1The opinions expressed in this paper are those of the authors and not necessarily the Federal

Trade Commission or any of its individual Commissioners. We would like to thank Steve Scutt for his

assistance in putting together the data set, and Sara Harkavy and Morgan Long for providing excellent

research assistance. We would also like to thank Jim Ferguson and Aileen Thompson for their helpful

comments on previous drafts.

How do Retailers Adjust Prices?: Evidence from Store-Level Data1 

Daniel Hosken, David Matsa, and David Reiffen

Federal Trade Commission

600 Pennsylvania Ave. NW

Washington, DC 20580 USA

January, 2000

ABSTRACT

Recent theoretical work on retail pricing dynamics suggests that retailers periodically hold sales -

periodic, temporary reductions in price, -even when their costs are unchanged. In this paper we

extend existing theory to predict which items will go on sale, and use a new data set from the BLS to

document the frequency of sales across a wide range of goods and geographic areas. We find a

number of pricing regularities for the 20 categories of goods we examine. First, retailers seem to have a

“regular” price, and most deviations from that price are downward. Second, there is considerable

heterogeneity in sale behavior across goods within a category (e.g. cereal); the same items are regularly

put on sale, while other items rarely are on sale. Third, items are more likely to go on sale when

demand is highest. Fourth, for a limited number of items for which we know market shares, products

with larger market shares go on sale more often. These final three observations are consistent with our

theoretical result that popular products are most likely to be placed on sale.
1

I. Introduction

Supermarkets’ pricing behavior differs across goods, and over time for many individual goods. 

Recent empirical studies of retailing behavior have revealed several regularities in retail pricing

behavior. First, most retail price changes reflect changes in retail margins, rather than changes in

wholesale prices (see Levy et al. [1999]). Second, most price reductions tend to be short-lived

(Warner and Barsky [1995], Hosken and Reiffen [1999], Pesendorfer [1997]). Together these

findings conform with the casual observation that sales, in the sense of temporary reductions in retail

prices that are unrelated to costs, are an important aspect of retailer pricing behavior. Third, sales

across various items within a supermarket are substitutes (Levy et al., Hosken and Reiffen) in the

following sense. Supermarkets apparently decide to place a group of products on sale each week, and

the identity of the specific items to be placed on sale is of somewhat secondary importance. Fourth,

the magnitude and frequency of sales differs across types of goods (Lach and Tsiddon [1996], Hosken

and Reiffen).

There is existing theoretical research on sales that provides an explanation for some of these

pricing patterns. One explanation found in this literature is that sales are a means to intertemporally

price discriminate for goods that either are infrequently purchased, or that can be inventoried by

consumers (e.g. Sobel [1984]). An alternative explanation is that sales result from retail competition

because consumers are heterogenous with respect to store loyalty (e.g. Varian [1980]). Hosken and

Reiffen linked these two models to show how multi-product retailers, e.g. grocery stores, behave when

they sell multiple goods. One implication of their work is that there should be systematic differences in

pricing dynamics among goods based on consumers’ costs of inventorying the good. 

The goal of this paper is to provide additional empirical evidence regarding empirical regularities

in pricing dynamics. The evidence extends previous empirical work and examines some of the

predictions of the theoretical work. Our primary data source is a non-public use data set provided to

us by the Bureau of Labor Statistics (BLS). This data set consists of 350,097 monthly price quotes on

twenty different food items collected from retailers in thirty different metropolitan areas from 1988-

1997. A key advantage of using this data set in studying sales is that we can observe a time series of
2

prices on a particular grocery item (e.g. z ounce container of brand x’s creamy peanut butter from

retailer y) for up to 5 years. Thus, we can examine how often different types of grocery products

experience sales. 

We establish a number of interesting facts about retail prices in the U.S. First, most products

appear to have a “regular price.” Using the BLS data, we find that for the 20 categories of products in

our sample, products are priced at exactly their annual modal price 62% of the time. Moreover, in

every category, products are priced at their annual mode at least 40% of the time. Consistent with

Hosken and Reiffen, we also find that when prices are not at their modes, they are overwhelmingly

more likely to be below the mode than above it. Second, products appear to go on sale more often

when consumer demand is high (e.g., eggs before Easter). This is a somewhat surprising phenomenon

in that most economists would assume that, other things equal, consumer prices would increase during

periods of high demand. Third, it appears to be the case that there is substantial heterogeneity

regarding which products within a category go on sale; i.e. in each category, certain brands and sizes

are far more likely to go on sale than others. 

We further explore this last finding using publically-available data provided by A.C. Nielsen,

Inc. The advantage of this data is that we can obtain more detailed information on each particular item

in the data set than we could using the BLS data. We focus on relating a product’s market share

(within a category) to the probability a retailer puts it on sale. We find definitive empirical results: for

each of the seven categories of goods we analyze in two geographic areas, products with higher market

shares are more likely to go on sale, and in all but one case, this result is statistically significant at

conventional levels. 

II. Theoretical Treatments of Retailer Behavior

This paper examines patterns in the pricing behavior of supermarkets. An important feature of

this industry is that each firm sells a large number of individual products and the typical consumer

purchases many individual products in each visit to a supermarket. Casual empiricism suggests that the

pricing policies adopted by these firms differs across goods and varies over time for each good. 
2Because each consumers’ demand for each product is completely inelastic in the model up to a

reservation value, there is a one-to-one relationship between consumer surplus and retailer profit. 

3

Specifically, a typical pattern is for a group of products to be put on sale by supermarkets (and

advertised as such) each week, with the products in the advertised group changing from week to week. 

The literature on price promotion by a multi-product retailer tends to focus on the information

value of the advertising. A contribution which is particularly relevant in the supermarket context is the

work of Lal and Matutes ([1989] and [1994]), who model competition between multi-product retailers

located at either end of a Hotelling line, with consumers uniformly distributed along the line. They show

that in equilibrium, competition between retailers results in prices which yield consumer surplus to all

consumers.2 The equilibrium level of surplus reflects consumer’s costs of traveling between retailers. 

Their 1994 paper considers the question of how that surplus is obtained; i.e., whether prices

are set so that consumers obtain roughly equal amounts of surplus on all of products they buy, or

whether some prices are set “low”, so that the surplus is primarily derived from relatively few products. 

In the model, advertising conveys price information to consumers, and consumers (correctly) believe

that any product whose price is not explicitly advertised will yield zero surplus (i.e., retailers charge

consumers’ their reservation value (H) for all non-advertised products). Based on this expectation and

the prices of the advertised goods, a consumer will buy from the retailer whose prices yield the most

greatest consumer surplus net of the transportation cost of reaching the retailer, as long as the net

consumer surplus is positive. In equilibrium, the number of products each retailer chooses to advertise

reflects a trade-off between two effects. Given that there is a cost for advertising each good, a

retailer’s advertising costs of guaranteeing any particular level of consumer surplus will be minimized by

advertising a low price on a single product (with the expectation that prices will be equal to H on the

remaining goods). Such a strategy may not constitute an equilibrium, however. If retailer i offers a

price of (H - x) on a single good (charging H for all other goods), retailer j may find it profitable to offer

two other goods at a price of (H - x/2) each, so that the surplus to the median consumer from buying

all goods at retailer j is the same as the surplus obtained by buying that bundle from retailer i. In this
3Lal and Narasimhan [1996] also conjecture that more popular items will be featured in the

retailer’s advertisements.

4

case, if transportation costs are sufficiently low, consumers will “cream skim”, buying some items at

each retailer. If consumers behave in this manner, such a strategy by retailer j will be profitable,

because retailer j will be selling a larger number of goods at higher margins than retailer i. More

generally, the “cream skimming” effect works in the opposite direction as the advertising cost effect,

inducing retailers to spread the consumer surplus across multiple goods. 

Lal and Matutes [1994] demonstrate in the two product/two firm case that the only equilibria

are characterized by both retailers advertising the same good(s) at the same price(s). Any good not

advertised will be sold at consumers’ reservation value for the good. It follows that in equilibrium no

consumer buys from both retailers. When advertising costs are relatively small, then there are three

equilibria. In two of the equilibria, a single product is advertised and sold at a price below H (one

equilibrium in which each good is advertised). In the third equilibrium, both goods are advertised, and

both are sold at less than H. If advertising costs are somewhat higher, but not prohibitive (i.e., not

greater than half of consumers’ cost of traveling between retailers), the only equilibria feature a single

product being advertised and sold at a price below H. They suggest that in a model with more than

two goods, all equilibria would feature multiple goods being advertised if advertising costs are

sufficiently low. 

While Lal and Matutes’ equilibria suggests that either (or both) of the two goods may have low

prices, their model has no direct predictions for which products will be priced low or high. However,

the logic of their analysis does suggest that more popular products will be put on sale more often.3 

Consider their two retailer case, but suppose each retailer sells more than two products and that two of

these products, A and B, are substitutes (as made clear below). We assume that "% of all consumers

have a reservation value of H for one unit of product A and $ (>")% of consumers have a reservation

value of H for one unit of product B. The remaining (1-")% consumers place a zero value on

consuming A, and likewise (1-$)% place a zero value on consuming B. Since $ > ", product B is

more popular than product A. Further, we assume that A and B are close substitutes, in the following
5

sense: *k% (k = A,B) of those consumers that derive utility from product k view the products as

perfect substitutes, and (1-*k)% do not value j (...k) at all. In addition, the value a consumer places on

product A and B are independent of whether they purchase any other good. We assume that ", $, *A, 

and *B are the same over the entire Hotelling line. 

Within this framework, we would not expect to see a retailer advertise good A and not good B

in the symmetric equilibrium. To see the why, consider the extreme case in which everyone who values

A values B, but the converse is not true; i.e., *A=1, *B < 1. In that case, there cannot be a symmetric

equilibrium in which A is advertised at a “low” price, but B is not advertised, and priced at H. The

reason is that if retailer i deviates by switching the prices and advertising strategies for the two products

(i.e., advertise B instead of A), all of the customers who would have would have bought their bundle of

goods from retailer i will continue to do so (since their utility is the same from buying A or B). Hence

retailer i will retain all of the customers it would have had in the proposed equilibrium. In addition,

retailer i will attract customers who value product B but not product A. Therefore, for the same

advertising expenditure, a strategy of advertising B instead of A will be a more efficient means of

bringing customers to the store (see appendix for the formal proof).

This case is unrealistic, in that it is unclear why a retailer would stock product A at all. 

However, the intuition holds in the more realistic setting where some consumers like A but not B

(*A<1 and *B<1). If a sale on A alone is profitable, then a sale on B alone is more profitable, since B

attracts more customers and all customers have the same reservation value. In contrast to the extreme

case of *A = 1, it may be profitable to have both A and B on sale. Given the retailer has product B on

sale, the benefit of placing product A on sale is the incremental increase in store traffic that results, "(1-

*A). As A and B become more differentiated (*A, *B become smaller), the retailer will have a greater

incentive to place product A on sale as well. Thus, other things equal, we would not expect to

simultaneously see sales on products that are very close substitutes. Hence, the prediction of this

analysis is that there should be considerable variation in the frequency of sales with a product category;

e.g., relatively popular brands of peanut butter have a higher probability of being on sale than relatively

unpopular brands. Further, one would not expect to see two brands of products that are very close
4

 Several other kinds of systematic price reductions have been documented. One pattern is that

prices for goods with a “fashion” element often systematically decline over a fashion season (see, e.g.,

Pashigian (1988), Pashigian and Bowen (1991), Warner and Barsky (1995)).

5Lal and Matutes (1989) use a similar explanation for competing multi-product retailers using

different (static) pricing strategies for their array of goods. In their model, each retailer has a low price

on a different good, which causes low transportation cost consumers to buy at more than one store

each period, but allows the retailers to charge high prices on some items to high transportation cost/high

reservation value consumers. Banks and Moorthy (1999), show that coupons can be another way of

offering low prices to low reservation price/low search cost customers, while maintaining high prices to

high reservation price/high search cost consumers.

6

substitutes, e.g. Skippy and Peter Pan peanut butter on sale at the same time.

The Lal and Matutes framework explains why a retailer advertises a group of goods, charges

low prices for those goods, and also provides some insight into which goods will be advertised. 

However, because the model is static, it does not provide an explanation for why the goods chosen to

be advertised changes weekly, nor provide any predictions for the dynamics of retail pricing.

The main dynamic phenomenon we wish to investigate are sales, defined as temporary

reductions in retail price which are unrelated to cost changes.4 Two kinds of explanations have been

offered for the sales phenomenon. First, Conlisk et al. [1984] have suggested that sales can be used to

price discriminate between consumers based on differences in demand elasticity and willingness to wait

(which is analytically similar to differences in costs of inventorying). If these differences are correlated

(low elasticity customers are also less willing to wait), a seller can price discriminate by making highelasticity customers wait for low prices. Hence, sales arise because periodic price reductions lead to a

large volume of purchases by high-elasticity customers, while allowing the seller to charge high prices

most of the time to low-elasticity customers.5

Varian [1980] provides an alternative explanation for changes in price that are unrelated to cost

changes. In Varian’s model, competing retailers each have some customers that are loyal to their store

(buying from their preferred retailer as long as that retailer’s price is below the consumer’s reservation

price). In addition, there are customers that buy from whichever store offers the lowest price. Each

retailer has a choice between charging a “high” price, and selling only to store-loyal customers, or
6More precisely, in contrast to the monopoly retailer, with competing retailers the probability

that a sale may occur becomes positive as soon as the expected profit from selling to the accumulated

low-value consumers at a low price equals the profit from selling to the loyal consumers at their

reservation value.

7

charging a "low" price and potentially selling to non-loyals as well. Varian shows that the only

symmetric equilibrium features mixed strategies, where all retailers choose their price from a continuous

distribution. Hence, price changes in each period, even though the basic cost and demand conditions

do not.

Sobel [1984] combines these two elements in his explanation of sales. In his model, there are

multiple retailers, and high-value consumers are not only willing to pay more for the good and are less

willing to wait (as in Conlisk et al.), but they also are loyal to one retailer (as in Varian). The primary

difference between this model and Conlisk et al. is that while low-value consumers are willing to wait

for a low price, they will buy from whichever retailer offers that low price. Hence, an individual retailer

may miss the opportunity to sell to the group of low-value/non-loyal consumers because these

consumers may have purchased elsewhere. In the multiple retailer model, each retailer faces the same

basic decision: Is it preferable to sell to the group of high value customers at a high price, or to cut his

price and sell to both these customers and the accumulated low value/non-loyal consumers before a

rival does? As the length of time since any retailer had a sale increases, the number of low-value

consumers rises as well, and this later option becomes more attractive.

The basic characteristics of the equilibrium in Sobel’s model resembles the Conlisk et al.

equilibrium. Retailers charge a high price when the number of non-loyal customers is small, but as the

number grows, it eventually becomes profitable to reduce price to attract non-loyal customers. The

key difference between the monopoly and multiple retailer equilibria is that in the latter case, competing

retailers will consider having a sale sooner than a monopolist.6 Hence, sales occur more frequently (and

at deeper discounts) when there are multiple retailers. Another difference is that there will are a range

of “sale” prices in the Sobel model. Finally, one can extend the model to show that the difference

between the monopoly and multiple retailer cases is a general one. That is, a reduction in the number of

competing retailers reduces the frequency and depth of sales, but does not affect the non-sale price of
7One empirical regularity that we do not discuss concerns the use of markdowns. Markdowns

differ from the sales in the sense used here in that markdowns refers to price reductions that are not

reversed, but rather increase over the course of a fashion season. Pashigian [1988] and Pashigian and

Bowen [1991] document this phenomenon for apparel, and show evidence that the extent of

markdown is related to the demand uncertainty for the good. Warner and Barsky [1995] provide

additional evidence of this pattern, as the only good in their sample that has a fashion element 

(sweaters) displays this markdown pattern. 

8

any good.

Hosken and Reiffen [1999] extend the Sobel analysis by considering competition between

multi-product retailers. They show that pricing dynamics will differ across goods sold by multi-product

retailers; goods which consumers can readily inventory will be characterized by less-frequent, but larger

sales than goods which are less readily inventoried. Their model also implies that competition between

retailers leads to some goods being on sale in each period. Because any individual good will only be on

sale infrequently, the identity of the goods sold at low prices changes from period to period. As such,

this analysis complements the Lal and Matutes model by explaining why the items that are advertised

change from week to week.

III. Recent Studies of Retail Pricing Dynamics

Several recent empirical studies have examined the dynamics of retail pricing behavior. These

studies have uncovered a number of empirical regularities that are broadly consistent with the theoretical

literature described in section II.7 

 Levy et al. [1999] present detailed information on the cost and frequency of retail price

changes for five supermarket chains. They exploit the fact that one of the five is located in Connecticut,

a state which requires that each unit (e.g., individual cans) of most products be stamped with a price. 

They estimate that this law more than doubles the cost of changing a product’s price. This difference

provides them with evidence on the effect of higher cost of changing prices on the frequency of price

changes. According to Levy et al., on average there was a change in the retail price for nearly 16% of

all of items sold in the non-Connecticut chains each week in 1991/92. In contrast, the chain in

Connecticut changed price on about 6% of their items in the average week (the total number of items

carried by the Connecticut supermarket was similar to the other four chains). In addition, they present
8Specifically, Levy et al. had information about wholesale price changes for one chain. They

find that wholesale prices increased for about 3.5% of goods each week, and assuming wholesale price

reductions and increases are equally common, this implies that wholesale price changed for slightly less

than 7% of items in the average week. In contrast, more than 17% of items have retail price changes in

the average week for this chain. 

9

data on a group of products at that chain which are exempt from the individual pricing law. They find

that about 21% of these items had price changes in the average week. Hence, it appears that the law

induces more frequent sales on products in the exempt group than would occur absent the law. This

kind of substitution of price reductions across goods is consistent with existing theory (especially Lal

and Matutes [1994]). They also address the question of whether observed changes in retail prices

solely reflect wholesale price changes, or whether some of the changes are changes in retail margins. 

They find that retail prices changes are 2 1⁄2 times more common than wholesale price changes, so that

most retail price changes are actually margin changes.8

Pesendorfer [1997] and Hosken and Reiffen [1999] examine prices at individual stores for

specific product groups. Pesendorfer studies ketchup prices and finds evidence of the sale

phenomenon. Consistent with Sobel, Pesendorfer finds that the probability a store has a sale, and

depth of the price reduction increases with the length of time since the most recent sale. In addition, he

finds that the percentage of days that the price of a bottle of ketchup is at a given level increases with

the price level. That is, price is usually at a “high” level, and then periodically declines to a lower level

for a short period of time. Finally, consistent with the Conlisk et al. and Sobel models, he finds that the

volume of purchases made during a sale is larger the longer the period since the previous sale, and on

average is seven times as large as when the product is not on sale.

Hosken and Reiffen [1999] address a different set of predictions, those regarding pricing

dynamics of multi-product retailers. They examine the pricing of two products, in order to test whether

the frequency and depth of sale differ between goods based on inventorying costs. Consistent with the

theory, they find evidence that the good with low inventorying cost (peanut butter) has less frequent, but

deeper sales than the good with higher inventorying cost (margarine). They also find evidence that the

probability of sales on the two items is negatively correlated, suggesting that a store can substitute
10

between goods when deciding how to offer surplus to consumers. In addition, they find that the

correlation of a product’s price across stores in an area is quite low, and often negative. They interpret

this to imply that most retail price changes are not driven by wholesale price changes, since fixed retail

margins combined with frequent wholesale price changes would imply a high correlation. 

Warner and Barsky [1995] collect and analyze daily data on retail prices for 7 infrequentlypurchased durable goods (such as televisions, drills, and cameras). They find that most price

reductions are short-lived, fairly significant (between 8 and 25 percent) and followed by a return to presale prices. This suggests that the sale phenomenon exists for multi-product retailers other than

supermarkets.

Lach and Tsiddon [1996] use data from the Israeli Central Bureau of Statistics to analyze retail

prices for products in two food categories - meat and wine. The data is sampled at monthly intervals

for a group of specialty stores in 1978/79. Their primary interest was documenting the frequency with

which retailers adjust prices for their goods. Despite the fact that overall inflation in Israel was nearly

4% per month for the period covered by the Lach and Tsiddon data, they find that meat retailers were

adjusting their prices only every other month, and wine retailers were adjusting their price only every 4-

5 months. One other difference between the pricing dynamics for the two types of goods is

noteworthy; they find that real price reductions large enough to cause a fall in nominal price are

significantly more likely for wine than meat, even though the lower frequency of price change for wine

would imply the opposite. This is consistent with Hosken and Reiffen’s prediction that goods that are

readily inventoried (like wine) have larger price reductions, conditional on a sale occurring.

An earlier study analyzing toy pricing by general merchandise retailers provides additional

evidence regarding sales. Steiner (1973) finds that these multiproduct retailers primarily advertise price

reductions on toys in the month prior to Christmas, when demand for toys is greatest. Moreover, within

this category, advertised sales were most common for the most popular items. As a consequence,

retail margins were generally inversely related to a toy’s popularity. This provides some evidence that

popular items are most likely to be placed on sale.

Taken as a whole, these studies suggest that a large portion of the observed variation in retail
9Because these products cannot be readily stored, firms cannot intertemporally price

discriminate against high and low valued consumers of these products

10For example, Pesendorfer (1997) finds that seven times as much ketchup is purchased in sale

weeks than non-sale weeks. 

11Where a category is a fairly narrow classification of consumer goods, e.g. cola drinks, eggs,

and white bread are BLS categories.

11

prices is driven by changes in retail margins. As discussed above, the theoretical literature provides two

potential explanations for why sales occur. First, firms could be playing a mixed strategy in prices (as in

Varian). Second, firms could be using sales to intertemporally price discriminate between high and low

value consumers (e.g. Conlisk et. al.). A theory based on the Varian model appears to provide the

best explanation of why highly perishable products that are frequently consumed (e.g. milk and eggs)

are placed on sale.9 For easily storable non-perishable products (e.g. ketchup or canned tuna) or

infrequently consumed perishable products (e.g. fresh salmon), either the price discrimination or mixed

strategy in prices models could describe retail pricing behavior. However, some empirical evidence

suggests that consumers “stock-up” during sale period, thus, the price discrimination model may be

more appropriate in describing why firms offer sales on non-perishable items.10 Section V provides

some additional evidence regarding the prevalence of sales, and some evidence regarding the

characteristics of those products that are put on sale by supermarkets. Section IV describes the data

used. 

IV. Data Description

This paper identifies and provides an explanation for some empirical regularities in retail price

variation. We use two different data sets in our analysis. The first is a non-public use data set we

obtained from the Bureau of Labor Statistics (BLS). To our knowledge, this data has not been used in

previous academic studies. For this reason, we provide background information on this data source. 

In collecting the data used to calculate the Consumer Price Index, the BLS samples food retailers in 88

geographic areas, collecting prices of specific items in up to 94 categories of goods.11 Within each
12These areas are: Atlanta, Boston, Buffalo, Chicago, Cleveland, Dallas, Dayton, Denver,

Detroit, El Paso, Greater Los Angeles, Jacksonville, Kansas City, Los Angeles, Miami, Minneapolis,

New Orleans, New York and Connecticut suburbs of New York City, Philadelphia, Portland,

Richmond, St. Louis, San Diego, San Francisco, Scranton, Seattle, Syracuse, Tampa, Tucson, and

12

category, the BLS samples the price of a specific item at the same store monthly for up to 5 years. 

That is, if in the first month, the BLS uses a 2-liter bottle of Pepsi as its cola product in a specific store,

it will continue collecting pricing data on 2-liter bottles of Pepsi as a cola item as long as the store

remains in the sample, and 2-liters bottles of Pepsi remain on the shelf at that store. The number of

retailers sampled in each area increases with the area’s population. In each geographic area the BLS

changes all of the stores in its sample every five years. Hence, the largest potential number of

observations in any individual price series is 60. The choice of which specific item(s) in a category to

sample from each supermarket is based on a weighted-average randomization. For example, if Pepsi in

the 2-liter bottle represents 10% of cola revenue in a supermarket, then the BLS randomization results

in a 10% chance that 2-liter Pepsi will be the sampled cola product.

The data we use in this study consist of individual price series for specific products. For

example, each price series in the cola category in Chicago contains observations on the price of a

specific brand and container size of cola at a retail outlet in the Chicago area, each month for up to 60

consecutive months. Most product categories have multiple price series in each geographic area. 

Unfortunately, the price series provided to us do not contain information that identifies the specific

product and package size sampled within each category. We only know that all of the prices within a

price series correspond to prices for a specific product at a specific store within a category. We do

not know is, for example, whether that specific cola product is a 12-pack of Coca-cola or a 2-liter

bottle of Pepsi-cola. 

The data we received from the BLS contains all of the price series the BLS collected on 20

categories of goods (cereal, white bread, cookies, crackers, ground beef, hotdogs, eggs, cheese,

bananas, lettuce, frozen concentrated orange juice, margarine, peanut butter, cola drinks, canned soup,

frozen dinners, snack foods, baby food, soap and detergents, and paper towels) from 30 geographic

areas12 for the period 1988-1997. Tables 1-4 provide some descriptive information about the data set. 
Washington D.C.

13Some of the price series have lengths longer than 5 years because the BLS collected an

additional year of data for the regions that were rotated out in 1997 for the update of the CPI.

13

Table 1 shows that the observations are fairly evenly distributed throughout the sample period, although

some years do have more observations than others. Table 2 presents both the number of unique price

series and number of observations for each product category. Our data contains far more information

on some grocery products (e.g. ground beef and white bread) than others (e.g. baby food and paper

products). This reflects a policy on the part of the BLS to collect more data on products that are

viewed as more important in measuring the CPI. Table 3 shows the number of price series and items

by geographic area. The sample contains much more information from larger population areas than

smaller areas.

Table 4 presents a frequency distribution of the length of the individual price series separately

for each product category. As discussed earlier, under the BLS sampling scheme, an individual price

series can be as long as 5 years. However, as seen in Table 4, only a small fraction of price series in

our sample attain a length of 5 years. In fact, the majority of price series are less than 2 years in length

for all product categories except ground beef, eggs, orange juice, and lettuce. According to the BLS,

there are two reasons why most of our price series have relatively short lengths.13 The first reason is

that we obtained the same ten calendar years (1988-97) of data for all cities. Because the BLS

changes its sample of stores for 20% of its cities each year, 80% of the observations in the first year of

our data are part of a series that began in a previous year. Hence, 80% of the observations for 1988

will be part of a time series that began outside of our sample period. Similarly, 80% of the observation

for 1997 will be part of a time series that will conclude outside of our time period. This means that for

the 80% of 1988 observations that are parts of prices series that began before 1988, the maximum

series length will be 48 months, and for 60% of the observation the maximum series length will be 36

months, etc.

A second reason is that if the BLS surveyor arrives at the store and cannot find the exact

product and package size of a particular item, she selects a new product in that category and creates a
14We have considered five different price decreases in our definition of sale - 5%, 10%, 15%,

20%, and 25%, although in the interest of brevity, only the results for the 10% and 20% definitions are

presented here.

14

new price series. In the data set, it appears this is the primary reason why most of the time series are

so short. For some of the product categories, e.g. canned soup or frozen dinners, this explanation

seems plausible. These product categories have many different individual brands and package sizes,

and it seems reasonable to believe that the life span of a randomly selected product is short. However,

for more stable categories, e.g. cola drinks, we find this explanation less credible. It is well known that

there are two major brands of cola (Coke and Pepsi) that come in four different varieties (the

permutations of with and without sugar and caffeine) that have been on the market with a commanding

market share throughout the sample period. It seems unlikely to us that changes in the product mix

would result in 40% of the price series for cola drinks being less than one year in length. The

unexpectedly short duration of many of the individual price series appears to be the major shortcoming

of the BLS data set. However, while the short length of some of our price series weakens our ability to

detect price changes, it does not induce any bias into our analysis.

In order to examine sale behavior, we must operationalize the idea of a sale as a significant

temporary reduction in the price of a retail item. We do this by saying that a sale occurs if a product’s

price falls by some fixed amount in a given period and then rises by a similar amount in the next time

period.14 In many ways, the BLS data is well-suited to measure sales. We typically observe the same

product over a relatively long time period and can observe when it experiences a temporary reduction

in price. Furthermore, because we have observations on many products for a large cross-section of

U.S. cities, we feel confident that our results are robust. 

Nevertheless, there are two significant weaknesses in using this data set to determine whether

popular products go on sale. First, prices are sampled monthly, whereas previous research suggests

that sales last either one or two weeks and the ideal frequency of observation would be weekly (See

Hosken and Reiffen, [1999], Pesendorfer [1997]). In a large sample, this should not affect the

proportion of our observations that are sales, but will reduce our ability to detect sales. The reason
15The data can be found at the ftp site: gsbper.uchicago.edu.

15

that sales are more difficult to observe is only partially due to the reduced number of observations. A

more fundamental problem arising from having less-frequent observations is that the retailer’s costs are

more likely to change between observations than if the data were weekly. Thus, some of the price

movements we detect may reflect wholesale price changes rather than sales. A second weakness is

that, because we do not know the exact product and package size sampled, it is impossible to relate a

product’s characteristics, such as its market share, to the likelihood it goes on sale. 

 The second data set we use comes from a public use data set provided by A.C. Nielsen.15 

This data set contains daily product prices for seven categories of goods (peanut butter, tub margarine,

stick margarine, tuna, ketchup, and facial tissue) at the individual store level for two medium-size cities

in the mid-western U.S. (Springfield, MO and Sioux Falls, SD) for the 124 week period beginning

January 23, 1985 through June 3, 1987. In addition, the data set contains market shares based on

product revenues for each product category and city. There are five supermarket chains in Sioux Falls,

and four chains in Springfield. An attractive feature of this data set is that the researcher knows daily

product prices for each brand and package size within a product category (e.g. 18 ounce Peter Pan

creamy peanut butter). Hence, using this data set we can directly relate a product’s popularity (as

measured by the its market share) to the likelihood a retailer puts the product on sale. The weakness of

the data set is that in covers a relatively small set of products for a short time period in only two cities.

V. Empirical Findings

In this section we present some empirical evidence related to the predicted pricing dynamics

described in Section II. One implication of the analysis in Section II that seems to have empirical

support is that most products should have a predictable “regular price”, and irregular downward

deviations from that price. Another implication is that within each category, popular products should

have more frequent sales.

To examine the question of whether products have a “regular price”, we first calculate how

often an individual product’s price is at its “typical” level. Specifically, we conduct the following
16At the same time, lettuce, and to a lessor extent, bananas and eggs have more seasonality in

wholesale prices than most of the other goods in our sample. Hence, some of the differences in the

observed percentage of time at the mode are undoubtably due to differences in the variability of

wholesale prices.

17Implicitly we assume there is no systematic pattern in wholesale price changes, e.g.

manufacturers changing prices every March.

16

calculation: we first divide the data set into individual time series for each calender year (e.g. the tenth

price series for peanut butter in Chicago for 1996). Next, for each annual time series, we calculate the

modal price. We then calculate how often the store’s price for the item was equal to the modal price. 

Finally, we compile frequency distributions describing how often the prices in each individual time series

are equal to their modal values for each product category. Summary statistics from these frequency

distributions are presented in table 5. With the exception of eggs and lettuce, the products’ prices are

equal to their modal value at least 50% of the time. Furthermore, with the exception of eggs, lettuce,

and bananas more than 25% of products are at their modal prices at least 75% of the time. Clearly,

most products have a “regular” price. Another interesting observation from table 5 is the difference

between goods based on inventory costs. Eggs, lettuce, and bananas are clearly the most difficult

products in our sample for consumers to inventory, and are the least likely to be equal to their modal

prices (consistent with the analysis in Section II).16

Having established that most products have a regular price, we next examine whether most of

the variability in product prices is the result of relatively permanent changes in wholesale prices or the

result of temporary decreases in product prices, i.e. sales. We address this question by calculating the

percentage of deviations from the modal price that are above or below the mode for each type of

product in our sample. If product prices only change as the result of permanent changes in wholesale

prices, we would expect the percentage of prices above the mode to be about the same as the

percentage of deviations below the mode.17 Conversely, finding that when the price is not at its mode,

it is generally below the mode suggests that price changes are driven by retailer behavior. As seen in

Table 6, for every category, prices below the mode are much more likely to occur than prices above

the mode. In each product category, the difference between the number of downward deviations from
18Where a sale as defined as observing at least a certain percentage decrease in a product’s

price between month t-1 and t, followed by a the same percentage price increase from month t to t+1. 

Since there is no obvious definition of how large the relevant change has to be, we consider sales of

5%, 10%, 15%, 20%, and 25%. Only the 10% and 20% results are presented here, but the results are

quite similar for other definitions, and are available from the authors upon request. 

17

the mode is higher than the number of upward deviations by a statistically significant amount. Thus, the

data suggests that sales are the leading cause of retail price variation for a wide variety of goods sold by

retailers. 

As discussed earlier, our extension of Lal and Matutes’s [1994] theory suggests that popular

products (defined as products consumed by a large proportion of consumers) should be the items

placed on sale most frequently. An implication of this result is that products should systematically differ

in their likelihood of going on sale. In particular, in a cross-sectional comparison one would expect to

find that popular products should go on sale fairly frequently while unpopular products should go on

sale less frequently. We propose to indirectly test this prediction as follows. If all products are equally

likely to go on sale, then knowing whether a particular product went on sale in a given year should not

help predict whether the product will go on sale in subsequent years. Thus, we wish to test the null

hypothesis of whether the probability of observing a sale on a particular product in year t is independent

of whether that product was on sale in year t-1. The alternative implied by the theory is that the

probability of observing a sale in period t is higher for products which had a sale in period t-1. 

To test this hypothesis we perform the following calculation. First, for the first twelve months of

every price series in the data set, we record whether that price series experienced a sale.18 Next, we

divide the sample into two parts: The first contains price series that have a sale in the first twelve months

and the second contains those price series that do not have a sale. Within each product category we

then calculate two conditional probabilities; the probability that a price series would experience a sale

during the second year of the sample (so that the probabilities are calculated only for series with at least

24 observations) conditional on the product being in the first group (i.e., having a sale within the first 12

months), and the probability of a sale in the second year conditional on being in the second group. We

then test the null hypothesis that the conditional probability of observing a sale is the same for both
19The corresponding number of z-statistics over 2.5 using all 5 sale definitions was 91 out of

100. Note that for some of the comparisons of conditional probabilities, the number of price series is

very small. In these cases it is incorrect to assume that the difference in proportions is approximately

normal, and instead we simply interpret the computed z-statistics as measures of the size of the

difference between conditional probabilities.

20From existing data sources we have found, it is difficult to determine which categories of

goods are most popular with consumers. For example, while we can find information on aggregate

consumption of peanut butter, however, it is unclear what proportion of people consume peanut butter

or given they consume peanut butter, how often they consume it.

18

groups. The results appear in table 7. For every product category in our sample the conditional

probability of observing a sale is larger, often substantially larger, if the price series experienced a sale

within the first 12 months. In fact, in 38 of the 40 hypothesis tests listed there, we reject the null

hypothesis with a z-statistic greater than 2.5.19 For example, as panel a shows, of the 77 cereal price

series that experienced a 10% sale within their first 12 months in the sample, 53.2% experienced at

least one additional 10% sale in the second 12 months of the sample period, while only 29.2% of the

336 price series that did not experience a sale within the first 12 months experienced at least one 10%

sale in the second 12 months. The difference in these conditional probabilities is significant at virtually

any level of statistical significance (z=5.29). We interpret this as strong evidence that there is substantial

heterogeneity across products in the likelihood of having a sale. Retailers appear to systematically

place some products within a category on sale more often than others. This result is robust across 20

large categories of goods, over time, across the U.S. and for five different definitions of sales (5%,

15%, and 25%, as well as the 10% and 20% reported here). Unfortunately, using the BLS data it is

not possible to relate which product characteristics (e.g. a product’s market share) are associated with

going on sale, however, the data does suggest that products differ widely in the frequency with which

they are put on sale.

Thus far, the discussion has focused on the relative popularity of goods within a category (e.g.

different types of peanut butter or bread). However, one would also expect that retailers would be

more likely to have sales on categories of goods that are more popular. While it is difficult to determine

which categories of goods are most popular with consumers,20 we know some goods become more
19

popular at certain times in the year; that is, there is seasonal demand for certain products. Of the

twenty products in our sample, we identify five which have predictable seasonal changes in demand. 

The demand for soup increases in the fall and winter (October thru March), peanut butter demand

increases as part of back to school planning in August and September, egg demand increases around

Easter, and ground beef and hot dog demand increases in the summer (June, July and August). 

Further, because the costs of producing these items are not seasonal, we are reasonably confident that

any change in sale behavior is a result of retailers’ reactions to changes in demand rather than supply. 

Thus, an additional test of the analysis is determining if sales on these products are more likely to occur

in periods of high demand. The results of these tests are presented in table 8. Again, the results

strongly support the theoretical analysis. We see for any of the sale definitions we consider, retailers

are more likely to put these items on sale in periods of high demand, and that these differences are

statistically significant in virtually all cases at any standard significance level. Thus, our data suggest that

retailers systematically lower the prices of items which experience increases in demand. While these

results are not surprising to anyone who shops in a grocery store, the analysis presented here provides

an explanation for this phenomenon: A retailer attracts a consumer by offering more consumer surplus

than its rival does. In order to inform consumers of the surplus that can be obtained, retailers invest

resources in advertising sale prices. Thus, other things equal, retailers will choose to put items on sale

that are attractive to the widest audience possible. Hence, when products have known upward spikes

in demand, we would expect retailers would find it more attractive to put these items on sale.

Using the BLS data we have seen that products appear to have a regular price and that most

deviations from that price appear to be sales. Further, we have seen that there is substantial

heterogeneity across products in the likelihood a retailer puts a product on sale. Within each product

category, e.g. peanut butter, some packages are far more likely to go on sale than others. Finally, we

have seen some evidence that suggests that products that are more popular, e.g. eggs at Easter, are the

products that retailers are most likely to put on sale. To further explore the relationship between

product popularity and the likelihood that the retailer puts the product on sale we use a data set from A.

C. Nielsen which allows us to relate a product’s market share to the probability it goes on sale.
21Where a sale is defined as before, a temporary price decrease of a given amount followed in

the next week by a similar increase.

22While these results are consistent with the hypothesis that more popular products are put on

sale, it is also consistent with the causality running in the opposite direction; products with lower

average prices have greater market shares. In any case, the empirical finding of a positive relationship

between the two seems robust. 

20

 Specifically, using the Neilsen data, we regress the probability a product goes on sale on the

product’s share of revenue within its category. We define a product as a particular brand and size of

a product (e.g. 18 ounce container of Skippy Creamy peanut butter) and the probability a product goes

on sale is the proportion of store weeks that particular size is on sale.21 Similarly, the market share for

a product is the share for that specific brand and size, calculated at the city level over the entire time

period. Hence, each observation in the data set consists of a product’s estimated probability of going

on sale and its market share. We estimate this regression separately for each of the seven product

categories in the data set (ketchup, tub margarine, stick margarine, peanut butter, sugar, facial tissue,

and tuna) and for both cities (Sioux Falls, South Dakota and Springfield, Missouri). For each product,

city, and both definitions of a sale (as well as definitions not reported here), we find a positive

relationship between a product’s market share and the likelihood it goes on sale (see table 9). Further,

for Springfield, Missouri for all products but tub margarine, the result is statistically significant at

conventional levels, and for Sioux Fall, South Dakota using a 10% sale definition the result is statistically

significant for all products except peanut butter. Considering the very small sample sizes in the

regression, these results imply that a strongly positive relationship exists.22

VI. Conclusion

Several recent papers have provided empirical evidence suggesting that retailer competition

results in periodic price changes even when costs are unchanged. However, each of these studies

provides evidence about sale behavior for a relatively small number of products from a few retail

establishments. This paper attempts to broaden our understanding of these pricing dynamics by

providing more systematic evidence about retail prices. Our data covers a large number of products
21

across a variety of urban areas for a ten year period. Our results suggests that a number of pricing

regularities exists for all of these goods. First, for each of twenty categories of goods in our BLS

sample, stores seem to have a “regular” price, and most deviations from that price are downward. 

Second, we find there is considerable heterogeneity in sale behavior across goods in each category;

within each category of goods, the same items are regularly put on sale, while other items are rarely, if

ever, put on sale. Third, the probability of a sale on an item appears to be greater when demand for

that item is highest. Fourth, for the limited number of items for which we know category market

shares, there is a statistically significant positive relationship between the likelihood a product is on sale,

and its market share.

 These latter three observations are consistent with the extension of the Lal and Matutes model

presented in Section II. This analysis predicts that relatively popular items should have more frequent

sales than relatively unpopular items. More generally, we view this evidence as consistent with the

premise that retailers adjust retail prices over time independent of wholesale price changes. 

The evidence we have presented here combined with the work of others (both empirical and

theoretical) suggests that retail sales are an important component of retail price variation, and that many

of the observed instances of sales are consistent with intertemporal price discrimination. Further, these

results imply that different types of consumers will effectively face different prices for the products they

purchase. Consumers who can inventory (alternatively, those who can wait for a “sale”) will pay a

lower price than those who cannot inventory (or who choose not to wait for a “sale”). 

These results have several implications for empirical analysis of retailing behavior. One clear

implication concerns estimating demand for individual consumer products. For instance, researchers

are often interested in estimating the own and cross-price elasticities between different products. To

estimate demand curves, researchers need to observe changes in price that are not associated with

changes in demand; i.e. movements of a supply curve. However, if the retail price changes are

primarily changes in retail margins (rather than exogenous changes in retailers’ costs) that are the result

of intertemporal price discrimination, then the estimated demand elasticities will be mis-measured. This

occurs because the relationship derived from contemporaneous price and quantity data (even using
22

instrumental variables to control for exogenous demand changes) does not correspond to the

experiment of changing price and observing the resultant change in quantity along a demand curve. 

Empirically, the process that causes changes in retail price also causes changes in the position of the

demand curve. In particular, as the length of time since the last sale increases, the volume of purchases

consumers will make at a particular “low” price increases, and hence so does the retailer’s incentive to

offer a low price. Correctly measuring demand curves in this type of environment requires explicitly

modeling the pricing dynamics (e.g. taking into account past prices in the demand equation).

The observation that effective prices are difficult to measure and vary across individuals implies

that researchers should take care when comparing average retail prices. For example, examining the

effects of a change in retailing structure (e.g., a merger) on consumers could be quite difficult. The

models of sale behavior imply that the effect of a merger is to increase the length of time between sales

and raise the expected sale price. This implies that consumers who purchase at the normal price will

not be harmed by the merger while the inventorying customers will be. In any event, for products

where sales and consumer inventory behavior are important, simply comparing the average prices of a

group of items (e.g., pre and post-merger) could be a relatively uninformative measure of harm. 

Instead, the best way for researchers to examine the effects of changes might be to examine changes in

the frequency or depth of sale or changes in shelf price. 
23

References

Banks, Jeffrey and Sridhar Moorthy (1999) “A Model of Price Promotions with Consumer Search,”

International Journal of Industrial Organization; 17, pp. 371-98. 

Conlisk, John, Eitan Gerstner, and Joel Sobel (1984) "Cyclic Pricing by a Durable Goods Monopolist," 

Quarterly Journal of Economics; 99, pp. 489-505

Hosken, Daniel and David Reiffen (1999) “Pricing Behavior of Multi-Product Retailers” Federal

Trade Commission Bureau of Economics Working Paper 225

Levy, Daniel, Mark Bergen, Shantanu Dutta, and Robert Venable (1997) “The Magnitude of Menu

Costs: Direct Evidence from Large U.S. Supermarket Chains,” Quarterly Journal of

Economics; 112, pp. 791-825

Lal, Rajiv and Carmen Matutes (1994) "Retail Pricing and Advertising Strategies," Journal of

Business; 67, pp. 345-70.

Lal, Rajiv and Carmen Matutes (1989) "Price Competition in Multimarket Duopolies" Rand Journal of

Economics; 20, pp. 516-37. 

Lal, Rajiv and Chakravarthi Narasimhan (1996) The Inverse Relationship Between Manufacturer and

Retailer Margins: A Theory,” Marketing Science; 15, pp. 132-151

Lach, Saul and Daniel Tsiddon (1996) “Staggering and Synchronization in Price-Setting: Evidence from

Multiproduct Firms,” American Economic Review; 86, pp. 1175-96.

Pashigian, B. Peter (1988) "Demand Uncertainty and Sales: A Study of Fashion and Markdown 

Pricing," American Economic Review; 78, pp. 936-53.

___ and Brian Bowen (1991) "Why are Products Sold on Sales?: Explanations of Pricing 

Regularities," Quarterly Journal of Economics; 106, pp.1014-1038. 

Pesendorfer, Martin (1997) "Retail Sales: A Study of Pricing Behavior in Super Markets" Mimeo. 

Sobel, Joel (1984) "The Timing of Sales," Review of Economic Studies; 51, pp. 353-68. 

Steiner, Robert (1973) “Does Advertising Lower Consumer Prices?” Journal of Marketing; 37, pp.

19-26
24

Varian, Hal R. (1980) "A Model of Sales", American Economic Review; 70, pp. 651-9.

Warner, Elizabeth J. and Robert B. Barsky (1995) “The Timing and Magnitude of Retail Store

Markdowns: Evidence from Weekends and Holiday,” Quarterly Journal of Economics;

110, pp. 321-52.
23The analysis here can be generalized to n > 3 goods with appropriate reinterpretation of (.

25

Appendix

The appendix generalizes the analysis in Lal and Matutes (1994) by considering differences in

popularity across products within a category. The Lal and Matutes model features two retailers, one at

each end of a Hotelling line. Consumers are located uniformly over the line, and face unit transportation

costs of T. Each retailer sells the same two goods, and for both goods, all consumers value one unit of 

the good at H, and have no value for a second unit of that good. Because they assume the retailers’

cost of the good is zero, H can be thought of more generally as the consumers’ value in excess of the

retailers’ cost. Finally, they assume that it costs F per good to inform consumers of the prices of

individual goods. Each consumer makes their decision as to which retailer(s) to visit based on the

advertised prices of the two retailers, their cost of reaching the retailers, and her expectation regarding

the price of any unadvertised good.

Lal and Matutes first show that consumers correctly anticipate that the price of any

unadvertised good will be H. They then show that the price of any advertised good will be strictly less

than H. Finally, they show that any equilibrium will feature symmetric behavior by the two retailers;

they both will advertise the same good(s) and charge the same price(s) for each good. As long as H >

2T, this equilibrium will feature all consumers buying from one of the two retailers, with all consumers

buying from their nearest retailer. 

We extend their analysis in three ways. First, we assume retailers sell 3 goods.23 Second, we

assume that customers are not all identical in their tastes for goods in that some consumers value each

good at H, while others value it at zero. In particular, (% of consumers place a value of H on the first

unit of good C, "% of consumers place a value of H on the first unit of good A and, $% place a value

of H on the first unit of good B, where $ > ". The goods are distinguished in that while the values

consumers place on goods A and B are independent of whether or not they value good C at H,
24Note that in the equilibrium derived in Lemma A.1, PC could be negative. However, most

consumers will pay a positive price for the product(s) they buy, since the sum of PC and either PA or PB

is positive. Specifically, PC is more likely to be negative (i.e., negative for a larger range of values for

H and T) when ($- ")/(1-") is large, which is to say, when $ is closer to 1. The closer $ is to 1, the

larger the number of customers who are buying a positively-priced bundle. Hence, the condition under

which PC is negative also implies most consumers are buying both C and another good. Moreover, 

PC is not literally negative - since we have normalized the retailer’s cost at zero, negative “prices” are

26

demand for products A and B are not independent. Specifically, goods A and B are substitutes in the

sense that all of the consumers that derive utility from product A view the products as perfect

substitutes, while ($ - ") of the customers that derive utility from B do not derive any utility from

consuming A. In this sense, B is more popular than A. Conditional on consuming one unit of either

good, consumers place zero value on consuming another unit of either A or B. We assume that (, "

and $ are the same everywhere on the Hotelling line. 

The proposition we demonstrate is that putting good A, but not good B on sale can never be an

equilibrium. To do so, we first derive the equilibrium to the subgame in which both retailers put A on

sale. We then demonstrate in Proposition A.1 that retailers will never choose this subgame; instead it

will always be more profitable to place product B on sale instead.

 

Lemma A.1: In the subgame in which products A and C are advertised and product B is not, the

symmetric equilibrium prices will be 

for both retailers.24
properly interpreted as negative margins. Finally, the possibility of negative margins is not unique to

our formulation, negative margins are also possible in Lal and Matutes’ model. 

27

(1)

(2)

Proof: As Lal and Matutes show, the price of any unadvertised good will be H. To derive the prices

for the other two goods, write retailer 1's profits as

where x1 defines the position of the consumer who likes both A and C and is indifferent between

purchasing those goods from the two retailers (i.e., x1 = 1⁄2 + (PA

2

 + PC

2

- PA

1

 - PC

1

)/2T), and x2 and 

x3 similarly respectively define the position of the marginal consumer who buys both products B and C

(but not A) and A only. Maximizing B1 with respect to PA

1

 and PC

1 yields the following first-order

conditions

Substituting in the definitions of the xi, and using the fact that PA

2

 = PA

1

 and PC

2 = PC1 we find

that equation (1) implies PA

1

 + (PC

1 = T. Similarly, using PA2

 = PA

1

 and PC

2 = PC1

, equation (2)

implies 

and substituting PA

1

 = T - (PC

1

, we get 
28

(3)

(4)

(2')

Solving yields 

Proposition A.1: Given the above assumptions, there is no perfect Nash equilibrium in which both

retailers advertise product A but not product B.

Proof: Consider an equilibrium in which product A is advertised by both retailers at PA

1

 < H, and

product C is advertised. Suppose retailer 1 deviates by advertising B at a price of PA

1

 instead of 

advertising A, and charges H for A. The change in retailer 1's profit consists of four components. 

The first term is the change in profits due to sales to customers who valued neither goods A nor

C, but do value B. The second term is the lower profit due to a price decrease for B charged to

customers who would have bought both goods B and C from retailer 1, even at the initial prices. The

third term is the profit from additional customers who would have bought products B and C from

retailer 2 at the initial price ((H - PA

1

)/2T is the number of additional customers), and the fourth term is

the profit from customers located between the midpoint of the Hotelling line and retailer 2 who would

have bought nothing in the initial equilibrium, but now buy product B from retailer 1. Rewriting these

latter three terms as 
29

using equation (1) we can substitute PA

1

 = T - ( PC

1 into this expression, to show that the term in

brackets is equal to (1-()T, and that the expression (3) is equal to 

Using the results from Lemma A.1, we see that this expression is positive. That is, it is

profitable for retailer 1 to deviate, implying that advertising A and C, but not B can never be an

equilibrium. #

It is easy to see that both retailers advertising A

alone is not an equilibrium either. If both retailers were only advertising A, advertising B instead of A

would allow retailer 1 to retain all of the customers who would have purchased from him in the initial

“equilibrium.” Moreover, these customers would pay exactly the same prices as they would have in the

initial equilibrium, so that retailer 1's profits from these customers are unchanged (the per-customer

expected profits are PA

1

 + (H). In addition, the retailer now earns these same profits from two groups

of additional customers; ($-") customers located between retailer 1 and the midpoint of the Hotelling

line, and ($-") customers located between the midpoint and the midpoint plus (H - PA

1

)/T (i.e., those

customers who are located beyond the midpoint who would receive zero surplus from retailer 2, but get

some surplus from retailer 1).#
30

Table 1: Description of Data Set

by Year

Year Proportion of Observations

1988 11.4%

1989 10.0%

1990 9.6%

1991 9.9%

1992 10.1%

1993 9.2%

1994 9.3%

1995 10.3%

1996 9.8%

1997 10.4%
31

Table 2: Description of Data Set

By Product

Product Number of Price Series Number of Observations

Baby Food 299 6579

Bananas 1142 26284

Canned Soup 1310 26480

Cereal 1631 26603

Cheese 1233 27183

Snacks 1288 21654

Cola Drinks 1116 19343

Cookies 750 14125

Crackers 311 6982

Eggs 905 27915

Frozen Dinners 561 7561

Frozen Orange Juice 491 13703

Ground Beef 909 27551

Hotdogs 471 9594

Lettuce 672 25687

Margarine 477 11826

Paper Products 620 7018

Peanut Butter 342 9188

Soap and Detergents 820 10158

White Bread 1043 24663

Total 16391 350097
32

Table3: Descriptive of Data Set

by Region

Region Number of Price Series Number of Observations

Atlanta 361 6547

Boston 570 11022

Buffalo 317 5866

Chicago 1765 40019

Cleveland 492 9730

Dallas 536 10657

Dayton 289 6733

Denver 341 6231

Detroit 1069 21404

El Paso 323 7312

Greater Los Angeles 557 15682

Jacksonville 297 7118

Kansas City 374 6033

Los Angeles 1694 35487

Miami 387 7116

Minneapolis 337 6379

New Orleans 375 6812

Suburbs of New York City 685 17816

Philadelphia 830 17270

Portland 289 5565

Richmond 385 8102

St. Louis 654 13530
33

San Diego 331 5556

San Francisco 947 25186

Scranton 335 6752

Seattle 355 6566

Syracuse 311 8577

Tampa 280 5515

Tucson 369 7658

Washington, D.C. 536 11856

Total 16391 350097
34

Table 4: Sample Description:

Frequency Distribution of Length of Time Series

Less than

1 year

1 to 2

years

2 to 3

years

3 to 4

years

4 to 5

years

5 years or

more

All Products 37.8% 24.4% 15.7% 10.1% 8.8% 3.2%

Baby Food 44.1% 17.4% 16.1% 11.0% 7.4% 4.0%

Bananas 23.6% 28.4% 26.4% 21.5% 0.1% 0%

Canned Soup 37.3% 30.5% 12.7% 9.1% 7.9% 2.5%

Cereal 51.5% 24.5% 10.1% 7.2% 5.2% 1.5%

Cheese 37.0% 23.1% 16.4% 8.7% 11.3% 3.5%

Snacks 45.3% 28.3% 12.8% 8.4% 4.7% 0.5%

Cola Drinks 40.9% 25.7% 21.1% 10.8% 1.5% 0%

Cookies 43.9% 24.2% 15.1% 6.5% 7.8% 2.5%

Crackers 31.2% 28.6% 18.0% 9.3% 10.6% 2.3%

Eggs 19.0% 23.2% 16.3% 13.2% 19.5% 8.8%

Frozen Dinners 56.7% 24.4% 11.8% 4.8% 2.1% 0.2%

Frozen Orange Juice 26.5% 20.3% 16.7% 14.5% 15.1% 6.9%

Ground Beef 19.0% 23.4% 17.8% 13.5% 18.3% 8.0%

Hotdogs 40.3% 22.5% 18.1% 8.7% 8.9% 1.5%

Lettuce 6.8% 17.9% 19.1% 15.4% 27.7% 13.1%

Margarine 32.1% 24.3% 14.2% 9.3% 15.9% 4.2%

Paper Products 64.4% 22.2% 9.4% 2.0% 0.9% 0.6%

Peanut Butter 28.4% 16.0% 22.6% 13.1% 13.2% 6.7%

Soap and Detergents 61.0% 23.6% 9.4% 2.2% 3.1% 0.6%

White Bread 34.6% 21.8% 17.4% 10.6% 11.8% 3.8%
35
36

Table 5: Summary of Frequency Distributions of 

How Often Price Quotes are at Their Modal Value 

Product Proportion of Time

Series at Modal

Price less than or

equal to 25% of

Time

Proportion of Time

Series at Modal

Price less than 50%

of Time

Proportion of Time

Series at Modal

Price more than

75% of Time

Annual

Price

Series

Baby Food 0.4% 12.7% 47.3% 790

Bananas 17.6% 42.8% 17.5% 3788

Canned Soup 2.1% 19.7% 39.3% 3570

Cereal 3.2% 21.5% 39.9% 3709

Cheese 6.1% 28.7% 37.5% 3568

Snacks 2.0% 14.1% 50.6% 3074

Cola Drinks 10.3% 34.7% 36.2% 2855

Cookies 4.0% 19.2% 48.6% 1917

Crackers 4.9% 26.3% 35.7% 892

Eggs 48.4% 75.7% 11.1% 4465

Frozen Dinners 1.4% 18.5% 46.0% 1247

Frozen Orange

Juice

8.5% 35.0% 24.9% 1672

Ground Beef 7.8% 35.6% 28.2% 3240

Hot Dogs 7.2% 31.9% 36.7% 1274

Lettuce 93.0% 96.6% 1.7% 12213

Margarine 7.4% 31.5% 34.8% 1461

Paper Products 4.3% 19.9% 41.5% 1552
37

Peanut Butter 5.1% 27.1% 34.3% 1099

Soap and

Detergent

4.1% 18.0% 42.5% 2194

White Bread 2.9% 21.5% 56.9% 3063
38

Table 6: Percentage of Prices Above and Below the Annual Modal Price By Product

Percentage Above

Modei

Percentage Below

Modei

Z-Statisticii 

(P value)

Baby Food 9.5

(592)

16.6

(1032)

3.95

(.0000)

Bananas 14.0

(3371)

28.2

(6791)

15.88

(.0000)

Canned Soup 10.5

(2615)

20.3

(5043)

10.81

(.0000)

Cereal 11.6

(2885)

20.3

(5038)

9.85

(.0000)

Cheese 12.8

(3238)

19.7

(4986)

8.15

(.0000)

Snacks 7.0

(1453)

17.2

(3581)

9.40

(.0000)

Cola Drinks 10.5

(1872)

 23.5

(4184)

11.80

(.0000)

Cookies 7.8

(1049)

18.6

(2491)

8.09

(.0000)

Crackers 7.8

(516)

25.7

(1699)

8.66

(.0000)

Eggs 25.6

(5795)

32.4

(7346)

8.55

(.0000)

Frozen Dinners 7.8

(552)

21.6

(1531)

7.24

(.0000)
39

Frozen Orange Juice 12.3

(1560)

27.5

(3479)

11.86

(0000)

Ground Beef 11.8

(2996)

25.6

(6480)

15.22

(0000)

Hotdogs 10.2

(908)

24.3

(2170)

8.92

(0000)

Lettuce 18.2

(4206)

65.0

(15007)

53.84

(0000)

Margarine 11.1

(1222)

23.4

(2576)

8.95

(0000)

Paper Products 9.2

(602)

22.3

(1454)

6.94

(0000)

Peanut Butter 11.5

(984)

22.2

(1904)

7.03

(0000)

Soap and Detergents 8.7

(832)

20.8

(1996)

7.79

(0000)

White Bread 10.6

(2462)

18.0

(4183)

8.11

(0000)

i Number of observations in parentheses.

ii P-Values in parentheses.
40

Table 7 - Percent of Price Series Experiencing at Least One Sale in the Second Year of the 

Sample, Conditional on Whether there is a Sale within the First Year

Panel a - sale = 10% reduction

Product Conditional on at

least one sale within

the First Year

(number of price

series)

Conditional on no 

Sale within the First

Year

(number of price

series)

Z-Statistic

(p-value)

Baby Food 26.7%

(15)

3.7%

(82)

3.17

(.0016)

Bananas 84.0%

(401)

52.9%

(87)

6.41

(0)

Canned Soup 51.8%

(110)

17.4%

(265)

6.81

(0)

Cereal 53.2%

(77)

22.0%

(259)

5.29

(0)

Cheese 56.1%

(139)

21.0%

(257)

7.07

(0)

Snacks 68.5%

(124)

25.8%

(151)

7.08

(0)

Cola Drinks 72.0%

(157)

25.4%

(122)

7.72

(0)

Cookies 66.7%

(63)

20.0%

(115)

6.18

(0)

Crackers 84.9%

(53)

25.5%

(51)

6.10

(0)
41

Eggs 63.5%

(244)

38.5%

(218)

5.37

(0)

Frozen Dinners 60.9%

(46)

34.2%

(38)

2.43

(.015)

 Frozen Orange Juice 64.6%

(113)

36.4%

(118)

4.28

(0)

Ground Beef 70.3%

(246)

36.1%

(216)

7.37

(0)

Hot Dogs 65.1%

(83)

37.5%

(56)

3.20

(.0014)

Lettuce 96.1%

(417)

70.0%

(40)

6.59

(0)

Margarine 66.2%

(74)

32.1%

(109)

4.54

(0)

Paper Products 76.5%

(17)

32.3%

(31)

2.93

(.0034)

Peanut Butter 49.0%

(51)

17.4%

(109)

4.17

(0)

Soap and Detergent 64.5%

(31)

21.2%

(33)

3.51

(.0004)

White Bread 60.9%

(151)

15.0%

(233)

9.34

(0)
42

Panel b - sale = 20% reduction 

Product Conditional on at least

one Sale within the

First Year

(number of price

series)

Conditional on no Sale

within the First Year

(number of price

series)

Z-Statistic

(p-value)

Baby Food 50.0%

(2)

3.2%

(7)

3.29

(0.0012)

Bananas 72.4%

(333)

49.0%

(155)

5.03

(0)

Canned Soup 32.0%

(50)

10.8%

(325)

4.08

(0)

Cereal 54.5%

(44)

14.7%

(292)

6.16

(0)

Cheese 44.0%

(75)

13.1%

(321)

6.15

(0)

Snacks 56.8%

(88)

23.0%

(187)

5.53

(0)

Cola Drinks 52.8%

(108)

17.5%

(171)

6.19

(0)

Cookies 44.8%

(29)

13.4%

(149)

3.98

(0)

Crackers 60.0%

(35)

25.0%

(64)

3.57

(.0004)
43

Eggs 49.6%

(121)

15.5%

(341)

7.48

(0)

Frozen Dinners 60.0%

(35)

16.3%

(49)

4.15

(0)

Frozen Orange Juice 56.5%

(85)

24.7%

(146)

4.85

(0)

Ground Beef 54.6%

(130)

21.1%

(332)

7.04

(0)

Hot Dogs 52.7%

(55)

32.1%

(84)

2.42

(.0156)

Lettuce 83.0%

(358)

71.7%

(99)

2.50

(.0124)

Margarine 54.8%

(42)

18.4%

(141)

4.67

(0)

Paper Products 50.0%

(6)

21.4%

(42)

1.51

(0.131)

Peanut Butter 28.6%

(21)

5.8%

(139)

3.45

(.0006)

Soap and Detergent 42.9%

(14)

10.0%

(50)

2.88

(.004)

White Bread 44.1%

(102)

12.1%

(282)

6.86

(0)
44

Table 8: Probability of Sale for Various /

Products in Relatively High and Low Periods of Demand

Panel a - Sale = 10% reduction

Product Probability of Sale in

High Demand Period

Probability of Sale in

Low Demand Period

Z-Statistic for

difference in

Probability

Ground Beef 0.0899 0.0675 3.99

Hot Dogs 0.1022 0.0730 2.93

Eggs 0.1342 0.0623 4.49

Canned Soup 0.0404 0.0264 6.14

Peanut Butter 0.0474 0.0336 2.64

Panel b - Sale = 20% reduction

Product Probability of Sale in

High Demand Period

Probability of Sale in

Low Demand Period

Z-Statistic for

difference in

Probability

Ground Beef 0.04562 0.03039 3.95

Hot Dogs 0.06080 0.04432 2.10

Eggs 0.03896 0.02536 1.30

Canned Soup 0.01850 0.01171 4.14

Peanut Butter 0.02306 0.01119 3.68
45

Table 9 - RELATIONSHIP BETWEEN PROBABILITY OF A SALE ON A PRODUCT AND ITS

CATEGORY MARKET SHARE

Panel a: Sioux Falls, Sale =10 %

Product

Intercept Market Share P Value for

Slope Coef.

R-squared Obs.

Estimate Error Estimate Error

Ketchup 0.0023 0.0038 0.0022 0.0004 0.0001 0.6843 15

Margarine - 0.0161 0.0096 0.0047 0.0009 0.0003 0.7073 13

Margarine - -0.0045 0.0044 0.0045 0.0007 0.0001 0.6673 20

Peanut Butter 0.0142 0.0074 0.0029 0.0020 0.1681 0.0692 29

Sugar 0.0067 0.0077 0.0050 0.0018 0.0129 0.3120 19

Tissue 0.0180 0.0076 0.0050 0.0019 0.0177 0.2299 24

Tuna 0.020 0.012 0.002 0.001 0.0333 0.350 13
46

Table 9 - (con’t)

Panel b: Springfield, Sale =10 %

Product

Intercept Market Share P Value for

Slope Coef.

R-squared Obs.

Estimate Error Estimate Error

Ketchup -0.0033 0.0029 0.0026 0.0004 0.0001 0.7003 19

Margarine - -0.0014 0.0029 0.0036 0.0003 0.0001 0.8919 17

Margarine - Tubs 0.0037 0.0023 0.0002 0.0006 0.7340 0.0040 31

Peanut Butter -0.0008 0.0028 0.0035 0.0006 0.0001 0.6289 24

Sugar 0.0091 0.0113 0.0043 0.0016 0.0246 0.4114 12

Tissue 0.0141 0.0081 0.0048 0.0018 0.0145 0.2639 22

Tuna 0.0080 0.0043 0.0023 0.0003 0.0001 0.7624 17
47

Table 9 - (con’t)

Panel c: Sioux Falls, Sale = 20 %

Product

Intercept Market Share P Value for

Slope Coef.

R-squared Obs.

Estimate Error Estimate Error

Ketchup 0.0006 0.0032 0.0012 0.0003 0.0052 0.4637 15

Margarine - 0.0156 0.0080 0.0021 0.0008 0.0186 0.4091 13

Margarine - Tubs -0.0069 0.0022 0.0032 0.0004 0.0001 0.8075 20

Peanut Butter 0.0047 0.0029 0.0004 0.0008 0.6252 0.0090 29

Sugar 0.0057 0.0030 0.0001 0.0007 0.8595 0.0019 19

Tissue 0.0100 0.0049 0.0017 0.0012 0.1943 0.0753 24

Tuna 0.0096 0.0071 0.0012 0.0005 0.0209 0.3973 13
48

Table 9 - (con’t)

Panel d: Springfield, Sale = 20 %

Product

Intercept Market Share P Value for

Slope Coef.

R-squared Obs.

Estimate Error Estimate Error

Ketchup -0.0022 0.0017 0.0016 0.0002 0.0001 0.7254 19

Margarine - -0.0046 0.0020 0.0031 0.0002 0.0001 0.9308 17

Margarine - 0.0014 0.0016 0.0002 0.0004 0.6909 0.0055 31

Peanut Butter -0.0018 0.0021 0.0025 0.0004 0.0001 0.5974 24

Sugar 0.0080 0.0107 0.0042 0.0015 0.0197 0.0197 12

Tissue 0.0068 0.0053 0.0034 0.0012 0.0032 0.3598 22

Tuna 0.0070 0.0037 0.0019 0.0003 0.0001 0.7497 17