1) + βB − k =
log(max(1, k)) + 1 + max(1, k) − k ≥ log(1) + 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.
∂f
To complete the proof we need to show uniqueness. First, consider the fact that ∂m
=
β
1
+ β > 0 as the function is defined for m > β . Therefore the function f (.) is strictly
βm−1
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
Moreover since f (.) is strictly increasing we must have the inverse g(.) is strictly increasing.
This proves this claim that
P there is a unique m(.) that satisfies equation 6 and moreover
the higher the value of log( k∈Θ eδk −βck ) 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 P
m(.). By the claim above we must have that these profits are an increasing
function of k∈Θt eδk,t −βck,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
δk,t − βck,t and pick the top nt 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 Mt (m(Θt ) −
Θt ⊆Ωt
1
)
β
Subject to
|Θt | ≤ nt
is the same as the solution to the problem
max
Θt ⊆Ωt
X
k∈Θt
eδk,t −βck,t
Subject to
|Θt | ≤ nt
P
as profits are a strictly increasing function of k∈Θt eδk,t −βck,t .
Now, suppose that picking the nt products with the highest δk,t −βck,t was not the optimal
solution. It must be the case that ∃ j ∈ Θt and l ∈
/ Θt with δl,t − βcl,t > δj,t − βcj,t . However,
we have
X
X
eδk,t −βck,t + eδl,t −βcl,t >
eδk,t −βck,t + eδj,t −βcj,t
k∈Θt ,k6=j
k∈Θt ,k6=j
X
=
eδk,t −βck,t
k∈Θt
which contradicts the optimality of Θt .
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
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
X
−
(pj,t − cj,t )sj,t (Θt , Pt , Θ−
max Mt max
t , Pt )
Θt ⊆Ωt
Pt
j∈Θt
subject to
|Θt | ≤ nt
−
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
1
1
P
pj,t − cj,t =
−
β
1 − k∈Θt sk,t (Θt , Pt , 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:
X
X
δk,t −βck,t
−
−
−
eδk,t −βpk,t )
e
)
−
log(1
+
log(βm(Θt , Θ−
,
P
)
−
1)
+
(βm(Θ
,
Θ
,
P
))
=
log(
t
t
t
t
t
k∈Θt
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
Pt
X
−
−
−
Mt (pj,t − cj,t )sj,t (Θt , Pt , Θ−
t , Pt ) = Mt (m(Θt , Θt , Pt ) −
j∈Θt
15
1
)
β
Proof.
X
X
−
−
−
−
Mt (pj,t − cj,t )sj (Θt , Pt , Θ−
Mt (m(Θt , Θ−
max
t , Pt ) =
t , Pt ))sj,t (Θt , Θt , Pt )
Pt
j∈Θt
j∈Θt
−
= Mt (m(Θt , Θ−
t , Pt ))
X
−
sj,t (Θt , Θ−
t , Pt )
j∈Θt
= Mt
X
1
1
−
P
sj,t (Θt , Θ−
t , Pt )
−
β 1 − j∈Θt sj,t (Θt , Θ−
,
P
)
t
t
j∈Θ
t
1
= Mt
β
= Mt
1
β
= Mt
1
β
−
− !
eδj,t −β(cj,t +m(Θt ,Θt ,Pt ))
P
1 + k∈Θ−t eδk,t −βpk,t
!
!
P
δj,t −βcj,t
1
j∈Θt e
P
−
−
1 + k∈Θ−t eδk,t −βpk,t
eβm(Θt ,Θt ,Pt )
!
P
δj,t −βcj,t
e
1
j∈Θt
P
−
−
1 + k∈Θ−t eδk,t −βpk,t
eβm(Θt ,Θt ,Pt )
P
j∈Θt
−
−
−
1 eβm(Θ,Θt ,Pt ) (βm(Θ, Θ−
t , Pt ) − 1)
= Mt
−
−
β
eβm(Θ,Θt ,Pt )
−
1 βm(Θ, Θ−
t , Pt ) − 1
= Mt
β
1
1
−
= Mt (m(Θ, Θ−
)
t , Pt ) −
β
This claim is important as it shows that the best response (profit) function for the retailer
−
is strictly increasing in m(Θt , 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 nt products
with the highest δj,t − βcj,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 assortments2 . 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
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.
3.4.1
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
ui,j,m = αm Xj,m − βm pj,m + ξj,m + i,j,m
where Xj,m is the demand characteristics, these include all product attribute information.
pj,m is the price charged by the retailer. In addition to the common assumptions we will
assume that the random shocks ξj,m are distributed from the Normal distribution with mean 0
and variance σξm . 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 ∈ Θm , this includes all retailers)
log(sj,m ) − log(s0,m ) = αm Xj,m − βm pj,m + ξj,m
3.4.2
(9)
Marginal cost
The optimal markup for all product in Θm,r (assortment for an assortment for any one
retailer) in our model is given by
!
1
1
P
pj,m,r − cj,m,r =
βm
1 − k∈Θm,r sk,m,r (Θm,r , Θm,−r , Pm,−r )
17
Alternatively this can be written as
cj,m,r = pj,m,r −
1
βm
1−
P
1
k∈Θm,r sk,m,r (Θm,r , Θm,−r , Pm,−r )
!
We parametrize marginal cost such that
cj,m,r = γm Zj,m + νj,m = pj,m,r −
1
βm
1
P
1 − k∈Θm,r sk,m,r (Θm,r , Θm,−r , Pm,−r )
!
(10)
where the Zj,m variables are possible marginal cost shifters, here we include all product attributes in this equation. γm describes how these impact marginal cost. The νj,m term is
a cost shock for product j in market m. We assume νj,m ∼ N (0, σνm ); 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]).
3.4.3
Assortments
In this paper we have shown that the optimal assortment for a retailer consists of selecting
the nm,r products with the highest δj,m,r − βcj,m,r . Therefore we must have the following
relationship for all products in the choice set Ωm,r :
min δj,m,r − βm cj,m,r > max δk,m,r − βm ck,m,r
j∈Θt
k∈Θ
/ t
(11)
where δj,m,r = αm Xj,m,r + ξj,m,r . Notice that in equation 9 conditional on βm we can point
identify δj,m,r , for all j ∈ Θm,r directly from the data (without any error). Similarly in
equation 10, conditional on βm we can point identify cj,m,r , for all j ∈ Θm,r directly from the
data. Therefore conditional on βm 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
δk,m,r − βck,m,r < min δj,m,r − βcj,m,r
j∈Θt
⇒ αXk,m,r + ξk,m,r − βm γm Zk,m,r − βm νk,m,r < min δj,m,r − βm cj,m,r
j∈Θm,r
⇒ ξk,m,r − βm νk,m,r < ( min δj,m,r − βcj,m,r ) − αm Xk,m,r + βm γm Zk,m,r
j∈Θm,r
(12)
Now notice that equation 12 can be written as a CDF as we know the joint distribution of
2
ξk,m,r − βm νk,m,r is N (0, σξm + βm
σνm ). Therefore conditional on model parameters we write
down the likelihood of those products that are not in the market.
To estimate Fm,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 Fm,r . Thus, the marginal profit of adding the last product is
minj∈Θm,r Mm,r [m(Θm,r , Θm,−r , Pm,−r ) − m(Θm,r − j, Θm,−r , Pm,−r )] where Θm,r − j refers to
18
the set of product Θm,r without the product j. Notice that our estimation procedure guarantees that for all k ∈
/ Θm,r , the marginal profit of adding product k to the assortment Θm,r is
less that Fm,r . Also note that we estimate a Fm,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 Fm,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 βm . 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:
αm ∼ N (ᾱ, Σα )
log(βm ) ∼ N (β̄, σβ )
γm ∼ N (γ̄, Σγ )
Fm,r ∼ N (F¯m + F̄t , σF )
(13)
(14)
(15)
(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
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 2007. 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
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
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.
4.2.1
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
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.
4.2.2
Canned Tuna
We define the Canned Tuna category as all products defined by IRI as “Canned Tuna4 ”.
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 Wikipedia5 , 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 steak6 , 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
The Wikipedia definition of Albacore can be found on http://en.wikipedia.org/wiki/Albacore
6
Other cuts include spreadable, fillet, and flaked
5
23
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.
4.2.3
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
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.
4.2.4
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.
4.2.5
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
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.
4.2.6
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 0.225 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
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.
4.2.7
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.
4.2.8
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
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 125-150 strips8 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
125-150 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.
4.2.9
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
[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.
4.2.10
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
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 coffee9 , 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 UPCs10 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 value12 , 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
61 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
10
30
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 category13 . 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
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 cost14 per retailer square foot is
reported to be between $7.5 and $13 per square foot per month15 . 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
Fixed
cost
numbers
are
estimated
on
many
websites
such
as
http://retail.about.com/od/startupcosts/f/startupcosts2.htm and http://wiki.answers.com/Q/How much inventory per squa
15
32
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.
[Table 17 about here.]
5.3
Coffee
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 -3.30. 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
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 -2.36 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.
[Table 21 about here.]
5.5
Frozen Dinners
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 -2.02. 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
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 -3.18 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.
[Table 25 about here.]
5.7
Orange Juice
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 -1.71 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
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
-3.92. 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.
[Table 29 about here.]
5.9
Toothpaste
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
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.
[Table 31 about here.]
5.10
Cookies
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
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 0.37. 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
-1.51 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.
5.12
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 -1.74. This is about half of the -3.93 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 -3.17 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
-0.90. 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 sensi38
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.
5.13
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 costs16 . 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
cost17 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
[Table 35 about here.]
5.14
Summary of the estimates
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
6.1
Counterfactual predictions
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
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 term18 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
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.
[Figure 4 about here.]
6.2
Importance of competition
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
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
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.
[Table 38 about here.]
6.4
Manufacturer demands
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
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
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
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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50
A
Optimal pricing
Claim 7. The optimal pricing in the logit is derived as
pj,t − cj,t =
1
1
P
β 1 − k∈Θt sk,t (Θt , Pt )
(17)
Proof. Remember the first order conditions provided the following
sj,t + (pj,t − cj,t )
∂sj,t X
∂sk,t
+
=0
(pk,t − ck,t )
∂pj,t k6=j
∂pj,t
This simplifies as follows
sj + (pj,t − cj,t )(−βsj,t (1 − sj,t )) +
X
(pk,t − ck,t )(βsj,t sk,t ) = 0
k6=j
sj − (pj,t − cj,t )βsj,t + (pj,t − cj,t )(βsj,t sj,t ) +
X
sj − (pj,t − cj,t )βsj,t +
X
(pk,t − ck,t )(βsj,t sk,t ) = 0
k6=j
(pk,t − ck,t )(βsj,t sk,t ) = 0
k
1 − (pj,t − cj,t )β +
X
(pk,t − ck,t )(βsk,t ) = 0
k
(pj,t − cj,t )β = 1 + β
X
(pk,t − ck,t )sk,t
k
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 pj,t − cj,t = pk,t − ck,t for all j, k. Therefore
we must have
X
(pj,t − cj,t )β(1 −
sk,t ) = 1
k
1
1
P
(pj,t − cj,t ) = ( )(
)
β 1 − k sk,t
B
Gibbs sampler
In this estimation we will consider two augmented parameters, for each product in the
consideration set, they are δj,t and cj,t For all products in the assortment can do the following:
• Calculate base markup is given by
1
1
P
m(Θt ) =
β
1 − l∈Θt sl,t
51
• Calculate the costs
cj,t = pj,t − m(Θt )
• Calculate the δj,t
δj,t = log(sj,t ) − log(s0,t ) + βpj,t
• Calculate the counter factual markup (m(Θt − j)) by inverting the relation
X
X
eδk,t −βpk,t )
log(βm(Θt − j) − 1) + (βm(Θt − j)) = log(
eδk,t −βck,t ) − log(1 +
k∈Θt
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, δk (∀k ∈
/ Θt ), σξ , ck,t (∀k ∈
/ Θt )
– Method: Metropolis
– Prior given by log(β) ∼ N β̄, A−1
– Likelihood for products in the market given by two equations, first from demand
we have
P (δj,t = log(sj,t ) − log(s0,t ) + βpj,t
δj,t ∼ N (Xj,t α, σξ2 )
Second, from marginal cost we have
P (cj,t = pj,t − m(Θt ))
cj,t ∼ N (µZj,t , σµ2 )
Additionally we know have information from the inclusion equations for products
in/out of the assortment. ∀k ∈
/ Θt
δk,t − β ∗ ck,t < min δj,t − β ∗ cj,t
j∈Θt
This acts like a CDF as we know δk,t − β ∗ ck,t ∼ N (Xj,t α − βµZj,t , σξ2 + β 2 σµ2 )
– Note that here we also estimate deltaj,t (∀k ∈
/ Θt ) and cj,t (∀k ∈
/ Θt )
• draw δk,t , ck,t (∀k ∈
/ Θt )|(α, β), σξ , σµ , δj,t , cj,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
– “Prior” given by δk,t ∼ N (Xj,t α, σξ2 ), ck,t ∼ N (γZj,t , σµ2 )
– The posterior draw is based on fact that
δk,t − β ∗ ck,t < min δj,t − β ∗ cj,t
j∈Θt
• draw γ, σµ2 |c.,t
– Method: Gibbs - linear regression (see Rossi et al. [2005])
• draw α, σξ2 |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
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
Figure 2: Marginal profit for each product added in Tuna category in Jewel Osco Chicago
first 9 UPCs
55
Figure 3: Marginal profit for each product added in Tuna category in Jewel Osco Chicago
last 12 UPCs
56
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
Attribute
Analgesics
Canned Tuna
Mustard
Ice Cream
Orange Juice
Paper Towels
Frozen Dinner
Cookies
Toothpaste
Coffee
Products sold
87.33
52.39
48.05
208.05
48.43
27.30
46.13
373.09
153.20
189.97
Products available
133.62
65.41
74.49
253.39
52.57
35.52
57.50
625.88
217.20
300.69
Table 1: Products offered in each category
58
Attribute
Mean
Number of pills
63.27
0.16
< 10 pills
> 100 pills
0.30
Regular flavor
0.90
Tablets
0.39
Caplets
0.35
0.16
Gelcap
Plastic container
0.76
0.09
Box container
Low strength
0.32
0.51
Extra strength
Children’s indication
0.05
No caffeine
0.05
200mg to 400mg dose
0.56
More that 400mg dose 0.11
Not swallowed
0.12
Less than 4 hours
0.18
More than 6 hours
0.22
Acetaminophen
0.43
Ibuprofen
0.19
0.27
Aspirin
Naproxen Sodium
0.05
Coated
0.39
J&J manufacturer
0.26
Bayer manufacturer
0.18
Novartis manufacturer 0.18
0.11
Wyeth manufacturer
Tylenol
0.20
Bayer
0.14
Advil
0.12
Excedrin
0.17
Aleve
0.05
Median
50
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Maximum
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Minimum
300
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Table 2: Descriptive statistics for the 348 UPCs in the Analgesics Category.
59
Attribute
Less than 4 Oz
4 Oz to 8 Oz
6 Oz to 8 Oz
8 Oz to 10 Oz
10 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
Mean
0.14
0.20
0.42
0.09
0.10
0.45
0.90
0.77
0.35
0.50
0.06
0.15
0.21
0.51
0.20
0.19
0.27
Median
0
0
0
0
0
0.375
1
1
0
0.5
0
0
0
1
0
0
0
Maximum
1
1
1
1
1
1.5
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0
0
0
0
0.1875
0
0
0
0
0
0
0
0
0
0
0
Table 3: Descriptive statistics for the 182 UPCs in the Canned Tuna Category.
60
Attribute
Low end
High end
< 4 oz
4 oz to 8 oz
8 oz to 10 oz
10 oz to 12 oz
12 oz to 16 oz
16 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
Mean
0.32
0.13
0.13
0.07
0.07
0.18
0.42
0.12
0.73
0.14
0.05
0.07
0.13
0.11
0.13
0.08
0.06
0.20
0.78
0.09
0.01
0.11
0.09
0.03
0.27
0.16
0.16
0.06
0.02
0.02
0.04
0.06
0.06
0.02
0.01
Median
0
0
0
0
0
0
0
0
0.75
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Maximum
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0
0
0
0
0
0
0
0.0263
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 4: Descriptive statistics for the 1366 UPCs in the Coffee Category.
61
Attribute
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
Mean
0.21
0.10
0.63
0.25
0.15
0.12
0.52
0.36
0.20
0.12
0.56
0.23
0.18
0.12
0.01
0.06
0.02
0.05
0.03
0.02
0.03
Median
0
0
0.5625
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
Maximum
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0
0.0625
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 5: Descriptive statistics for the 322 UPCs in the Mustard Category.
62
Attribute
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
Mean
0.09
0.27
1.11
0.20
0.28
0.06
0.77
0.46
0.06
0.11
0.01
0.15
0.09
0.04
0.06
0.07
Median
0
0
1.0625
0
0
0
1
0
0
0
0
0
0
0
0
0
Maximum
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0
0.2769
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 6: Descriptive statistics for the 332 UPCs in the Frozen Dinners Category.
63
Attribute
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
Mean
0.25
2.95
0.21
0.19
0.07
0.08
0.31
0.13
0.21
0.12
0.04
0.06
0.12
Median
0
3.5
0
0
0
0
0
0
0
0
0
0
0
Maximum
1
10
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0.225
0
0
0
0
0
0
0
0
0
0
0
Table 7: Descriptive statistics for the 886 UPCs in the Ice Cream Category.
64
Attribute
Units
Carry Bottle
Carry Jug
Not from concentrate
No sugar
Additives added
Brand Tropicana
Brand Minmaid
Brand Florida
Mean
62.11
0.31
0.28
0.68
0.49
0.32
0.31
0.19
0.08
Median
64
0
0
1
0
0
0
0
0
Maximum
128
1
1
1
1
1
1
1
1
Minimum
8
0
0
0
0
0
0
0
0
Table 8: Descriptive statistics for the 126 UPCs in the Orange Juice Category.
65
Attribute
Small
Large
Units
Absorb extra
Color white
Size Mega
Size Upick
Strength extra
Manuf P & G
Manuf Kimberly
Manuf Georgia
Mean
0.34
0.34
2.91
0.35
0.49
0.43
0.16
0.31
0.36
0.27
0.26
Median
0
0
1.516
0
0
0
0
0
0
0
0
Maximum
1
1
9.825
1
1
1
1
1
1
1
1
Minimum
0
0
0.397
0
0
0
0
0
0
0
0
Table 9: Descriptive statistics for the 147 UPCs in the Paper Towel Category.
66
Attribute
Mean
Tiny or Travel
0.06
0.16
Small
Large
0.11
Units (16oz)
0.36
Added Fluoride
0.72
Added Multiple
0.12
Flavor mint
0.47
Type Gel
0.55
Container Bottle
0.07
Form Tartar protection
0.15
Form White and Tartar protection 0.19
Color white
0.09
0.21
Color multicolored
Adult only
0.09
0.08
Child
Manuf P & G
0.29
0.22
Manuf Colgate
Manuf Church
0.12
0.11
Manuf GSK
Manuf Tom Maine
0.09
Manuf J & J
0.03
0.00
Brand Gerber
Median
0
0
0
0.375
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Maximum
1
1
1
2.625
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Minimum
0
0
0
0.0469
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 10: Descriptive statistics for the 664 UPCs in the Toothpaste Category.
67
Attribute
Mean
Volume (16Oz)
0.64
Chocolate
0.12
0.03
Vanilla
Assorted
0.04
Carry Box
0.31
Carry Bag
0.20
0.04
Carry Tin
Carry Tray
0.17
Cookie
0.73
Sandwich Cookie
0.11
0.06
Sugar Wafer
Shape Round
0.50
0.16
Shape Square
Shape Assorted
0.05
Form Patty
0.43
0.24
Form Piece
Form Bar
0.10
Seasonal
0.12
Base Unflavored
0.26
Base Flavored
0.25
0.10
Base Choc. Chip
Base Shortcake
0.05
Base Oatmeal
0.05
0.03
Base Macaroon
Base Biscotti
0.02
Manuf Altria
0.09
Manuf Archway
0.08
Manuf Kellogg
0.06
0.04
Manuf Campbell
0.04
Manuf Lofthouse
Manuf Pepsico
0.03
Manuf Voortman
0.03
Manuf Mckee
0.02
Manuf Rab
0.01
Manuf Hershey
0.01
Median
0.5678
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Maximum
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Minimum
0.0463
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 11: Descriptive statistics for the 2,620 UPCs in the Cookies Category.
68
Number of
Quarter
stores
Q1 Q2 Q3 Q4
Analgesics category
DFF, Chicago (6 stores)
0
6
13
15
11
9
8
11
6
1
2
11
5
9
5
3
8
9
9
3
4
12
15
12
9
21
16
13
15
5
6
51
50
43
45
Total
118 116 112
94
% not in all 54% 51% 56% 46%
Alberstons, Seattle(4 stores)
23
26
39
32
0
1
28
32
33
28
24
24
49
45
2
45
36
33
33
3
4
24
30 NA NA
144 148 154 138
Total
% not in all 80% 75% 71% 69%
Shop and shop, MA (5 stores)
0
13
12
13
15
1
22
20
15
13
18
16
20
20
2
3
10
13
5
12
4
20
22
22
19
31
31
39
32
5
Total
114 114 114 111
% not in all 69% 70% 61% 67%
Coffee category
Jewel Osco, Chicago (6 stores)
0
65
51
66
52
1
36
39
56
49
2
8
6
14
6
3
8
11
18
8
4
25
28
20
23
5
50
70
53
56
6
146 115 145 146
Total
175 177 172 160
% 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
69 represents the fact that 9 UPCs are sold in
6 stores we consider. The 9 in the second row,
only one of the DFF stores
Store
Store
Store
Store
Store
Store
Store
1
2
3
4
5
6
Store
Store
Store
Store
Store
Store
1
2
3
4
5
6
Store
Store
Store
Store
1
2
3
4
Store
Store
Store
Store
Store
1
2
3
4
5
Number of
% of UPCs
UPCs sold Same in all quarters Different
Analgesics category
Jewel Osco, Chicago
150
55%
179
60%
166
73%
173
73%
185
66%
173
64%
DFF, Chicago
110
65%
97
53%
107
59%
104
62%
107
63%
104
40%
Alberstons, Seattle
58
43%
109
67%
117
60%
134
57%
Shop and shop, MA
113
77%
85
68%
72
57%
98
70%
72
63%
across quarter
45%
40%
27%
27%
34%
36%
35%
47%
41%
38%
37%
60%
57%
33%
40%
43%
23%
32%
43%
30%
38%
Table 13: Variation in assortment across quarters within a chain
70
Demand estimates
Attribute
Estimate 95% credibility
log(Price)
2.07
2.02 2.12
Constant
-7.11
-7.47 -6.73
< 10 pills
2.28
2.04 2.53
1.43
1.17 1.68
> 100 pills
Number of pills
-0.01
-0.11 0.09
Regular flavor
0.13
-0.04 0.31
Tablets
0.34
0.18 0.50
0.79
0.61 0.95
Caplets
Gelcap
0.43
0.27 0.59
Plastic container
2.12
1.92 2.32
Box container
1.53
1.33 1.75
Low strength
-0.25
-0.42 -0.09
Extra strength
-0.25
-0.40 -0.10
Children’s indication
-0.48
-0.67 -0.28
No caffeine
0.39
0.21 0.57
200mg to 400mg dose -0.36
-0.51 -0.21
More that 400mg dose -1.65
-1.82 -1.48
Not swallowed
-0.43
-0.59 -0.26
Less than 4 hours
0.10
-0.06 0.26
0.62
0.49 0.75
More than 6 hours
Acetaminophen
-0.19
-0.38 0.01
Ibuprofen
-0.74
-0.98 -0.50
Aspirin
-1.17
-1.40 -0.95
-1.42
-1.69 -1.15
Naproxen Sodium
Coated
0.08
-0.05 0.21
J&J manufacturer
0.88
0.73 1.03
0.70
0.50 0.91
Bayer manufacturer
Novartis manufacturer 0.71
0.52 0.90
Wyeth manufacturer
1.24
1.02 1.47
Tylenol
-0.46
-0.67 -0.25
Bayer
-0.36
-0.59 -0.13
Advil
-0.24
-0.44 -0.03
Excedrin
-1.06
-1.23 -0.89
Aleve
-0.81
-1.03 -0.60
Weeks on display
0.27
0.14 0.41
Feature B or C
0.61
0.49 0.72
Feature A or A+
0.58
0.43 0.72
Marginal cost estimates
Estimate 95% credibility
0.30
0.53
0.13
0.00
-0.02
-0.04
0.04
0.02
0.16
0.11
-0.04
-0.10
0.06
-0.03
0.04
-0.07
-0.06
-0.11
0.03
-0.08
-0.22
-0.12
-0.23
0.00
0.02
0.01
-0.10
0.05
-0.12
-0.12
0.00
-0.04
-0.08
-0.02
-0.05
-0.10
0.17
0.41
0.00
-0.10
-0.13
-0.15
-0.07
-0.09
0.06
0.00
-0.15
-0.21
-0.05
-0.15
-0.07
-0.17
-0.17
-0.22
-0.07
-0.19
-0.34
-0.25
-0.36
-0.11
-0.08
-0.10
-0.21
-0.07
-0.23
-0.24
-0.11
-0.14
-0.20
-0.12
-0.15
-0.21
Table 14: Demand and marginal cost estimates for Analgesics
71
0.44
0.64
0.25
0.10
0.09
0.07
0.15
0.13
0.27
0.22
0.07
0.01
0.17
0.08
0.15
0.03
0.05
0.00
0.14
0.03
-0.10
-0.01
-0.11
0.10
0.13
0.13
0.01
0.17
-0.01
0.00
0.12
0.07
0.03
0.08
0.05
0.00
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
1.93
3.27
3.41
3.25
3.31
2.75
-0.51
-0.44
-0.21
95%
1.07
2.45
2.47
2.14
2.39
1.75
-1.34
-1.31
-1.12
credibility region
2.82
4.07
4.30
4.42
4.24
3.75
0.32
0.45
0.65
Table 15: Fixed cost estimates for Analgesics
72
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-0.46
-0.52 -0.41
Less than 4 Oz
-4.20
-4.71 -3.68
4 Oz to 8 Oz
-0.13
-0.32 0.08
-0.63
-0.82 -0.43
6 Oz to 8 Oz
8 Oz to 10 Oz
-0.60
-0.76 -0.45
-0.18
-0.34 -0.02
10 Oz to 16 Oz
Ounces
-0.70
-0.92 -0.49
Regular
-0.33
-0.46 -0.20
Can
-0.70
-0.87 -0.54
Albacore
1.28
1.12 1.44
Cut chunky
-0.40
-0.52 -0.28
0.29
0.11 0.46
Cut Steak
In pure water
-0.17
-0.29 -0.04
In oil
-0.63
-0.75 -0.51
Color light
0.37
0.21 0.54
Bumble Bee manuf
1.32
1.05 1.59
Chicken of the sea manuf 0.92
0.64 1.20
1.26
0.97 1.56
Del Monte manuf
Minor display
0.29
0.17 0.42
0.31
0.19 0.43
Major display
C feature
0.01
-0.25 0.28
0.28
0.18 0.39
B feature
A, A+ feature
0.29
0.16 0.42
Marginal cost estimates
Estimate 95% credibility
6.93
2.06
1.63
-0.33
0.93
-0.96
-0.20
-2.07
1.11
-0.58
1.12
0.48
0.14
-0.19
-1.73
-2.04
-2.19
-0.21
-0.20
-0.39
-0.48
-0.71
6.48
1.89
1.46
-0.47
0.78
-1.14
-0.32
-2.19
0.92
-0.69
0.93
0.36
0.02
-0.37
-2.06
-2.37
-2.51
-0.34
-0.32
-0.64
-0.59
-0.85
Table 16: Demand and marginal cost estimates for Canned Tuna
73
7.39
2.22
1.80
-0.19
1.08
-0.78
-0.07
-1.95
1.29
-0.46
1.30
0.60
0.26
-0.01
-1.42
-1.73
-1.87
-0.09
-0.09
-0.14
-0.37
-0.57
Attribute
Estimate
Chicago markets
6.10
5.00
Washington markets
Massachusetts markets 3.72
4.09
California markets
Colorado markets
3.22
Georgia markets
2.58
Quarter 1
1.28
Quarter 2
1.16
-0.54
Quarter 3
95%
4.91
3.93
2.51
2.57
2.03
1.30
0.16
0.03
-1.68
credibility region
7.27
6.03
4.92
5.65
4.42
3.87
2.38
2.33
0.60
Table 17: Fixed cost estimates for Canned Tuna
74
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-1.13
-1.20 -1.06
Constant
-7.83
-8.51 -7.12
Low end
-0.21
-0.33 -0.09
-0.03
-0.15 0.10
High end
< 4 oz
2.94
2.55 3.32
2.80
2.41 3.21
4 oz to 8 oz
8 oz to 10 oz
1.38
1.04 1.72
0.89
0.54 1.23
10 oz to 12 oz
12 oz to 16 oz
1.12
0.77 1.47
0.13
-0.08 0.33
16 oz to 35 oz
Units (16 Oz)
0.49
0.26 0.73
Regular flavor
0.85
0.69 1.00
-0.65
-0.80 -0.50
Chocolate flavor
Espresso flavor
-0.21
-0.39 -0.03
Blended
0.21
0.07 0.34
French roast
0.12
-0.02 0.25
-0.37
-0.50 -0.23
Added flavor
Colombian roast
0.19
0.05 0.33
-0.09
-0.23 0.06
Regonal coffee
Carried in Can
-0.57
-0.74 -0.40
Caffine stated
0.59
0.43 0.75
Organic
-0.84
-1.04 -0.64
Coff subsitute
-0.21
-0.52 0.09
0.48
0.32 0.64
Decafinated
Instant coffee
0.22
0.06 0.37
Instant decafinated
0.49
0.29 0.70
-0.36
-0.50 -0.23
Whole bean
Manuf P & G
-0.32
-0.53 -0.11
Manuf Altria
-0.20
-0.38 -0.02
Manuf Saralee
0.13
-0.06 0.32
Manuf Gryphon
0.04
-0.32 0.38
Manuf Nestle
-1.01
-1.25 -0.77
Brand Maxwell
0.53
0.32 0.74
Brand Starbucks/seattle 1.40
1.16 1.66
Brand Folgers
1.05
0.85 1.25
Brand Hills
0.01
-0.22 0.25
Brand Tasters choice
2.96
2.70 3.22
Minor display
0.30
0.17 0.43
Major display
0.28
0.16 0.40
B, C feature
0.52
0.39 0.64
A, A+ feature
0.54
0.39 0.68
Marginal cost estimates
Estimate 95% credibility
9.42
-0.07
0.23
6.40
5.61
1.20
-0.11
-0.34
-0.39
-1.66
0.69
-0.42
0.35
-0.21
-0.29
-0.49
-0.17
-0.17
-3.60
-0.15
0.66
1.81
0.17
-0.76
-0.61
0.68
-0.99
-3.41
-1.64
-1.65
-2.61
1.67
4.03
-0.02
-0.18
5.66
-0.30
-0.29
-0.53
-0.72
Table 18: Demand and marginal cost estimates for Coffee
75
8.50 10.35
-0.22 0.08
0.05 0.40
5.59 7.19
4.93 6.30
0.53 1.87
-0.69 0.45
-0.86 0.17
-0.73 -0.04
-1.98 -1.36
0.47 0.89
-0.69 -0.15
0.06 0.65
-0.39 -0.03
-0.47 -0.11
-0.70 -0.28
-0.37 0.02
-0.39 0.05
-3.90 -3.30
-0.36 0.05
0.29 1.04
1.19 2.46
-0.06 0.41
-1.09 -0.43
-1.06 -0.17
0.49 0.87
-1.36 -0.61
-3.69 -3.12
-2.05 -1.22
-9.88 7.54
-3.14 -2.10
1.35 1.98
3.64 4.44
-0.40 0.37
-0.59 0.26
5.22 6.11
-0.49 -0.11
-0.44 -0.14
-0.67 -0.39
-0.90 -0.53
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
4.61
2.51
3.84
3.63
2.24
1.29
-1.70
-1.63
-1.38
95% credibility region
5.48 6.37
3.29 4.08
4.76 5.66
4.89 6.30
3.13 4.01
2.21 3.15
-0.85 -0.03
-0.79 0.03
-0.51 0.34
Table 19: Fixed cost estimates for Coffee
76
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-0.69
-0.76 -0.61
Constant
-5.13
-5.50 -4.75
Small
0.32
0.15 0.49
0.09
-0.12 0.31
Large
Units
-0.81
-1.13 -0.50
Regular
0.14
0.01 0.27
Honey flavored
-0.14
-0.28 0.01
0.18
0.04 0.31
Dijon flavored
Carry in glass
0.06
-0.12 0.26
-0.21 0.09
Carry in squeeze -0.05
Hot
-0.04
-0.17 0.09
0.14
0.00 0.30
Sweet
Spreadable
-1.12
-1.33 -0.92
Pourable
-1.07
-1.30 -0.86
Squeezable
-0.86
-1.10 -0.64
Manuf Beaver
0.11
-0.04 0.27
Manuf Heinz
1.18
0.85 1.51
Manuf Reckitt
2.10
1.94 2.27
Manuf Conagra
1.84
1.62 2.07
0.25 0.66
Manuf Plochman 0.45
Manuf Hunts
0.05
-0.23 0.33
2.73
2.48 2.99
Manuf Unilever
Manuf Altra
2.78
2.63 2.93
Minor display
0.35
0.23 0.47
Major display
0.35
0.16 0.54
0.36
0.21 0.51
B, C feature
A, A+ feature
0.12
-0.17 0.41
Marginal cost estimates
Estimate 95% credibility
6.95
0.82
-0.13
-3.19
-0.34
-0.43
0.10
-0.38
-0.72
0.14
0.44
-0.66
-1.28
-1.20
-1.10
-1.50
-1.55
-2.43
-0.96
-0.96
2.64
0.11
-0.19
-0.25
-0.24
-0.30
6.46
0.59
-0.45
-3.63
-0.49
-0.62
-0.06
-0.70
-0.92
-0.02
0.27
-0.90
-1.66
-1.56
-1.32
-1.98
-1.78
-2.75
-1.19
-1.37
2.14
-0.09
-0.31
-0.47
-0.41
-0.80
Table 20: Demand and marginal cost estimates for Mustard
77
7.46
1.06
0.17
-2.76
-0.20
-0.25
0.26
-0.06
-0.53
0.31
0.61
-0.41
-0.93
-0.84
-0.89
-0.99
-1.34
-2.13
-0.73
-0.57
3.14
0.31
-0.07
-0.02
-0.08
0.20
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
2.23
2.59
2.03
2.21
2.20
1.91
-0.35
-0.57
-0.47
95% credibility region
1.81 2.65
2.18 3.02
1.59 2.48
1.68 2.78
1.76 2.65
1.44 2.40
-0.76 0.06
-1.02 -0.15
-0.90 -0.06
Table 21: Fixed cost estimates for Mustard
78
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-1.10
-1.15 -1.04
Constant
-6.27
-6.53 -6.00
Small
1.30
1.11 1.48
0.19
-0.02 0.41
Large
Units
0.25
0.03 0.47
Chicken
0.00
-0.12 0.12
Meat (beef or pork)
-0.05
-0.16 0.07
Carry vaccum packed 0.06
-0.10 0.21
Carry plastic
-0.08
-0.21 0.04
Sauce added
-0.01
-0.13 0.11
Cheese added
-0.72
-0.99 -0.45
Pre cooked
-0.87
-1.05 -0.69
Seasonal
0.34
0.06 0.62
Manuf Hormel
0.60
0.45 0.74
Manuf Smith
-0.41
-0.67 -0.16
Manuf Harry
-0.48
-0.85 -0.12
Manuf Perdue
2.01
1.71 2.31
0.65
0.50 0.80
Manuf Tyson
Minor display
0.35
0.13 0.58
0.55
-0.15 1.23
Major display
B, C feature
0.41
0.31 0.51
0.45
0.31 0.59
A, A+ feature
Marginal cost estimates
Estimate 95% credibility
4.21
2.21
1.08
-1.28
-0.16
0.02
-0.21
-0.29
-0.39
-0.56
-0.12
0.32
-0.05
-0.85
-1.55
0.90
0.08
0.04
0.12
-0.23
-0.28
3.92
2.01
0.81
-1.57
-0.29
-0.09
-0.40
-0.43
-0.52
-0.87
-0.31
0.03
-0.21
-1.09
-1.96
0.62
-0.08
-0.17
-0.60
-0.33
-0.44
4.50
2.41
1.35
-0.98
-0.04
0.13
-0.03
-0.15
-0.26
-0.24
0.07
0.62
0.10
-0.61
-1.11
1.18
0.23
0.26
0.84
-0.13
-0.11
Table 22: Demand and marginal cost estimates for Frozen Dinners
79
Attribute
Estimate
Chicago markets
11.59
10.55
Washington markets
Massachusetts markets 6.04
7.67
California markets
Colorado markets
9.64
Georgia markets
8.72
Quarter 1
1.98
Quarter 2
1.50
-1.14
Quarter 3
95%
8.75
7.85
2.88
3.89
6.69
5.37
-0.86
-1.42
-4.00
credibility region
14.55
13.31
9.08
11.42
12.62
11.87
4.81
4.34
1.75
Table 23: Fixed cost estimates for Frozen Dinner
80
Demand estimates
Attribute
Estimate 95% credibility
log(price)
0.51
0.44 0.59
Constant
-8.05
-8.37 -7.75
Small
-0.43
-0.59 -0.27
-0.09
-0.19 0.01
Units
Flavor Chocolate
-0.04
-0.12 0.05
0.33
0.25 0.42
Flavor Vanilla
Flavor Assorted
-0.10
-0.21 0.01
-0.31
-0.41 -0.21
Flavor Fruit
Carry Sqround
-0.25
-0.39 -0.11
Sugar low
-0.46
-0.57 -0.36
Fat Free or low fat -0.19
-0.28 -0.09
Brand breyer
-0.02
-0.16 0.13
0.92
0.76 1.08
Brand Benjerry
0.53
0.38 0.67
Brand Haagendaz
Any display
0.31
0.22 0.41
B, C feature
0.50
0.41 0.59
0.45
0.37 0.52
A, A+ feature
Marginal cost estimates
Estimate 95% credibility
1.58
0.20
-0.52
0.02
0.03
0.01
-0.03
0.12
0.00
-0.02
-0.23
0.57
0.61
-0.03
-0.05
-0.07
1.48
0.11
-0.59
-0.05
-0.04
-0.07
-0.10
0.05
-0.07
-0.09
-0.32
0.48
0.52
-0.10
-0.12
-0.14
Table 24: Demand and marginal cost estimates for Ice Cream
81
1.69
0.29
-0.44
0.09
0.10
0.08
0.04
0.20
0.08
0.05
-0.15
0.66
0.69
0.04
0.02
0.00
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
2.33
3.10
1.79
2.67
2.48
1.54
-1.62
-1.06
-0.80
95% credibility region
3.02 3.69
3.72 4.36
2.50 3.21
3.56 4.45
3.15 3.84
2.27 3.00
-1.00 -0.36
-0.41 0.24
-0.14 0.54
Table 25: Fixed cost estimates for Ice Cream
82
Attribute
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
Demand estimates
Estimate 95% credibility
3.43
3.37 3.49
-5.15
-4.93 -4.71
-0.06
0.00 0.07
0.08
0.18 0.28
-0.03
0.07 0.17
0.29
0.42 0.55
0.25
0.34 0.44
-0.16
-0.08 0.01
0.18
0.28 0.39
-0.06
0.07 0.20
0.00
0.11 0.22
0.06
0.18 0.29
0.11
0.21 0.31
-0.01
0.06 0.13
-0.05
0.02 0.10
Marginal cost estimates
Estimate 95% credibility
0.05
-0.07
-0.08
-0.08
-0.10
-0.08
-0.09
-0.11
-0.14
-0.13
-0.09
-0.08
-0.08
-0.08
0.14
0.00
-0.01
0.00
0.00
-0.01
-0.02
-0.03
-0.05
-0.05
0.00
0.00
-0.01
-0.01
Table 26: Demand and marginal cost estimates for Orange Juice
83
0.24
0.07
0.07
0.08
0.09
0.07
0.05
0.05
0.05
0.04
0.08
0.07
0.06
0.06
Attribute
Estimate
Chicago markets
8.40
14.84
Washington markets
Massachusetts markets 2.14
18.77
California markets
Colorado markets
4.76
Georgia markets
6.37
Quarter 1
-4.60
Quarter 2
-8.54
-6.03
Quarter 3
95% credibility region
13.77 19.28
19.93 24.97
7.91 13.74
25.78 32.87
10.36 15.93
12.57 18.82
0.52 5.77
-3.18 2.14
-0.61 4.75
Table 27: Fixed cost estimates for Orange Juice
84
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-0.58
-0.64 -0.51
Constant
-4.68
-5.07 -4.29
Small
0.06
-0.10 0.22
0.22
0.01 0.41
Large
Units
-0.30
-0.39 -0.22
Absorb extra
0.09
-0.11 0.29
Color white
0.30
0.17 0.44
Size Mega
0.53
0.36 0.69
Size Upick
0.49
0.33 0.66
Strength extra
0.65
0.43 0.87
Manuf P & G
2.27
1.96 2.59
Manuf Kimberly 1.81
1.52 2.10
1.32
1.05 1.60
Manuf Georgia
Minor display
0.23
0.07 0.39
Major display
0.31
0.20 0.41
B, C feature
0.47
0.36 0.57
0.44
0.32 0.57
A, A+ feature
Marginal cost estimates
Estimate 95% credibility
1.84
0.33
-0.28
-0.11
0.09
0.12
-0.06
-0.20
0.30
0.33
0.56
0.11
-0.09
-0.09
-0.16
-0.13
1.70
0.23
-0.40
-0.18
-0.02
0.03
-0.17
-0.30
0.18
0.20
0.42
-0.03
-0.18
-0.16
-0.24
-0.21
1.99
0.43
-0.16
-0.04
0.20
0.21
0.04
-0.11
0.41
0.46
0.68
0.24
0.01
-0.01
-0.08
-0.04
Table 28: Demand and marginal cost estimates for Paper Towels
85
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
16.30
23.47
15.94
36.26
13.44
18.17
-8.75
-9.26
-5.96
95% credibility region
10.11 22.57
17.45 29.79
9.42 22.58
27.49 45.43
7.14 19.97
10.97 25.34
-14.79 -2.60
-15.29 -3.08
-12.33 0.27
Table 29: Fixed cost estimates for Paper Towels
86
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-1.76
-1.82 -1.69
Constant
-5.02
-5.48 -4.54
Tiny or Travel
0.63
0.40 0.83
0.21
0.04 0.37
Small
Large
0.06
-0.08 0.22
-3.81
-4.47 -3.21
Units
Added Fluoride
-0.19
-0.31 -0.08
0.42
0.29 0.55
Added Multiple
Flavor mint
0.24
0.14 0.34
Type Gel
-0.05
-0.15 0.06
Container Bottle
-0.01
-0.14 0.13
Form Tartar protection
-0.11
-0.23 0.00
-0.12 0.10
Form White and Tartar protection -0.01
Color white
0.49
0.37 0.60
Color multicolored
0.18
0.07 0.29
Adult only
-0.23
-0.39 -0.08
Chlidrens
-0.18
-0.31 -0.06
Manuf P & G
-0.27
-0.45 -0.11
Manuf Colgate
-0.50
-0.67 -0.34
-0.59
-0.78 -0.39
Manuf Church
Manuf GSK
0.15
-0.03 0.32
-0.66
-0.86 -0.48
Manuf Tom Maine
Manuf J & J
1.38
1.17 1.59
6.81
6.17 7.44
Brand Gerber
Display
0.30
0.21 0.41
0.69
0.58 0.79
B, C feature
0.72
0.59 0.85
A, A+ feature
Marginal cost estimates
Estimate 95% credibility
18.53
2.50
6.32
1.87
-17.38
-1.87
0.34
0.46
-0.47
-0.75
-1.33
0.29
0.55
-1.19
2.06
-1.66
-6.77
-7.94
-9.14
-4.28
-5.70
6.43
41.45
-0.70
-1.14
-1.79
Table 30: Demand and marginal cost estimates for Toothpaste
87
17.44 19.62
1.64
3.33
5.70
6.95
1.41
2.32
-19.02 -15.76
-2.15 -1.58
0.00
0.68
0.28
0.65
-0.67 -0.28
-1.06 -0.44
-1.58 -1.09
0.07
0.50
0.26
0.82
-1.41 -0.96
1.59
2.51
-1.98 -1.37
-7.42 -6.10
-8.59 -7.26
-9.79 -8.50
-4.93 -3.62
-6.43 -4.91
5.61
7.22
34.31 49.53
-0.89 -0.51
-1.32 -0.97
-2.05 -1.53
Attribute
Estimate
Chicago markets
3.71
2.19
Washington markets
Massachusetts markets 2.07
2.24
California markets
Colorado markets
2.64
Georgia markets
3.01
Quarter 1
-0.24
Quarter 2
-0.22
0.00
Quarter 3
95%
3.14
1.68
1.52
1.56
2.05
2.44
-0.75
-0.79
-0.59
credibility region
4.29
2.69
2.65
2.93
3.19
3.61
0.29
0.29
0.55
Table 31: Fixed cost estimates for Toothpaste
88
Demand estimates
Attribute
Estimate 95% credibility
log(price)
-0.69
-0.75 -0.64
Constant
-7.20
-7.51 -6.90
Volume
-0.99
-1.14 -0.84
Chocolate
-0.02
-0.16
0.11
Vanilla
0.70
0.47
0.93
-0.01
-0.21
0.18
Assorted
Carry Box
0.97
0.81
1.12
-0.23
-0.37 -0.10
Carry Bag
Carry Tin
-0.27
-0.47 -0.07
-0.04
-0.17
0.10
Carry Tray
Cookie
0.16
0.03
0.29
0.24
0.09
0.38
Sandwich Cookie
Sugar Waffer
-0.42
-0.61 -0.23
Shape Round
-0.38
-0.52 -0.25
Shape Square
-0.23
-0.37 -0.09
-0.76
-0.96 -0.56
Shape Assorted
Form Patty
-0.25
-0.38 -0.12
Form Piece
0.12
-0.01
0.25
Form Bar
0.07
-0.07
0.22
Seasonal
-0.07
-0.28
0.15
Base Unflavored
-0.23
-0.36 -0.10
-0.38
-0.52 -0.25
Base Flavored
Base Choc. Chip
-0.28
-0.42 -0.15
0.24
0.09
0.39
Base Shortcake
0.30
0.15
0.45
Base Oatmeal
Base Macaroon
-1.12
-1.39 -0.86
Base Biscotti
0.30
0.08
0.53
Manuf Altria
0.68
0.53
0.83
Manuf Archway
0.48
0.29
0.67
Manuf Kellogg
0.71
0.55
0.88
Manuf Campbell
1.63
1.46
1.81
Manuf Lofthouse
0.95
0.71
1.19
Manuf Pepsico
-1.91
-2.16 -1.65
Manuf Voortman -1.03
-1.73 -0.43
Manuf Mckee
-1.38
-1.68 -1.09
Manuf Rab
-24.33
-38.00 -13.22
Manuf Hershey
-0.49
-0.83 -0.17
Minor display
0.34
0.23
0.45
Major display
0.32
0.21
0.43
B or C Feature
0.57
0.46
0.69
A or A+ feature
0.51
0.39
0.63
Marginal cost estimates
Estimate 95% credibility
8.75
-4.29
0.69
1.24
0.76
0.96
-0.21
0.76
0.03
-0.73
-0.81
-0.74
-0.10
-0.91
-0.57
0.00
0.82
0.93
1.23
0.03
-0.62
-0.21
0.61
-0.05
-1.32
0.44
-2.00
-1.80
-2.15
-0.21
-1.47
-2.89
4.38
-4.16
35.74
-0.59
-0.19
-0.22
-0.37
-0.27
8.49 9.01
-4.46 -4.13
0.53 0.85
0.90 1.59
0.50 1.01
0.76 1.16
-0.39 -0.04
0.50 1.02
-0.14 0.21
-0.89 -0.57
-0.99 -0.64
-1.00 -0.48
-0.28 0.08
-1.11 -0.73
-0.88 -0.27
-0.15 0.14
0.65 0.98
0.73 1.13
0.91 1.56
-0.11 0.18
-0.77 -0.46
-0.36 -0.06
0.44 0.78
-0.23 0.12
-1.74 -0.90
0.05 0.82
-2.20 -1.82
-1.98 -1.61
-2.34 -1.96
-0.40 -0.04
-1.82 -1.11
-3.21 -2.57
-0.09 10.46
-4.47 -3.85
14.68 61.81
-1.97 1.47
-0.30 -0.08
-0.33 -0.11
-0.49 -0.26
-0.39 -0.15
Table 32: Demand and marginal cost estimates for Cookies
89
Attribute
Chicago markets
Washington markets
Massachusetts markets
California markets
Colorado markets
Georgia markets
Quarter 1
Quarter 2
Quarter 3
Estimate
1.55
1.40
1.19
1.74
1.56
1.28
-0.15
-0.25
-0.16
95%
1.22
1.10
0.79
1.30
1.21
0.89
-0.47
-0.58
-0.50
credibility region
1.88
1.70
1.62
2.20
1.91
1.69
0.18
0.09
0.19
Table 33: Fixed cost estimates for Toothpaste
90
Category
Orange Juice
Paper towels
Frozen Dinner
Tuna
Coffee
Ice cream
Analgesics
Toothpaste
Mustard
Cookies
Storage
Fixed cost
Refrigerated
$14.09
Shelf (large UPC) $13.59
Refrigerated
$10.03
Shelf (small UPC) $4.83
Shelf (small UPC) $3.38
Refrigerated
$2.68
Shelf (small UPC) $2.67
Shelf (small UPC) $2.50
Shelf (small UPC) $1.89
Shelf (small UPC) $1.30
Assortment Size
48
27
46
87
190
209
87
153
48
373
Price Elasticity
-1.71
-3.92
-2.02
-3.31
-3.30
-3.18
-1.63
-1.92
-2.36
-2.82
Table 34: Summary of assortment estimates, numbers represent the average across stores
and quarters
91
Category
Ice cream
Coffee
Tuna
Frozen
Orange Juice
Toothpaste
Paper towels
Mustard
Cookies
Analgesics
Ice
Orange ToothCream Coffee Tuna Dinner
juice
paste
1.00* 0.36* 0.37* 0.34* 0.29* 0.26*
0.36* 1.00* 0.40* 0.37*
0.21
0.28*
0.37* 0.40* 1.00* 0.48* 0.39*
0.23
0.34*
0.37* 0.48*
1.00*
-0.04
0.39*
0.29*
0.21
0.39*
-0.04
1.00*
0.19
0.26*
0.28*
0.23
0.39*
0.19
1.00*
0.36*
0.24* 0.30*
0.11
0.52*
-0.07
0.34*
0.09
0.25*
0.42*
-0.07
0.12
0.19
0.10
0.23
0.23
0.04
0.28*
0.22
0.10
0.09
0.10
0.24*
0.13
Table 35: Correlations of fixed costs
92
Paper Musttowels
ard
Cookie
0.36* 0.34* 0.19
0.24* 0.09
0.10
0.30* 0.25* 0.23
0.11
0.42*
0.23
0.52* -0.07
0.04
-0.07
0.12
0.28*
1.00*
0.07
0.02
0.07
1.00*
0.15
0.02
0.15
1.00*
0.08
0.00
0.17
Analgesics
0.22
0.10
0.09
0.10
0.24*
0.13
0.08
0.00
0.17
1.00*
Fixed
Cost
$5
$50
$150
$1,000
Variable
Number of UPCs
Markup
Number of UPCs
Markup
Number of UPCs
Markup
Number of UPCs
Markup
sold
sold
sold
sold
Duopoly
Monopoly
Store 1 Store 2 Store 1 Store 2
208
187
206
187
$5.23
$6.10
$6.91
122
111
97
108
$5.17
$6.06
$6.74
45
47
31
47
$4.97
$5.93
$6.37
1
12
1
12
$4.54
$5.62
$5.68
Table 36: Understanding the effect of competition on assortment decisions in coffee
93
Fixed
Cost
UPCs by
Colgate
$0.50
Other manuf
Colgate
$8.00
Other manuf
Colgate
$30.00
Other manuf
Colgate
$100.00
Other manuf
Colgate
$150.00
Other manuf
Colgate wholesale discounts
Current 10% 25%
40%
44
52
56
63
142
142
142
141
37
37
38
39
57
57
57
56
27
29
31
32
32
32
31
31
10
10
11
13
12
12
12
12
9
9
9
9
4
4
4
4
Table 37: Understanding the effect of wholesale discounts, with cost constraint and no space
constraint, table contains the number of UPCs stored
94
Fixed
Cost
UPCs by
Colgate
$0.50
Other manuf
Colgate
$8.00
Other manuf
Colgate
$30.00
Other manuf
Colgate
$100.00
Other manuf
Colgate
$150.00
Other manuf
Colgate wholesale discounts
Current 10% 25%
40%
44
51
56
62
142
135
130
124
37
37
38
39
57
57
56
55
27
28
29
30
32
31
30
29
10
10
11
12
12
12
11
10
9
9
9
9
4
4
4
4
Table 38: Understanding the effect of wholesale discounts, with cost constraint and with
space constraint, table contains the number of UPCs stored
95
Manufacturer
Bayer
Glaxo Smith-Kline
Insight
Johnson and Johnson
Little drug store
Little necessities
Novartis
Polymedica
Upsher-Smith
Wyeth Labs
Total UPCs
Total profits
% of optimal profits
UPC
Fixed cost $10
offered Optimal tying
√
28
82%
√
3
100%
2
√
43
72%
1
2
√
22
77%
√
1
100%
1
√
15
53%
118
83
112
$9,904
$9,637
97%
Fixed cost $75
Optimal tying
√
43%
√
33%
35%
14%
41%
0%
9%
0%
53%
45
$5,828
√
46
$2,731
47%
Table 39: Understanding the effect of tying contracts
96
Fixed cost $150
Optimal tying
25%
33%
20%
19
$3,668
√
15
$842
23%