Private Label Positioning: Vertical vs. Horizontal Differentiation from the National Brand

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1 Private Label Positioning: Vertical vs. Horizontal Differentiation from the National Brand By S. Chan Choi and Anne T. Coughlan May 004 Please do not uote or distribute without ermission. Marketing Deartment, Rutgers Business School, 80 University Ave., Newark, NJ 070, , Fax: Marketing Deartment, Kellogg School of Management, Northwestern University, Evanston, IL , , Fax:

2 Private Label Positioning: Vertical vs. Horizontal Differentiation from the National Brand Abstract Among major benefits rivate labels bring to the retailer, we focus on the retailer s ability to coordinate the rices of both the national brand and its store brand counterart. By using roduct-line ricing, the retailer can exloit the differentiated nature of the two brands. This aer investigates the retailer s roblem of ositioning her rivate label and the subseuent ricing issues. While most revious studies concentrate either on vertical i.e., uality or horizontal i.e., trade dress differentiation, we view the rivate label s differentiation from the national brand as a combination of the two. In contrast to the location theory literature, which generally suggests maximum differentiation in both dimensions as the best strategy for the retailer, our results are mixed: when the two dimensions are considered searately, the retailer s rofit is maximized by minimum vertical differentiation and maximum horizontal differentiation. However, when the two dimensions are correlated, the retailer is generally better off increasing its uality u to the level of the national brand, rovided that the uality cost is negligible. We also extend the model to the case of two national brands, and show that the rivate label s otimal level of differentiation deends on the existing differentiation between the two brands. KEY WORDS: Private Label, National Brand Private Label Cometition, Private Label Positioning, Vertical and Horizontal Differentiation.

3 INTRODUCTION By 999, rivate label roducts or euivalently, store brands accounted for over 0 ercent of suermarket unit sales and 5.7 ercent of dollar sales Williams 000. In 77 of 50 suermarket roduct categories, rivate labels in the U.S. collectively have higher unit market shares than their strongest nationally branded cometitor, while they are second or third in 00 of those categories Quelch and Harding 996. Among other benefits, rivate labels add diversity to a retailer s roduct line in a category Raju, Sethuraman and Dhar 995; Soberman and Parker 004. This diversity or roduct differentiation can be vertical or horizontal in nature or both, of course. Changes in both dimensions have been artially resonsible for rivate label sales growth in U.S. grocery retailing Wellman 997 refers to imrovements in ackaging and selection as well as uality in the late 980s as driving forces. Vertical differentiation is essentially uality-driven, where rivate labels are usually erceived as a lower uality substitute to the corresonding national brands e.g., Ann Page canned sous the A&P grocery chain s former rivate label were widely viewed as lower uality than Cambell s canned sous. Vertical differentiation is based on the notion that the characteristic on which differentiation occurs is one for which all consumers value the highest ossible level. A suerior uality national brand may lose its vertical differentiation from the rivate label if rivate-label retailers are eventually able to match the national brand s technology and ercetion e.g., President s Choice cookies. However, the economics literature indicates that a second roduct a rivate label in our context in the market would find it otimal to vertically differentiate itself from the market leader Shaked and Sutton 98; Moorthy 988. In articular, using a uniform distribution of consumer s willingness to ay for uality, Moorthy obtains a uality-rice euilibrium where the two brands are ositively but finitely searated. A key assumtion in his analysis is a uadratic cost function: The finite, market-uncovered euilibrium arises because the firms find it too costly to roduce a roduct with a uality higher than a certain level. Desai 00, on the other hand, assumes a model with two distinct uality segments, in which firms offer different uality roducts for different markets. Desai uses Hotelling s location model structure to cature uality-rice cometition in monooly and duooly settings.

4 In contrast, horizontal differentiation means that roducts may have different forms, sizes, or ackaging, but there is not a uniform ideal oint for such an attribute. The economics literature is divided between two oosite results when there are two brands of eual uality: minimum differentiation Hotelling 98 and maximum differentiation d Asremont, Gabszewicz, and Thisse 979, deending on the underlying assumtions. Sayman, Hoch, and Raju 00 add a third brand a rivate label in their model, in which the two incumbent national brands are assumed to be maximally differentiated in the horizontal dimension. They find that it is otimal for the rivate label to imitate the stronger national brand. Positioning at a midoint would never be otimal. For examle, a rivate label mouthwash would imitate either Listerine or Scoe, but never osition somewhere in between the two. In addition, their emirical study reveals that a store brand that imitates a national brand horizontal differentiation may not have much imact on uality ercetions vertical differentiation. Du, Lee, and Staelin 004 similarly model two national brands and one store brand, but in a location model structure derived from consumer utility. They examine retailer rivate-label ositioning strategies assuming fixed maximum category demand and a constraint on the horizontal osition of the rivate label secifically, the rivate label may osition only between the two national brands. Our model investigates a similar context of national brand-rivate label cometition, but we investigate both vertical and horizontal differentiation using a utility theory-based demand function that allows for flexible category demand. One of our key findings is that, when the two national brands are horizontally undifferentiated, the retailer is better off by maximally differentiating her rivate label from the national brands. Meanwhile, when they are horizontally differentiated, the rivate label s otimal strategy is to imitate one of the national brands. This indicates that there is no single best differentiation strategy for a rivate label in all market conditions, which is suorted by the real market examles summarized in Table. [Insert Table about here] Many rivate label retailers have urosely sought to minimize horizontal differentiation from the national brand, by making their ackaging, sizes, tyeface, and labeling extremely similar to those of the national brand. This strategy gave rise in the mid-990s to a trademark lawsuit by Unilever, the maker of Vaseline Intensive Care Lotion, against Venture Stores, Inc.,

5 alleging that the virtually identical roduct form and trade dress the legal term for the brand, trademark, logo, and ackaging that identify a roduct of Venture s lotion constituted trademark infringement Conoco, Inc. v. May Deartment Stores Co., 995; see also Harvey, Rothe, and Lucas 998 and Harvey, Rothe, Kasulis and Lucas 999 for discussions in the Marketing literature. The court ruled in Venture s favor, saying that the Venture store brand s label exlicitly invited the consumer to comare Venture s roduct with Vaseline Intensive Care. One of the core conditions for trademark infringement, that consumers would be confused into thinking the imitator is in fact the original branded roduct, therefore did not hold. Hence, the legality of virtual imitation of the national brand by the rivate label i.e., the minimization of horizontal differentiation was uheld. Two interesting features of this case deserve mention in our context. First, the rincile uheld was the legality of minimum horizontal differentiation; but one of the basic insights of location modeling is the otimality of maximum horizontal differentiation. Second, while the aarent issue is ure horizontal differentiation through trade dress imitation, it would seem intuitively that Venture was also trying to aear to offer a roduct of similar uality to its consumers and to signal this through similar trade dress. This suggests that in many real-world cases, the retailer s ositioning of the rivate label inherently involves both horizontal and vertical ositioning messages to its consumers. The concet of differentiation of the rivate label from the national brand is thus not a unidimensional concet. The overall interchangeability or substitutability between them is a function of both vertical and horizontal roduct differences, and the retailer s ositioning choice for its rivate label will naturally reflect both dimensions. The rimary focus of this aer is an investigation of the otimal vertical and horizontal ositioning strategies of the rivate-label retailer that also sells the national brand in a given category. We use a standard consumer utility maximization foundation to build our analysis, as it allows for both vertical and horizontal differentiation between roducts. We show that the otimal ositioning strategy can be uite different from that suggested by the location modeling literature, suggesting that it is imortant to consider category by category whether total consumtion is essentially fixed, or whether it can be exanded with roduct variety investments. 3

6 A related model was roosed by Vandenbosch and Weinberg 995, who assume a two-dimensional attribute sace. Their euilibrium solution is max-min differentiation in which the strong brand locates at the best osition and the second brand chooses maximum differentiation in one attribute dimension and minimum differentiation in the other in a large art of the arameter sace. Note that their model has two vertical dimensions, whereas ours has one vertical and one horizontal dimension. In addition, theirs is a location model with fixed total category demand, as oosed to our flexible demand utility-based model. In what follows, we first introduce the base model with one national brand. It is shown that the rivate label is better off differentiating horizontally from the national brand counterart. Then we extend the model to the case in which there are two national brands. When the national brands are substantially differentiated and the rivate label s otential osition is limited to the sace between the two national brands, our result is the same as Sayman et al. s 00: it is better to imitate the stronger national brand. On the other hand, when the two national brands are horizontally undifferentiated, the result is the same as that of our base case: it is better for the rivate label to horizontally differentiate from the national brands. THE DEMAND MODEL AND THE RULES OF THE GAME In this section, we resent a duooly demand function derived from a consumer utility framework. This is a base demand function with one national brand and a rivate label. In a later section, we will extend this base model to a more general case of two national brands. Our consumer utility function for two substitutes takes the following standard uadratic form widely used in economics Häckner 000: U, = /, where i is the uantity of roduct i consumed and i is the rice of roduct i i=,, and subscrit reresents the rivate label. The other arameters have standard interretations in utility theory, that can be seen by examining the marginal utility of consumtion for roduct i: U i = i i i j i, i =,. 4

7 Clearly, the higher is i, the higher is the marginal utility of consumtion of roduct i; thus, reresents the intrinsic value or uality of roduct i. Without loss of generality, we assume that >. The difference between and is a measure of the vertical differentiation between the two roducts. The arameter i measures the rate at which the marginal utility of consumtion for roduct i declines with units of roduct i itself consumed. It is natural to assume that <, reflecting a steeer marginal utility decline for the less valued rivate label. Finally, the arameter [ 0, ] measures the rate of decline of marginal utility of consumtion for roduct i with resect to the consumtion of the other roduct, j. This arameter thus reresents the interchangeability or substitutability of roducts and, and is a measure of horizontal differentiation Häckner 000. When = 0, the two roducts are indeendent; and when =, the roducts are erfect substitutes. Therefore, the utility function catures both vertical and horizontal roduct differentiation between the national and store brands. The assumtion of decreasing marginal utility allows the consumer to otimally allocate his budget between the two differentiated roducts. The utility-maximizing consumer will otimally allocate the uantities consumed by U U solving the first-order conditions: = 0 and = 0. The second-order conditions for a i utility maximum reuire that > ; this condition intuitively imlies that cross-roduct utility effects are not as large as own-roduct utility effects. 3 The otimal solution results in the following demand system: = [ ] = [ ] 3 In order to guarantee ositive demand when all rices are zero, we reuire that 0 > and 0. Note that these demand functions are in the same linear form as that of the > most oular linear demand function, but the coefficients of the demand functions are exlicitly 5

8 exressed in terms of the underlying utility arameters. It is easy to see that changing the substitutability arameter, for examle, nonlinearly affects the intercet, the own-rice derivative of demand, and the cross-rice demand derivative. Therefore, our demand structure rovides clear insights into the effects of changes in utility arameters on market outcomes. Other commonly-used demand functions in the marketing literature cannot rovide these insights because they are not derived directly from utility maximization. While the national brand manufacturer determines the wholesale rice w for his roduct whose uality level is, the retailer s decision is to choose the otimal level of vertical differentiation of her store brand from the national brand, the degree of horizontal substitutability between the national and store brands, the national brand s retail margin, eual to w, and the retail rice for the rivate label. Since the focus of our aer is on the retailer s decisions, we assume that is already given. Observing the uality level of the national brand and anticiating subseuent rice euilibrium, the retailer vertically and horizontally ositions her rivate label. Thus, the euilibrium concet is a sub-game erfect euilibrium, in which the second-stage rice euilibrium is reached immediately after the differentiation decisions. Price cometition is modeled as a manufacturer-stackelberg game, in which the manufacturer sets the national brand s wholesale rice m anticiating the retailer s ricing reaction that sets the retail margin m for the national brand and the retail rice of her rivate label. w THE SHORT-RUN PRICE EQUILIBRIUM In this section, we assume the two brands uality levels and to be fixed and derive the retailer s otimal ricing strategy and euilibrium values of all rices, uantities, and rofits in the system. The retailer is assumed to use roduct-line ricing as art of category management. The manufacturer-stackelberg ricing game is solved recursively, starting from the retailer s ricing decision. The retailer maximizes her combined rofit: Maximizem, Π = m R, 4 6

9 where is the unit variable cost of the rivate label, which is an increasing function of that is, creating a higher-uality rivate label roduct results in a higher marginal cost of roduction. 4 Π R Π R Solving the first-order conditions = 0, = 0 for m and, and then m adding and to obtain, we obtain the following retailer reaction functions: m w w = and =. 5 to note that To guarantee that the retail margin is ositive, we reuire that w. It is interesting is indeendent of the national brand s wholesale rice, even though the two roducts are interrelated in demand. The retailer chooses the rivate label s rice based only on its own uality and variable cost. 5 That is, roduct-line ricing imlies that it is in the retailer s best interest not to link the rivate label s rice to the level of the national brand s wholesale rice: Proosition. When the retailer emloys roduct-line ricing, the rivate label s otimal rice is indeendent of the national brand s wholesale rice. The retailer s otimal margin for the national brand w is negatively related to its wholesale rice and ositively related to its intrinsic uality. When the wholesale rice increases, the retailer absorbs half the increase and asses through only the other half to the national brand s retail rice. This ass-through rate is consistent with McGuire and Staelin s 983 and Coughlan s 985 buffer effect and Lee and Staelin s 997 vertical strategic substitutes roerty of the linear demand function. Given the retailer s reaction functions 5, the manufacturer s ricing decision is to choose his wholesale rice so as to maximize his short-term rofit: Maximize w Π = w m w, 6 M where is his unit variable cost w. Solving the first order condition, we have the otimal wholesale rice: 7

10 w =. 7 It is straightforward to verify the second order condition. The otimal wholesale rice increases ositively with the national brand s uality, its unit variable cost, and the rivate label s variable cost. It is negatively related to the rivate label s uality. All these directional changes make intuitive sense. Note that, to make an otimal wholesale ricing decision, the manufacturer needs to have information on all the utility arameters excet. Since we know 0 from the above discussion, w is nonnegative. We can obtain all related euilibrium values by substitution, which are summarized in Table. [Insert Table about here] DIFFERENTIATION OF THE PRIVATE LABEL Given the short-run rice euilibrium and the uality level of the national brand, the retailer s long-term decision is to choose the osition of her rivate label. The ositioning decision in this aer is different from that of Sayman, Hoch, and Raju 00 or Du, Lee, and Staelin 004, in which the rivate label s horizontal osition is constrained to lie between that of the two national brands. Our model lets the retailer choose both vertical and horizontal dimensions of differentiation in the context of the examles in Table. In what follows, we examine the effects of vertical and horizontal differentiations as well as their combined effects. Effects of Vertical Differentiation For the moment, we fix the value of, and consider the retailer s roblem of choosing the uality of her rivate label, anticiating the rice euilibrium in the short run. From Table, it is straightforward to show that the euilibrium demand for the rivate label ositive, and is an increasing function of, for greater than : is =. 8 8

11 If is less than or eual to, rivate-label uality is so oor that demand for it will not exist. Note that is a strictly ositive value. Further, the uality of the rivate label is bounded above by, the uality of the national brand. Given these bounds, the retailer chooses the level of so as to maximize her long-term rofit: Maximize Π = m 9 R Subject to. The exact exression of euation 9 is long and tedious, and is omitted here. Recall that we are assuming the rivate label s unit variable cost to be an increasing function of : a higher roduct uality can only be achieved at a higher average cost. The otimal solution deends on how the cost function is defined. If the cost increases fast and exonentially, the lowest value of would be otimal. Otherwise, the behavior of the rofit function deends on the assumed cost function. A number of studies use a simle uadratic function to obtain interior solutions for uality i.e., Moorthy 988; Tirole 989; Motta 993. We could also derive an otimal uality assuming a well-behaved cost function, but instead choose to examine more general imlications in this aer. Consider a limiting case in which increasing the rivate label s uality level is costless, so that is a constant. Then the second order derivative of the retailer s rofit with resect to can be derived as Π R 3 = 8, 0 which is unambiguously ositive and constant. Thus, with costless uality augmentation, the retailer s rofit is a uadratic convex function of. The minimum rofit occurs at. = 4 3 9

12 A brief comarison between euations 8 and shows that >. This imlies directly that all feasible values of lie in the range where retail rofit is increasing in. Therefore, under the assumtion that uality augmentation is costless, the otimal uality for the rivate label is : i.e., as high as that of the national brand. Figure shows the shae of the retailer rofit function. At first glance, this result seems trivial and uninteresting because uality imrovement is assumed to be costless. In fact, a number of studies have used uadratic cost functions in order to obtain interior solutions for the lower-uality roduct e.g., Motta 993; Desai 00. Our model would also result in a finite otimal value for rivate label uality when a uadratic cost function is used. However, we note that in either case, the imlied solution is in direct contrast to the maximum differentiation result in the location theory literature e.g., Shaked and Sutton 98, in which the second brand is maximally differentiated in uality from the major brand which here means it has the minimum uality level,. 6 this result as follows: We formalize Proosition : For a fixed value of the horizontal substitutability arameter, and costless rivate label uality imrovement, it is otimal for the retailer to seek minimum vertical differentiation from the national brand. [Insert Figure about here] In addition, it can be shown that the national brand s euilibrium rice is higher than that of the rivate label, due to double marginalization and the differences in variable costs: Proosition 3: Even when the rivate label s uality is same as that of the national brand, the national brand s euilibrium rice is higher than that of the rivate label. Proof: See Technical Aendix. Consider Proositions and 3 in light of Table. For illustrative uroses, suose the rivate label is horizontally undifferentiated from the national brand, as in the Ann Page Cambell s case. Then Proosition imlies that the retailer s best strategy for the Ann Page brand is to increase its uality level to that of Cambell s; but Proosition 3 then imlies that 0

13 even so, we should still exect to see a retail rice differential between the two brands, due to the degree of horizontal differentiation between them. Effects of Horizontal Differentiation An emirical study by Sayman, Hoch, and Raju 00 found that a store brand can exlicitly target a national brand by imitation i.e., horizontal imitation via trade dress design, even if this has no effect on the ercetion of its uality vertical differentiation. This imlies that the two differentiation dimensions can be searately oerated in some roduct classes. Assuming the uality level of the rivate label is fixed, therefore, we now turn our attention to the role of the substitutability arameter. It is straightforward to show that the retailer s euilibrium rofit from Table decreases as goes u: Π R = 8 < 0. This means that the retailer s total rofit is maximized at the lowest ossible : hence the maximum degree of overall cross-roduct differentiation is otimal for the rivate label, in the absence of any uality changes. We formalize this as: Proosition 4: When the substitutability arameter can be changed without changing, the lowest ossible is the otimal solution for the retailer. That is, maximum horizontal differentiation is otimal. The intuition for this horizontal differentiation result is seen most clearly by considering the form of the utility function itself. The lower is, the higher is consumer utility, all other things constant, because consumers value variety; and higher utility levels lead to greater willingness to ay and greater consumtion, all of which lead to higher retail rofitability. 7 In short, if the retailer can reduce the extent to which the rivate label is viewed as interchangeable with the national brand, the marginal utility of consumtion for both roducts is higher.

14 Comaring this result with those found in location models in the Economics literature, our finding of maximal horizontal differentiation is similar to that in Gabszewicz and Thisse s 979 location modeling framework. 8 Our minimum vertical differentiation result is artially consistent with Vandenbosch and Weinberg 995 although the models are not directly comarable, as Vandenbosch and Weinberg look at a location model with two dimensions of vertical differentiation and no ossibility of horizontal differentiation. Consider this result in light of the examle of Sears Kenmore aliances in Table. Many Kenmore aliances are in fact manufactured for Sears by General Electric GE, and hence have virtually eual uality to GE aliances hence, little vertical differentiation. Given the lack of vertical differentiation, Sear s best strategy for Kenmore is to differentiate it horizontally e.g., in lacement of control knobs and dials, or in colors and facades from GE s refrigerators, while maintaining a uality level eual to GE and a ositive rice differential for GE over Kenmore. Combined Effects The above two analyses show that when the rivate label can be differentiated urely in the vertical dimension, minimum differentiation i.e., the maximum ossible level of is otimal from the retailer s oint of view. When the rivate label can be differentiated urely in the horizontal dimension, maximum differentiation i.e., the minimum ossible level of is otimal. Thus, we are temted to conclude that in the combined situation, the rivate label should be vertically undifferentiated and horizontally differentiated, as in the Kenmore GE examle in Table. But does this mean, for instance, that President s Choice makes an error in minimally differentiating both horizontally and vertically its chocolate chi cookies from Chis Ahoy, the national brand? Not necessarily: our analysis shows that the result deends on how searable the two differentiation dimensions are in any articular roduct class. The temting conclusion that low vertical differentiation and high horizontal differentiation are the otimal combination rests on the imlicit assumtion that these dimensions are in fact set indeendently of one another. We roceed to consider the imact of relaxing this imlicit assumtion here.

15 In the cookie examle in Table, it is reasonable to suose that a higher can come at the exense of a higher as well. That is, a higher uality rivate label cookie can be also viewed as very similar horizontally to the national brand. This is bad news for the retailer, who would increase but minimize the value of if she could. The strategic decision of the retailer therefore becomes how high to let rise, which may deend on the extent to which this also raises the substitutability arameter. So logically, if a rise in is accomanied by a rise in, the ossibility exists that retailer rofits could actually be harmed by an increase in. In general, the change in retail rofit for a change in is given by dπ d R Π = R Π R Π R Π R, where > 0, < 0, and > 0. The derivative will be negative imlying it is not otimal to increase to its maximally limiting value if Π R > Π R / /. The uestion then is whether this ineuality is ever met, and if so, when. To examine this issue, we assume for the moment that differentiation is once again costless since uality increases in the rivate label could always be costly enough to dissuade the retailer from undertaking them. Recall from euation 0 that the convexity of the retailer s rofit function with resect to is established by: Π R 3 = 8 > 0. Clearly, the convexity of the retail rofit function with resect to increases with increases in that is, the derivative becomes greater in value when increases. This means euivalently that the more interchangeable are the rivate label and the national brand the higher is, the greater is the marginal rofit increase to be had by increasing roduct uality, assuming no incremental cost of doing so. From a utility ersective, this makes sense: a higher means a lower marginal utility of consuming either roduct, the more the other is consumed, and this decreases consumer willingness to ay and rofitability. Marginal increases in roduct uality then have a greater imact on rofitability. 3

16 Further, note that an increase in has three effects on the osition of the euilibrium retail rofit function as a function of : a it shifts the minimum of the function to the right i.e., to a higher value of ; b it causes the minimum of the retail rofit function to occur at a higher level of retail rofit; and c it causes maximum achievable retail rofits at = to dro in value. We summarize these roerties of the retail rofit function in the following Lemma: Lemma : Absent marginal cost imacts, the euilibrium retail rofit function is not only convex in, but exhibits the following roerties: i its degree of convexity increases with increases in ; ii increasing causes the minimum of the euilibrium retail rofit function with resect to to occur at a higher level of ; iii increasing causes the minimum of the euilibrium retail rofit function with resect to to occur at a higher level of euilibrium retail rofit; and iv increasing reduces the maximum achievable level of euilibrium retail rofit. Proof: See Technical Aendix. Figure shows a set of reresentative euilibrium retail rofit functions as functions of, for different values of that illustrate these four roerties recall that the feasible values of for each curve are ones in the uward-sloing ortion of the curve; the entire curve is shown merely for illustrative uroses. As the set of curves shows, whether or not retail rofit increases when the retailer invests in increasing the uality of its rivate label deends on how much this increase affects the overall differentiation between the roducts, reresented by increasing, and also deends on the starting value of. For examle, consider the arameter values in Figure, with =. and =0.8 as a starting oint for the rivate label. In this situation, the rivate label s vertical uality is reasonably close to that of the national brand which has =, and the roducts exhibit fairly low overall interchangeability, reresented by the difference between and its maximum value of 0.3 the value of in this examle. Given these values, euilibrium retail rofit euals Now, suose that the retailer 4

17 wishes to increase the uality of its rivate label. For these starting values, as long as the retailer can achieve a rivate label uality level of at least = , it can increase its total rofitability even if this means that total interchangeability between the rivate label and the national brand rises to =.9, very close to its maximum ermissible level given by the level of in this examle. If it can increase uality to its maximum level of = = accomanied by a rise of to its maximum value of.9 as well, total retail rofit rises to , a net increase even given the loss due to a higher value of. [Insert Figure about here] On the other hand, with the other arameter values as deicted in Figure, imagine a starting oint of =.94 and =0.05, generating a retail rofit of The retailer cannot make herself better off by increasing to its maximum value of if this would cause to rise to 0.9, as this generates a rofit of only A similar situation occurs if the starting oint is =.96 and =0., which generates a retail rofit of These examles show that increasing the rivate-label uality level is unrofitable if a the retailer s starting oint is a high-uality, highly horizontally differentiated roduct i.e. a high value of counterbalanced by horizontal differentiation sufficient to kee uite low, and b a further increase in the uality is accomanied by a large enough increase in overall interchangeability between the rivate label and the national brand. Under such circumstances, imitating the trade dress of the national brand would be a bad idea for the rivate-label retailer, for examle. increase in without a corresonding increase in marginal roduction costs., but However, if the retailer s starting osition for the rivate label is not so fortuitous, then increasing the uality of the rivate label is likely to be a rofitable exercise, if it only induces an These examles show that the tradeoff between increasing rivate-label uality and associated increases in interchangeability have a strong imact on whether a retailer finds it rofitable to imrove rivate label uality. That is, when an increase in the rivate label s uality is accomanied by an increase in the overall interchangeability of the rivate label and the national brand i.e., a higher, the otimal uality level is not always the maximum ossible, even when this does not increase the retailer s marginal cost of roduction for the rivate label. 5

18 They further show that the lower is the starting value of and the higher is the starting value of, the less likely this is to be a good investment. We formalize these results in the following Proosition: Proosition 5: Suose the vertical and horizontal dimensions are correlated. Increasing the uality of the rivate label to its maximum value is less likely to be rofitable, the less is the initial vertical uality differentiation between the rivate label and the national brand i.e., the higher is, and the less is the initial interchangeability between the rivate label and the national brand i.e., the lower is. Note that the above calculations have treated the retailer kindly, in that they assume no increase in the marginal cost of roduction of the rivate label when is increased. Proosition 5 oints out that even with no increase in marginal cost, it may not be otimal to increase rivate label uality to its maximum ossible level; but for this to be true, the initial ositioning of the rivate label must be extraordinarily favorable in terms of and. One might ask whether it is ever likely that we would observe such conditions in the real world; erhas not, but it is also more realistic to assume that an increase in the uality of the rivate label,, carries with it an increase in its marginal cost of roduction for the rivate label,. In the limit, it is reasonable to assume that when = =, the level of should rise to eual the marginal cost of roduction of the national brand as well as increasing the level of. It is straightforward and not surrising to show that euilibrium retailer rofits are unambiguously decreasing in. Thus, any increase in the marginal cost of roduction of the rivate label accomanying other arametric changes will worsen the rofit icture for the retailer, relative to the cases discussed immediately above. An extension of the examles above suffices to show the attern. Figure 3 shows two curves that are identical to those in Figure : one of retailer rofit for =. and =., and one of retailer rofit for =.9 and the same value of =.. However, suose that increasing rivate label uality to = can only be achieved 6

19 with an increase in to.9 and an increase in to the level of =.3. Then it is also relevant to lot the retail rofit curve for =.9 and =.3, which also aears in Figure 3. If rivate label uality of = means that both =.9 and =.3, the resulting retail rofit is If the rivate-label retailer starts out with a rivate label described by =. and =., any starting value of greater than or eual to makes it imossible for the retailer to imrove its rofit osition by investing in increasing the vertical uality of its rivate label roduct. This contrasts with the situation we analyzed when discussing Figure above, where we assumed that there was no marginal-cost enalty for increasing rivate label uality. In that case, where a rivate label uality of rivate label and the national brand i.e., the lower is. = means that =.9 but that remains at its starting value of 0., retailer rofit is ; if the rivate-label retailer started out with a rivate label described by =. and =., the starting value of would have to be greater than or eual to for it to be imossible for the retailer to imrove its rofit osition by investing in increasing the vertical uality of its rivate label roduct. This illustrates the imact of the marginal-cost enalty on the retailer s decision rocess in fixing the uality of its rivate label. While the ualitative nature of our conclusions does not change, the likelihood that the retailer will choose not to invest in a uality level close to that of the national brand is much greater when we take account of the marginal-cost effect of roducing a higher-uality rivate label roduct. We summarize this insight as: [Insert Figure 3 about here] Proosition 6: When an increase in the rivate label s uality is accomanied by both an increase in its overall interchangeability with the national brand and an increase in the marginal cost of roduction of the rivate label, the otimal uality level is not always the maximum ossible. Increasing the uality of the rivate label to its maximum value is less likely to be rofitable, the less is the initial vertical uality differentiation between the rivate label and the national brand i.e., the higher is, and the less is the initial interchangeability between the 7

20 This result of course does not imly that the rivate-label retailer rarely or never finds it rofitable to invest in increasing rivate-label uality, but does rovide redictions about underlying conditions on consumer utility for the roducts that make it more or less likely to occur. Clearly, cost is a critical factor that kees retailers from investing more in their rivate labels; one business ress article states, Many retailers balk at marketing their store brands, envisioning exensive ad camaigns aimed at building brand euity. No matter how much [retailers] talk about reinvesting three ercent back into the [rivate label] brand, [retailers] don t do it Wellman 997. This uote suggests that even beyond the marginal-cost increases we examine here, there may be significant fixed costs of investing in rivate-label branding which further deter the retailer from seeking to imitate the national brand. TWO NATIONAL BRANDS CASE In this section, we extend the simle demand model to the case where there are two national brands. These national brands can have various degrees of horizontal differentiation. In some roduct categories such as canned sous, the two leading national brands Cambell s and Progresso are barely differentiated horizontally. On the other hand, in the analgesics category, roducts are widely differentiated even with the same ingredients. For examle, both Tylenol and Midol have acetaminohen as their rimary ingredient. However, Tylenol is ositioned as the general ain reliever, while Midol is strongly entrenched for menstrual crams. In the latter category, the retailer s decision is to osition its rivate label between the two claims, and Sayman et al. 00 find that the rivate label should imitate the stronger brand i.e., Tylenol. However, in the former case, the rivate label sou may have another otion than imitating the two national brands it may differentiate outside the sace between the two national brands. These two scenarios are examined searately in the following two subsections. Case : National Brands are Sufficiently Differentiated We first generalize our base demand model and 3 assuming the two national brands are differentiated. Later we examine the case where these national brands are horizontally 8

21 undifferentiated. The consumer utility function can be extended as follows by adding the second national brand denoted by subscrit : /,, U =, 3 where s and s have the same interretation as in the base case. Solving the three first-order conditions of utility maximization for, we obtain the following demand system: 3 and,, ] [ B T =, 4 ] [ B T =, and 5 ] [ 3 3 B T =, 6 where = T, B =, B =, 3 = B. For the demand coefficients to have correct signs and for the second order conditions to be satisfied, we reuire jk i for all k j i,,,, =, and i for =, i. That is, the rates of decrease in own-marginal utilities are greater than cross-marginal utilities, and satiation occurs faster when consuming the rivate label than when consuming a national brand. The retailer s rofit maximization roblem with resect to the retail rices is euivalent to euation 4 but with three brands. The retailer s reaction functions are found as: /, /, / w w = = =. 7 9

22 As in the base case euation 4, the rivate label s rice is indeendent of the uality levels of the national brands. We obtained the euilibrium solution for the Nash game between the two national brands that act as Stackelberg leaders against the rivate label results, but they are not resented here because the euations are long and not immediately meaningful. Interested readers can find the solution in the Technical Aendix. Instead, we simlify the solution by normalizing =. Note that i =. Without loss of generality, we assume national brand is = the higher uality brand:. Let x [0,] denote the level of vertical differentiation such that = x. A larger x reresents less vertical differentiation. We also assume the variable cost of rivate label is normalized to zero = 0. In addition, since we are focusing on the case of intermediate differentiation for now, we restrict the horizontal differentiation arameter to be such that =, and and having the following relationshi: When the rivate label imitates national brand, = = and =, and vice versa. The linear rule imlied is: = k and = k, where k [ 0, ]. When k = 0, the rivate label is horizontally imitating national brand ; and when k =, it imitates national brand. As in the base case above, we are interested in finding the behavior of retailer rofit as a function of the two tyes of differentiation. However, the function is olynomial and very long even with the simlification. Therefore, we resort to a numerical aroach to evaluate its roerties. An extensive comutation reveals that the general shae of the rofit function is consistent, and it is convex in both dimensions within the arameter domain. Figure 4 resents a tyical rofit surface. Note that x varies between 0 and, and indicates the level of vertical differentiation x = means the rivate label has the same uality level as the lower-uality national brand. k reresents the horizontal location of the rivate label between the two national brands k = 0 means the rivate label horizontally imitates national brand. [Insert Figure 4 and 5 about here] In interreting Figure 4, we need to focus on the arameter region in which the rivate label s demand is ositive Figure 5. When its uality is low, the rivate label s demand is negative with negative rice, leading to a false ositive rofit level. Combining insights from 0

23 the two figures, we find that it is otimal for the retailer to osition the rivate label a with minimum vertical differentiation from national brand x=, and b with minimum horizontal differentiation from the higher uality national brand s trade dress k=0. The minimum vertical differentiation result contradicts those from the location models in the economics literature e.g., Shaked and Sutton 98; Tirole 989. Note, however, that this latter result is obtained without considering the cost of increasing the uality of the rivate label. When it is costly to increase rivate label uality, minimum differentiation will not always be the best decision. If the uality levels of the two national brands are eual = and they are substantially horizontally differentiated, imitating either brand is otimal for the rivate label. However, when the national brands are allowed to be asymmetric different levels, the rivate label is better off imitating the higher uality brand. This is consistent with Sayman et al. s 00 result. Positioning in between is never an otimal solution. Case : The Two National Brands are Horizontally Undifferentiated When the two national brands lack horizontal differentiation, the rivate label might have another otion for its horizontal ositioning horizontally differentiated from both national brands. 9 The car battery market rovides an examle of this henomenon. Two major national brands, ACDelco and Exide, are virtually undifferentiated; would the Sears rivate label battery, DieHard, be better off imitating them? We in fact observe that the rivate label differentiates itself as the tough battery. In this section, we modify our model to the secial case of two undifferentiated national brands. In our demand functions 4-6, having undifferentiated national brands would mean that P = P = P from our rivate label s oint of view: that is, the rivate label is eually horizontally differentiated from both national brands. Further, a lack of horizontal differentiation between the two national brands means that consuming a unit of either one has an eual effect on the marginal utility of consuming an incremental unit of one of the brands. Mathematically, this imlies that the cross-rice demand arameter is essentially the same as the own-rice demand arameter; but to insure that the roblem has an interior solution, we need to introduce a small number ε such that = ε, where we recollect that is the cross-roduct substitutability arameter between the two national brands.

24 We derive the euilibrium rofits of the retailer and manufacturer, as well as euilibrium rices and uantities, with these assumtions. While they can be straightforwardly derived, the exressions are too unwieldy to resent here. As in the discussion of differentiated national brands above, we therefore assume = =. As above, P =. Hence, =ε =. For simlicity, we first examine the case where the two national brands are characterized by the same vertical uality: = = P. Let x [0,] denote the level of vertical differentiation such that P = x. An analysis of the euilibrium demand for the store brand shows that storebrand sales are ositive only when < P x, a condition we need to imose to evaluate realistic situations where the store brand in fact cometes with the two similarly-ositioned national brands. Intuitively, this condition imlies that if the store brand is too inferior in uality to the national brands i.e., if x <, store-brand demand will be negative. Alternatively, the P condition imlies that the relative uality of the store brand as comared to national brands laces a limit on how horizontally differentiated the store brand can be from the national brands, and still garner ositive sales; the higher is the store brand s uality, the more horizontally differentiated it can be and still survive in the market. Without loss of generality, we therefore restate as = y x, with y [0,]. Euilibrium retailer rofits in this situation, as ε aroaches zero, are given by [ x y ] 4 P x y P. The uestion of what is the otimal degree of horizontal differentiation of the store brand from the national brands translates in this context to a choice of the value of P y in the ermitted range of 0 y that maximizes these euilibrium retailer rofits. It is straightforward to show that this rofit exression is decreasing in y: the otimal value of y is thus zero, imlying maximal horizontal differentiation of the store brand from the national brands. We can also easily show that if it were costless the retailer would choose minimal vertical differentiation of the store brand from the national brands, that is, x =. Finally, it is also easy to show that in this situation, maximal horizontal store brand differentiation also maximizes unit sales of the store brand. Interestingly, therefore, the nature of cometitive ositioning between the national brands affects the relative osition the retailer wishes to establish for its store brand. In the case of horizontal differentiation between the national brands, the retailer otimally ositions the store

25 brand at the same horizontal osition as one or the other of the national brands minimizing horizontal differentiation with one of the national brands similar to the result in Sayman, Hoch and Raju 00. But here, when the national brands themselves are undifferentiated, it is no longer in the retailer s best interest to choose a horizontal osition eual to those of the national brands; instead, retail rofit is maximized by maximally horizontally differentiating the store brand from the national brands. Neither Sayman et al. 00 nor Du et al. 004 derive this result, because they do not consider the ossibility that the rivate label horizontally differentiates from two horizontally undifferentiated national brands. Thus, in a multi-nationalbrand world, rivate-label ositioning decisions otimally take account of the existing nationalbrand cometition. We can also extend our results to a case where the two national brands, while horizontally undifferentiated, are vertically differentiated, with > P. We show a numerical examle of this more comlicated case in the Technical Aendix to illustrate that a the more uality differences there are between the two national brands, the more stringent is the condition on minimum uality of the store brand to guarantee ositive store-brand sales; and b it is still otimal for the retailer to maximize the horizontal differentiation of the store brand from the national brands subject to ositive sales of the store brand, as above. Thus, our results on the otimality of maximum horizontal differentiation of the store brand, given national brands that lack horizontal differentiation, holds regardless of the uality differences between the national brands. In sum, our analysis of the case of two national brands cometing with the rivate label shows that otimal ositioning of the store brand should take into account the relative horizontal ositions of the national brands. When national brands are significantly differentiated only in the horizontal dimension, the rivate label can horizontally osition euivalently to one of the national brands. If the national brands are of different uality, the retailer horizontally ositions the rivate label euivalently to the stronger national brand. But when national brands are not differentiated horizontally, the results are uite different: the retailer otimally maximizes the horizontal differentiation between the rivate label and the national brands. 3

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