Download Structural Demand Models for Retailer Category Pricing

Structural Demand Models
for
Retailer Category Pricing
Eric Anderson
University of Chicago
and
Naufel Vilcassim
London Business School
December 21, 2001
Structural Demand Models
for
Retailer Category Pricing
Abstract
One critical aspect of retailer category management is pricing the brands within
the category in order to maximize total category profits. Unlike the manufacturer, a
retailer must carefully assess how changes in brand prices affect substitution between
brands and overall category profits. In this paper, we demonstrate that structural demand
models have inherent advantages over commonly used non-structural approaches, such as
the linear and log-linear demand models. While numerous papers have utilized these
non-structural demand models, we show that these models have unappealing theoretical
properties for category pricing.
We then show that a variant of the AIDS model provides for very flexible
substitution effects and category expansion effects. In addition, the model specification
allows for prices and merchandising (display/feature) to separately affect brand
substitution and category expenditure. We compare this model to the logit model with an
outside good, which can also been used for category pricing. We describe how the
underlying assumptions and structure of each model yield different implications. Finally,
we apply each model to a retail category pricing problem in three different categories.
The results show how the AIDS model can be used to assist in retailer pricing decisions
and illustrate its comparative advantages/limitations with respect to the logit model.
Introduction
Category management is a complex process that is of considerable importance to
retailers. In the 1990s, category management emerged as a dominant retail practice and
an integral part of efficient consumer response programs (ECR). A.C. Neilson, one of the
industry leaders in this area, defines category management as a “process that involves
managing product categories as individual business units and customizing them
according to customer preferences within stores. (Neilson 1996). Industry surveys reveal
that over 90% of all manufacturers and retailers indicate that category management is of
concern and importance to the entire channel (Cannondale Associates, 1998). Brandweek
concludes that “The real value of category management is in analyzing the overall
profitability and productivity of the category, identifying best practice solutions and
applying micro-marketing approaches to those solutions.” (Dusek, 1999) While most
channel members recognize category management as an opportunity, many are frustrated
by its mixed success (Cannondale Associates, 1998).
One key to successful retail category management is correctly pricing multiple
brands within a category. This task is analogous to the manufacturer problem of pricing a
product line and involves a two-step procedure (e.g., Zenor 1994). The first step is
estimation of a demand system that yields own- and cross-price effects, promotional
effects, and any other factors that drive demand. In the second step, estimated price and
promotion effects are used to compute brand prices that maximize category profits.
While a number of different demand models have been used as an input for the
optimization phase (e.g., Reibstein and Gatignon 1984, Montgomery and Bradlow 1999,
and Chintagunta 2001), we demonstrate that they differ in their appropriateness for retail
category pricing decisions. We identify three key properties that differentiate these
demand systems and hence their appropriateness. We then show that a variant of the
AIDS (Almost Ideal Demand System) model offers very flexible properties and
demonstrate its application to retail category pricing. In the remainder of this section, we
describe these three properties, outline our model, and summarize our findings.
The first property that is critical for category pricing is that the demand system be
derived from consumer’s utility maximizing behavior. In the economics literature, this is
referred to as a demand model that is structural. In deriving demand from first-principles,
the critical aspect of consumer behavior that must be captured is substitution inside and
-- 1 --
outside a category. In other words, the demand system must explicitly consider sales of
an individual brand and total category sales. A demand system that only considers
substitution within a category or only considers individual brand sales fails this criterion.
The implication for retail category pricing is that such a demand system may imply
unrealistic optimal pricing strategies. We discuss these details in a later section of the
paper.
A second property of demand systems is that there is consistency between the
underlying individual choice process and the derived aggregate demand. For example, if
the model assumes a discrete choice process, then it is critical that consumers actually
make discrete choices. If consumers purchase multiple units or multiple brands on a
single shopping occasion, then this assumption is violated. A model that places fewer
restrictions on the individual choice process may be more desirable if the retailer is
uncertain about the choice process. However, if the retailer is certain about the choice
process (e.g., for automobiles the choice is clearly discrete), then adding this information
may result in a superior model.
A third property of demand systems that is critical for retail category pricing is
that they allow for flexible patterns of within-category brand competition as measured by
the cross-price elasticities. These elasticities capture the degree of substitution between
brands when the retailer changes one brand’s price. The presence of cross-price effects is
what distinguishes category pricing (retailer’s problem) from brand pricing
(manufacturer’s problem). If the true cross-price elasticities are zero (or negligible), then
the retailer’s problem simplifies to maximizing profits on each brand independently.
However, if the true cross-price elasticities are non-zero, the retailer must select brand
prices to maximize joint brand profits. Thus, retailer category management requires a
demand system that allows for flexible patterns of brand substitution. Demand systems
that impose severe restrictions on brand substitution are less desirable for category
pricing.
A main premise of this paper is that many of the demand systems used previously
to study retailer category pricing falls short on one or more of these three criteria. Failure
to capture these three criteria has significant implications for category pricing. For
example, failure to capture category substitution may result in a retail category profit
function that is not well behaved. In a later section, we explain how the theoretical
-- 2 --
optimum for such demand systems predicts in an infinite price for one or more brands. In
response to these three issues, we introduce an extended version of the well-known AIDS
(Almost Ideal Demand System) model developed by Deaton and Muellbauer (1980).
Unlike choice models, the basic AIDS model works with expenditure shares of each
brand. Each brand’s expenditure share is a function of its own-price effect, cross-price
effects, and a category expenditure effect. An important feature of the model is that total
category sales affect relative brand expenditure either positively or negatively; these are
referred to as marginal expenditure effects. We modify the AIDS model to include
promotion effects and also model total category expenditure as a function of brand prices,
brand promotions, and other factors.
This approach endogenizes total category
expenditure and we refer to this as the “AIDS system.” In a later section, we discuss the
advantages and limitations of our model compared to other demand systems.
We apply our model to three grocery store categories: toilet tissue, refrigerated
orange juice, and canned tuna. We analyze the pricing decision at the store level because
the retail chain for which we have data implements a zone-pricing policy, whereby store
prices are customized to accommodate local demand and competitive conditions. To
illustrate the relative properties of our model, we also consider a logit model with an
outside good. Our main findings, different or beyond those from previous studies, are as
follows:
•
Unlike logit demand models, the optimal product line pricing policy in our model
closely approximates a percent markup rule.
•
Unsupported price cuts require deeper discounts than those supported by in-store
display and store feature advertising.
•
When one or more brands are promoted, profits and sales of non-promoted brands
may increase due to category expansion effects. In some cases, profits of all
brands may increase.
•
For a retailer, it is less profitable to promote brands with negative marginal
expenditure effects.
•
Promoting multiple brands in a category on the same week may be sub-optimal,
particularly when brands have negative marginal expenditure effects or strong
cross-price effects.
•
Neither the retailer nor the manufacturers benefit from promoting brands that are
close substitutes in the same week.
-- 3 --
We also demonstrate how our model can be used to address how total store
expenditures affect expenditures on a particular category. For the categories we consider,
we find that category sales are positively correlated with increases in total store
expenditure. Importantly, in response to an exogenous increase in store expenditure (e.g.
holiday week), our model enables retailers to gauge expected changes in category profits
and whether a price response is necessary. For the categories we examine, we find that a
minimal change (0%-2%) in product line price is required.
However, we find
considerable variation in the expected changes in brand/category sales and profits.
The remainder of the paper is organized as follows. In the following section we
evaluate the properties of alternative demand systems for retail category pricing. Next,
we describe the AIDS model and describe how we endogenize category expenditures. We
then state the retailer’s problem and describe how our model addresses many of the issues
relating to retailer product category pricing. In the following section, we describe the
data, the estimation method, and report the results of the demand system estimation.
Next, we analyze the retailer’s category pricing problem and determine the optimal
regular and sale prices under a variety of scenarios that a retailer typically confronts. In
the final section, we summarize our main results and implications and address the
relevance of our analysis for other product line pricing situations.
-- 4 --
Alternative Aggregate Demand Models for Category Pricing
Previous researchers have used two broad types of aggregate demand models to
analyze retailer category pricing. For example, Reibstein and Gatignon (1984), Zenor
(1994), Montgomery and Bradlow (1999), and Basuroy et al. (2001) use log-linear or
linear models to represent aggregate demand. Besanko et al. (1998) and Nevo (2001)
have used Logit models of market share, along with an outside good to represent
aggregate demand. Each of these aggregate models has its advantages and limitations
vis-à-vis retailer category pricing. In this section, we evaluate these models in terms of
the three criteria discussed in the Introduction.
i) Structural Demand System and Category Substitution
Linear and log-linear models have often been used to study retailer category
pricing because they are simple and provide a good fit to data. Recall that solving a
product line pricing problem involves two-steps: estimation and optimization. These
reduced form models often perform well when estimating demand. However, problems
with these models appear when one considers maximizing product line profits. Neither
the linear or log-linear model offers finite product line prices. Instead, these models
predict that it is globally optimal to set at least one price as high as possible (infinity). As
an illustration of this problem, consider Reibstein and Gatignon (1984). The authors use
a log-linear demand model and find that the optimal prices involve setting the price of
one offering to an exogenously defined upper bound.
Before we formalize the result, let’s consider the intuition for this finding. The
key feature that distinguishes product line pricing from pricing a single product is crossprice effects. It is well known that for substitutes, the cross-price effects are positive.
Hence, raising the price of brand 1 increases the sales of brand 2. If the gains on brand 1
profits outweigh losses on brand 2 profits, total category profits increase. In a log-linear
demand system, high prices for brand 2 results in sales and profits of approximately zero
for brand 2. While brand 2 profits decline to zero, the quantity sold of brand 1 continues
to increase. Thus, category profits are strictly increasing as the price of brand 2
increases. To illustrate this graphically, we plot the category profit function versus the
price of each brand for the log-linear and linear demand systems in Figure 1.
-- 5 --
Figure 1: Retail profit function results in infinite price
The left panel is the profit function for a log-linear demand system and the right
for a linear demand system. The global maximum for both models is to set one price at
infinity and the other price at the monopoly price. As a technical note, for the linear
r
r
demand system, we assume that the demand for brand i is qi = max(qi( p ),0) where p is
a vector of brand prices. In practice, if the price of an item is high then sales are zero
sales; our assumption captures reflects this.
More technically, two conditions of an aggregate demand system may yield
infinite product line prices for a retailer. These are:
r
∂qi ( p)
> 0 for all pj,
∂p j
(C1)
r
lim π j ( p) = 0 .
(C2)
p j →∞
The first condition is that there are positive cross price effects, and this occurs
when the product line includes substitutes rather than complements. Notice that this
condition implies that profits of brand i are strictly increasing in the price of brand j. The
second condition is that as the price of a brand increases the profits on that brand must
converge to zero. Because margins are positive as price increases, this condition implies
that quantities are non-negative. These two conditions are sufficient to ensure that
product line profits are always increasing in the price of brand j.
-- 6 --
The logit and probit demand systems model market shares rather than quantities.
However, if an outside good is not included then category substitution is not modeled and
this leads to an analogous retail category pricing problem. The theoretical optimal
solution is to raise the prices of all brands to infinity. Because market shares, by
construction, sum to 1 and margins are infinite the retail category profits are infinite.
These results are summarized in Claim 1.
Claim 1
Consider a product line with two or more products. If an aggregate demand
system satisfies C1 and C2 or a market share demand system does not include an
outside good, then the optimal price of one or more brands is infinite and retail
category profits are infinite.
Proof:
In an aggregate demand system, a sufficient condition for category profits to be
increasing in the price of brand j is:
r
r
∂πi ( p) ∂π j ( p )
>
∑
pj
pj
i≠ j
C1 implies the left hand side is strictly positive and C2 implies the right hand side
converges to zero. Together, they imply on price is infinite and category profits
are infinite. In a share demand system with no outside good, the prices of all
goods can be increased and market shares remain positive. More technically let
ur *
Qi = MarketSize * Si , where Si ∈ [0,1]. Then for any p = ( p1* , p2* ,..., pJ* ) , there
ur
exists a vector p = ( p1 , p2 ,..., pJ ) such that p j > p*j and S j = S *j for all j. This
implies all prices are infinite and category profits are infinite.
QED
Intuitively, a demand system yields theoretically infinite profits when it fails to
explicitly separate brand substitution and category substitution. For example, in an
aggregate demand system we expect that a small increase in the price of a brand results in
substitution to another brand. However, we also expect that the increase in demand is
bounded – perhaps by the size of the market. Unfortunately this latter effect is not
captured in many aggregate demand systems.
-- 7 --
Similarly, if a market share demand
system fails to capture substitution outside the category, the optimization model assumes
customers are willing to pay infinite prices. Obviously this is not realistic and illustrates
a problem with the specification of the demand system. Failure to account for category
substitution explains why both types of models offer reasonable estimates of demand
elasticity but are unattractive for price optimization.
Previous analyses of retailer category pricing using linear and log-linear aggregate
demand systems have varied in their approach to this problem. In analytic models with
linear demand, it is common to ignore the condition that quantity is non-negative.
Assuming the concavity conditions hold, the optimal prices and profits are finite. Other
solutions to this problem are ad-hoc. For example, Reibstein and Gatignon (1984) fix the
price of one product ‘as high as possible’ while, Montgomery and Bradlow (1999)
decompose a brand’s retail price into an overall mean category price and a brand
adjustment component and bound the latter so as to get finite prices. Neither of these adhoc solutions addresses the issue of whether prices determined are indeed optimal and
maximize total category profits.
In market share models, introduction of an outside good addresses the problem of
substitution away from the category and hence, the optimal prices are finite. As the price
of a brand increases, the shares of all other brands and the outside good also increase.
Total sales and profits are bounded because total market share is 100%, by construction,
and the size of the market is fixed.
While the outside good captures category substitution, a practical limitation of the
logit model is defining the outside good and measuring its quantity and price. Although
aggregate household store traffic in a given week allows one to proxy for quantity sold of
the outside good, one does not easily obtain a measure of its price. One might use all
categories in the store to construct a weekly store price index, but to our knowledge this
approach has not been pursued. Instead, the price of the outside good is typically
normalized to one.
Both the elasticities from the estimation phase and the price
optimization can be sensitive to the manner in which the outside good is operationalized.
ii) Consistency between individual choice and aggregate demand
A second desirable property of a demand system is that it reflects the underlying
consumer choice process. This process includes choices over categories, brands, and
-- 8 --
quantities. In some settings, customers may purchase multiple brands and multiple units
within a category. For example, on a single shopping trip a customer may purchase 2 sixpacks of Diet Coke and 1 two-liter bottle of Coke. In other settings it may be clear that a
customer will purchase a single product (e.g., a customer only purchases one
automobile). An appropriate demand model should capture ones knowledge, or lack of
knowledge, about the consumer choice process.
In environments where one is uncertain about the consumer choice process, a
demand system that places fewer assumptions on consumer choice may be more
desirable. An advantage of reduced form models, such as the linear and log-linear
demand systems, is that they are flexible and place few restrictions on consumer choice.
In contrast, the aggregate logit makes very strong assumptions about consumer behavior.
Every consumer is assumed to purchase one unit of one brand on each shopping trip. If
some consumers purchase multiple brands or multiple units on a shopping trip, then the
model may yield inaccurate measures of brand substitution. In contrast, when it is clear
that the choice process is discrete, incorporating this information in the demand model
may improve estimates.
iii) Flexible pattern of substitution
Brand substitution within the category is what distinguishes retailer pricing from
manufacturer pricing, and therefore it is important that the demand model allow for
flexible substitution patterns. In this regard, linear and log-linear demand systems are
fairly flexible and allow for varied substitution patterns. However, a limitation of the
aggregate logit formulation is its well-known property of unappealing cross-price effects,
which has two implications for pricing.
A first implication is that the aggregate logit implies constant absolute dollar
markups for all brands (see Besanko et al. 1998). This is generally inconsistent with
empirical evidence and managerial wisdom (Steiner, 1973; Berkowitz, 1992; Ortmeyer
1993). A second implication is that current-period category expansion effects of price
promotions may be underestimated. To understand why, one must first recognize that the
"market share" of the outside good reflects customers who visit the store, but do not
purchase in the category. In empirical applications, the non-purchase option often has a
very large relative share. While a price promotion induces switching between purchases
-- 9 --
and non-purchases of the category, many share models assume this is proportional to
market shares. As the market shares of the n brands are small relative to the “(n+1)th”
brand (the outside good), category expansion effects may be underestimated.
Recently, researchers such as Nevo (2000) have made the logit model more
flexible by incorporating unobserved heterogeneity. This model, which is referred to as
the random coefficients logit or the heterogeneous logit, has more flexible cross-price
effects. However, even after incorporating heterogeneity, reported cross price effects in
these models can still be quite small (Chintagunta, 2001; Berto Villas-Boas, 2001).
Underestimation of cross-price effects will offer misleading implications about category
pricing.
To illustrate the importance of modeling cross-price effects for retail category
pricing, it is instructive to compare the retailer and manufacturers’ incentives. In a
product line with two goods, the retailer’s optimal percent markup on product 2 is given
by:
%Markup on Product 2 =

 p1q1  η12  
100-100 



η21η12  
 p2 q2  η11  
η
−
 22

η11 

−1
(1)
In this expression, ηij is the cross price effect of pj on qi. In contrast to the above
expression, the optimal markup for the manufacturer is -1/η22. Notice that if brand 2’s
price does not affect brand 1’s sales (i.e., η12 = 0), then the retailer and manufacturer
incentives are aligned and the optimal markups are equivalent. When the price of brand 2
affects the sales of other brands (i.e., η12 ≠ 0), this is no longer the case. The extent to
which the retailer and manufacturers’ incentives are not aligned depends on the
magnitude of cross-price effects. For retail product line pricing, it is critical that the
demand system allow for flexible patterns of brand substitution.
Model Development
In the previous section, we identified three desirable properties of a demand
model for retail category pricing. The linear, log-linear, and logit demand models fail to
satisfy these criteria and in this section we present a model that meets these criteria. We
consider a retailer selling J different brands of a given product category who wishes to
maximize total category profits. Our solution to this problem is in two stages: demand
-- 10 --
specification and optimization. We first outline our demand model, which is a variant of
the Almost Ideal Demand System (AIDS) of Deaton and Muelbauer (1980)1. We then
describe the properties of our model for retail optimization.
Our Model: AIDS System
We chose the AIDS model as our demand specification for two reasons. First, the
model has attractive theoretical properties. The specification is consistent with utility
maximization (i.e. a first order approximation to any arbitrary utility function) and places
few restrictions on the price elasticities.
Second, the demand system naturally
incorporates category expenditures. As we show later in this section, modeling category
expenditures is critical for price optimization.
The basic demand system is:
J
w jt = a j + ∑ γ jk log( pkt ) + b j log( xt / Pt ) + c j DF jt + ε jt .
(2)
k =1
In this equation, wjt is the expenditure share of brand j in period t, pjt is the price of brand
j in period t, xt is total expenditure on all J brands, Pt is a price index of the J brands, and
DFjt is a measure of weekly feature and display. In the original AIDS model, there are no
marketing mix variables (e.g. cj = 0) and the theoretical restrictions on parameters aj, γjk,
and bj that follow from utility maximization are ∑ a j = 1 , ∑ b j = 0 , and ∑ γ jk = 0 . These
j
j
k
restriction hold in our model if we include cross-promotion effects (i.e., cjk), and imply an
analogous adding up restriction, ∑ c jk = 0 .
k
For parsimony, we only include own-
promotion effects in our model.
In most applications of this model, total expenditure (xt) is considered exogenous.
In our approach, we consider a second equation to model total category expenditure:
xt = z0 + z1 X t + z2 Pt + z3 DFt + νt .
(3)
In this equation, Pt is identical to equation (2), DFt captures the extent of category feature
and display, and Xt is a measure of net store expenditure (i.e. expenditure outside the
category). This is a linear expenditure system, as described by Deaton and Muellbauer
1
See Cotteril et al. (2000) for an application of the AIDS model to study the interaction between national
and private label brands.
-- 11 --
(1982).2 We simultaneously estimate both equations using an instrumental variables
approach, which endogenizes category expenditure. Modeling total category expenditure
is necessary if one is to consider optimal retail pricing. Extreme pricing strategies (i.e.
one or more prices at infinity) are no longer optimal if category expenditure decreases as
brand prices increase (∂xt/∂pjt < 0).
It is also important to note that total category expenditure is not well defined from
equation (2) alone. To see this, set cj = 0 and add up the brand expenditures (wjt).
Because the shares must sum to one, this gives:
J
∑ w jt = 1 = ∑ a j + ∑ ∑ γ jk log( pkt ) + ∑ b j log( xt / Pt ) + ∑ ε jt .
j
j k =1
j
j
j
(4)
Given that ∑ a j = 1 , ∑ b j = 0 , and ∑ γ jk = 0 , total expenditure is indeterminate.
j
j
j
Thus, if we only considered brand expenditure shares, this again admits unreasonable
solutions in price optimization because total expenditure is not bounded. As we are
interested in price optimization, this rationalizes the need for a total expenditure equation.
Such a formulation can also be justified theoretically by treating the demand (or
share equations) and the expenditure equations as a two stage budgeting process. In the
first stage, the total expenditure on the product category is determined based on the prices
of the brands within the category and an overall store price index. The store price index
represents competition from other categories for a share of the total, within-store
expenditures (see Deaton and Muellbauer 1982). At the second stage, the expenditure
determined in the first stage is allocated to the brands within the product category, based
on the observed prices. The AIDS model is used for the second stage analysis, while a
variation of Stone's (1954) linear expenditure system is used for the first stage analysis.
Retail Price Optimization
We now turn to optimizing the retailer's profit function. Given marginal cost cj,
for brand j, the retailer optimizes total category profit:
J
π = ∑ ( p j − c j )q j
j =1
s.t.
2
r
q j = max(q j ( p ), 0)
(5)
∀j = 1...J .
We considered a model with log(xt) rather than xt, and this produces a similar model fit.
-- 12 --
We assume that the prices and quantities are consistent with the posited demand
systems and total category expenditure in equations (2) and (3). Assuming quantities are
non-negative, the retailer’s first order condition for product j is
r
J
dqk ( p)
dπ
= q j + ∑ ( pk − ck )
=0
dp j
dp j
k =1
(6)
In this expression, the quantity of brand j is q j = xt w j ,t / p j , which is a function of
category expenditure (equation (3)), brand expenditure share (equation (2)), and brand
price. Given the AIDS model functional form, we cannot obtain closed-form expressions
for the optimization of (2) and (3). Hence, we numerically compute the optimal prices
given the required parameter estimates from the demand system and the expenditure
model. We require that the optimal prices satisfy the first order conditions (equation 6)
and lie on the demand system (equations 3 and 4)3.
In our model specification, the expenditure share equations allocate a fixed level
of category expenditure to each of the brands. The expenditure equation endogenizes the
level of expenditure as a function of category prices. As the prices inside the category
increase, category expenditures decrease as customers substitute to products in other
categories. In turn, the expenditure on each brand decreases. This addresses the issue of
infinite category profits and is summarize claim 2.
Claim 2
For the demand system specified in (2) and (3), if z2 < 0 the optimal product line
profits and prices are finite.
Claim 2 follows directly from our earlier arguments. Notice that if category expenditure
is not a function of category prices (z2 = 0), our specification may lead to the same
optimization problem.
In Table 1, we compare the three properties of demand systems discussed in the
previous section for our model, market share demand models, and aggregate demand
models. Demand models that fail to capture category substitution are unattractive for
retail category pricing because they may predict infinite profits, which is obviously false.
3
An alternative approach is to use parameter estimates and observed quantities to compute optimal prices
from the first order conditions. However, this does not ensure that the observed quantities and optimal
prices are consistent with the estimated demand system.
-- 13 --
Share models that include an outside good and the AIDS system both model category
substitution, and therefore overcome this problem. With respect to the consumer choice
process, the relative attractiveness of the logit model or AIDS system depends on the
application. There is considerable evidence that in packaged goods, consumers often
purchase multiple units and/or multiple brands on a shopping trip (Dube, 2001). This
suggests that the AIDS model is slightly more attractive than the logit in our application.
With respect to flexibility in brand substitution, the AIDS model is very flexible. As
mentioned earlier, empirical studies often report small cross-price effects; as this is the
critical aspect of retail category pricing, the logit model is relatively less attractive than
the AIDS model.
Table 1: Properties of Demand Models for Category Pricing
Property
Logit Demand Models
Aggregate
Demand Models
AIDS
System
(Linear, Log-Linear)
No Outside
Good
Outside Good
Category Substitution
No
No
Yes
Yes
Consumer Choice Process
No Assumption
Discrete Choice
Discrete Choice
No Assumption
Flexible Brand Substitution
Yes
No
No
Yes
Comparison Models
The previous discussion suggests that an appropriate benchmark for our model is
the logit model with an outside good. Similar to Besanko et al. (1998), we assume that
each customer who visits the store could purchase up to one unit per visit. Thus, the
quantity of the outside good (non-purchases) is the number of customers that visit a store
each week minus weekly unit sales for the focal category. The share of brand j in week t
is:
s jt =
V jt
e
J +1 V
e kt
,
(7)
∑
k =1
where
V jt = a j + b jt p jt + cDF jt ,
j = 1...J ,
VJ +1 = 1.
-- 14 --
(8)
In the next section, we describe our data and estimation results for the AIDS
system and the logit model with an outside good.
Data and Estimation
Description of the Data and Variables
We apply our model to data from three grocery store categories: toilet tissue,
refrigerated juice, and canned tuna. A complete description of the data for each category,
including
the
individual
UPCs,
is
available
at
http://gsbwww.uchicago.edu/research/mkt/Databases/DFF. The data includes variables
indicating whether an item was sold on promotion that week, together with the number of
units sold, the price of each item, the wholesale cost of an item, and whether a major
holiday fell during that week. The nature of the variables is described in some detail on
the University of Chicago web site. As the description of the promotion variable is not
very complete, we interpret the variable in the same way as Kadiyali, Chintagunta and
Vilcassim (2000).
In each category, we focus our attention on the most popular package size: 4-rolls
of toilet tissue, 64 oz. refrigerated juice, and 6 ounce canned tuna. The time series of
approximately 145 weeks covers the time period January 1991 to September 1993. As
shown in Table 2, we consider the 3 top-selling brands, the store brand, and a fifth
“other” brand in each category. The “other” brand is a composite of all other brands in
the category.
Table 2: Brands Used in Analysis
Toilet Tissue
Canned Tuna
Refrigerated Juice
Brand 1
Store Brand
Store Brand
Store Brand
Brand 2
Charmin
Chicken of The Sea
Minute Maid
Brand 3
Northern
Starkist
Tropicana Season’s Best
Brand 4
Cottonelle
Bumble Bee
Tropicana Pure Premium
Brand 5
“Other”
“Other”
“Other”
Summary statistics for all of the brands are provided in Table 3. As expected, the
store brand price and wholesale cost are significantly less than the national brand price
and cost. The market share of the store brand ranges from 5.7% (toilet tissue) to 28.3%
-- 15 --
(refrigerated juice) while the national brand shares range from 16.6% (refrigerated juice)
to 28.8% (toilet tissue). There is considerable use of promotions in all three categories.
INSERT TABLE 3 ABOUT HERE
In refrigerated juice, we split Tropicana into two brands (Season’s Best and Pure
Premium) because Tropicana Pure Premium has significantly greater wholesale cost
($1.89 vs. $1.50) and average retail price ($2.49 vs. $2.00). In canned tuna, a low market
share, premium brand dominates the “other” category. While equivalent in size, this
brand of tuna has significantly higher price and wholesale cost. For toilet tissue and
refrigerated juice, the “other” brands are priced similarly to national brands 2-4.
While our model can accommodate multiple stores, we chose to focus on one
randomly chosen store (store 59) to demonstrate that our model can be applied in that
setting. Our primary motivation is to demonstrate that a single store retailer can apply the
model. For a multi-store retailer, including more stores in the analysis would mainly
improve the efficiency of the parameter estimates.
We were careful to verify the
robustness of our results by estimating the model on different stores.
We aggregate UPCs to the brand level by adding weekly unit sales, adding
weekly dollar sales, and taking the unit volume weighted weekly average price. Note that
because we use the same brand size within each category, we do not need to normalize
price per unit size. Further, there is minimal within brand variation in the weekly price
because the sizes of all UPCs are equal. In the Dominick’s data, the binary (0/1)
variables “bonus” and “special” are used to indicate some form of promotion (i.e., instore display or feature). The promotion variable in our model, DFjt, is computed as the
percent of UPCs within a brand that have either a “bonus” or “special” indicator of 1.
Our specification of (3) requires us to construct three category variables: Pt, DFt,
and Xt. For Pt, we use the Stone price index (see Deaton and Muellbauer (1980)):
J
log( Pt ) = ∑ w jt log( p jt )
(9)
j =1
This index is a well-established price index in applications of the AIDS model and its
main advantages are that it renders the AIDS model linear in the parameters, and has
performed well empirically in past studies. We construct the category promotion variable
analogous to (9): an expenditure share weighted brand promotion variable
-- 16 --
( DFt = ∑ w jt DF jt ). For net store expenditures, Xt, we calculate the weekly total dollar
j
expenditures in all categories listed in the Dominick’s web site and subtract weekly dollar
expenditures on the focal category. These 29 categories include primarily dry-goods and
some frozen foods, and a complete description of all categories is contained on the web
site.
Instruments
Similar to recent models in marketing (Villas-Boas and Winer 1999; Kadiyali et
al 2000), we recognize that price is an endogenous variable in our model. To address
this, we use an instrumental variables approach and seek variables correlated with pjt but
uncorrelated with εjt. As our data contains wholesale price, we use both current and 1week lagged wholesale price as instruments. Similarly, it is common to use lagged price
as an instrument and posit that it is uncorrelated with εjt. (Villas Boas and Winer, 1999).
As such, we use both 1-week and 2-week lagged prices. Finally, we take advantage of
the fact that Dominick’s uses multiple price zones that vary in their competitive
conditions. For example, stores located near a low-priced competitor, such as Cub
supermarket, are in an aggressive price zone. Conversations with the former CEO of
Dominick’s indicate that there are separate decision rights for each price zone.
If
endogeneity is due to response to a competitor action in a specific price-zone (e.g. actions
by a rival such as the Cub Stores), then the current price from a different price zone
serves as an instrument. This is approach is similar to using prices in different markets as
instruments (Hausman et al. 1994; Nevo 2001). However, we note that if there is a
chain-level shock, these instruments are potentially contaminated. We address this in our
estimation by considering various combinations of instruments.
Estimates
We jointly estimate the system of equations in (2) and equation (3) using
instrumental variables. The IV estimation for canned tuna, refrigerated juice, and toilet
tissue are given in Table 4 and we include all the instruments in this estimation. As we
were concerned that contemporaneous prices from other price zones may be
contaminated, we also estimated the model without these instruments. Fortunately, we
did not find any substantial differences. These estimates and the OLS estimates are
available from the authors in a technical appendix.
INSERT TABLE 4 ABOUT HERE
-- 17 --
We note from Table 4 that for all three categories the estimated own-price
coefficients (γjj) are negative as expected, while the cross-price coefficients are positive,
where significant. In addition the coefficients of the feature/display variable (cj) are all
positive for all three categories, though not all are significantly different from zero. The
estimated coefficients of the variables in the category expenditure model are also
consistent with prior expectations. The coefficient of the category price index variable
(z2) is negative and significant, the store expenditure coefficient (z1) is positive and
significant, and the coefficient of the feature/display variable is positive and significant.
Finally, we note that the adjusted R-square values seem reasonable. Hence, from a
descriptive standpoint the AIDS system model seem to fit the data well and provides
reasonable results. In the next section, we analyze the implications of these results for
category pricing.
INSERT TABLE 5 ABOUT HERE
To benchmark our model, we also estimate a logit model with an outside good
and use the same instruments for price (Table 5). We operationalize the outside good by
using the customer count data available in the Dominick’s data. This variable captures
the number of store shoppers each week and we assume that each shopper could purchase
one unit on each shopping trip. As expected, our estimation yields brand price and brand
display/feature coefficients that are very significant. Based on the adjusted R-square, we
note that the model fit of the logit and our model are comparable. While both models
offer reasonable coefficients and “fit” of the data, in the next section we demonstrate that
they have quite different implications for product line pricing.
INSERT TABLE 6 ABOUT HERE
In table 6, we report the own- and cross- price elasticities for the AIDS system
(conditional on category expenditures) and the logit model. We see from table 6 that the
most striking difference between the AIDS and the logit models is that the estimated
cross-price elasticities for the latter are all much smaller compared to the former. For
example, for the tuna category, the cross-price elasticity between brands 3 and 2 is 1.172
for the AIDS model, while it is 0.011 for the logit model. In general, the AIDS model
estimates show significant brand substitution effects, while for the logit they are almost
negligible. The large share of the outside good in the logit model drives these results.
-- 18 --
Price Optimization
Given the applied nature of our problem, it is important that our approach
incorporates managerially relevant phenomena. In a recent study of the dimensions of
retailer pricing, Shankar and Bolton (1999) identified four important considerations. We
use these considerations to guide our application of the model.
In particular, we
demonstrate that the model can be used to assist in determining and adjusting regular
price levels, promotion depth, the benefit of supported versus unsupported price cuts, and
synergies/costs of promoting multiple brands in the same week. We are also able to
address the degree of price pass-through, which is an important channel consideration.
Finally, we show how the model can be used to estimate the impact of exogenous
increases in total store expenditures on category profits, sales, and prices. A limitation of
our static model is that we cannot address long run, dynamic issues such as store format
(e.g., EDLP vs. HiLo) and promotion timing and frequency.
Description of Scenarios
To illustrate the properties of the model, we consider three pricing scenarios that
are summarized in Table 7.
Table 7: Pricing Scenarios
Type of Promotion
Scenario
Base Case: Regular Price
Scenario 1:
(a) Unsupported Price Cut
(b) Supported Price Cut
Scenario 2:
(a) Unsupported Price Cut
(b) Supported Price Cut
Scenario 3:
Synergies and losses from
promoting multiple brands
Promoted Brands
None
Manufacturer
Allowance
None
Display/Feature
National Brand
20%
(a) None
(b) Yes
Store Brand
20%
(a) None
(b) Yes
Multiple Brands
Both at 20%
None
Both Brands
In the base case scenario, we examine category pricing at average wholesale costs
and no promotion support. The resulting prices might be thought of as “regular” prices.
In scenarios 1 and 2, we consider how pricing strategies change in response to
manufacturer allowances (i.e. decrease in wholesale price) and retail display/feature. In
the trade, these are referred to as supported versus unsupported price cuts.
-- 19 --
These
scenarios offer insight into retail markups, retail pass through, and category expansion
due to price cuts and promotion.
In scenario 3, we consider how retail prices and profits change when two brands
are promoted in the same week.
Note that in our model, price promotions and
display/feature increase category expenditure. However, the marginal expenditure effects
(bj) influence how this additional spending is allocated between brands. Because a
brand’s relative expenditure share may increase or decrease (holding prices constant), it
is not a priori clear whether there are synergies or costs from promoting two brands in the
same week. However, by combining our results from scenarios 1 and 2, we can address
whether a retailer should promote multiple brands in the same week or different weeks.
Before describing our results, we recognize that the marketing literature has taken
at least two approaches to the treatment of regular and promoted prices. One approach is
to explicitly separate regular prices from promoted prices and treat these as separate
decision variables. For example, Blattberg and Wisniewski (1989) separate the observed
retail price into a “regular” price component and a “deal value” component and estimate
separate demand effects for each variable. An alternative approach, which we take in this
paper, is to use a single price variable that includes any deal value in the demand
estimation. While this approach may ignore behavioral features such as reference effects
(Thaler 1985) in the demand specification, there are several advantages.
First, regular prices are by definition stable and change less frequently, which
implies less variation in the data and more imprecise estimates of the regular price
coefficient. More technically, if the data includes only one store it is not clear what
separately identifies (i.e. econometrically) both deal effects and regular price effects. A
second problem with using this approach in our setting is that the estimated “deal value”
effect on demand is often larger (in magnitude) than the “regular price” effect (Blattberg
and Neslin 1990). The implication for optimal pricing is that the retailer should set the
regular price as high as possible and offer a very high deal value, and this is perhaps an
unrealistic scenario.
On the other hand, by having a single price in the demand
estimation and the profit maximization, we can avoid such a problem and the retailer can
infer easily what the optimal deal value should be, for any given reduction in
manufacturer wholesale price.
-- 20 --
In finding optimal prices and quantities, we note that our demand system only
implicitly defines the expenditure shares (they appear on both sides of equation 2). This
is a standard feature of the AIDS model and in demand estimation it is common to treat
the expenditure shares on the right hand side as exogenous. However, in the optimization
stage this is an inappropriate assumption. Therefore, we use an iterative non-linear
optimization routine and ensure that our optimal prices and quantities are consistent with
the underlying demand system4.
As a technical note, we use plug-in estimates to
calculate expenditure shares and this ignores uncertainty in the parameter estimates5.
In the discussion that follows, we report first the overall category level results for
the three categories and then discuss detailed results for the canned tuna category.6 Of
the five canned tuna brands we analyze, one is a store brand, one is a premium
price/quality brand (brand 5), and the remaining three are moderately priced.
The
diversity of brands in this category allows us to illustrate key properties of the model.
Category Level Results
For each scenario, we evaluate the overall impact on category profits,
expenditures, unit sales, and price. These results are summarized in Table 8 for both the
AIDS system and the logit model.
INSERT TABLE 8 ABOUT HERE
As noted earlier, one drawback of the logit model is that it tends to underestimate
category expansion effects. This is easily seen in Table 8 by comparing results from the
AIDS system and the logit model. For every category and scenario we consider, the logit
model predicts relatively smaller increases in unit sales for each brand. This translates
into relatively smaller increases in category expenditure and category sales.
These
differences increase for supported features, where category expansion is even greater.
For example, in scenario 3b for canned tuna, the logit model predicts a 74.9% increase in
volume while the AIDS system predicts a 154.5% increase in sales.
4
Technically, we fix the price vector and calculate expenditure shares. These shares are used in the
computation of the price index. We then numerically solve for the optimal price vector. We iterate until
the initial and optimal price vector converge.
5
Given the linear structure of the AIDS model, it is not well suited for exploring this issue. See Rossi,
McCulloch, and Allenby (1996) for a formal treatment of this issue in the logit model.
6
The detailed results for the other categories (refrigerated juice and toilet tissues) can be obtained from the
authors.
-- 21 --
These results also illustrate differences in promotional prices predicted by the
AIDS system and the logit model. In Table 8, we report the Stone price index and its
analog in the logit model (i.e. market share weights). For interpretation, the share
weighting implies that the percent changes in the price index more closely relate to
changes in the price paid rather than changes in the price available. To see the difference
in the models, first compare changes in the price index for an unsupported versus a
supported price cut. The logit model always predicts that the price index is lower for a
supported price cut than for an unsupported price cut. As we will see later, this is due to
the fact that there is virtually no change in the price of non-promoted brands and a deeper
price cut on the promoted brand. In contrast, in the AIDS system there is considerably
less change in the price index for a supported price promotion. In some cases, the price
index actually increases. For example, for refrigerated juice the category price index is
lower for an unsupported price cut than for a supported price cut in all three scenarios.
Brand Level Results
The category level results provide an overview of the differences between the
AIDS system and the logit model. We focus on the canned tuna category to illustrate
additional features of the AIDS system for determining markups, regular prices, and
promoted prices. In Table 9 we report the pricing results for the base case and scenarios
1a and 1b for the AIDS system, while those for the logit model are given in Table 10.
We discuss results from these scenario analyses next.
INSERT TABLES 9 AND 10 ABOUT HERE
Regular Prices and Markups
Recall that in canned tuna, brand 1 is the store brand, brands 2-4 are national
brands, and brand 5 is the “other brand” category but is dominated by a
premium/specialty brand. We see from Table 9 that for the base case scenario the
absolute mark-ups vary across the different brands, but the percent mark-up is relatively
stable (16%-18%). This translates into $0.10 to $0.11 markups on brands 1-4 and a $0.23
markup on brand 5. By contrast, the logit model must have constant dollar markups
(Besanko et al. 1999); in the base case a $0.20 markup is predicted for all brands. When
there is considerable variation in wholesale cost (brand 5 vs. brands 1-4), this may yield
unrealistic prices. For canned tuna, one might expect that the logit over-prices low cost
brands and under-prices high cost brands. The difference in results between the two
-- 22 --
models (absolute constant mark-ups vs. constant percent mark-ups) is also noteworthy
from a managerial perspective. Steiner (1973) (toy industry), Wiegand (1998) (restaurant
wine prices), and Ortmeyer (1993) (department store) each offer examples of managers
using a percent markup, which suggests percent markups may be more consistent with
managerial decision-making.
Promoted Price of National Brand and Store Brand
Our base case enables us to benchmark the effect of various promotion activities
on brand prices. We first consider the optimal promotion strategy of a national brand and
then turn to promotion of a store brand. Finally, we discuss promotion strategies when
both a national and store brand are promoted in the same week.
In scenario 1a, we consider a 20% reduction ($0.11) in the wholesale price by a
national brand, Starkist (brand 3). This results in a decrease in the price of Starkist from
$0.65 to $0.56, or $0.09. However, note that the optimal prices of the non-promoted
brands increase. The intuition for this result is that because there are significant crossprice effects, if the retailer raises prices on non-promoted brands this shifts demand to the
promoted brand. The price increases in scenario 1a range from $0.03 to $0.07, or
approximately 5% of the retail price. When Starkist is supported by retail display/feature
(scenario 1b), we also find that prices increase.
Note that in the AIDS system,
display/feature serve as demand shifters and this implies that retailers are able to charge
higher prices, a result analogous to findings in Villas-Boas (1993). Compared to scenario
1a (unsupported price cut), the prices of all brands increase. Again, this is due to the
retailer strategically affecting substitution between brands. By raising the price of nonpromoted brands, the retailer is able to offer a smaller price cut on the promoted brand.
Results of the logit model offer a stark contrast to the AIDS system. Due to small crossprice effects, the prices of the non-promoted brands are virtually unchanged in all
scenarios for the logit model.
When the store brand is promoted (scenarios 2a and 2b), the effects on price are
analogous to scenarios 1a and 1b (a technical appendix is available from the authors).
However, the increases in sales, category expenditures, and category profits are
somewhat smaller in scenario 2b vs. scenario 1b (supported price cut of Starkist, brand
3). (see Table 8) The explanation can be directly related to the negative marginal
expenditure effect for the store brand. As the category expands due to display/feature,
-- 23 --
the store brand loses relative share. Thus, the promotion support is less effective at
driving traffic toward the store brand. This demonstrates that a brand with a negative
marginal expenditure effect is less attractive from the retailer’s perspective.
In scenario 3 we analyze the promotion policy when both Starkist (brand 3) and
the store brand (brand 1) are promoted in the same week (a technical appendix is
available from the authors). The results are directionally consistent with the previous
scenarios. When neither brand’s price cut is supported by display/feature, there is a
decrease in profits for national brands 2 and 4. However, when the price cuts are
supported the profits on all brands increase. We also find that prices increase relative to
scenarios 1 and 2. Intuitively, the retailer raises the price on non-promoted brands to
increase the attractiveness of the promoted brands.
Features of AIDS System
A comparison of Tables 9 and 10 illustrate the AIDS system and the logit model
offer very different predictions with respect to: (i) the relationship between category
expansion and brand profits and (ii) channel pass-through. We now discuss each of these
in detail.
Category Expansion and Brand Profits
The AIDS system predicts that profits of non-promoted brands may either
decrease or increase when a competing brand is promoted. The change in brand profits is
related to the extent of category expansion, the marginal expenditure effect (bj), and
cross-price effects (γij). All non-promoted brands benefit from category expansion, and
the benefit is greater when the marginal expenditure effect is positive (bj > 0). Two
factors that may decrease profits of non-promoted brands are negative marginal
expenditure effects and strong cross price effects (γij > 0). The overall effect of a
promotion on each individual brand depends on the magnitude of these effects.
To illustrate, consider scenario 1a for canned tuna (Table 9). When brand 3 is
promoted, category expenditures increase by 32% and unit sales increase by 46%.
Because of category expansion, profits of all non-promoted brands could increase – but
profits on brands 2 and 4 decline while profits on brands 1 and 5 increase. Brands 2 and
4 gain relative share as the category expands because each brand has a positive marginal
expenditure coefficient (b2 > 0, b4 > 0). However, the price elasticities in Table 6
indicate that brand 3 is particularly strong at stealing share from brands 2 and 4. The
-- 24 --
decrease in profits for brands 2 and 4 is explained by a strong substitution effect. Brands
1 and 5 have negative marginal expenditure effects, but cross-price effects with brand 3
are negligible. Profits increase for brands 1 and 5 because the category expansion effect
outweighs the negative marginal expenditure and cross-price effect.
When the category expansion effect is large it can dominate any negative effects.
The result is that profits on all non-promoted brands may increase. To illustrate, consider
scenario 1b in Table 9. A supported price promotion by Starkist (brand 3) yields an 82%
increase in total category expenditure relative to the base case. While the lion’s share of
this increase is directed towards Starkist, the profits of all brands in the category increase.
Note that in the logit model, this does not occur as profits on non-promoted brands either
decrease or remain constant.
More practically, the AIDS system offers predictions that show that all
manufacturers and the retailers can benefit from a promotion. A retailer would like
manufacturers to believe that as the category grows, all brands can benefit. The AIDS
model offers such a prediction while the logit model does not.
Channel Pass Through
Analysis of channel pass-through follows directly from our scenario analysis, and
is shown for all scenarios in Table 11.
Table 11: Channel Pass Through for Canned Tuna
AIDS System
Scenario
Promoted
Brand(s)
1a
1b
2a
2b
3a
3b
Store
Brand
Display/
Feature
National
National
Wholesale
Price Cut
20%
20%
Store
Store
20%
20%
No
Yes
86.5%
99.4%
72.2%
98.8%
Store & National
Store & National
20%
20%
No
Yes
60.9%
22.3%
No
Yes
National
Brand
Logit Model
Store
Brand
86.0%
53.1%
68.1%
28.2%
National
Brand
99.2%
97.9%
98.7%
96.4%
98.6%
96.5%
We define pass through as (∆ Retail Price)/(∆ Wholesale Price); thus a pass
through less than 100% implies that the retailer “pockets” part of the price cut and a pass
through greater than 100% implies the retailer pays for some of the promotion. A
limitation of the logit model is that it predicts a pass-through of approximately 100% for
-- 25 --
all categories and all scenarios. In contrast, the AIDS system predicts that pass through
varies by brand, category, and the extent of promotion. For tuna, the pass through ranges
from as low as 22% to as high as 86%. While not shown here, we find pass through for
refrigerated orange juice and toilet tissues as high as 134% and 127%, respectively.
Table 9 also illustrates that for the AIDS system, pass through tends to decrease as
category expenditures increase. Thus, supported promotions have less pass through than
non-supported promotions because of the demand shifting effects.
Similarly, pass
through decreases when multiple brands are promoted. In sum, the AIDS system offers
insight into factors that affect channel pass through while the logit model is noninformative.
Application of AIDS System
In the remainder of this section, we demonstrate how the AIDS system can be
used to assess three important retail decisions. First, we show how the model might be
applied to determine whether a retailer should promote multiple brands in the same week.
Importantly, we link promotion timing strategies to the marginal expenditure effect and
the substitution effect. Second, we recognize that it is common for a retailer to only
adjust the price of a promoted brand during a promotion week. By maintaining “regular
prices” on non-promoted brands, the retailer incurs an opportunity cost that our model
can measure. Finally, a critical issue for retailer is understanding how changes in overall
store traffic impact category profits and brand profits. While the logit model is silent on
these issues, the AIDS system can be used to assess each and we discuss these next.
Promotion Timing
An important consideration for the retailer is whether promoting multiple brands
in the same week yields synergies or opportunity costs. For example, the retailer can
clearly control the timing of a store brand promotion. Should the retailer time the
promotion to coincide with other promotions? Or, should the retailer prefer to promote
only one brand each week? Similarly, should a retailer promote two national brands in
the same week or in different weeks?
We suggest that two important considerations for the retailer are whether the
brands have strong cross-price effects and whether the brands have negative marginal
expenditure effects. Recall that when there are positive cross price effects, a retailer may
slightly increase the price of a non-promoted brand to increase sales of a promoted brand.
-- 26 --
As we illustrate next, when two brands with positive cross price effects are promoted the
effectiveness of this strategy may be reduced. A second consideration is how a brands
relative share changes as the category expands. When a brand has a negative marginal
expenditure effect, a brand loses relative share as the category expands. As we illustrate,
promoting two brands with negative marginal expenditure effects may result in greater
opportunity costs.
To determine optimal promotion timing, we allow a retailer to consider two
strategies. In the sequential promotion strategy, the retailer can promote only one brand
but in two different weeks. In the joint promotion strategy, the retailer promotes both
brands the same week and neither brand in a second week. For each strategy, the
incremental profits are measured relative to the case of no promotion in both weeks.
Optimal promotion timing is determined by the strategy that offers the largest
incremental profits.
To show how cross-price effects influence optimal promotion timing we analyze
brands 3 and 4. In the sequential promotion strategy, incremental profits are $186.78;
under the joint promotion strategy incremental profits are $166.43. The net gain of
$20.35 (11%) from the sequential promotion strategy is due to the strong cross-price
effects between these brands. To verify that these losses were indeed related to the crossprice effects, we set the cross price effects for brands 3 and 4 to zero and then conduct the
same exercise. In this case, we find that joint promotions yields incremental synergies
and a gain of +$15.19; this suggests the loss from joint promotion is due to the positive
cross price effect. Finally, neither the retailer nor the national brand manufacturers prefer
the joint promotion strategy when there are strong cross price effects.
A second factor that affects promotion timing is the marginal expenditure effects.
To explore this issue we first assume the retailer promotes the store brand and then
consider the incremental effect of promoting either brand 2, 3 or 5. Brand 2 (Chicken of
the Sea), has a positive marginal expenditure effect; Brand 3 (Starkist) has a marginal
expenditure effect close to zero; Brand 5 (“other” Brand) has a negative marginal
expenditure effect. The incremental gains/loss from promoting these brands sequentially
or jointly is illustrated in Table 12.
-- 27 --
Table 12: Net Gain(Loss) from Promoting Multiple Brands in the Same Week
Incremental Profits from Sequential Promotion
Incremental Profits from Joint Promotion
$ Gain (Loss): Joint vs. Sequential Promotion
% Gain (Loss): Joint vs. Sequential Promotion
Store Brand Store Brand Store Brand
& Brand 2 & Brand 3 & Brand 5
(b2 > 0)
(b3 ≈ 0)
(b5 < 0)
$134.11
$129.15
$58.34
$140.65
$131.54
$42.40
$6.54
$2.38
($15.94)
+4.9%
+1.8%
-27.3%
Results in Table 12 show that the gains from joint promotions are increasing in
the marginal expenditure effect. When the marginal expenditure is positive or neutral,
there may be benefits from jointly promoting the store brand with a national brand. In
contrast, when the national brand has a negative marginal expenditure effect there are
significant opportunity costs, which is illustrated by the absolute (-$15.94) and percent
(-27.3%) dollars lost.
A potential confound with this analysis is that other factors may differ between
brands 2, 3 and 5. For example, the cross price effects for the store brand and brands 2
and 3 are small but there are positive cross price effects between brands 1 and 5 (γ15 =
4.2). To isolate whether the losses from joint promotion can be attributed to negative
marginal expenditure effects, we performed numerical comparative statics by varying b5.
As expected, incremental profits are increasing in the marginal expenditure effect. This
suggests the losses from jointly promoting a store brand and a brand with a negative
marginal expenditure effect is not optimal.
While the previous discussion focused on canned tuna, we obtain similar results
in the other categories. More generally, while synergies from promotion are possible, in
the few instances where this occurred the incremental gains were quite small. In contrast,
we found many instances of losses from joint promotion and in some cases these loses
were very large. Overall, this supports the conventional wisdom that retailers should be
cautious promoting and supporting more than one brand at a given point in time. Our
results offer some insight as to why retailers might prefer this strategy. Positive cross
price effects and negative marginal expenditure effects may decrease incremental gains
from promoting multiple brands in the same week.
-- 28 --
Opportunity Cost of Regular Prices
A second policy decision the AIDS system can address is whether the retailer
should adopt a “regular price” policy and only adjust the prices of brands that receive
wholesale price cuts. To assess the possible opportunity cost of such a policy, we assume
that prices from the base case reflect regular prices. We then evaluate scenarios 1-3 and
only adjust the price of the promoted brand(s). In Table13, we report the estimated
opportunity costs of not varying the prices of the non-promoted brands. Note that a
similar analysis for the logit model is uninteresting as there is virtually no change in the
price of non-promoted brands.
Table 13: Opportunity Cost of Regular Price Policy
Canned Tuna
Refrigerated Juice
Toilet Tissue
% Loss
$ Loss % Loss
$ Loss % Loss
$ Loss
Scenario
Unsupported National Brand Promotion
-7.2%
($5.43)
-3.1%
($7.38)
-1.0%
($5.10)
Supported National Brand Promotion
-20.6%
($25.84)
-9.5%
($36.10)
-2.3%
($13.40)
Unsupported Store Brand Promotion
Supported Store Brand Promotion
-14.1%
-24.2%
($10.34)
($22.25)
-0.5%
-3.6%
($1.03)
($8.86)
-1.3%
-3.2%
($6.82)
($19.18)
Unsupported Store and National Brand Promotions
-24.6%
($25.61)
-3.9%
($10.38)
-2.8%
($16.61)
Supported Store and National Brand Promotions
-36.5%
($64.22)
-12.7%
($57.20)
-5.7%
($41.56)
We note from Table 13 that the opportunity costs (percent profits foregone) are
greatest for the canned tuna category and least for the toilet tissue.
This result is
consistent with the previous results that the gains from promotions are greatest for the
tuna category. Further, the opportunity costs of maintaining constant regular prices are
greatest when price promotions are supported and when multiple brands are promoted in
the same week. The results allow a retailer to determine whether it is worthwhile bearing
the costs of price changes for the different categories (Bergen et al. 1997). If these
adjustment costs are significant (the so-called "menu costs"), maintaining regular prices
and incurring these opportunity costs may be optimal. Note that the decision to maintain
regular prices needs to be made concurrently with promotion timing and support
decisions.
Impact of Store Traffic
A final issue the AIDS system allows us to assess is the impact of store traffic on
category profits and brand prices, sales and profits. To examine this issue, we consider
an exogenous 10% increase in store expenditure (e.g. during a major holiday weekend).
We then compute the optimal brand prices and the expected change in sales and profits
-- 29 --
for each brand. Category-level results for canned tuna, refrigerated juice, and toilet tissue
are shown in Table 14.
Table 14: Effect of 10% Increase in Store Expenditure
%∆ in Profit
%∆ in Quantity
Largest Brand Increase in Q
Largest Brand Decrease in Q
Average %∆ in Price
Canned Refrigerated
Juice
Tuna
21%
9%
11%
3%
18%
9%
0%
-14%
2%
2%
Toilet
Tissue
9%
4%
9%
-14%
1%
For the canned tuna category, profits and unit sales increase by 21% and 11%,
respectively. The corresponding results for refrigerated juice category are 9% and 3%,
while for the toilet tissue category they are 9% and 4%, respectively. However, for all
three categories, price changes are almost negligible (1%-2%). At the brand level, there
is considerable variation in profits and quantities because brands with positive marginal
expenditure effects gain more from the increase in category expenditures. For example,
in both refrigerated juice and toilet tissue, brands with large negative expenditure shares
may lose up to 14% in unit sales. While category expenditures increase in all three
categories that we consider, our approach allows for a negative response. Thus, our
approach enables retailers to assess the interaction between the overall store expenditure
and category level expenditure.
Summary and Directions for Future Research
The issue of optimally pricing the brands within a product category is a critical
task facing retailers. This is one aspect (albeit, a very important one) of retailer category
management and has thus received attention in both academic research and practitioner
literature. In this paper, we have highlighted some serious, practical shortcomings of the
models discussed for category pricing and propose the use of an easily implemented
aggregate demand system that addresses those limitations.
An important aspect of our model is allowing the category expenditures to be
determined endogenously as a function of the category price, total store expenditures
(excluding the category), and category support activities. We believe that our study is
one of the first to examine explicitly the relationship between category expenditures, its
-- 30 --
drivers, and the allocation across different brands within the category. Our empirical
results show promotions can expand category profits, expenditures, and unit volume, and
that brands with positive marginal expenditure effects are more attractive from the
retailer's standpoint for promotional and support activities. In addition, even when such
brands are not explicitly promoted, they gain when the promotions of other brands induce
consumers to spend more on the product category.
The AIDS system indicates that a somewhat constant percent mark-up rule can be
optimal for pricing brands within the category. Further, the model can be used to
estimate that percentage. Our results show that the optimal pass through amount of a
brand price promotion can exceed 100%, implying that the AIDS model is quite flexible.
We also find that optimal pass-through amount is lower for a promotion supported by
feature and display, which implies smaller price cuts for supported promotions.
Our demand model also demonstrates that in many instances the incentives of the
retailer and all manufacturers may be aligned. For example, growing the category is a
fundamental premise of category management and our model shows that category
expansion can benefit all manufacturers brands and the retailer. Similarly, we show that
neither the retailer nor the manufacturers profit from promoting brands that are strong
substitutes in the same week. Thus the fact that two competing brands are promoted in
different weeks may be in both the retailer’s and manufacturer’s best interest.
In contrast to the results from the AIDS system, the logit model with an outside
good produces some unappealing price optimization results. For example, all brands
must have the same absolute margins, irrespective of factors such as price elasticity and
promotion support.
More importantly, the logit model underestimates category
expansion effects of promotions and brand price reductions, largely because of the
manner in which the outside good is operationalized. From the retailer's perspective, the
logit model offers less flexibility in the pricing of the brands.
A pertinent question that can be asked is whether these shortcomings of the logit
model for retailer category pricing can be overcome were one to estimate the model
parameters by using a random coefficient logit. For optimal product line pricing, the
main advantage of this model is flexibility in the cross-price effects. The amount of
variation and magnitude of the cross-price effects is largely an empirical question. In
packaged goods, Chintagunta (2001) implements the random coefficients logit and finds
-- 31 --
that the cross-price elasticities vary but are quite small in magnitude. If these results
were used for retail category pricing, we might expect little difference between the logit
and random coefficients logit. Finally, introducing heterogeneity does not address issues
related to the the large share of the outside good. We expect results driven by this effect
(e.g, underestimation of category expansion) to be unchanged in the random coefficients
logit.
Our analysis of the retailer category-pricing problem did not consider any demand
dynamics and to the extent that they exist and are significant, the pricing implications can
change. For example, if promotions induce consumers to stockpile or inventory a brand,
then the profit implications must be addressed using a dynamic formulation for the
category expenditure, demand and profit functions. While recent empirical studies have
shown that often there are no long run dynamic effects (Nijs et al. 2001), other studies
have shown that there are in many cases short run dynamic effects in the form of post
promotions dips (see Blattberg and Neslin 1990). Hence, a more comprehensive analysis
should allow for such possible effects.
Another issue for future research would be to examine how the chosen overall
pricing position (e.g., EDLP vs. Hi-Lo) affects retailer prices. This will be of particular
interest when the two types of stores compete in a given retail trading area and face
common manufacturer pricing. If a retailer is constrained to maintain reasonably constant
average category prices, then how should individual prices be determined in the wake of
manufacturer price reductions and support activity?
In summary, we have attempted to develop a simple and easily implementable
pricing model that can help a retailer better manage product categories for optimal
performance. We have identified and addressed several shortcomings of some of the
extant pricing models and have provided insights into brand pricing not obtainable from
those other models. Extending the analysis to include dynamic effects will provide the
retailer with a comprehensive pricing tool that enhances profits form the category.
-- 32 --
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-- 34 --
Table 3: Summary Statistics
Canned Tuna
Brand
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5*
Average
Price
$ 0.60
$ 0.72
$ 0.70
$ 0.66
$ 1.43
Average
Cost
$ 0.52
$ 0.55
$ 0.54
$ 0.51
$ 1.08
Average
Promotion
0.140
0.350
0.224
0.119
0.268
Expenditure
Share
21.3%
14.0%
26.5%
20.6%
17.6%
Conditional
Market Share**
21.5%
21.2%
25.2%
24.9%
7.2%
Average
Promotion
0.425
0.361
Expenditure
Share
21.3%
20.4%
Conditional
Market Share**
28.3%
20.6%
0.324
0.377
0.213
15.4%
21.9%
21.0%
17.1%
16.6%
17.5%
Expenditure
Share
5.8%
17.4%
26.5%
18.1%
32.2%
Conditional
Market Share**
5.7%
21.8%
28.8%
17.2%
26.5%
Refrigerated Juice
Brand
Brand 1
Brand 2
Average
Price
$ 1.51
$ 1.95
Average
Cost
$ 1.07
$ 1.58
Brand 3
Brand 4
Brand 5*
$
$
$
$
$
$
2.00
2.49
2.07
1.50
1.89
1.60
Toilet Tissue
Brand
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5*
Average
Price
$ 0.98
$ 1.15
$ 1.15
$ 1.12
$ 1.22
Average
Cost
$ 0.73
$ 1.00
$ 0.99
$ 0.98
$ 1.02
Average
Promotion
0.402
0.246
0.202
0.450
0.196
* In canned tuna, Brand 5 is a specialty brand with higher price and cost.
** Conditional Market Share is within category market share.
-- 35 --
Table 4: Model Estimates for AIDS System1
Brand
Intercepts
Brand 1
Price
Effects
Brand 2
Price
Effects
Brand 3
Price
Effects
Brand 4
Price
Effects
Brand 5
Price
Effects
Marginal
Expenditure
Effect
Brand
Display/Feature
Intercept
Store Expenditure
Category Price
Category Display/Feature
Parameter
a1
a2
a3
a4
a5
γ11
γ12
γ13
γ14
γ15
γ21
γ22
γ23
γ24
γ25
γ31
γ32
γ33
γ34
γ35
γ41
γ42
γ43
γ44
γ45
γ51
γ52
γ53
γ54
γ55
b1
b2
b3
b4
b5
c1
c2
c3
c4
c5
z0
z1
z2
z3
Canned Tuna
coefficient
t-value
0.333
(2.42)
-0.599
(-3.03)
0.265
(1.45)
0.136
(0.70)
0.857
(9.09)
-0.573
(-5.65)
0.159
(1.41)
0.173
(1.54)
0.249
(2.64)
0.909
(3.49)
0.076
(0.55)
-1.041
(-6.22)
0.368
(2.24)
0.079
(0.60)
0.308
(0.81)
0.269
(2.13)
0.299
(1.92)
-1.054
(-6.12)
0.501
(3.82)
0.172
(0.49)
0.171
(1.28)
0.638
(3.96)
0.845
(5.23)
-0.946
(-6.94)
-0.312
(-0.81)
-0.028
(-0.56)
0.018
(0.30)
-0.048
(-0.80)
-0.009
(-0.18)
-0.677
(-3.14)
-0.083
(-4.68)
0.073
(2.82)
-0.001
(-0.06)
0.062
(2.40)
-0.077
(-8.26)
0.012
(0.56)
0.096
(4.35)
0.071
(2.72)
0.040
(1.16)
0.031
(1.77)
-357
(-2.53)
0.00395
(2.32)
-1362
(-8.11)
164
(2.65)
Refrigerated Juice
coefficient
t-value
-0.548
(-1.68)
-0.516
(-1.73)
-0.256
(-0.96)
0.960
(4.39)
1.386
(5.94)
-0.626
(-6.04)
0.314
(2.11)
0.178
(1.55)
0.183
(1.57)
-0.077
(-0.28)
0.315
(3.49)
-1.010
(-6.49)
0.174
(1.64)
0.162
(1.54)
0.828
(3.17)
0.133
(1.68)
0.321
(2.65)
-0.762
(-6.84)
0.186
(1.97)
0.453
(1.97)
0.156
(2.40)
0.058
(0.58)
0.115
(1.49)
-0.826
(-9.36)
0.388
(2.12)
-0.022
(-0.32)
0.407
(3.77)
0.369
(4.33)
0.316
(3.69)
-1.765
(-8.06)
0.084
(2.19)
0.056
(1.59)
0.020
(0.64)
-0.068
(-2.61)
-0.103
(-3.64)
0.012
(0.38)
0.045
(1.36)
0.061
(2.02)
0.013
(0.51)
0.040
(0.69)
1591
(3.69)
0.01206
(2.56)
-1595
(-4.91)
470
(2.61)
Toilet Tissue
coefficient
t-value
0.164
(2.41)
-0.150
(-0.85)
0.019
(0.10)
0.032
(0.17)
0.971
(4.38)
-0.305
(-5.31)
0.102
(2.17)
0.079
(1.37)
0.249
(5.11)
-0.046
(-0.79)
0.043
(0.40)
-1.511
(-11.00)
0.643
(4.30)
0.336
(2.66)
0.794
(5.38)
0.083
(0.69)
0.656
(4.76)
-1.187
(-5.34)
0.201
(1.41)
0.199
(1.18)
0.097
(0.86)
0.384
(2.97)
0.509
(3.17)
-1.384
(-7.20)
0.352
(2.22)
-0.039
(-0.30)
0.294
(1.95)
0.580
(3.12)
0.507
(3.27)
-1.310
(-6.59)
-0.024
(-2.49)
0.033
(1.33)
0.033
(1.18)
0.015
(0.56)
-0.088
(-2.88)
0.015
(1.35)
0.076
(2.72)
0.187
(4.49)
0.032
(1.07)
0.206
(2.65)
546
(1.37)
0.00697
(1.52)
-1551
(-2.58)
752
(3.25)
0.306
0.436
0.411
0.632
Adjusted
0.426
0.580
R-Square
0.499
0.464
0.415
0.378
0.241
0.225
1
We instrument for price using costs, lagged prices, and price from a different price zone. OLS estimates
and other IV estimates are available from the authors.
Eqn 1
Eqn2
Eqn3
Eqn4
Eqn5
Cat Eqn
0.393
0.470
0.362
0.388
0.521
0.492
-- 36 --
Table 5: Logit Model Estimates
Canned Tuna
coefficient
t-value
-1.805
(-7.03)
-2.191
(-6.84)
-1.266
(-4.21)
-1.677
(-5.89)
1.310
(2.16)
-5.028
(-12.00)
0.500
(8.52)
Parameter
a1
a2
a3
a4
a5
b
c
Refrigerated Juice
coefficient
t-value
-1.918
(-10.00)
-1.324
(-5.85)
-1.876
(-7.81)
-0.410
(-1.46)
-0.920
(-3.97)
-1.789
(-16.58)
0.469
(6.93)
Adj R2
0.022
0.272
0.300
0.257
0.089
Equation
s1
s2
s3
s4
s5
Adj R2
0.271
0.385
0.315
0.479
0.184
Toilet Tissue
coefficient
t-value
-4.259
(-17.85)
-2.915
(-10.63)
-2.288
(-8.50)
-3.045
(-11.19)
-1.984
(-6.97)
-1.772
(-7.85)
0.854
(13.57)
Adj R2
0.288
0.248
0.467
0.486
0.214
Table 6: Price Elasticities in AIDS System and Logit Model
AIDS System
Logit Model
Canned Tuna
Canned Tuna
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
-3.527 0.763 0.887 1.213 4.216
-0.497 -8.573 2.836 0.530 2.421
0.053 1.172 -4.128 1.964 0.674
-0.263 2.974 3.903 -4.514 -1.529
-1.058 0.148 -0.157 0.042 -3.734
Refrigerated Juice
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5
Refrigerated Juice
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
-4.081 1.446 0.824 0.755 -0.456
0.613 -5.450 0.902 0.804 4.361
-0.068 2.260 -5.468 1.293 3.194
-0.172 0.350 0.608 -3.957 1.981
-1.003 1.974 1.769 1.577 -7.938
Toilet Tissue
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
-2.962 0.011 0.030 0.023 0.020
0.024 -3.619 0.030 0.023 0.020
0.024 0.011 -3.415 0.023 0.020
0.024 0.011 0.030 -3.222 0.020
0.024 0.011 0.030 0.023 -7.123
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
Brand 1 -2.714 0.034 0.016 0.037 0.038
Brand 2 0.029 -3.475 0.016 0.037 0.038
Brand 3 0.029 0.034 -3.642 0.037 0.038
Brand 4 0.029 0.034 0.016 -4.500 0.038
Brand 5 0.029 0.034 0.016 0.037 -3.752
Toilet Tissue
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
-6.023 1.766 1.393 4.168 -0.633
-0.734 -9.919 4.158 2.145 5.115
-0.619 3.072 -5.641 0.917 0.884
-0.429 2.244 3.002 -8.213 2.068
-1.103 0.942 1.848 1.630 -3.950
-- 37 --
Brand 1 Brand 2 Brand 3 Brand 4 Brand 5
Brand 1 -1.704 0.014 0.026 0.014 0.037
Brand 2 0.004 -1.988 0.026 0.014 0.037
Brand 3 0.004 0.014 -1.960 0.014 0.037
Brand 4 0.004 0.014 0.026 -1.904 0.037
Brand 5 0.004 0.014 0.026 0.014 -2.038
Table 8: Scenario Analysis Category Level Results
Canned Tuna
Scenario Promoted Brand Description
1a
National Brand Unspported 20% Wholesale Price Cut
1b
AIDS System
Logit Model
Category Category Category Category Category
Category Category Category
Profit Expenditure Sales Price Index Profit
Expenditure Sales Price Index
70.5%
31.9%
46.0%
-37.4%
19.1%
10.2%
18.6%
-45.4%
183.7%
82.3%
100.4%
-42.8%
48.4%
30.9%
46.7%
-65.7%
National Brand
Supported 20% Wholesale Price Cut
2a
Store Brand
Unspported 20% Wholesale Price Cut
65.1%
32.8%
42.4%
-27.4%
11.8%
6.0%
11.5%
-31.6%
2b
Store Brand
Supported 20% Wholesale Price Cut
107.7%
52.3%
62.7%
-28.4%
30.4%
18.9%
29.5%
-51.4%
3a
Store & National Unspported 20% Wholesale Price Cut 134.5%
59.0%
83.6%
-58.6%
30.8%
16.1%
29.8%
-67.8%
3b
Store & National Supported 20% Wholesale Price Cut
124.8%
154.5%
-60.6%
78.1%
49.1%
74.9%
-90.7%
296.8%
Refrigerated Juice
AIDS System
Logit Model
Category Category Category Category Category
Category
Category Category
Profit Expenditure Sales
Price Index
Profit
Expenditure
Sales Price Index
Scenario Promoted Brand Description
1a
National Brand Unspported 20% Wholesale Price Cut 15.9%
1b
National Brand Supported 20% Wholesale Price Cut 29.1%
9.0%
15.2%
-5.9%
7.7%
4.7%
7.4%
-3.7%
19.2%
25.2%
-5.4%
18.7%
13.6%
18.0%
-5.3%
2a
Store Brand
Unspported 20% Wholesale Price Cut 19.6%
12.4%
28.4%
-10.9%
10.5%
4.4%
10.1%
-8.8%
2b
Store Brand
Supported 20% Wholesale Price Cut
36.3%
22.6%
36.5%
-8.2%
29.9%
16.9%
28.7%
-15.1%
3a
Store & National Unspported 20% Wholesale Price Cut 34.3%
20.4%
42.7%
-16.3%
18.1%
9.0%
17.4%
-11.5%
3b
Store & National Supported 20% Wholesale Price Cut
40.0%
60.6%
-13.2%
48.3%
30.2%
46.0%
-17.2%
63.0%
Toilet Tissue
AIDS System
Logit Model
Category Category Category Category Category
Category
Category Category
Scenario Promoted Brand Description
Profit Expenditure Sales
Price Index
Profit
Expenditure
Sales Price Index
1a
National Brand Unspported 20% Wholesale Price Cut 35.2%
14.7%
19.2%
-12.3%
10.8%
7.9%
10.6%
-16.8%
1b
National Brand Supported 20% Wholesale Price Cut 111.5%
62.1%
61.0%
2.4%
21.8%
17.1%
21.5%
-24.8%
2a
Store Brand
Unspported 20% Wholesale Price Cut 12.7%
8.3%
15.1%
-14.5%
15.0%
8.0%
14.8%
-47.7%
2b
Store Brand
Supported 20% Wholesale Price Cut 37.9%
23.1%
27.4%
-5.4%
19.1%
12.1%
18.8%
-45.8%
3a
Store & National Unspported 20% Wholesale Price Cut 47.4%
22.1%
33.9%
-26.6%
25.7%
15.9%
25.4%
-58.3%
3b
Store & National Supported 20% Wholesale Price Cut
151.1%
82.8%
86.4%
-- 38 --
-3.5%
55.4%
37.1%
54.4%
-84.2%
Table 9: Scenario Analysis in Canned Tuna with AIDS System
Base Case
Expenditure Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
Brand 1
12.4%
52
$0.62
$0.52
no
$0.00
$5.20
Brand 2
11.5%
45
$0.66
$0.55
no
$0.00
$5.03
Brand 3
28.8%
114
$0.65
$0.54
no
$0.00
$12.83
Brand 4
18.2%
77
$0.61
$0.51
no
$0.00
$7.99
Brand 5
29.1%
57
$1.31
$1.08
no
$0.00
$13.27
Category Expenditure
Markup
$258.76
16%
17%
17%
17%
18%
Total
100.0%
345
$44.31
Scenario 1a: Unsupported Price Cut by National Brand
Expenditure Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
%∆ in Profit
Category Expenditure
Markup
Pass-Through
Brand 1
10.4%
54
$0.66
$0.52
no
$0.00
$7.40
Brand 2
5.3%
26
$0.69
$0.55
no
$0.00
$3.76
Brand 3
56.3%
343
$0.56
$0.54
no
$0.11
$43.73
Brand 4
3.9%
21
$0.64
$0.51
no
$0.00
$2.78
Brand 5
24.1%
60
$1.38
$1.08
no
$0.00
$17.86
Total
100.0%
504
42%
$341.36
21%
-25%
241%
-65%
35%
70%
21%
23%
86.0%
21%
22%
$75.54
Scenario 1b: Supported Price Cut by National Brand
Expenditure Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
%∆ in Profit
Category Expenditure
Markup
Pass-Through
Brand 1
11.0%
74
Brand 2
5.4%
35
Brand 3
59.7%
474
Brand 4
8.7%
60
Brand 5
15.1%
49
Total
100.0%
692
$0.70
$0.52
no
$0.00
$13.30
$0.74
$0.55
no
$0.00
$6.59
$0.59
$0.54
yes
$0.11
$77.15
$0.69
$0.51
no
$0.00
$10.61
$1.45
$1.08
no
$0.00
$18.09
$125.73
156%
$471.82
26%
31%
502%
33%
36%
184%
26%
27%
53.1%
26%
25%
-- 39 --
Table 10: Scenario Analysis Model in Canned Tuna with Logit Model
Base Case
Mkt Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
Brand 1
17.6%
60
$0.72
$0.52
no
$0.00
$12.31
Brand 2
10.5%
35
$0.75
$0.55
no
$0.00
$7.20
Brand 3
27.2%
94
$0.74
$0.54
no
$0.00
$19.08
Brand 4
20.9%
72
$0.71
$0.51
no
$0.00
$14.71
Brand 5
23.8%
81
$1.28
$1.08
no
$0.00
$16.60
Category Expenditure
Markup
$296.12
28%
27%
27%
29%
16%
Total
100.0%
343
$69.90
Scenario 1a: Unsupported Price Cut by National Brand
Mkt Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
%∆ in Profit
Category Expenditure
Markup
Pass-Through
Brand 1
14.8%
60
$0.72
$0.52
no
$0.00
$12.26
Brand 2
8.5%
35
$0.75
$0.55
no
$0.00
$7.16
Brand 3
39.2%
160
$0.64
$0.54
no
$0.11
$32.69
Brand 4
17.7%
72
$0.71
$0.51
no
$0.00
$14.65
Brand 5
19.8%
81
$1.28
$1.08
no
$0.00
$16.52
Total
100.0%
407
0%
$326.32
28%
0%
71%
0%
0%
19%
27%
32%
99.2%
29%
16%
$83.27
Scenario 1b: Supported Price Cut by National
Brand
Mkt Share
Unit Sales
Price
Wholesale Cost
Promotion
Mnf. Allowance
Profit
%∆ in Profit
Category Expenditure
Markup
Pass-Through
Brand 1
11.7%
59
$0.73
$0.52
no
$0.00
$12.17
Brand 2
6.8%
35
$0.76
$0.55
no
$0.00
$7.11
Brand 3
51.6%
260
$0.64
$0.54
yes
$0.11
$53.53
Brand 4
14.0%
71
$0.72
$0.51
no
$0.00
$14.54
Brand 5
16.0%
80
$1.29
$1.08
no
$0.00
$16.40
$103.75
-1%
$387.52
28%
-1%
181%
-1%
-1%
48%
27%
32%
97.9%
29%
16%
-- 40 --
Total
100.0%
503