Rehabilitating Cherry-Picking. Xavier Drèze*

Transcription

1 ll-rev5.wpd January 6, 1999 Rehabilitating Cherry-Picking Xavier Drèze* * Xavier Drèze is Assistant Professor of Marketing at the Marhsall School of Business, University of Southern California. The author would like to express his gratitude to Sanjay Dhar, Steve Hoch, Abel Jeuland, Peter Pashigian, Peter Rossi and Duncan Simester for their helpful comments on this manuscript.

2 Abstract Cherry-picking is traditionally seen as an undesirable side effect to loss leader pricing. Indeed, retailers use loss leader prices to attract customers into their stores, hoping that these consumers will also buy regular priced goods and that the profits generated on these sales will more than compensate for the loss incurred on the loss leader products. However, if consumers buy only the loss leader goods (i.e., cherry-pick), the loss leader strategy backfires and retailers lose money. Hence, cherry-picking is viewed as a parasitic behavior that should be prevented at all cost. In this paper, we show, using both an economic model and supporting empirical evidence, that contrary to common wisdom, it is often in the best interest of retailers to encourage cherrypicking and avoid direct competition on promotions. By not competing with each other, retailers can afford to give shallow discounts (making promotions profitable) and still attract price conscious consumers. At the same time, by encouraging a fraction of the population to cherrypick, retailers increase promotion lifts (making promotions even more profitable). There are however situations in which retailers are forced to use loss leader pricing. When they do so, it is not to steal consumers away from competitors, but rather to prevent their core consumer segment from shopping at other stores. Retailers then fight each other head to head, in a classic prisoner's dilemma setting. This competition has no effect on store traffic and precludes cherry-picking. In short, we show that (1) cherry-picking is not an undesirable behavior, but rather a behavior that can be taken advantage of for greater profit, (2) loss leader prices are not aimed at stealing consumers away from the competition, but are rather defensive moves to protect one s consumer base, (3) cherry-picking and loss leader are mutually exclusive. Keywords: Promotion, Pricing, Loss Leader, Cherry-Picking

3 3 I. Introduction Store traffic is one of the main concerns of retailers worldwide. Indeed, every purchase starts with a store visit. With this in mind, retailers expend significant resources to convince consumers to shop at their stores rather than at a competitor's. To achieve this goal they use marketing techniques such as radio announcements, television spots, or frequent shopper cards. One of the most widely used tools is the weekly advertising of temporary price reductions. It is commonly assumed that retailers generate traffic by mailing consumers weekly flyers that advertise loss leaders promotions. Loss leaders are products priced at very low margins (sometimes negative) to generate traffic by diverting customers away from competitive stores. The rationale behind this pricing scheme is that, once in the store, consumers buy additional goods which are priced at full margin. The loss of profit on the loss leader is more than compensated by the profits generated by the other goods the consumers buy. One problem hindering the effectiveness of loss leader pricing is cherry-picking. Cherrypicking occurs when consumers hop from store to store, buying only items that are on sale. In so doing, they manage to buy a full basket of goods without having to buy the full margin items that make loss leader pricing profitable. As such, cherry-picking is an undesirable behavior that limits the effectiveness of loss leader pricing. Both empirical and theoretical papers have been written about loss leader pricing and its effect on store attendance. The general consensus is that loss leaders are a good way to generate traffic and that cherry-picking is a necessary evil that has to be tolerated in order to maximize profits. Lal and Matutes (1988), for instance, studied the case of two stores competing in a heterogeneous market (two types of consumers: rich and poor), with full price information. Their analysis shows that, depending on the cost of transportation of rich consumers, three different situations can arise: (a) For small transportation costs, no pure strategy Nash equilibrium exists. (b) For medium transportation costs there are two possible equilibria, one in which retailers encourage cherry-

4 4 picking, and one in which they prevent it. There are however some parameter values for which the two equilibria coexist. (c) For large transportation cost, firms will choose different products as loss leaders, yielding a situation where loss leader pricing and cherry-picking happen concurrently. Cherry-picking by the poor segment is tolerated because it is too expensive to prevent it. The empirical research however has failed to demonstrate the impact of loss leaders on store traffic while showing at the same time that cherry-picking does indeed occur. Walters and MacKenzie (1988) conducted an empirical analysis of loss leaders and found that loss leader pricing produced only a small increase in store traffic. They found no evidence that loss leader sales have a positive spillover effect on the sales of non-promoted brands. However, they found strong evidence that store traffic has a positive influence on sales of both promoted and non-promoted products. Using data from two Midwestern fabric stores, Walters (1988) later confirmed that traffic has a positive impact on sales, and found that advertised promotions have a positive spillover on complementary products, and a negative impact on substitute ones. Walters (1991) looked at 26 weeks of scanner data for four product categories (cake mix, frosting, spaghetti, and spaghetti sauce). He reported that although promotions affect sales of the promoted products, they have only a modest impact on substitute and complement products and little, if any, impact on competing store sales. Kumar and Leone (1988), looking at diaper sales in 10 stores (five different chains), found that not only are a brand's sales affected by its own promotion, but they are also affected by promotion from directly competitive stores. They further discovered that sales of product categories are also influenced by in-store displays in competitive stores, showing that consumers frequently cross-shop. This finding has been recently confirmed by a study commissioned by the Coca-Cola Company (1995). By analyzing data from frequent shopper programs, they discovered that consumers will shop at three to four different supermarkets on a regular basis. Examining this empirical and theoretical work leads to some puzzling questions: Why are loss leaders not generating the traffic predicted by theory? Why are loss leaders not having any spillover

5 5 effects on other categories? If loss leaders have no spillover effects on other categories, why do retailers keep selling turkeys below cost on Thanksgiving? If cherry-picking is truly a side effect of loss leaders and loss leaders are ineffective, why not dispose of both? Are retailer doing things wrong? In this paper, we develop a framework that proposes to answer these questions. We do so by reconciliating the theoretical work with the empirical findings. To that effect, we extend the work of Lal and Matutes in a few significant ways. First we show that, if one takes trade deals into account, a Nash equilibrium always exists. Second, the equilibrium is always unique, although different parameter values will yield different optimal strategies. Third, we show that, when used optimally, loss leader prices and cherry-picking are mutually exclusive. The analysis shows that, in most situations, retailers are better off promoting different products than their competitors. This allows them to offer shallow discounts on promoted products (i.e., they still keep a substantial positive margin on the promoted products), and at the same time will induce a portion of the population to cherry-pick, thus increasing store traffic. This combination of positive margins and increased traffic is what makes the promotions profitable. In some circumstances, however (when manufacturer incentives are large), this alternate promotion scheme will leave the retailers too vulnerable to predatory moves by competitors, and they will be forced to protect their businesses by offering deep discounts on promoted goods at the same time as their competitors. This situation will yield loss leader prices on the promoted goods (retailers are fighting head to head in a Bertram style competition), and will prevent cherry-picking (since both retailers are promoting the same products, consumers have no opportunities to cherry-pick). In this framework, loss leader prices are not predatory moves to steal consumers away from competitors, but rather defensive moves aimed at retaining core customers. Fourth, we offer empirical support for the model. Concentrating on soft drinks (a category widely believed to be a loss leader) we show that, when promoted, two liter bottles of Coke or Pepsi

6 6 still retain a margin of 30% (hardly a loss leader). we also show that when two competing retailers (Dominick s Finer Food and Jewel, the two major retailers in Chicago) fight head to head on multipacks of Coke and Pepsi, their store traffic is smaller than when they don t. At the same time, when Dominick s and Jewel allow their consumers to cherry-pick on soft drinks, they generate higher store traffic and higher overall store sales. The theoretical framework for this paper is laid out in the next section (Section II). The actual analysis is then carried out in Section III, with the empirical work exposed in Section IV. II. Model When modeling the promotional activities of competing retailers, it is important to recognize that most promotions are subsidized by manufacturers. Each week, retailers receive hundreds of trade deal offers. These trade deals are used by manufacturers to encourage retailers to promote their brands. They usually involve discounted merchandise and an advertising allowance in return for guaranteed ad space and/or special displays. The practice is so widespread that retailers will not advertise products without payment from manufacturers. Of all the trade deals offered each week, retailers typically accept only 25 to 30%. Once retailers have accepted a trade deal (different retailers can make different decisions), they have to decide when and how to use it. Indeed, retailers have some flexibility in terms of the timing of the promotion, the size of the pass-through (the percentage of the discount passed on to the consumers) and the discount vehicle (Dhar and Hoch 1995, Tellis and Zufryden 1995). To model the decisions retailers face regarding the trade deal offers made by manufacturers, we will use a classic Hotelling style game. We consider the case of two retailers (A and B), competing in a oneperiod game. They are located at the ends of a unit-length segment. The retailers compete for the demand of two goods that are neither complements nor substitutes. They acquire the products at a marginal cost which is set to zero without loss of generality.

7 7 Consumers are uniformly located along the segment line and are divided into two groups. The first group of people consists of price-insensitive consumers who are characterized by a reservation price of H for each product and a transportation cost of c/2. Consumers in the second group are price-sensitive and are characterized by a lower reservation price of $H ($ < 1) and a lower transportation cost (c/2 (( «1, and in particular, (c $H). The proportion of priceinsensitive consumers is ". One should note at this point that our definition of transportation cost encompasses not only the cost of physically traveling one or two miles, but also the opportunity cost of time (time spent looking at flyers, going to a store, standing in line, and so on). This transportation cost is assumed to be very small for price-sensitive people. However, it is not set to zero since this would provide price-sensitive consumers with the ability to visit both stores before making a choice, thereby gaining perfect information. The transportation cost of price-insensitive people is assumed to be large, but not so large that price-insensitive people located at the halfway point between the two stores would choose not to shop if products were priced at a level acceptable for price-sensitive people (i.e., c/2+$h < H). Price Insensitive Price Sensitive Proportion " 1 - " Reservation Price H $H Transportation Cost c/2 (c/2 Table 1: Model Parameters It is generally assumed that consumers are fully aware of the prices of the goods they are interested in purchasing. They are capable of comparing prices across stores, and can recognize when a product is priced at a discount. However, empirical research shows that price knowledge is

8 8 very low in practice. For instance, Dickson and Sawyer (1990) showed that 23% of the people they surveyed could not give any estimate for the price of an item they had bought less than 30 seconds ago. And of those who could give an estimate, 40% gave an incorrect price (by about 30 cents on a two-dollar item). Only 21% of the consumers surveyed had made a price comparison between two supermarkets in the previous week, and 45% had never made price comparisons between supermarkets. Therefore, we will assume here that consumers have limited price knowledge. They know about price only through advertising or store visits, and no learning takes place from one period to another. Hence a multi-period horizon can be viewed as a series of independent one period games. At the beginning of the game, the manufacturers of both products will offer a trade deal to the retailers. The offer has two components: first a fixed amount of money, F, if they advertise their product at a price below $H in the weekly feature (co-op money); second a scanback of D on each unit sold during the promoted week. In response to this offer, stores can choose to advertise up to one product (the advertisement will reach every consumer). The trade deal, as described in our model, mimics the scanback practice that is now gaining popularity among manufacturers. A scanback trade deal is structured as follows: manufacturers offer retailers a three- or four-week window during which they can run one one-week promotion. After running the promotion, retailers tell the manufacturer how many units were sold, and receive money back based on that number (e.g., 20 cents for each unit sold). The popularity of scanbacks is growing with improved scanner technology -- out of the 26 categories that were tracked at

9 9 Dominick's Finer Food (Dominick s) as part of the Micro-Marketing project 1, only three (cigarettes, front-end-candy and beer) did not use any scanbacks. Given our assumptions, the weekly profit function for a retailer who advertises one product can be formulated as 2 : A ' (P A %D)[g ia "%g sa (1 & ")]%P NA [g ina "%g sna (1 & ")] (1) Where: A refers to the non&advertised product NA refers to the non&advertised product i refers to the price insensitive consumers s refers to the price sensitive consumers P p is the price of product p 0(A,NA) g cp is the proportion of the consumers of type c 0(i,s) who are buying product p 0(A,NA) Given the prices advertised, consumers will form expectations about the non-advertised prices and then, depending on these expectations, decide to visit one store, both stores, or neither store. In the event that consumers decide to visit both stores, they will visit the closest store first. Once at a store, consumers are free to revise their shopping plan according to the discrepancies between actual and expected prices. We will assume that consumers are rational in their expectations. They understand that retailers are opportunistic and, in an attempt to maximize profit, set prices by taking into account transportation costs and consumer heterogeneity. Our model explicitly prevents the retailers from advertising promotions on both products in the same period. This assumption is made in an attempt to be realistic. Indeed, of the 45,000 skus 1 The Micro-Marketing project was a three-year research venture between The University of Chicago, Dominick's Finer Food and 20 major packaged goods manufacturers. 2 In the remainder of the paper, we will ignore the fixed incentive F given by the manufacturer. Since it is a constant amount, it does not affect the profit maximization results.

10 10 that a retailer carries, a typical promotion-driven operator will promote 2,000-3,000 items every week. Advertising every item would be prohibitively expensive, and would be of doubtful value since consumers would be unable to process the massive number of messages they would receive. Even if we constrained stores to advertise only one product per category, we would still send information about hundreds of products every week (Dominick s carries 350 different product categories; IRI tracks 750 different categories in their INFOSCAN database). Our model assumes that every week each store selects a limited number of categories to advertise (Dominick's features products from different categories). III. Analysis of the Model We show in Appendix A that given consumers' limited knowledge of prices, stores that do not advertise will not attract any clientele. We therefore assume that each store advertises and that the only decisions to be made are: (a) Which products should be advertised? (b) When should the advertising take place? And (c) what are the profit-maximizing prices? Furthermore, in the event that the size of the price-sensitive segment, or its willingness to pay, is sufficiently large (i.e., $ > ") 3, it will always be in the best interest of the retailers to advertise prices that will attract customers from both price-sensitive and price-insensitive groups, even without receiving trade deals from the manufacturers. Consequently, we limit our analysis to cases where " > $ so that under normal circumstances, retailers would prefer selling to price-insensitive people only. This may seem to be a quite arbitrary constraint. It is however not unrealistic. All it is saying 3 When $>", a retailer with a trading area of size M has the choice between setting a price of H and selling to the price-insensitive only, for a profit of "MH, or setting a price of $H and selling to the whole population, for a profit of M$H. Since $>", he will chose to cater to both price-sensitive and priceinsensitive consumers.

11 11 is that there is enough heterogeneity among consumers that a one price fits all strategy is not optimal. Retailers are better off treating the two groups of consumers differently and pricing the products strategically. We will perform the analysis of the theoretical model in two phases. First, we look at the general case where consumers are free to switch stores given the right incentive. Second, we look at the changes in equilibrium when we constrain the price-insensitive segment to be store-loyal (they go to the closest store and cannot be induced to switch). These two models correspond to two different types of products. The second model captures secondary products such as toothpaste or ketchup. For these products the amounts of money involved and the frequency of purchase are too small to make it worthwhile for the price-insensitive consumers to switch stores. The first model deals with more important items such as soft drinks or frozen entrees where the quantities involved and the size of the discounts traditionally offered are big enough to entice price-insensitive consumers to switch retailers. III.1 Full Model In this first model, all consumers are free to shop at either or both stores. They will plan their shopping trips based on the advertising campaigns put forth by the retailers, and are free to revise their plans after visiting one or both stores. Thus, the problem facing the retailers is: What advertising strategy will maximize profits? The advertising strategy will revolve around two issues: (1) what product should be advertized, and (2) at what price? In terms of product selection, the question is: Should retailers compete head to head and advertise the same product, or should they try to influence consumers by advertising different products?

12 12 To compare these two situations, we will first study the case of head-to-head competition. Second, we will look at retailers advertising different products. Lastly we will compare the profit generated by each strategy (Proposition 1). LEMMA 1: When the price-insensitive segment can be induced to switch stores, retailers who promote the same product will advertise prices that are below cost. This situation is a Nash equilibrium. PROOF: The derivation of the equilibrium prices when price-insensitive shoppers can switch stores, and retailers advertise the same product is given in Appendix B.1. The equilibrium prices are, assuming that product 1 is the advertised good: Advertised prices: P ( 1A ' "((c & H) P( 1B ' 1 & " %"( &D Non&advertised prices: P ( 2A ' P( 2B ' H (2) (3) As we can readily see, the advertised prices are negative (c < H). The rationale for the negative prices is quite straightforward. When both retailers are advertising the same product, consumers gain perfect information about the advertised products. Retailers are then in a classic Bertram style type of competition. However, while in Bertram competition prices fall to a point of zero profits, in our case retailers are willing to lose money on the advertised product because priceinsensitive consumers who are attracted by the promotion will also buy the non-advertised products. Retailers can thus subsidize the sale of the advertised product with the revenue generated from the sale of non-advertized products. Although retailers are losing money on the advertised products, the situation is still a Nash equilibrium. Indeed, if one of the retailers (let's say A) decided to forgo sales to the price-sensitive segment and concentrate on sales to the price-insensitive segment only, he would maximize his profits by advertising a price of (see Appendix B.2 for details):

13 13 P (( 1A ' P 1B %c&d&h 2 or using equation 2: P (( 1A ' "((c&h) 2(1&"%"() & 2D%H&c 2 (4) This new advertised price is smaller than the price of equation 2; it will therefore attract both segments and yield lower profits than equation 2 (equation 2 yields maximum profits when advertised prices attract both consumer segments). Thus, retailers have no incentive to deviate from the price of equation 2; it is a Nash equilibrium. The promoted prices are below cost because retailers need to attract as many consumers as they can. They are willing to lose money on the promoted brand in order to attract price-insensitive consumers who will buy the non-advertised product (i.e., the advertised product is a true loss leader). In doing so, they split the market in half with price-insensitive consumers buying both products, and price-sensitive ones buying only the advertised one (referring back to equation 1, we have g ia = g sa = g ina = ½ and g sna = 0). Since the promoted products are the same in each store, and that retailers price the non-advertised products in a monopolistic fashion, consumers do not gain anything from visiting both stores, and cherry-picking does not occur. LEMMA 2: In a Nash equilibrium where retailers advertise different products, price-insensitive shoppers will not cherry-pick. PROOF: When retailers advertise different products (let us say that retailer A advertises product 1 while retailer B advertises product 2), shoppers will first visit the store which is closest to their location and buy the advertised product. Then they will compare the price of the non-advertised product to the price posted by the competitor. They will buy the second product if the posted price

14 14 is below their reservation price and if it is cheaper to buy it at their current store than to travel to the other store and buy the good there at the promoted price (i.e., cherry-pick). A price-insensitive shopper located at g (0 # g # 1) who has entered store A will be indifferent between buying product 2 at A and Figure 1: Optimal response going to store B to buy product 2 if the sum of the purchase price of product 2 in store A and the cost of returning home (g c/2) is the same as the sum of the cost of traveling to store B (c/2), the purchase price of product 2 in store B, and the cost of returning home from store B ((1 - g) c/2) 4. Hence, one can find the point at which price-insensitive consumers will be indifferent between buying product 2 at retailer A or retailer B with: P 2A % g c 2 ' P 2B % c 2 % (1 & g) c 2 Y g ( ' P 2B & P 2A %c c (5) If P 2A is larger than P 2B +c, then anyone entering store A is better off traveling to store B to purchase product 2 than buying it at A, leaving retailer A with no sales of the good (see Figure 1). As a result, retailer A will never price product 2 higher than P 2B +c. With prices between P 2B +c/2 and P 2B +c, retailer A will sell product 2 to some of the price-insensitive shoppers who will visit his store. The maximum share of price-insensitive consumers that retailer A can get will be 1/2 if he sets his 4 One could argue that the cost of traveling back home from store A should be allocated to product 1 and not product 2. This would not change the location of the indifference point since the shopper passes in front of his house on the way to store B.

15 15 price at P 2B +c/2. He cannot reach a higher market share since one half of the price-insensitive consumers will already have purchased product 2 at retailer B before entering store A. Hence, no additional sales will be made unless prices are lowered below P 2B +(c, the price at which product 2 becomes attractive to price-sensitive people. The profit function on product 2 for retailer A is then: for P 2B % c 2 # P 2A # P 2B % c: A 2A ' P 2A (" P & P %c 2B 2A ) c Y MA 2A MP 2A ' " P 2B & P 2A % c c & " c P 2A ' 0 Y P ( 2A ' P 2B 2 % c 2 Using the restriction that P 2A $P 2B % c 2 œ P 2B $ 0:P ( 2A ' P 2B % c 2 we have: (6) Hence, it is always in the best interest of the retailer to price the non-advertised good so that every price-insensitive shopper who enters the store and hasn t already bought the product will buy it. The optimal price of P 2A =P 2B + c/2 is a corner solution where every price-insensitive shopper who visits a store to purchase the advertised product will also purchase the non-advertised one. Reducing the price any further would not increase sales to the price-insensitive segment since any increase in sales would come from consumers who have already bought the product at the other store. Since price-insensitive shoppers buy both products in the same store, they do not cherry-pick! LEMMA 3: When retailers advertise different products, the following prices constitute a Nash equilibrium:

16 Advertised Prices: P 1A ' P 2B ' c 2&" 2" &D (7) 16 Non&advertised Prices: P 2A ' P 1B ' P 1A % c 2 PROOF: See Appendix B.3 for the derivation of the equilibrium prices when retailers advertise different products. The situation here is quite different from the situation described in Lemma 1. The two main differences are that: (1) since retailers are trying to prevent price-insensitive shoppers from cherrypicking, they cannot price the non-advertised good monopolistically at H as in Lemma 1, but have to price it defensively as prescribed by Lemma 2. Consequently, any attempt to attract price-insensitive consumers by lowering the advertised price will also render these consumers less attractive by lowering the gain made on the non-advertised product, (2) in this situation, price-sensitive consumers can and will cherry-pick. This will further reduce the incentives retailers might have to lower prices since more consumers will buy the advertised product, yielding a higher opportunity cost of promotion. At the same time, a reduction in advertised prices will not increase the sales made to price-sensitive consumers since they are already buying the advertised products. Compared to Lemma 1, we are in a situation where the costs associated with lowering advertised prices are higher, and where the potential benefits from low advertised prices are lower. As a result, the advertised prices will naturally be higher than in Lemma 1. Retailers actually will be generating profits from the promoted good instead of losing money on it. At these prices, the price-insensitive shoppers will buy both products at the store which is closest to them, while price-sensitive shoppers will visit both stores, and buy both products on sale (i.e., cherry-pick). Referring back to equation 1, we have: g ia =g ina =1/2, g sa =1, g sna =0.

17 17 PROPOSITION 1: When the price-insensitive segment can be induced to switch, the size of the scanback incentive will determine which promotion strategy the retailers will use. For small scanbacks, retailers will promote different products; for large scanbacks, they will promote the same products. PROOF: Lemma 1 tells us which prices will be posted by retailers who are advertising the same products. At these prices, each retailer will sell both products to half the price-insensitive shoppers, and the promoted product to half the price-sensitive shoppers. Lemma 3 gives us the posted prices when retailers are advertising different products. In this case, each retailer sells both products to half of the price-insensitive consumers (as in Lemma 1), and sells the promoted product to all the pricesensitive consumers. We can now compute the profits generated by each strategy: Number Non Number Promoted of Advertized of Prices plus Customers Prices Customers Scanback A Same Product ' " 2 ( H % 1 2 ( "((c & H) 1 & " % "( (9) A Different Product ' " 2 ( ( c " & D) % (1 & " 2 ) ( c 2 & " 2" (10) Retailers will then advertise the different products if A Same Product < A Different Product, or: " 2 H % 1 " ( (c & H) 2 1 & " % " ( < (1 & " 2 ) c 2&" 2" %" 2 ( c 2 &D) ( (c & H) Y H % 1 & " % " ( < c "2 & 2 " % 4 &D 2 " 2 Y D < c "2 & 2 " % 4 ( (c & H) & H & 2 " 2 1 & " % " ( (11) As we can see, the optimal strategy for a retailer will depend on the size of the scanback incentive the manufacturer gives. If the incentive is small (i.e., satisfies equation 11) then retailers

18 18 will profit from advertising different products. However, if the scanback D is too large to satisfy equation 11, retailers will be better off advertising the same product. One can look at this result in the following way: when retailers promote different products, they are trying to generate profits by increasing the size of the pie (every consumer buys both products); when retailers promote the same products, they are trying to generate profits by grabbing a bigger slice of the pie. By giving large scanbacks, manufacturers are lowering the costs of competing head-to-head, making it more attractive to try to grab a large piece of the pie rather then trying to make the pie bigger. Example: As an illustration, let us look at the profits generated by each strategy for the following parameter values: H=1, c=0.4, "=0.7, $=0.4, (=0.1. With these parameters, the break-even point (from equation 11) is D=0.42. As can be seen in Figure 2, for scanback incentives smaller than 0.42, retailers are better Figure 2: Scanback off promoting in different weeks (and using the prices of equation 7). Conversely, for scanbacks larger than 0.42, they are better off advertising the same products (with the prices of equation 2). III.2 Constrained Model We can now look at what happens if the price-insensitive segment of the population is loyal to the store that is closest to their domicile. This case is interesting because there is a wide range of products for which the savings from a promotion are too small to justify switching stores except for

19 19 consumers who are price-sensitive. A 30 cent price reduction on tooth brushes or a 25 cents off promotion on margarine is unlikely to attract price-insensitive shoppers. Weekly flyers, however, are filled with dozens of such offers. Does the fact that these ads will be considered by only a fraction of the population affect the equilibria described in the previous section? The answer is: Yes! The most noticeable difference with the full model is that when retailers have a loyal segment, they will never advertise the same product (See Appendix C for a complete analysis). Indeed, advertising the same product never leads to an equilibrium situation (at least not in pure strategy). The reason for this is simple. If retailers were to advertise the same product, competition for the price-sensitive segment would drive the advertised prices down to a point at which retailers would be better off raising their prices and selling to the price-insensitive segment only (Lemma 4 in Appendix C). The second difference is that when retailers are advertising different products, they do not need to price the non-advertised product in a defensive fashion. Indeed, since only the priceinsensitive consumers buy the non-advertised product, and since price-insensitive consumers are store loyal, retailers can price the non-advertised good monopolistically (i.e., P NA =H). At the same time, the pressure to lower the price of the advertised good is lessened. With advertised prices of $H - (c, retailers will sell their goods to all the price-sensitive consumers and to all of their store loyal customers. A unilateral decrease in advertised prices would not increase sales since the only additional sales remaining would be to consumers who are loyal to the competing store. By definition, these consumers cannot be induced to switch. As a result, when there is a segment of loyal customers the only possible equilibrium is one when retailers advertise different products at the following prices (Lemma 5, Proposition 2, in Appendix C):

20 20 Advertised Prices: P A = $H - (c (12) Non-advertised Prices: P NA = H (13) At these prices, the price sensitive segment will cherry-pick. This cherry-picking is beneficial to retailers since the advertised prices yield positive profits of $H - (c + D. IV. Empirical Validation of the Model The theoretical analysis we have just performed is an attempt at modeling a real-life phenomenon: the reaction of a retailer to a manufacturer s trade deal, and the consequence it has on the timing of promotions (to encourage or prevent cherry-picking) as well as the pricing policy (loss leader or profitable promotion). The equilibria we have derived have definite practical implications as far as store traffic and posted prices are concerned. Some of these implications (Implications 1 and 2) are straightforward and could stem from a wide variety of models. Other implications (Implications 4 to 6) are less intuitive and are a direct result of the model developed in this paper. A first implication of the model is that whenever stores are promoting different products, there is an opportunity for price-sensitive consumers to cherry-pick. We should then see an increase in store traffic during these weeks as compared to weeks when retailers promote the same items: I1: The number of customers visiting a store will be greater when competing retailers advertise different products than when they advertise the same ones. A secondary implication is that cherry-pickers do not buy a full basket of goods at each store they visit, while non-cherry-pickers do. Hence, one expects average spending per customer to be smaller when cherry-picking occurs than when it does not: I2: Average customer expenditures (check size) will be greater when competing retailers advertise the same products than when they advertise different ones.

21 21 Our model shows that price-insensitive shoppers do not cherry-pick (in any situation). Therefore, the increase in traffic due to cherry-picking must translate into higher store sales, even though the size of the average transactions diminishes: I3: Total store sales will be larger when competing retailers advertise different products than when they advertise the same products. In terms of posted prices, we can generate implications regarding both the advertised and non-advertised prices. We can first look at products that are likely to influence the store choice of price-insensitive people. If we look at equations 3 and 8, we see that products that are promoted on different weeks have to be priced defensively when they are not being promoted while products that are promoted in the same week can be priced monopolistically during non-promoted weeks. In practice, it would be meaningless to compare the prices of two different products since they probably have different wholesale costs. We can however compare the gross margins for two products as long as they belong to the same category. This will be more meaningful since Dominick s sets average margin goals for each of its categories, and then sets the prices of individual items in each category by deviating from the target margin in accordance with their estimate of the competitive pressure on that item. We can then formulate the following implication: I4: Within a product category, non-promoted margins will be larger for products that are always promoted at the same time as the competition than for products that are never promoted at the same time. Similarly, if we look at the promoted prices of such products (equations 2 and 7), we can see that products that are promoted at the same time by competitors are promoted as loss leaders (negative margins according to the model) while the other products are promoted for profits. Hence, again speaking in terms of gross margins, we can say that:

22 22 I5: Within a product category, promoted margins will be smaller for products that are always promoted at the same time as the competition than for products that are never promoted at the same time. Going one step further, one can derive from the model that if a product is such that, depending on the size of the trade deal incentive, it is sometimes jointly promoted by two retailers, and is at other times promoted on different weeks, then it must be the case that the promoted price will be lower when the retailers promote the product during the same week (loss leader situation) than when they promote it on different weeks (cherry-picking). Since here we are looking at two different situations for the same product, we can compare prices directly rather than using margins as a proxy. Hence, we can formulate implication 6: I6: For products promoted both at the same time as the competiton and at different times, the promoted prices will be lower when promoted the same week. Data Description In order to test our implications, we need to look at a major category that exhibits enough variety in its promotion schedule. Indeed a category such as bathroom tissues is a good loss leader candidate, unfortunately we cannot use it for our analysis since there is always a four-pack on sales at both Dominick s and Jewel. Hence, we will concentrate our analysis on the soft drink category. Due to the wide range of packaging styles in this category (cans, bottles, 6-packs, 24 packs, 2 liters, and so on) there is enough variety in the promotion pattern to allow us to run the analysis we require. The interaction between Dominick s and Jewel in the Chicagoland market is such that when Dominick s promotes 6-packs of Coke and Pepsi (in Chicago, Coke and Pepsi are always promoted together), Jewel always has a similar promotion (and vice-versa). The exact format of the promotions (use of coupons, multiple pricing, and so on) might however be different. Conversely, 2 Liters are never promoted together except during the Fourth of July, Labor Day or Halloween week.

23 23 As far as multi-packs (12 and 24 packs) are concerned, they are jointly promoted by Dominick s and Jewel less than 50% of the time. This wide range in promotion scheduling makes soft drinks the ideal category upon which to base our analysis. To test the validity of our hypotheses, we look at a database that merges data from three sources. The first set of data contains one year (1991) of feature advertising from both Jewel and Dominick's Finer Food. The second data set records daily department (e.g., produce, grocery, etc.) level sales and traffic for each of the Dominick s stores. The last data set captures weekly upc level sales in each of Dominick s stores for 26 packaged goods categories. Implications 1, 2 and 3: To test the validity of the first three implications we look at the impact of weekly feature ads on the following three performance measures: weekly customer count, as captured by the total number of rings at the check out registers; weekly total store sales; and average customer expenditure (i.e., total store sales/customer count). Each measure is used as the dependent variable in a log-linear regression. A set of 7 dummy variables describes the weekly features as independent variables, two dummy variables control for weeks when employees receive their paychecks (monthly or bi-monthly), and 82 dummies are used for the 83 stores in the data set (n=2,898). The regression equation for customer count is (the equations for store sales and average checks are similar):

24 24 log(customer ij ) ' Intercept % " i Store i % $ 1 DFF&Multi j % $ 2 Jewel&Multi j % $ 3 DFF&Jewel&Multi j % $ 4 6&Pack j % $ 5 2&Liter j % $ 6 Special j % $ 7 Holiday j % $ 8 Monthly j % $ 9 Bi&Monthly j %, ij Where: Customer ij is the number of customers visiting store i during week j. DFF-Multi j is 1 if 12 or 24 Packs are featured at Dominick's week j. Jewel-Multi j is 1 if 12 or 24 Packs are featured at Jewel week j. DFF-Jewel-Multi j is 1 if 12 or 24 Packs are featured by both Jewel and Dominick's. 6-Pack j is 1 if 6-Packs are featured week j. 2-Liter j is 1 if 2-Liter bottles are featured at Dominick's week j. Special j is set to 1 if the weekly flier for week j features a special event (10 cents sales, BOGO 5,... ) on the front page. Holiday j is set to 1 if week j is a holiday (Christmas, Easter, Halloween,... ). Monthly j is 1 if monthly payrolls are paid during week j. Bi-Monthly j is set to 1 if bi-monthly payrolls are paid during week j. We chose a log-linear model to account for the multiplicative effect that promotions have on sales. The variables of interest in the model are DFF-Multi, Jewel-Multi and DFF-Jewel-Multi. The other variables are only control variables. As far as the payroll variables are concerned, we 5 Buy One Get One Free.

25 25 understand that not everybody is remunerated on a monthly or by-monthly schedule. However, we need not concern ourselves with households paid on a daily or weekly basis since the data is analyzed at the week level. The parameter estimates (with their p-values) for the three regressions are summarized in Table 2 (although they account for most of the variance explained, we have omitted the intercept and store dummies since they are of little practical interest). Customer Count Average Check Store Sales DFF-Multi Jewel-Multi DFF*Jewel Pack Liter Special Holiday Monthly Bi-Monthly Overall R 2 93% 94% 94% Table 2: Regression Estimates To better understand the net impact of multi-pack advertising by Dominick's and/or Jewel, we can plot the expected traffic and sales data for each of the four conditions (Figure 3; store traffic, average check and store sales are scaled to 1 in the no-promotion condition). As predicted by Implication 1, store traffic is greater when only one of the two retailers is advertising multi-pack.

26 26 Conversely, the average check is smaller when only one retailer advertises multi-packs (supporting implication 2). Implication 3 is also validated since store sales at Dominick s are greater when Dominick s does the opposite of what Jewel does. Our analysis shows that store traffic is greater and customer spending is smaller when retailers advertise different products. This is clear evidence that cherry-picking does occur. Furthermore, the fact that store sales are larger when Dominick s does not advertise at the same time as Jewel shows that it is indeed in Dominick s best interest to encourage cherry-picking. A four percent change in sales or store traffic might seem trivial, but when one considers that Dominick s sees a quarter million customers every week, the question studied becomes important. Figure 3: Advertising Impact Implications 4 and 5: Our full model predicts that when products are always promoted at different times by two competitors, retailers will price the products defensively when they are not being promoted. Conversely, when products are always promoted at the same time, retailers can set monopolistic prices when the products are not being promoted. To validate this finding, we look at weekly sales of two-liter bottles and 6-packs of soft drinks. Indeed, in Chicago, 6-packs of Coke and Pepsi are always promoted simultaneously by

27 27 Dominick s and Jewel. Two-liter bottles, on the other hand, are promoted on different weeks except on three occasions: Fourth of July, Labor Day and Halloween. Therefore, we can test Implication 5 by running a regression with weekly profit margins of 6-packs and two-liters 6 as a dependent variable, and two dummy variables (promotion and package size) plus an interaction term as independent variables. The regression equation can be written as: Margin ijk ' $ 0 % $ 1 2&Liter i % $ 2 Promotion ik % $ 3 Interaction ik %, ijk Where: Margin ij is the profit margin on product i at store j during week k; 2-Liter i = 1 if product i is a 2 Liter bottle, 0 otherwise; Promotion ik = 1 if product i is on promotion during week k, 0 otherwise; Interaction ik = 1 if product i is both on promotion during week k and a 2 Liter product, 0 otherwise. The estimated coefficients for this regression (n = 36914, R 2 = 0.37) are presented in Table 3. Figure 4 depicts the effect graphically. Estimate p-value Intercept Liter Promotion Liter*Promotion Table 3: Regression Coefficient The data supports both implications. 6 Excluding the three holiday weekends.

28 28 Implication 6: If a product is sometimes promoted simultaneously by competitors, and sometimes promoted on different weeks, then Implication 6 says that the price reductions will be greater when the products are promoted at the same time. We tested this implication by looking at the promotions of three different package sizes in the soft drink category: 24-packs, 12-packs and 2 liter bottles. For each of these products, we conducted an ANOVA comparing Figure 4: Profit Margins promoted prices when the promotions occur at the same time at Dominick s and Jewel and promoted prices when only Dominick's is promoting the goods. The results of the ANOVA are summarized in Table 4. Size Regula r Price Promoted Price (DFF Only) Promote d Price (Both) Proportion of Concurrent Promotion n p-value 24 Packs % Packs % Liters % Table 4: Promoted Prices As we can see, the effects measured are in the right direction, but not all of the effects are significant. The data moderately support Implication 6.

29 29 V. Conclusions This paper views cherry-picking and loss leader pricing in a way that goes against mainstream beliefs. We see cherry-picking not as a parasitical behavior that is tolerated because it is too expensive to prevent it, but rather as an opportunity to increase profits by taking advantage of the increased traffic. At the same time, we do not see loss leader pricing as an aggressive pricing strategy aimed at luring consumers away from the competition, but rather as a defensive strategy used to prevent current customers from fleeing to the competition. Lastly, we showed that cherrypicking is not a side effect of loss leader pricing, but rather that loss leaders and cherry-picking are mutually exclusive. The basic rationale for this is that cherry-picking will only occur when two retailers promote different products. When the promoted products are different, the retailers do not need to make them loss leaders, they need only to price them below the competitor s regular price (which will still allow for generous margins given the manufacturers trade deals). Choosing between encouraging cherry-picking and preventing it with loss leader prices will depend on two factors: the type of product, and the size of the trade deal offered by the manufacturer. For products that carry a small price or have too small a demand to induce priceinsensitive consumers to switch stores (e.g., toothbrushes), it is always in the best interest of retailers (and a Nash equilibrium) to encourage cherry-picking by offering shallow deals and to time the promotion in a different week than their competitor. For products that are important enough to have an impact on the behavior of priceinsensitive consumers, the optimal strategy for a retailer will depend on the size of the trade deal offered. For a small trade deal (but big enough to induce the retailer to promote), it will also be a Nash equilibrium for retailers to encourage cherry-picking. If the trade deal is large, however, the equilibrium falls apart and retailers will have no choice but to resort to loss leader prices by offering