Using Price Cues. December Eric T. Anderson Northwestern University. Edward Ku Cho MIT. Bari A. Harlam. Duncan Simester MIT

Transcription

1 Using Price Cues December 2007 Eric T. Anderson Northwestern University Edward Ku Cho MIT Bari A. Harlam Duncan Simester MIT This paper forms the basis of a portion of the second author s PhD dissertation at MIT. The authors would like to thank the anonymous company that participated in the field study and generously provided the data for this study.

2 Using Price Cues Many firms employ an array of price cues, such as sale signs, to convince customers that their prices are low. While there is an extensive literature studying how to set prices, use of price cues has received relatively little attention. In this paper, we study how firms should use price discounts and price cues. We develop theoretical predictions regarding both demand and profits, and then test these predictions in a large-scale empirical study that combines survey metrics and a field experiment. We show that customer price knowledge moderates the impact of both price discounts and price cues. However, the profitability of price discounts and price cues are both determined by a different force. This common force makes it profitable to use price discounts and price cues on the same products, which in turn explains why consumers can rely on price cues as a credible source of price information.

3 1. Introduction Many firms employ an array of price cues to convince customers that their prices are low. These cues include Sale signs and other explicit low price claims, together with more subtle signals, such as 9-digit price endings. There is now extensive evidence that these cues are effective (see for example Inman, McAlister and Hoyer 1990) and so a simple response for firms is to place them on every product. However, we also know that they lose effectiveness if used too frequently (Anderson and Simester 2001), and so it is generally optimal to place price cues on some, but not all products. While there is an extensive literature studying how to set prices, use of price cues has received relatively little attention. In this paper, we study how firms should use price discounts and price cues. We develop theoretical predictions about both demand and profits, and then test these predictions in a large-scale empirical study that combines survey data and a field experiment. The economic theory of price cues explains that customers with poor price knowledge use them to evaluate whether it is worthwhile to search elsewhere for lower prices. Customer price knowledge plays an important role in this theory: while most people know the price of some products (gasoline), price knowledge is poor for many other products (spices). Our results confirm that price knowledge does moderate how customers respond to price changes and prices cues. Price cues are most effective when many customers have poor price knowledge, while price changes are more effective when customers have good price knowledge. This suggests a simple pricing strategy: lower prices on products for which price knowledge is good, and place price cues on products for which it is poor. We will show that this is not an optimal strategy. Our empirical results reveal that the profitability of price discounts and price cues is determined by a common force, demand sensitivity. Because of this common force a profit maximizing firm will tend to use price discounts and price cues on the same products. Page 1

4 The source of our empirical findings is a large-scale study that combines survey metrics and a field experiment. The survey data include almost six thousand price knowledge measures collected from actual customers waiting in line to checkout at two retail stores. We conduct the field experiment in eighteen convenience stores and exogenously vary prices and price cues on the same 192 products for which we collect survey measures. We combine the survey and experimental data to examine how price knowledge moderates consumer responses to price changes and price cues. We then calculate the profitability of the experimental treatments to identify where a profit maximizing retailer would lower prices and place price cues. Prior Literature The findings link several streams of previous research, including literatures on price knowledge, price cues and price elasticity. Asking customers to recall the price of products is not unique; the price knowledge literature includes a series of studies comparing the response to different price knowledge questions. These studies reveal that customers often cannot recall the prices of recently purchased products, including products that they have just placed in their grocery carts (see for example Allen, Harrell and Hutt, 1976; Conover 1986; Dickson and Sawyer 1990; and Vanhuele and Drèze 2002). Moreover, there is evidence that customers price knowledge varies across products. We will later exploit this variation when investigating how price knowledge moderates the response to low prices and low price claims. What is unique is that we link variation in price knowledge with demand elasticities. It is this connection that reveals how price knowledge moderates the response to price changes and price cues. Early research on price cues focused on measuring their effectiveness. For example, in laboratory experiments Inman, McAlister and Hoyer (1990) show that placing a sale sign on a product can increase demand, even if it is not accompanied by a change in the actual price. This finding survives when moving from the laboratory to the field. Inman and McAlister (1933) describe a field study conducted with a college campus store, while Page 2

5 Anderson and Simester (2001) report the outcome of an experiment conducted in a mailorder catalog. Similar findings have also been reported for other types of price cues, including price-matching policies (Srivastava and Lurie 2004) and price endings (Schindler and Kibarian 1996, Anderson and Simester 2003). Further evidence can be found in the discrete choice literature. Starting with Guadagni and Little (1983), this literature consistently reports that product displays and features, which often include low price claims, increase demand even after explicitly controlling for the impact of price changes. As we discussed, the economic theory of why price cues are effective interprets the cues as signals that prices are low. When customers have poor price knowledge they use the cues to evaluate whether to purchase. Anderson and Simester (1998) present an equilibrium model of this theory. When customers in their model are informed about prices, they respond to price changes rather than Sale claims. It is only when customers are uninformed that the Sale claims (price cues) influence demand. Our experimental results provide a test of these predictions. We also test a second prediction in this model: profit-maximizing firms prefer to place price cues on products for which they also charge low prices. This result is central to the credibility of price cues as a signal. If firms preferred to charge low prices on some products but to place price cues on other products, then price cues would not be an accurate signal that prices are low. Notice the apparent inconsistency in these two predictions. If firms offer low prices on products with good price knowledge and place price cues on (different) products for which price knowledge is poor, then products with price cues would not coincide with low prices. In the long-run this would undermine the credibility of price cues as a signal that prices are low. Our findings reconcile this apparent inconsistency by demonstrating that price knowledge alone does not provide a complete understanding of how prices and price cues affect firm profits. Our paper also contributes to literatures in marketing and economics that have sought to explain systematic variation in price elasticity. Tellis (1988) conducts a meta-analysis of Page 3

6 over three hundred price elasticity estimates and finds that brand life cycle and country of origin have significant moderating effects. While researchers have sought to link customer demographics and socioeconomic characteristics to price elasticity, many of these studies have found weak or insignificant relationships (see for example Blattberg, Buesing, Peacock and Sen 1978; Elrod and Winer 1982; Rossi and Allenby 1993). A notable exception is Hoch, Kim, Montgomery and Rossi (1996), who show that almost two thirds of the variation in store price elasticity is explained by demographic and competitive variables. Our research extends this literature by showing that customer price knowledge significantly moderates the demand response to price discounts and price cues. Ethical Concerns Claiming that a price is low raises ethical concerns if it misleads customers about true price levels. We will present evidence that it is profitable to use low price claims on products for which prices truly are low, suggesting that these claims are at least partially self-regulating. Nevertheless, while beyond the scope of this paper, study of the inherent ethical issues is called for. Such a review would be particularly valuable given the very widespread use of low price claims in both retail and industrial settings. We certainly do not intend that readers interpret our results as a recommendation that firms engage in unethical practices. In the next section we motivate our empirical analysis by presenting a series of testable hypotheses. We then describe how we will test these hypotheses using our survey and experimental data. 2. Consumer and Firm Theory We begin with a standard profit function: π = QM, where M = p - c and Q, M, p and c denote the quantity sold, profit margin, price and cost (respectively). The incremental profits when lowering the price by λ can be written as: π = QM Q λ, (1) λ λ Page 4

7 where Q λ is the change in demand. The incremental profits when placing a price cue on a profit is similar, though there is no change in the profit margin: π =QM, (2) Δ Δ whereq describes the demand change. We would normally expect both Q and Q to be Δ positive, and so the change in profits is determined by three factors: the profit margin (M), demand (Q), and the sensitivity of demand to price changes ( Q ) and price cues ( ). We will later investigate the relative contribution of these factors by testing the Q Δ following predictions: λ λ Δ Prediction 1 Prediction 2 Prediction 3a Prediction 3b It is more profitable to lower prices and place price cues on products with higher initial profit margins. It is more profitable to lower prices on products for which initial demand is smaller. It is more profitable to lower prices on products for which demand is more sensitive to price changes. It is more profitable to place price cues on products for which demand is more sensitive to price cues. Notice that demand sensitivity, profit margins and demand vary with the price of the product and so (as with all comparative statics) these predictions must be evaluated at a specific price. We will evaluate the predictions using the regular price as our benchmark or Control. For this reason we measure Q and M at the regular price, and measure Qλ and Q by the incremental demand that each treatment yields over demand at Δ this benchmark price. This issue is discussed in greater detail in both Sections 3 and 5, including a description of what is meant by the regular price. We can further diagnose the profitability of price changes and price cues by investigating the determinants of demand sensitivity ( Q and λ Q Δ ). We will investigate two Page 5

8 determinants: (1) product competition; and (2) customers price knowledge. Standard economic models predict that demand is more sensitive to actual or perceived price changes in markets that include more close substitutes. Intuitively, variation in the availability of substitutes leads to customers caring more about the prices of some products than others. We would expect this to moderate the response to both prices and price cues, suggesting that if the response to price changes is large, then the response to price cues will also be (relatively) large: Prediction 4 The sensitivity of demand to price changes and price cues is positively correlated across products. This strawman prediction has an important corollary. Positive correlation in the demand responses makes it more profitable to lower prices and place price cues on the same products (Predictions 3a and 3b). Moreover, it is this relationship that connects our analysis of demand in Section 4 with the profit analysis in Section 5. Anderson and Simester s (1998) investigation of the role of sale signs suggests an alternative prediction. In their model, demand sensitivity depends upon customers price knowledge. When customers have good price knowledge they respond to price changes, but when price knowledge is poor customers are more responsive to price cues: Prediction 5a Prediction 5b Demand is more sensitive to price changes when more customers have good price knowledge. Demand is more sensitive to price cues when fewer customers have good price knowledge. These predictions suggests that variation in price knowledge will lead to negative correlation in the response to price changes and price cues: Prediction 4 The sensitivity of demand to price changes and price cues is negatively correlated across products. Notice that price knowledge yields an opposite prediction to product competition (Predictions 4 and 4 ). For completeness, we illustrate our four demand predictions more Page 6

9 formally in the Appendix. We use a standard Hotelling model to demonstrate how customers with different knowledge of prices respond to price changes and price cues. Testing the Predictions Our first four predictions focus on firm profits, while the remaining predictions focus on demand. We use this distinction to help structure this paper. After describing the design of the field study in Section 3, we begin our analysis in Section 4 by testing the demand predictions. We test Predictions 5a and 5b by measuring how the response to price changes and price cues is moderated by customers price knowledge. We then measure whether there is positive or negative correlation across products in the demand response to price changes and price cues (Predictions 4 and 4 ). In Section 5 the focus shifts to testing the profit predictions. We identify products on which a profit maximizing firm would lower prices and/or place price cues. We then evaluate how variation in profit margins, demand and demand sensitivities contribute to these outcomes. The paper concludes in Section 6 with a summary of the conclusions and limitations. 3. Design of the Field Study Our study was conducted with the cooperation of a large chain of convenience stores. The stores sell a typical array of private label and national brand products in the grocery, health and beauty and general merchandise categories. The stores are smaller than most supermarkets and are located in convenient residential and urban locations. At the time of the study the firm also operated an Internet channel, but few customers purchased through this channel. The field study was conducted in eighteen stores located within approximately five miles of each other in the metropolitan area of a major US city. The study involved a total of 192 Test Products were selected from almost 20,000 SKUs sold by the retailer. Because the study manipulated prices and price cues for multiple products within the same store, Page 7

10 we selected products to minimize any cross-product effects amongst the 192 Test Products. For example, if a shampoo is discounted, it may affect demand for both substitutes (other shampoos) and complements (conditioners). For this reason we avoided including any products that were close substitutes or complements. We began with the retailer s classification of products into almost one thousand categories. Within each of these categories, we randomly selected a single SKU. A team of retail managers, the authors and research assistants then independently reviewed all of the candidate products. If there was a possibility that two products were close substitutes or complements, we randomly removed one of the products. The design of the field experiment included three conditions: Price Cue: A price cue was attached to the shelf. Price Discount: The price was reduced by 12%. Control: No change. In the price cue condition a 2 x 2 sticker was affixed to the shelf. The sticker had the words LOW prices in a red circle on a yellow background, as depicted in Figure 1. In the Control condition the price was reduced by 12%. This was an unannounced price reduction; there were no LOW prices stickers or any other indications that the price had been changed. In the Control condition the price was left unchanged (at the regular price) and there was again no sticker or other announcement of a price change. The regular price is the price that the firm charges for these products across a large number of stores in this geographic region. Although promotions sometimes result in temporary deviations from this regular price, an inspection of the historical data (and discussions with management) confirm that these regular price levels are relatively stable over time. It would have been ideal to include a fourth condition, in which prices were reduced and the LOW prices sticker was used. This would have allowed us to measure any interactions between the two treatments. Unfortunately, managerial and legal constraints prevented us from including this additional condition. Page 8

11 Figure 1. LOW prices shelf sticker LOW prices Notice that the price was left (unchanged) at the regular price in the price cue condition. For this reason the sticker does not make an explicit claim that the price of that product was reduced. It is possible that such a claim would have had a larger impact on demand. However, our focus is on comparing the impact of this cue across products. Because we used the same sticker on each product, the LOW prices wording does not limit our ability to compare outcomes across products. Similarly, use of a 12% price reduction in the Discount condition would be expected to yield different demand effects than smaller or larger price reductions. To control for store effects we rotated the experimental treatments across the 18 stores and used a balanced experimental design. The 192 products were randomly assigned to six product groups and the stores were randomly assigned to three store groups. We then rotated the experimental treatments across the product and store groups as illustrated in Table 1. The random assignment of products to the stores is of particular importance. It ensures that we can compare the outcomes across products without concern for store differences. Page 9

12 Table 1. Experimental Design Store Group 1 Store Group 2 Store Group 3 Product Group 1 Price Discount Price Cue Control Product Group 2 Price Discount Control Price Cue Product Group 3 Control Price Discount Price Cue Product Group 4 Price Cue Price Discount Control Product Group 5 Price Cue Control Price Discount Product Group 6 Control Price Cue Price Discount It is possible that the discount and LOW prices treatments may lead to either crossproduct or inter-temporal substitution. To control for cross-product substitution, in Section 5 we extend our measures of incremental profits beyond the Test Products to measure the change in category profits. To mitigate the effects of inter-temporal substitution we maintained the experimental manipulations for four months (seventeen weeks) between April, 2006 and July, The treatments did not vary over these seventeen weeks and regular visits by the research team to each of the stores ensured compliance with the experimental design. To measure whether the impact of the treatments varied during these 17-weeks, in our preliminary results we compare the outcome at the start and end of the treatment period. Preliminary Results More than 600,000 units of the 192 Test Products were purchased during the seventeen weeks treatment period. We received transaction data describing the number of units of each product purchased in each store in each week, together with the price paid and the wholesale cost of those purchases. We report preliminary results using two approaches. First, we aggregate across products, weeks and stores to calculate total demand by condition. We then use these aggregate measures to calculate the percentage change in the discount and LOW prices conditions compared to the control. By aggregating across products we effectively give greater weight to products that have more demand. Page 10

13 Therefore, in our second approach we calculate the effect for each product and then average this effect across the 192 products. The findings from both approaches are reported in Table 2. As expected, the 12% discount and the LOW prices sticker resulted in significant increases in demand. Table 2. Preliminary Results Price Discount LOW prices Cue Aggregate Results Demand in Treatment Condition (units) 182, ,043 Demand in Control Condition (units) 155, ,796 Difference (units) 26,593 5,247 Difference (%) 17.3% ** 3.4% ** Product Level Results Average Difference 13.2% ** 8.4% ** Standard Error 2.8% 2.9% Sample size For the aggregate results we test whether demand in the Treatment Condition was significantly different than 50% of total demand in the two conditions. ** Significantly different from zero, p < * Significantly different from zero, p < To evaluate whether these outcomes varied across the 17-week treatment period we divided the period into two sub-periods, comprising the first 8 weeks and the last 8- weeks. We then re-estimated the findings using these sub-periods (the findings are reported in Table A1 in the Appendix). They reveal that the outcomes were very stable, with almost identical demand effects at the start and end of the 17-weeks for both treatments. While these preliminary results serve as a reassuring manipulation check, they are not the primary focus of this paper. Instead we focus on understanding how the impact of the Page 11

14 two experimental treatments varied across the different products. In the next section we investigate how these demand outcomes were moderated by customers price knowledge and the availability of substitutes. In Section 5 we investigate the profitability of the two treatments. 4. The Demand Response We begin by investigating how price knowledge moderated the response to the two experimental treatments (Predictions 5a and 5b). We then evaluate whether these demand responses were positively or negatively correlated across products (Predictions 4 and 4 ). Measuring Price Knowledge To measure customer price knowledge we collected price recall responses from a sample of actual customers inside two of the chain s stores. The responses were collected by a team of research assistants who approached customers standing in check out lines waiting to complete their transactions. Customers were asked to participate in a short survey about products and prices that takes roughly four and a half minutes. They were offered a free $5 gift card for participating. Pretests confirmed that the survey was generally completed in less than five minutes. Approximately 60% of customers who were asked to participate agreed, limiting the risk of non-response bias. Respondents were each shown actual examples of eight of the Test Products and asked: What is your best guess of the price that [store name] normally charges for this product? Respondents in the pretest were asked to describe in their own words to the interviewer what was meant by this question. Their responses confirmed that they had little difficulty interpreting the question. The 192 Test Products were randomly sorted into groups of eight products, and these groups were then rotated across the respondents. Thus, each customer provided price knowledge measures for eight randomly selected products. A total of 783 customers Page 12

15 participated in the survey and this yielded a total of 5,969 usable price recall measures across the 192 Test Products. This represents an average of just over 31 responses per product. All products had at least 25 responses and no product had more than 32 responses (the variation reflects the random assignment of products to survey groups). Although the response measures were conducted during the same time period as the experimental treatments, we do not believe the measures were influenced by the treatments. Customers were asked whether they had seen the prices of any of the products in the store on that visit. This occurred for just 1% (64) of the price recall responses, and omitting these observations has no affect on the results that follow. We use the 5,969 responses to calculate a measure of price recall accuracy (Accuracy i ). This measure is defined as the percentage of customers who recalled a price within X% of the regular price. Summary statistics for this accuracy measure are reported in Table 3. The standard for evaluating accuracy is somewhat arbitrary and so for completeness we report summary statistics when setting the standard at 10% and 20%. Table 3. Price Recall Accuracy Summary Statistics Within 10% Within 20% Mean 17.8% 30.6% Standard Deviation 11.5% 14.3% Maximum 59.4% 70.0% Minimum 0.0% 3.1% Number of Products ** Significantly different from zero, p < * Significantly different from zero, p < On average 17.8% of responses were within 10% of the actual price, though there is considerable variation across products. For one product almost 60% of the responses Page 13

16 were correct (within 10%), while for five of the products none of the responses were within 10% of the correct price. Our next step uses this accuracy measure to investigate whether the response to the discounts and LOW prices sticker was moderated by customers price knowledge. We use a multivariate approach to explicitly estimate how the interaction between price knowledge and the two treatments changed demand for the Test Products. Specifically, because demand is measured as a count of the number of units sold we use Poisson regression (which is well-suited to count data) to estimate the following equation: 1 ln ( λ ) =α+β 1 +β 2 +β3 Discount LOW prices Accuracy its is is i +β Discount * Accuracy + β LOW prices * Accuracy 4 is i 5 is i (3) The Discount and LOW prices variables are defined as follows: Discount is LOW prices is Equal to 1 if product i was discounted in store s and zero otherwise. Equal to 1 if product i had a LOW prices sticker in store s and zero otherwise. Under this specification, the β 1 and β 2 coefficients measure the percentage change in demand attributable to the discounts and LOW prices sticker (respectively). The interaction coefficients β 4 and β 5 measure how the outcome is moderated by the number of customers that can accurately recall prices. We will use these interaction coefficients to evaluate Predictions 5a and 5b. 1 In doing so we assume that the number of units of product i sold in week t in store s (Qits ) is drawn from a Poisson distribution with parameter λ its : where: ( ) coefficients. λ its e λits Prob ( Qits = q) =, q=0, 1, 2,... q! ln its its q X its λ =βx. The term denotes the independent variables, while β denotes the estimated Page 14

17 We estimate Equation 3 using 58,752 observations, representing demand for the 192 products in the 18 stores across the 17 weeks. We estimated separate models using our two accuracy standards (from Table 3) and also estimate a benchmark model in which we omit the interaction terms. The findings are reported in Table 4. Table 4. Moderating Effects of Price Knowledge Benchmark Model Within 10% Within 20% Accurate * Discount ** (0.024) ** (0.024) Accurate * LOW prices Cue ** (0.025) ** (0.024) Accurate ** (0.017) ** (0.017) Discount ** (0.003) ** (0.008) ** (0.011) LOW prices Cue ** (0.004) ** (0.008) ** (0.011) Intercept ** (0.003) ** (0.006) ** (0.008) Log Likelihood -844, , ,989 Sample size 58,752 58,752 58,752 ** Significantly different from zero, p < * Significantly different from zero, p < The results confirm that the price discounts were more effective and the LOW prices stickers were less effective on products for which customers have better price knowledge. Together, these findings offer strong support for Predictions 5a and 5b. This pattern of results is also precisely the outcome predicted by Anderson and Simester s (1998) model. On products for which they have good price knowledge, customers in their model can recognize when a price is low and so they respond to price changes. However, when they are unable to evaluate prices, customers use prices cue to evaluate whether to search elsewhere for lower prices. Page 15

18 The effects are large. To illustrate their magnitude we can use the interaction coefficients to compare the outcome on products for which Accuracy equals 1 (all customers can accurately recall the true price) versus 0 (no customers can recall the price). Price discounts lift demand by 79.7% more when customers can recall the price compared to when they cannot. In contrast, the demand increase from the LOW prices sticker is 66.0% smaller when customers can accurately recall prices. Rather than measuring price knowledge using survey responses, we can also measure price knowledge using product characteristics that are correlated with price knowledge. We consider two characteristics: the frequency with which customers purchase the products, and the variation in the regular price. We would expect customers to have more price knowledge on frequently purchased products but less price knowledge when the regular price varies frequently, and so we replicated the results using measures of both Purchase Frequency and Price Variation. These measures were constructed from a sample of 5 million historical transactions as follows: 2 Purchase Frequency i Price Variation i The number of times that product i was purchased in the sample of historical transactions. The coefficient of variation in the regular price of product i across this historical sample of purchases. To aid interpretation, we standardized both variables before re-estimating Equation 3. The results, which are presented in the Appendix (Table A2), replicate the pattern of findings reported in Table 4. Price discounts yielded a larger demand increase on products that customers purchase more frequently and on products for which the regular price varies less frequently. These interactions are reversed for the LOW prices cue. 2 These historical transactions were made by a randomly selected sample of approximately 650,000 customers who had all made at least one purchase at one of the 18 stores involved in the test. The transactions include every purchase made by these customers in the 20 months before the start of the test, including purchases at stores other than these 18 stores. Page 16

19 A Dilemma The results in Table 4 (and Table A2) confirm that price cues are more effective when customers lack price knowledge, which supports the theory that these cues serve a signaling role. However, the findings also highlight a difficulty with this theory. If firms lower the prices of some products (for which price knowledge is good) but place price cues on different products (where price knowledge is poor), then the cues and low prices will not coincide. In the long-run we would expect customers to discover this pattern and no longer rely on price cues as a signal that prices are low (indeed, customers could reasonably draw the opposite inference). There are two possible solutions to this dilemma. The first solution focuses on demand sensitivity. While price knowledge may introduce negative correlation in the response to prices and price cues (Prediction 4 ), price knowledge is not the only factor that influences these demand responses. As we discussed in Section 2, standard models predict that customers care about some prices more than others, and this will tend to introduce positive correlation in the response to the two treatments (Prediction 4). Resolving these opposing predictions is an important empirical question, which we focus on in the remainder of this section. The second solution recognizes that the firm s objective is to maximize profits not demand, and incremental profits depend not just upon the demand response but also upon both initial demand and the initial profit margin (Predictions 1 and 2). We delay investigation of these issues until our profit analysis in the next section. Correlation in the Demand Responses We begin by calculating the percentage change in demand under each treatment (we used the same response metric for the product-level results in Table 2). The correlation in this response metric for the two treatments across the 192 products is 0.58, indicating a highly significant (p < 0.01) positive relationship. We can illustrate this relationship in a scatter plot (Figure 2), where each point represents the change in demand for a single product under each treatment. To protect the confidentiality of the data the outcomes are rescaled Page 17

20 on a 1 to 7 scale (using the same re-scaling for each treatment). The figure reveals a strong positive relationship in the response to the two treatments. Figure 2. Demand Response to the Discounts and LOW prices Sticker 7 6 Price Cue Elasticity Price Elasticity Each point represent the percentage change in demand for a single product under each of the treatments. The scaled are scaled from 1 to 7 to disguise confidential information. We conclude that products that had a large demand response to the price discount also had a large response to the LOW prices sticker. This positive correlation favors Prediction 4 over Prediction 4, suggesting that the variation in response rates introduced by customers concern about prices overwhelms the variation introduced by price knowledge. For completeness we conducted a series of robustness checks. First, we can see from Figure 1 that there is an outlying result for one product that contributed to the positive correlation (depicted in the top right corner of the figure). However, omitting this outlying observation only lowers the correlation to We can also control for outliers by using a rank-order correlation. The rank order correlation in the response to the two Page 18

21 treatments is We conclude that the positive correlation is robust to the presence of outliers. Second we investigated whether the positive correlation resulted from a common set of control measures. Notice that we compare demand in stores that received the respective treatments with demand in the control stores that did not receive either treatment. It is possible that stochastic variation in demand at these control stores may have contributed to the positive correlations. We repeated the analysis when randomly assigning three of the six control stores as controls in the discount calculation and the other three as controls in the LOW prices calculation. The correlation remains positive and significant (ρ = 0.52), confirming that this positive relationship cannot be fully explained by the use of common control stores. More generally, all of the results that we report in both this section and the next section survive when using different control stores to evaluate the two treatments. Finally, we replicated the analysis using a Poisson regression model to calculate the response to each treatment for each product. We then used the coefficients from these models to calculate the correlation between the two treatments. The correlation coefficient was 0.57, essentially unchanged from the univariate approach. Customers Concern About Prices Correlation in the response to the two treatments does not directly measure customers concern about prices. Fortunately, for many of the products we have an independent measure of customers price sensitivities. Approximately 18-months before the present study the same retailer conducted a large-scale price test involving over 10,000 products. The study was conducted in a different geographic region and did not include any of the 18 stores used in this study. However, the study did include 168 of the 192 Test Products used in our study. From this earlier study we obtain a measure of price sensitivity (which we label Elasticity) for these 168 products, which we will interpret as an independent measure of how much customers care about prices. Adding this measure to Equation 3 allows us to evaluate how concern about prices moderated the response to the Page 19

22 experimental treatments in this study. For ease of interpretation we multiple the price elasticities by minus 1, so that larger positive values indicate more elastic demand, and standardized both the Elasticity and Accuracy variables. The findings are reported in Table A3 in the Appendix. Not surprisingly, products for which demand was highly elastic in the earlier price test were also more responsive to the discounts in this study. More importantly, we observe the same outcome for the LOW prices sticker: larger elasticities in the earlier study correspond to a larger response to the LOW prices stickers in this study. Summary We have shown that price knowledge moderates the response to price changes and price cues in the manner that was predicted by Anderson and Simester (1998). Demand is more responsive to price changes on products for which customers have more price knowledge, and more responsive to price cues when price knowledge is poor. Despite these results, we find that products that had a large demand response to the price discount also had a large response to the LOW prices sticker. This positive correlation in the response rates follows from a standard model in which customers care more about the prices of some products than others. In the next section our focus shifts to measuring firm profits. We identify the products on which it is most profitable to lower prices and place price cues. 5. Optimal Use of Actual and Perceived Price Changes In this section we use the results of the field test to investigate how a profit-maximizing firm would use price cues. We begin by calculating the change in profits earned from each product under the two experimental treatments. We then use these profit measures to rank the profitability across products, and identify where it is profitable to lower prices and place price cues. We evaluate alternative explanations for the findings and then conclude by extending the analysis to measure incremental profits at the category level. Page 20

23 Which Products Had the Largest Profit Increases? In Table 5 we list the twenty products that generated the largest incremental profit under each treatment. Seven of the products appear on both lists. Intuitively, if the retailer is restricted (for exogenous reasons) to lowering the price of twenty products and placing LOW prices stickers on twenty products, a profit-maximizing retailer would use both treatments on seven of the products. This is more overlap than we would expect through chance alone: if the retailer allocated the two treatments randomly across the 192 products then we would expect overlap on just 2.08 products. We can also compare the correlation in the two rankings across the complete set of 192 products. The Spearman rank-order correlation is 0.39 (the Pearson correlation is 0.45). This is significantly larger than zero (p < 0.01). Table 5. The 20 Products That Yielded the Largest Incremental Profits Rank Discount LOW Prices 1 Latex gloves Water filter 2 Lint brush Laxative 3 AAA batteries Cotton swab 4 Iced tea Nutrition bar 5 Mailing tape Hair trimmer 6 Canned tuna Anti-itch cream 7 Sheet protector Liquid soap 8 Baby wipes Lint brush 9 Baby powder Napkins 10 Hair pins Mailing tape 11 Anti-itch cream AA batteries 12 Peroxide Hair treatment 13 Water filter Sleep aid 14 Eye patch Plastic cups 15 AA batteries Sunscreen 16 Vitamin C Cleansing towelet 17 Nutrition bar Condoms 18 Marker pen Baby wipes 19 Pencil sharpener Chap stick 20 Pill box Candy We highlight the 7 products that appear in both lists with bold text. Page 21

24 The restriction to discounting twenty of the 192 products and using twenty LOW prices stickers is obviously arbitrary. While earlier research indicates that using too many LOW prices stickers may undermine the credibility of the low price claims (Anderson and Simester 1998 and 2002), there is no such restriction on the discounting treatment. In practice we might expect the firm to discount all of the products for which the discounts yield positive profits. The field test results reveal that the 12% discounts led to higher profits on 41 of the 192 products. If the firm maintains the discounts on these 41 products, we can ask whether it would also place LOW prices stickers on these products. In Table 6 we report how many of these 41 products would receive LOW prices stickers as we vary the total number of available stickers. We compare two policies: a profitmaximizing policy that places the stickers on the products for which they yield the largest incremental profits; and a policy that places the stickers randomly on the 192 products. Under the profit-maximizing policy up to half of the available stickers would be placed on these 41 products. In contrast, a random allocation of the stickers would on average lead to just 21% (41/192) of the stickers being placed on these 41 products. Table 6. Placement of LOW prices Stickers Total Number of LOW prices stickers Profit Maximizing Allocation Random Allocation In the first column we vary the total number of available stickers. In the second and third rows we describe how many of these stickers would be placed on the 41 products for which the discounts were profitable. Recall that a critical prediction from Anderson and Simester s (1998) model is that firms prefer to place price cues on products that have low prices. Our results can be thought of Page 22

25 as a first empirical test of this prediction. The implication is that when firms allocate discounts and price cues to maximize their profits, customers can use the cues to identify which products have low prices. We can illustrate this signaling role by comparing the probability that a product has a low price in the presence or absence of a LOW prices sticker. We report these probabilities in Figure 3 when varying the total number of available stickers. We again assume that the firm charges low prices on the 41 products for which doing so was profitable, and allocates the stickers so that they yield the greatest incremental profit. Figure 3. Information Revealed by the LOW prices Sticker Probability the Product Has a Discount Total Number of Products with LOW prices Stickers Products with LOW prices Stickers Products without LOW prices Stickers Irrespective of how many LOW prices stickers are used, products with stickers are more likely to have discounts than products without stickers. We conclude that rational customers can rely on these cues to infer which products have discounted prices. Notice that the cue is not fully revealing as not all of the products with stickers are truly discounted. In this respect the cue contains information, but the information is noisy. The noisy characteristic of the signal is also a feature of Anderson and Simester s (1998) Page 23

26 model. While sale signs are informative in their model, they are not perfectly accurate as not all products with sale signs are truly discounted. These results confirm that a profit maximizing firm will tend to use actual and perceived price changes on the same product. We next consider why this outcome is profitable. Why Are Price Cues Informative? Recall that in Section 2 we identified three factors that determine how much incremental profit a firm earns from a price change and a price cue: (1) the initial profit margin, (2) the initial demand, and (3) the sensitivity of demand to each treatment. We summarized the role of these factors in Predictions 1-3. To test these predictions we can evaluate the extent to which variation in each factor contributed to the rankings of the incremental profits earned from each treatment. We begin by calculating a measure of the initial profit margin (M), initial demand (Q), and the sensitivity of demand to each treatment ( Q and λ Q Δ ). As we discussed, the field experiment compares the profits earned under the two treatments to the profits in the control condition, where we charged the regular price for each product. For this reason, the initial profit margin (M) and initial demand (Q) are calculated using data from the control stores. The demand sensitivity measures ( Q and λ Q Δ ) were constructed by calculating the difference in demand between the (respective) treatment stores and the control stores (measured in units). To evaluate the contributions of each factor to the incremental profits earned under each treatment we calculated the Spearman rank correlations between the incremental profits and the M, Q, Q and Q metrics. These correlations, which are reported in Table 7, λ provide a test of each of our profit predictions. Δ The findings do not support Prediction 1; initial profit margins are not significantly correlated with the ranking of incremental profits from either of the two experimental treatments. However, there is support for Prediction 2. It is more profitable to offer Page 24

27 discounts on products with lower initial demand, reflecting the loss of margin when discounting the price. Because placing a price cue on a product does not change the price, initial demand was not expected to influence the profitability of the LOW prices sticker (see Equation 2). The findings are also consistent with this prediction. We do not observe any correlation between demand in the control condition and the incremental profits earned from the LOW prices stickers. Finally, there is strong support for Predictions 3a and 3b. Demand increases under each treatment were highly correlated with the incremental profits. We conclude that the incremental profits are primarily determined by the sensitivity of demand to each treatment. Table 7. Determinants of Incremental Profits Rank-Order Correlations Incremental Profits Discounts LOW prices Profit Margin (M) Demand (Q) ** Demand Sensitivity (Q and λ Q Δ ) 0.62 ** 0.87 ** Sample size The table reports rank order correlations between the incremental profits earned from each experimental treatment, and the different sources of those incremental profits. ** Significantly different from zero, p < * Significantly different from zero, p < Measuring Profits at the Category Level Recall that we earlier recognized that changing the price or placing a price cue on a product may lead to cross-product substitution, reducing demand for other products in the category. To control for this possibility we repeated our analysis using measures of category profits rather than product profits. This category-level analysis replicated the pattern of results that we report above. For example, the rank order correlation in the incremental profits earned under the two Page 25

28 treatments is 0.39 when using profits at the product level and 0.40 using profits at the category level. As a result, the tendency to place LOW prices stickers on products that also have discounts remains unchanged and so rationale consumers may use the cues to infer which products have discounted prices irrespective of whether the firm evaluates profits at the product or category level. We can also replicate the results in Table 7, revealing the determinants of incremental profits under each treatment. In Table 7a we report the rank order correlations between the initial profit margin, initial demand and demand sensitivities (all measured at the category level) with the incremental profits (also measured at the category level). Table 7a. Determinants of Incremental Profits at the Category Level Rank-Order Correlations Incremental Profits Discounts LOW prices Profit Margin (M) Demand (Q) Demand Sensitivity (Q and λ Q Δ ) 0.89 ** 0.90 ** Sample size The table reports rank order correlations between the incremental profits earned from each experimental treatment (measured at the category level), and the different sources of those incremental profits (also measured at the category level). ** Significantly different from zero, p < * Significantly different from zero, p < Although there is no longer a significant relationship between initial demand and incremental profits in the discount condition, the role of demand sensitivity is further strengthened. 3 We conclude that the key findings are robust to using either product-level or category-level measures. 3 As with all of our analysis, we investigated whether the positive correlation attributable to the demand changes could be explained by the use of common control stores by randomly assigning three of the control stores to each condition (see the discussion in the previous section). The results are essentially unchanged when using this approach. Page 26

29 Summary A comparison of the incremental profits earned under the two treatments reveals that a profit-maximizing firm would tend to lower prices and use the LOW prices cue on the same products. This has important implications for our understanding of why price cues are effective. A tendency to use both pricing strategies on the same products supports the interpretation that price cues serve as a credible signal that prices are discounted. Our results also reveal why it is profitable to lower prices and place price cues on the same products. The primary determinant of where firms will offer discounts and place price cues is the sensitivity of demand to these two treatments. This factor plays a much greater role in determining incremental profits than either the initial demand or the product s profit margin. Moreover, as we demonstrated in Section 4, the sensitivity of demand is positively correlated across products, so that the products on which discounts are effective tend to be the same products that price cues are most effective. We caution that because we were unable to include a fourth experimental condition in which products received both discount and LOW prices stickers, our findings do not account for possible interactions between the two treatments. We discuss this limitation and summarize the key conclusions from the study findings in the next section. 6. Conclusions We have presented a combination of data from a field experiment and customer surveys to evaluate where it is profitable to place price cues. The paper offers four key results. First, demand is more sensitive to price changes when customers have good price knowledge, and more sensitive to price cues when price knowledge is poor. This is consistent with the theory that customers with poor price knowledge use price cues to evaluate whether to search elsewhere for lower prices. Second, despite these price knowledge interactions, the demand response to discounts and price cues is positively correlated across products. We attribute this correlation to variation in product Page 27