In-Store Experiments to Determine theImpact of Price on Sales
Vishal Gaur • Marshall L. FisherDepartment of Information, Operations and Management Science, Leonard N. Stern School of Business,
New York University, 8-160, 44 West 4th St., New York, New York 10012, USAThe Wharton School, University of Pennsylvania, Jon M. Huntsman Hall, 3730 Walnut St., Philadelphia,
This paper describes an experimentation methodology to measure how demand varies with price andthe results of its application at a toy retailer. The same product is assigned different price-points in
different store panels and the resulting sales are used to estimate a demand curve. We use a variant ofthe k-median problem to form store panels that control for differences between stores and produceresults that are representative of the entire chain. We use the estimated demand curve to find a price thatmaximizes profit. Our experiment yielded the unexpected result that demand increases with price insome cases. We present likely reasons for this finding from our discussions with retail managers. Ourmethodology can be used to analyze the effect of several marketing and promotional levers employedin a retail store besides pricing.
Key words: retail operations; pricing; experiment design; short lifecycle productsSubmissions and Acceptance: Received January 2004; revision received July 2004; accepted October 2004 by
Kalyan Singhal.
1. IntroductionAn in-store experiment is a useful scientific tool for re-tailers to learn about consumer response to the use ofvarious marketing levers, such as pricing, promotions,store layout, presentation, etc. However, successful de-sign and execution of experiments involves many chal-lenges. A retailer must select such stores for the experi-ment that are representative of its entire chain, otherwisethe results of the experiment may be idiosyncratic andmay not be generalizable to the entire chain. Further, theretailer faces the choice whether to try all experimentaltreatments within a single store over time, or to trydifferent treatments across a cross-section of comparablestores. This choice depends on the length of productlifecycle and the seasonality of demand. Finally, the re-tailer must execute the experiment in a controlled envi-ronment, keeping the effect of non-experimental factorsto a minimum. These challenges can be daunting. Forexample, in a recent study of 32 large u.s. retailers, wefound that 90% of the retailers conduct price experi-ments. However, the retailers themselves rated the effec-
tiveness of their experiments as a median score of 6 outof 10.
This paper describes a controlled pricing experi-ment conducted at a toy retailer to measure how itsdemand varies with price and to determine the priceat which profit is maximized. The products consideredin the experiment are three different types of toysinvolving different buyer behaviors (a branded toy, anunbranded but technologically complex toy, and anunbranded but simple toy). None of the three prod-ucts is a repeat purchase item. A set of stores is se-lected for the experiment and the products are offeredat different prices in different stores. The originalprices of the products are changed so that the custom-ers see only the offered price and cannot tell if it hasbeen marked up or down. The experiment is carefullydesigned to ensure control and minimize the chancethat a customer may visit two stores and find the sameproduct at different prices. We present the experimentdesign methodology and then analyze the results fromthe experiment.
paper are: what stores to select for the experiment, andhow to map different price-points to each of thesestores. Let n denote the number of stores in the chainand suppose that each product in the experiment is tobe tested at p price-points in m stores (mp � n). Thus,at each price-point, we require m stores such that theyare similar to the stores at the other price-points and,moreover, are representative of the entire chain. Weselect such stores by using a clustering technique basedon a measure of distance or degree of dissimilarity be-tween stores. Then we design a randomized block layoutfor the experiment wherein p stores in each cluster areassigned one-to-one to different price-points.
Our paper contributes to the literature on pricingand field experiments in several ways. First, whiledesigning experiments has a long history in marketingand consumer research, in-store field experiments arenot that common. Instead, most existing research isbased on interviews and laboratory experiments in-volving the use of overt intervention to elicit con-sumer response; research on pricing additionally useshistorical time-series and panel data. An in-store ex-periment offers some methodological advantages. Itenables us to observe the relationship between priceand unit sales directly by changing prices systemati-cally in a controlled environment. Thus, it allows us todistinguish between consumer response to changes inregular price and consumer response to markdowns.Furthermore, while prior research on pricing largelyconsiders frequently purchased items, we considershort lifecycle and one-time purchase items. The buyerbehavior for such items is more complex than that forfrequently purchased items since consumers typicallyare less well informed about such items and rely onprice and other cues to make their purchase decisions(see Roberts and Lilien (1993) for a survey of con-sumer behavior models). A field experiment enablesus to study buyer behavior for such items withouthaving to assume a stylized pricing model.
Second, our experiment yields counterintuitivefindings and shows that the relationship betweenprice and demand is not straightforward. While two ofthe three products used in the experiment had down-ward-sloping demand curves, the third product haddemand increasing significantly with price in a part ofthe tested price range. Researchers in marketing havestudied the role of price in the consumer choice pro-cess as a budget constraint (allocative role) and as asignal of quality (informational role). Our finding pro-vides evidence to support existing theory and furthershows that the informational role of price can be sostrong as to dominate the allocative role and result indemand increasing with price. This finding is uniquebecause we show an increase in demand with price forthe same product whereas existing empirical researchtypically compares price and demand across compet-
ing products with different quality levels. We presentpossible explanations for this finding from our discus-sions with managers at several retailers, and discussmanagerial implications on assortment selection andsignals of quality other than price.
Third, we address the store selection problem inexperiment design. This problem is particularly rele-vant to seasonal or short-lifecycle products becausethere is a short time-span available for such products,and it is not possible to change prices in the samesubject store over time and observe the correspondingchange in sales. It is also not prudent to change pricesin the same subject store unless the goal is to study theeffect of price promotions. This is so because custom-ers who revisit the store may discover the changes inprice. Instead, a matched subset of stores must beidentified and different prices must be used simulta-neously in different stores. Several criteria must bemet in selecting the stores in order that the results ofthe experiment are accurately representative of theretailer’s customer segment, and the cost and execu-tion complexity of the experiment are minimized.
Our paper shows that in-store experimentation canbe a powerful tool for retail managers to learn abouttheir customers. Once designed, the experiment can beconducted regularly with different product groups.Further, it can be applied not only to price, but also toother marketing levers such as ‘item of the week’promotion, shelf-space allocation, presentation, sales-person push, etc.
In recent years, research using case based method-ology has gained emphasis in the operations manage-ment literature. Production management offers manyexamples of case based research, such as Chao andGraves (1998), Keizers et al. (2003), and Henderson etal. (1998). In addition, several papers attest to theincreasing use of case based research in retail opera-tions and supply chain management by the operationsmanagement community. See, for example, Agrawalet al. (2002), who present a decision support systemfor managing capacity, inventory, and shipments foran assortment of retail products produced by multiplevendors; Clark and Hammond (1997), who conduct across-sectional study showing the impact of continu-ous replenishment processes and electronic data inter-change on inventory reduction at food retailers; Ca-chon and Fisher (1997), who evaluate a continuousproduct replenishment program at Campbell SoupCompany; and Raman and Kim (2002), who study theimpact of inventory carrying costs on stockout costsand optimal capacity for a manufacturer of short life-cycle style goods. Our paper contributes to the litera-ture in retail operations by presenting case based re-search of the pricing problem in retail stores.
This paper is organized as follows. Section 2 de-scribes the relevant literature; Section 3 presents our
store selection model; Section 4 discusses the applica-tion of the methodology to the retailer; Section 5 pre-sents the results of the experiment; Section 6 discussesthe insights obtained for the pricing decision; andSection 7 concludes the paper with directions for fu-ture research.
2. Literature ReviewThere has been a vast amount of research on pricing inthe marketing literature. We focus on the main ideasrelated to our paper without providing a comprehen-sive survey.
Tellis (1988) conducts a meta-analysis study of mod-els estimating the price elasticity of demand for vari-ous products. He reports 367 estimates of elasticity for220 brands/markets obtained from 42 studies pub-lished during the period 1960 to 1985 and yielding 424sales models. These studies use time-series or panelsales data for frequently purchased products, and es-timate various market share models. They differ byproduct category, brand, lifecycle, estimation method,functional form, region, and demographic groups. Tel-lis finds that the mean price elasticity of demand issignificantly negative and that it differs significantlyacross product categories and even across brands inthe same product category. More significantly, hefinds 50 items with estimated price elasticities greaterthan zero and another 40 items with price elasticitiesbetween 0 and �1. See also Brodie and Kluyver (1984),Ghosh, Neslin and Shoemaker (1984), and Naert andWeverbergh (1981) for price elasticity studies usingdifferent datasets and pricing models.
It is recognized that price plays two distinct roles inthe consumer choice process: an allocative role (as abudget constraint) and an informational role (as asignal of quality); see Nagle (1984), Rao (1984, 1993),Rao and Sattler (2000) for reviews. Empirical measure-ment of price elasticity of demand is complicated bythe fact that only the net effect of price can be observedin practice, and the two roles cannot be distinguished.For example, in the aforementioned studies on priceelasiticity of demand, it is likely that the items withelasiticity greater than �1 had significant informa-tional role of price, and the ones with positive elasi-ticity had the informational role dominating the al-locative role. While there is a lack of research thatintegrates the two roles of price into a single model,several papers use experiments to identify these roles.
For example, several researchers have examined theeffect of price on consumers’ quality perceptions andon objective quality. Objective quality is defined as anunbiased measurement of quality based on character-istics such as design, durability, performance andsafety, and is often obtained from independent con-sumer reports published by the Consumers Union.
Research evidence suggests that while price is used asan indicator of quality, there is a lack of uniformityacross products as well as across individuals in boththe price-quality relationship and the perceived qual-ity-objective quality relationship (see Etgar and Mal-hotra 1981, Gerstner 1985, Zeithaml 1988). Several ex-planations have been offered for this lack ofuniformity. For example, Lichtenstein and Burton(1989) find that consumers perceive a stronger associ-ation between price and quality for durable productsthan for non-durable products, even though the objec-tive quality of products may be unrelated to or nega-tively correlated with price. They offer the followingexplanations for this finding: (i) less knowledge aboutdurable goods because the consumer makes fewer andmore infrequent purchases in a durable goods cate-gory, and (ii) greater difficulty in evaluating the qual-ity of durable goods as they are more complex prod-ucts.
Dodd et al. (1991) investigate how the price-per-ceived quality relationship influences buyers‘ percep-tion of value or their purchase intentions. They con-duct an experiment with two short lifecycle products(calculators and personal stereo) to identify the effectsof price, brand, and store name on the consumers’quality perceptions, value perceptions, and willing-ness to buy. They find that while price is positivelycorrelated with quality perceptions, it is negativelycorrelated with willingness to buy for both products.Their methodology differs from ours in that they use alaboratory experiment rather than in-store experi-ment.
The lack of uniformity in the relationship betweenprice and sales underscores the need for further em-pirical research to validate existing theory. It also im-plies that retailers must use proprietary data to learnabout their own consumers. The field experiment pre-sented in this paper fits these purposes. It differs infocus from the existing research in three importantways. First, we directly measure the effect of changesin regular price on sales rather than eliciting consumerattitudes and preferences. Second, existing empiricalresearch focuses on estimating market share modelsfor competing products or identifying the drivers ofbuyer behavior process, while we focus on a retailer’spricing decision. Finally, we consider short lifecycleone-time purchase items which have not been com-monly studied in prior research using actual salesdata.
We note that other researchers have used controlledexperiments at retail chains to estimate the price elas-ticity of demand, see, for example, Nevin (1974),Curhan (1974) and Neslin and Shoemaker (1983). Ex-periments have also been used to study the impact ofstore environmental variables such as music, lighting,behavior of store employees, and store design on con-
sumer behavior. See, for example, Baker, Levy, andGrewal (1992) and Gagnon and Osterhaus (1985).These studies differ from this paper in that they useaggregated data or data from a pre-selected set ofstores. Thus, they do not address the problem of storeselection for a retail chain selling short lifecycle prod-ucts.
Our paper is related to Fisher and Rajaram (2000),who present an experimental methodology for testingnew merchandise at a subset of stores prior to launchand demonstrate results from application to a wom-en’s apparel retail chain. Their paper differs from ours,since they do not consider price as a decision variable.Furthermore, their experiment design does not in-volve multiple treatment effects, and therefore, doesnot require a matched subset of stores to be selected.
3. Experiment Design:Store Selection Model
Let n be the number of stores in the retail chain, p thenumber of price-points to be tested in the experiment,and m the number of stores at which each price-pointis to be repeated (mp � n). In the terminology ofexperiment design, each price-point is called a ‘treat-ment’, so that we have p treatments and m repetitionsof each treatment. We construct a randomized blockdesign for the experiment. We first partition all thestores into m disjoint blocks such that each block has atleast p stores and the stores in each block are as ‘alike’as possible. We then select p stores in each block thatare geographically far from each other and randomlyassign them to the p price-points. Thus, each price-point is tested once in each of the m blocks.
The randomized block design is used because itsatisfies three principles of experiment design: replica-tion, randomization, and local control. The replication ofeach treatment m times gives a basis for the estimationof the experiment error. Randomization within eachblock is a necessary condition for obtaining a validestimate of the effects of the treatments on the exper-iment results since it controls for unknown differencesbetween stores that may be sources of error in theexperiment. Local control implies that the stores as-signed to each block be chosen as alike as possible forthe comparison of treatment effects within each block.These three principles were formulated by R. A. Fisher(1923, 1926). See Montgomery (1991), and Mason,Gunst, and Hess (1989) for an introduction to experi-ment design, and Ghosh and Rao (1996) for surveyarticles on the mathematical properties of experimentdesign methods.
Our experiment has one other requirement in addi-tion to these principles. We need to ensure that theresults of our experiment are representative, i.e., theyprovide an accurate forecast of the sales in the entire
chain at each treatment. Therefore, we require that thestores assigned to each price-point should representthe sales characteristics of the entire chain. When thenumber of experimental units per block is smallerthan the number of treatments, then an incompleteblock design is used. While we use a complete blockdesign, the method of store selection we present maybe used in conjunction with an incomplete block de-sign as well.
To measure the degree of (dis)similarity betweenstores, we use a metric given by Fisher and Rajaram(2000). They define the ‘distance’ or the degree ofdissimilarity between two stores as the difference be-tween their sales distributions across product catego-ries. Let l � 1, . . . , q index the product categories soldby the retailer, and fsl be the fraction of sales of store srealized from product category l. The distance be-tween the sales distributions of stores s and t, denoteddst , is computed using the Euclidean norm,
dst � ��l
� fsl � ftl �2. (1)
Fisher and Rajaram compare this distance metric withseveral alternatives. They find that the partition ofstores obtained using (1) provides a more accurateforecast of total chain sales than distance measuresdefined solely on store size or geographical location.Our methodology remains unchanged if an alternativemeasure of dissimilarity between stores is used.
We now assign stores to clusters (henceforth, ‘clus-ter’ is used synonymous with block). We use a variantof the k-median problem (see Nemhauser and Wolsey1988). Each cluster is represented by its median store.The degree of dissimilarity within each cluster is de-fined as the sum of the distances of all stores in thatcluster from the median store. The objective of theproblem formulation is to minimize the total sum ofdissimilarities within each cluster.
Let yk be 1 if store k is chosen as the median of acluster and 0 otherwise. Also, let xsk be 1 if store s isassigned to the cluster with store k as its median and0 otherwise. The problem formulation with decisionvariables yk and xsk is as follows:
xsk , yk � �0, 1� k � 1, . . . , n, s � 1, . . . , n. (7)
The objective function (2) is the sum of the distance ofeach store from the median of its cluster. Constraint(3) ensures that each store is assigned to exactly onecluster; (4) ensures that stores are assigned only to themedian stores of their respective clusters; (5) restrictsthe number of clusters to m; and finally, (6) defines theadditional constraint that each cluster has at least pstores. We solve this problem using the standardbranch-and-bound algorithm for integer program-ming using the CPLEX solver in GAMS.
We note that the k-median problem formulation is anon-hierarchical clustering technique. It gives the op-timal solution by solving an integer program for afixed k, but is NP-Hard, thus, computationally inten-sive and suited to smaller datasets. Additionally, it hasthe nice property that the clusters formed are convexin the Euclidean space. In contrast, hierarchical clusteranalysis uses a greedy algorithm that iteratively com-bines together clusters with the minimum distancebetween them in each step, but does not allow reallo-cation of stores that may have been poorly classified inan early iteration. Thus, it need not give the optimalsolution, but runs in polynomial time and is particu-larly suited to large datasets. Further, it is useful whenk is not known a priori. Hierarchical cluster analysisrequires a measure of distance not only between indi-vidual stores but also between clusters of stores. Sev-eral distance metrics have been proposed, such as thedistance between the centroids of the clusters, or as theaverage distance between all pairs of stores across thetwo clusters. For computing distance between single-ton clusters, these methods are identical to the Euclid-ean norm used by us. See Everitt et al. (2001) for acomparison of alternative clustering techniques.
4. ApplicationZany Brainy, Inc. is a specialty retailer of high qualityeducational toys for children less than 12 years old. Ithas 53 retail stores in the u.s. with total sales of about$200 million. It faces a pricing problem for its productsevery season when it launches new products and de-termines their prices. All data for Zany Brainy, Inc. arebased on the year 2000. The main characteristics ofZany Brainy’s business are as follows:
1. It sells products across eleven categories, such asgames and puzzles, arts and crafts, sport-theme toys,building toys and trains, infant development toys,electronic learning aids, and science-related toys, etc.The retailer has a unique image and does not sell toysthat reinforce gender stereotypes or encourage vio-lence.
2. Most products sold at Zany Brainy are exclusive,with only 30% of the products being common withdiscounters and mass-market retailers.
3. A typical store is 10,600 square feet and carries15,000 SKUs. Stores are located in suburban shoppingcenters, sharing retail space with destination, and life-style-oriented retailers.
4. Zany Brainy seeks to set prices that give value tothe customer, without trying to be the discount leaderin its market. Therefore, it does not use cost-pluspricing. Instead, merchandisers determine the markupfor each item individually using their experience andjudgement. Products vary in price from less than $1 upto $200, with the average price for a single productbeing less than $10. The average gross margin acrossall products is close to 50%.
Zany Brainy was interested in adopting a morescientific approach to pricing. As a first step towardsthis, it decided to conduct an in-store experiment witha subset of products in its chain to observe how theirdemand varies with price. It was also interested inexploring the long-term usefulness of in-store experi-mentation to learn about consumer response to vari-ous marketing levers employed in its stores, such as“item of the week” promotion, salesperson push, ad-vertisements, store layout, assortment planning, etc.
4.1. Store Selection ModelWe are given data for 53 stores, and each item is to betested at three price-points in six stores each. Thus, n� 53, m � 6, and p � 3. To measure the distancesbetween stores, we classify the annual dollar sales ofeach store into eleven product categories used by thefirm and compute the fraction of sales in each cate-gory. The average distance between stores thus com-puted is 0.5347. After solving the k-median problem,the average distance of a store from the median of itscluster is 0.2228, a 58% reduction. Since clustering perse does not provide tests of statistical significance, weuse an analysis of variance test to determine whetherthe clusters formed are representative of the chain, i.e.,whether they explain a statistically significant propor-tion of the variation in sales distribution of all stores.The test is statistically significant at p � 0.001.
Now, from each cluster, three stores are selected forthe experiment using additional criteria to further con-trol for dissimilarities within clusters. The selectedstores are similar in age and size (measured by totaldollar sales), and their geographical locations are rel-atively isolated from other stores belonging to thechain. Table 1 lists the stores selected for the experi-ment, their opening years, their total year-to-datesales, and the percentage of sales coming from the fivelargest product categories.
Ideally, we would like to conduct the experiment inas many stores as possible to obtain a large dataset for
analysis. However, the choice of the number of storeswas limited due to the opportunity cost of lost sales inthe stores under experimentation, and the complexityof managing the controlled experiment such that thereare no execution errors. The management of the firmwas also concerned about interference between storeslocated close to each other. If a large number of storeswere used in the experiment, then a customer visitingtwo neighboring stores would discover the differencein their prices. This would not only introduce an errorin the experiment but also result in a loss of goodwillfor the retailer.
4.2. Description of ItemsThe experiment was conducted for the following threeproducts: a family game center, ‘phonics traveler’, anda headset walkie-talkie. The family game center is anunbranded board game. It is a simple toy that custom-ers can try out in the store. The phonics traveler is abranded toy, produced by Leapfrog Enterprises, Inc. Itis a complex electronic product to teach spelling andreading to children through interaction. The headsetwalkie-talkie is also a complex electronic toy, but isunbranded. The family game center and the headsetwalkie-talkie are not carried by the competition. Eachitem is unique to avoid comparison with other brandsin the same category.
Table 2 lists the items, their price-points, and theirpurchase costs. The middle price-point in each case isthe existing list price and the high and low price-points are five dollars above and below the list price.These price-points were chosen by the firm’s merchan-dising managers to be sufficiently far from each otherin order that they cause observable changes in de-mand.
4.3. Experiment LayoutTable 3 shows the layout of the experiment. In eachcluster, one store is designated the control store andassigned each item at the middle price-point. Theremaining two stores are randomly assigned the highand low price-points for each item. For example, store103 is the control store in cluster 1, store 102 has theFamily Game Center at its highest price-point, and thePhonics Traveler and the Headset Walkie-Talkie attheir lowest price-points, and store 204 is assigned theremaining price-points. We note that, as an alternativeto this layout, all three prices could be randomizedacross all 18 stores. Doing so would eliminate a po-tential confound if there is interaction in demandacross the products under experiment. We did notconsider this possibility since the products in our ex-periment belong to different categories, and are phys-ically located in different parts of the store.
4.4. Data CollectionThe experiment was conducted for a period of sixweeks. The length of the time period was fixed as acompromise between our desire to have a long timeperiod to collect data, and the managers’ keenness to
Table 1 Summary of the Stores Used in the Experiment Classified into Cluster
Cluster Store Opening year Year to date sales ($ ’000)
avoid the experiment encroaching on their peak sell-ing season. The data collected at each store for eachweek were the unit sales of the three items, the num-ber of returns, the beginning-of-week inventories ofthe three items, and the total number of sales transac-tions in the store across all items. The total number ofsales transactions in the store was used to measurecustomer traffic in order to control for differences instore size.
Since store managers were kept unaware of theexperiment, inventory control and data quality weremanaged centrally. An inventory planner in the cor-porate office was responsible to monitor beginning ofweek inventories to ensure that there was no stock-out. Various studies on retail supply chains have dem-onstrated that data quality tends to be poor and thatmuch work needs to be done on upgrading data qual-ity, so that data could be useful in analysis (see, forexample, Raman, DeHoratius and Ton 2001). Thus, theinventory planner monitored sales data for the exper-iment daily to safeguard against data quality prob-lems.
Some precautions were observed during the exper-iment: (1) The price labels in each case were changedto reflect the new prices. The labels did not show theoriginal list price, so that customers would not per-ceive that a product was marked up or marked down;(2) Sufficient inventory was kept in the experimentalstores to avoid stock-outs; (3) The store managerswere not informed about the experiment to avoid anyexecution differences that may arise because of man-agers treating the experimental items differently, ortrying to promote them based on their price-points.
5. ResultsTable 4 summarizes the results of the experiment. Foreach item-store combination, it shows the list priceand the total number of units sold over six weeks.There were no stock-outs in the experiment stores assufficient inventory was provided. The last column inthe table gives the average number of sales transac-tions per week recorded in each store. Figure 1 showsa plot of the total sales of each product at each price-point.
Note that the total sales of the family game centerand the phonics traveler are downward sloping inprice. The family game center recorded total sales of 7units, 5 units, and 3 units at prices of $19.99, $24.99,and $29.99, respectively. The phonics traveler re-corded total sales of 33 units, 26 units, and 15 units atprices of $24.99, $29.99, and $34.99, respectively. How-ever, the headset walkie-talkie shows a different pat-tern. Its sales of 74 units at the middle price-point aremuch higher than the sales of 47 units at the lowestprice-point and the sales of 36 units at the highestprice-point. This finding was unexpected to us as wellas to the managers at the retail chain. To ascertainwhether this finding is statistically significant, we fit ademand model to the experimental data expressingdemand as a function of categorical variables for thethree price-points.
Since all three products are slow-moving items, werepresent weekly demand in each store with a Poissondistribution, and thus, use a Poisson regression modelfor statistical analysis (See Greene 1997, Chapter 19 fordetails). We assume that mean weekly demand fol-lows a multiplicative model and is given by a productof cluster-specific, price-specific, and store size specificvariables. Let ykit denote random demand in the storein cluster k at price-point i in week t, and �kit denotethe mean of ykit. Here, k � 1, . . . , m and i � {L, M, H},denoting low price, middle price, and high price, re-spectively. We write �kit as
�kit � ak bi � xkit �c, (8)
where ak is a cluster-specific constant to control fordifferences between clusters, bi is a price-specific con-
Table 3 Experiment Layout Showing the Random Assignment ofStores in Each Cluster to Price-Points for Each Product
stant, xkit is the number of transactions in the store incluster k at price-point i in week t, and c is a coefficientrepresenting the increase in mean demand with storesize.
The regression model is used to estimate ak, bi, andc. We represent the indices k and i by dummy vari-ables, so that ak and bi are the coefficients of theirrespective dummy variables. Since the coefficients’matrix must be non-singular, it is not possible to esti-mate all coefficients separately. Therefore, we set thevalue of bM to be 1 and use two dummy variables to
estimate bL and bH relative to bM. The model (8) isestimated by maximum likelihood estimation (MLE).The log likelihood function for Poisson distribution is:
log L � �k,i,t
��kit � ykit�log ak � log bi � c log xkit�
� log �ykit !�. (9)
We test whether demand is downward sloping withprice for the first two products using the followinghypothesis:
Hypothesis 1. For the phonics traveler and the familygame center, bL � bM � bH.
For the headset walkie-talkie, we test whether de-mand at the middle price-point is higher than that atlower and higher price-points using the following hy-pothesis:
Hypothesis 2. For the headset walkie-talkie, bL � bM
and bM � bH.
Since bM is set to 1, Hypothesis 1 is equivalent totesting that log bL � 0 and log bH � 0. Hypothesis 2 isequivalent to testing that log bL � 0 and log bH � 0.The Student’s t test is used in each case because theestimates of log bi are asymptotically normally distrib-uted.
Table 5 gives the parameter estimates obtained fromMLE. For each item, the first two rows of the table givethe estimates of log bL and log bH setting a value of zero
Table 4 Total Sales Recorded for Each Product in Each Store
Cluster Store
Family Game Center Phonics Traveler Headset Walkie Talkie Average numberof transactions
per weekPrice Total unit sales Price Total unit sales Price Total unit sales
for the middle price-point. The next six coefficientestimates give the values of log ak for the six clusters.The last estimate gives the value of c, the exponentof xkit .
We observe that bi decreases with price for the fam-ily game center and the phonics traveler. For example,for the family game center, the estimate of log bi is0.3277 at the lower price, 0 at the middle price, and�0.5249 at the higher price. Further, computing t-statistics and p-values, we observe that the values of bi
are statistically significant (p � 0.05) at the higherprice for the phonics traveler, and at both price levelsfor the headset walkie-talkie. Thus, Hypothesis 1 issupported for the phonics traveler at 95% confidencelevel, but not for the family game center. The lack ofsignificance for the family game center may be becausethe quantity of sales registered at each price-point forthis product is too small for statistical analysis.
For the headset walkie-talkie, Hypothesis 2 is sup-ported with a 99% confidence level. Thus, the findingthat the sales at the middle price-point exceed those atthe low and high price-points is statistically validated.
6. Discussion
6.1. Reasons for Upward Sloping DemandTo understand the reasons for the demand curve ob-served for the headset Walkie-Talkie, we discussed theresults with the managers of the subject firm andseveral other retailers. The following explanationsemerged from our discussions.
6.1.1. Price as an Indicator of Quality. The head-set walkie-talkie is a complex electronic item. Theconsumers find it difficult to judge its quality, andtherefore, use price as an indicator of quality. Themanagers used wine as another example where con-sumers might be expected to use price as an indicatorof quality. This argument did not apply to the familygame center because it is a board game, and easilyunderstood by the customer, so that price need not beused as an indicator of quality. It also did not apply tothe phonics traveler because it is a branded item.
This explanation is consistent with those given byDodd et al. (1991), Gerstner (1985), Lichtenstein andBurton (1989), Tellis and Wernerfelt (1987), andZeithaml (1988) for consumers using price as an indi-cator of quality. Our finding extends the insights fromthese articles because it is based on actual sales. Fur-ther, some of these papers are based on comparingprice and quality across products in a category, whilewe document the increase in sales with price for thesame product due to a likely increase in quality per-ception. For example, if a reputed and a not so reputedbrand sell the same toy for $30 and $25, respectively,then it is possible that the more reputed brand has ahigher quality, and thus a higher demand in spite ofthe higher price. However, our finding implies thatthe demand of the more reputed brand might increaseif its price is increased from $30 to $35.
6.1.2. Sweet Spot of Pricing. The price-point$19.99 is more popular for gift purchases than $14.99.Consumers may like the headset walkie-talkie as a giftitem, so that the unit sales at $19.99 exceed those at$14.99.
6.2. Implications of Informational Role of PriceWe first note that if price plays an informational role,then it leads to a reduction in the demand and theexpected profit for the subject item. To see this, con-sider the headset Walkie-Talkie. If price did not playan informational role and consumers had full infor-mation about the quality of this item from othersources, then the demand for this item would bedownward sloping in price. A conservative estimateof the price elasticity of demand is obtained from thetwo higher price points of $19.99 and $24.99. This
Table 5 Maximum Likelihood Estimates of the Effects of Price,Cluster, and Store Size on Unit Sales
estimate is conservative since the observed sales arenet of the informational and allocative roles of price.We find that the price elasticity is �3.16 (see Appendixfor the computations). With this price elasticity, theprice that maximizes the profit is $16.09 and the max-imum profit is $743.50. Compared to the profit of$665.26 realized at the middle price-point ($19.99), thisrepresents an increase of 12%. In such a case, it mightbe advantageous for the retailer to provide additionalsignals of quality to increase demand and profits.
However, the informational role of price can bebeneficial to the retailer due to product substitution.Suppose that the retailer offers an assortment of itemsat different price-points and that the consumers arewilling to substitute between these items. Then usingprice as a signal for quality could enable the retailer tocapture a larger consumer surplus by promoting sub-stitution.
7. ConclusionsWe have presented a methodology for conductingexperiments in a retail store that can help retailingmanagers learn more about their consumers. Thismethodology is useful not just for finding consumerreactions to different price-points, but also to test theeffects of other marketing levers on sales. The criticalaspect of the methodology is the selection of stores forthe experiment. We have shown how the differencesbetween stores may be defined using their sales char-acteristics and used to partition stores into a random-ized block design. This technique is advantageousbecause an experiment with a small number of exper-imental stores can yield accurate results applicable tothe entire chain.
While our paper shows the usefulness of in-storeexperimentation, it has some limitations that may beaddressed in future research. First, our paper providesa single statistically significant evidence that demandcan be upward-sloping in price. There is need forreplicating this finding through further experimenta-tion to demonstrate its validity. A wider range ofproducts and price points should be considered tosystematically study how consumers react to pricesand extend our results. Second, the experiment maybe conducted with fast-moving items or for a largernumber of weeks to collect more data for statisticalanalysis. Finally, the informational role of price maybe quantified in future research to investigate the con-ditions under which such a role is advantageous ordisadvantageous to the retailer. Such research wouldbe useful to retailers that use different pricing strate-gies and provide different levels of quality signals fortheir products.
Appendix
Estimation of Price Elasticity of DemandAssume that the mean demand depends on price accordingto a constant elasticity demand curve. Then, (8) in the Pois-son regression model of Section 5 is modified to
�kit � ak �Pki ��� xkit �
c,
where Pki is the i-th price-point in cluster k, � is the priceelasticity of demand, and the other variables have the samedefinition as before. The log likelihood function is thus givenby:
log L � �kit
��kit � ykit�log ak � � log Pki � c log xkit� � log �ykit!�.
We compute the maximum likelihood estimates of ak, �, andc. The price elasticity of demand for the phonics traveler isfound to be �2.02 (standard error � 0.90, p-value � 0.01).For the family game center, it is found to be �1.95 (standarderror � 1.64, p-value � 0.12). The lower significance level forthe family game center may be because it is a very slow-moving item with a few units sold at each price. For theheadset Walkie-Talkie, the price elasticity of demand esti-mated from the two higher price points of $19.99 and $24.99is �3.16 (standard error � 1.18, p-value � 0.01).
The optimal price is found by maximizing the standardexpected profit function,
E�� � Pki�kit � C�kit � constant �Pki1� � CPki
��,
where C denotes unit cost. This gives an optimal price of Pki
� �C/(1 �). Its value is $35.65 for the phonics traveler fora cost of $18 and a profit margin of $17.65. For the familygame center, it is equal to $22.58 for a cost of $11 and a profitmargin of $11.58. Thus, the price for the phonics traveler isfound to be higher than the existing price of $29.99, and theprice for the family game center is found to be lower thanthe existing price of $24.99 at this retail chain. The increase inexpected gross profit from moving to the optimal price is3.8% for the phonics traveler and 0.9% for the family gamecenter. The pricing problem for the headset Walkie-Talkie isdiscussed in Section 6.2.
AcknowledgmentsThis paper is based on a pricing experiment conducted atZany Brainy, Inc., a toys retailer based in King of Prussia,PA, and owned by F.A.O. The authors thank Gene Rosadinofor facilitating the experiment, and Young-Hoon Park (Cor-nell University) and Robert Shoemaker (New York Univer-sity) for helpful comments.
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