17 816 May 2017 Private Label Positioning and Produt Line Stéphane Caprie
Private Label Positioning and Produt Line Stéphane Caprie 29 May 2017 Abstrat This artile examines i) how retailers position private label produts, ii) why private labels are sold in some produt ategories but not in others, and why some national brand produts may have diffi ulty in aessing retailers shelves, iii) why some private label produts are positioned as "premium" brands, and iv) how onsumers surplus and total welfare are affeted by private labels. We find that private label positioning leads to less differentiation in produt ategory, whih struturally hanges a retailer s produt line in return. Consumer welfare and total welfare are lower. JEL Classifiation: L13, L81. Keywords: Private Label, National Brand, Produt Line. This paper is based on Chapter 2 of my PhD thesis Caprie, 2000). I thank Zhiqi Chen who enouraged me to revise this paper and provide an English version. I am very grateful to Anne Perrot, my PhD advisor. I also thank the ommittee for my PhD defense: Mihel Moreaux, Vinent Réquillart, Patrik Rey and Antoine Soubeyran. Toulouse Shool of Eonomis, INRA, University of Toulouse Capitole, Toulouse, Frane; email: stephane.aprie@inra.fr. 1
1 Introdution Private Labels PLs), also known as store brands, are typially goods sold under a retailer s brand whih an be the retailer s own name or a name reated exlusively by that retailer. Private-label goods are available in a wide range of industries from food to osmetis. Aording to a report by Nielsen 2014), private label produts aount for 18 perent of the U.S. and Canada retailing markets in value 2013 data) and more than twie this figure in some European ountries Switzerland at 45%, United Kingdom at 41%, Spain at 41%, 2013 data), and are now well developed in most ountries throughout the world. In India, PLs onstitute 5% of sales 2014 data; Nielsen report, 2014), and "they grew 27% between 2012 and September 2014". However, PL market shares and their positioning with respet to National Brand NB) produts exhibit widespread diversity aross produt ategories. For example, for 38 ountries the PLs aggregated value shares were, on average, 32 perent in refrigerated food, five perent in personal are produts and two perent in baby food ACNielsen, 2005). In addition, while PL produts were pried, on average, 31 perent lower than their manufaturer ounterparts, the average prie differentials on a ategory basis ranged from 46 perent in personal are produts to just 16% for refrigerated food. Interestingly, there was no diret orrelation between the lower prie and the largest market share: while the value shares of PLs were 32 perent in refrigerated food and two perent in baby food, refrigerated food and baby food were pried 16 perent lower and 24 perent lower respetively, than their manufaturer ounterparts. Moreover, at the individual ountry/ategory level, "there were a number of examples where PL produts had an average prie that was atually higher than the manufaturer brands" ACNielsen, 2005). One reason for this, is that while PL produts an be positioned as lower-ost alternatives to NB produts, some retailers have also positioned their PL brands as "premium" brands. Retailers suh as Teso in the U.K. and Loblaws in Canada, for example, have now both added these PL offerings to their produt assortments. 1 With growing market shares of PL produts and/or the premium brand 1 Alongside the Teso Value brand usually depited by blue and white stripes), Teso has a premium quality brand, Teso Finest, whih also spans most produt areas in the store ACNielsen, 2005). Overall, Teso has also developed Teso Organis with a variety of organi foods from ookies to sausages, and Teso Free, inluding over 150 produts whih are gluten, wheat or milk free. Sine President s Choie PC) produts were launhed in 1984, Loblaws has expanded the brand beyond a prie-point fous in order to offer quality, health-foused alternatives to onsumers in Canada, 2
positioning of some PL brands, some ategories exhibit a level of tension between NB produers and retailers, and NB suppliers may fae problems in aessing the shelves of retailers. To date, the literature on this subjet has studied a number of reasons for a retailer to launh PL produts with two main motivations suggested: first, segmenting the market, and seond, strengthening the bargaining power of a retailer. 2 In respet to market segmentation, by differentiating the produts in one produt line with several brands, firms are able to weaken the ompetition with their rivals, whih improves their market power see Shaked and Sutton, 1982, for example; see also Brander and Eaton, 1984, Champsaur and Rohet, 1989 and Gilbert and Matutes, 1993 in whih firms hoose their produt lines 3 ). Launhing a PL is also onsidered as an instrument to strengthen the retailer s bargaining power against NB suppliers. Earlier studies inlude Mills 1995), Bontems et al., 1999) and Mills 1999). 4 For example, Mills 1995) shows that PL produts are introdued beause they indue a prie onession of NB produers and, hene, limit the market power of NB produers. In other words, when a new substitute is supplied by the retailer and ompetes with the existing good, the problem of double marginalization is redued. When PL produts are introdued or beause of the threat of supplying PLs), industry surplus and onsumer surplus are higher, whih results in as well as the United States, the Caribbean, Hong Kong and Israel for example PC Blue Menu, PC Organis, PC Mini Chefs; ACNielsen, 2005). See also Caprie 2000), for examples in Frane Carrefour with "Filière Qualité", "Esapades Gourmandes"). 2 Other reasons have been used to justify the prodution of PL produts. For example, Bergès and Bouamra-Mehemahe 2012) shows that NB manufaturers may use their exess prodution apaities to produe PL produts. They study the retailer s and NB manufaturer s PL strategy for prodution in a setting featuring endogenous store brand quality, bargaining power, possible differenes in prodution tehnology and potential apaity onstraints for the NB manufaturer. Depending on the struture of apaity onstraint applying to both produts or to PL only), they find that the retailer may prefer to hoose an independent firm for the prodution of PL produt whereas the NB manufaturer is hosen in the ase of exess apaity. In an environment of imperfet information where onsumers do not know the quality of the PL produt before purhase, Bergès-Sennou and Waterson 2005) and Chen and Xu 2015) also examine what determines the presene or absene of private labels as experiene goods) in groeries. 3 These latter papers define multi-stage games in whih firms first hoose their produt lines and then ompete on the market. 4 More reently, see also Gabrielsen and Sorgard 2007) with brand loyalty onsumers. Other studies suh as Narasimhan and Wilox 1998) have also onsidered brand loyalty onsumers. By ontrast, Bergès-Sennou 2006) has onsidered store loyalty onsumers. In any ase, onsumers loyalty affets the retailer s bargaining position, but also the retailer s assortment, of available produts. See also Bergès et al., 2004) for a survey. 3
higher soial welfare as long as fixed osts are low). Results from empirial studies are more ambiguous on this issue. Some studies find that the prie of NB produts dereases when PL produts are introdued or when the market share of PLs is larger), while others find the opposite. 5 For example, Ward et al., 2002) show that an inrease in the PL market share is onsistent with an inrease or no hange) in the prie of national brands. While theoretial studies suggest that the impat of PLs on the retail pries of NB produts is negative, results from empirial studies are far from lear. Moreover, while previous theoretial papers assume that NB suppliers use linear priing, reent empirial analysis shows that non-linear priing is prevalent, espeially when suppliers ontrat large retailers. 6 In this paper, we onsider a simple setup where the produer of a NB sells its brand through a single retailer and the retailer onsiders the hoie of the harateristis of its PL produt. As it is ommon to argue that there are quality differenes between NB and PL, we assume that both produts are vertially differentiated. The marginal ost of the PL produt is inreasing and onvex in the quality objetive quality). Initially, we onsider the industry outome when the quality of PL produt is hosen in order to maximize industry surplus. Then, we restrit attention to the ase where the quality of the PL produt is lower than the quality of the NB produt and study the following three stage game where first, the retailer hooses the quality of the PL produt, seond, the NB produer offers a non-linear tariff, and finally, the retailer sets retail pries. The timing of the game is familiar as ontrating deisions present a lower degree of irreversibility than quality hoies. As the retailer owns and ontrols the brand, the hoie in regard to quality is made by the retailer. This timing underlines an essential feature of PL produts: the harateristis of PL produts are fixed by retailers and not by manufaturers. Moreover, these deisions are strategially taken in order to enable retailers to inrease their profits. As expeted, beause the retailer hooses the quality of the PL produt so as to maximize its disagreement payoffs, the quality is higher than the quality whih maximizes industry profits. This result highlights one major differene when we ompare the quality hoie of a NB produer and the quality hoie of a retailer 5 We an ite, for example, Putsis 1997), Cotterill et al., 2000), Chintagunta et al., 2002) and Ward et al., 2002); more reently, see also Bontemps et al., 2008). 6 See Villas-Boas 2007) and Bonnet and Dubois 2010) for seminal papers, showing evidene of suh ontrats in vertial ontrating. 4
on PL. While the former onsiders the inremental ontribution of its good to the surplus of the produt ategory, whih leads to industry surplus maximization, the latter takes into aount its disagreement payoff. As the quality hosen by the retailer for the PL produt is higher, the total demand whih is supplied in the produt ategory is smaller. Moreover, the retail prie of the NB produt is unhanged in this setting. We then show that onsumer surplus and total welfare are lower when the retailer hooses the quality of its PL produt in omparison with the situation in whih the quality would be hosen optimally. This is beause total demand is lower in the former ase. Thus, we haraterize in detail the retailer s produt line when the retailer positions its PL produt. In partiular, we show that the demand for the NB produt may be zero in some ases at equilibrium, whih raises the issue of aess to shelves for the NB produers. 7 By ontrast, the PL produt is not sold in some ases at equilibrium. Another situation an arise, in whih the retailer may hoose the quality of the PL produt whih is higher than the quality of the NB produt, whih may explain premium PL produts in some produt ategories. We then disuss our results with respet to different senarios: first, we onsider an alternative game in whih the NB manufaturer an ex-ante ommit to ontrat terms before PL positioning), and seond, we allow for ompetition between NB produers. In the former senario, the retailer not unsurprisingly hooses PL quality whih maximizes industry surplus. In the latter senario, similar insights arise when the ompetition between NB manufaturers is fiere. In both ases, PL positioning now allows the retailer to prie disriminate between onsumers. Our results are in line with the findings of Sott-Morton and Zettelmeyer 2004). 8 Using a bargaining framework, they study a retailer s deision whether to arry an additional NB or a PL and, if the retailer hooses to introdue the latter, where in produt spae to loate the PL produt. They show that the strategi positioning of a PL produt in a ategory hanges the bargaining over supply terms between a retailer and a NB manufaturer in that ategory, and learly differs from the strategi positioning of another NB manufaturer. PL positioning auses a redution of differentiation in produt ategory. However, in their analysis, PL and NB produts are always supplied 7 The result is due to the finiteness property Gabszewiz and Thisse, 1979; Shaked and Sutton, 1983) in vertially differentiated markets. In suh an analysis, the number of produts with a positive market share depends on the degree of onsumer heterogeneity. 8 See also, Choi and Coughlan 2006) for similar insights. 5
at equilibrium or another NB produt and the original NB). They assume onstant marginal ost of prodution for both PL and NB produts. By ontrast, we assume inreasing marginal ost in quality for the PL produt. We an thus study in detail the equilibrium produt line of the retailer with respet to the positioning of the PL produt. We find that the PL produt or the NB produt are not sold in some ases. Moreover, while their model is not designed to study premium PL produts suh as President s Choie for Loblaws in Canada, our model allows us to onsider this PL positioning. There is now a literature whih investigates the role of PLs in oligopolisti downstream markets Avenel and Caprie, 2006; Colangelo, 2008 and more reently Bonroy and Lemarié, 2012). For example, Avenel and Caprie 2006) onsider two ompeting retailers; they study a vertial differentiation model where a high quality item i.e., a NB) is offered by a monopolist, while low quality items i.e., PL produts) are offered by a ompetitive fringe. They show that the equilibrium produt line depends on the positioning of PL produts. When PL and NB produts are lose substitutes, the NB manufaturer prefers to deal with both retailers in order to affet retailers outside options, that is, the profits that retailers obtain with their PL produts. By ontrast, in this paper, we assume a monopoly retailer, leaving aside the issue of how PL produts interat with retailer ompetition. In doing so, we fous on interbrand ompetition i.e., ompetition between produts at one retailer), when the retailer is a monopoly. The rest of the paper is organized as follows. Setion 2 introdues the model. We analyze PL positioning when the industry is fully vertially integrated in Setion 3 this ase will be used as a benhmark ase). Setion 4 solves the model and presents results. Consumer surplus and total welfare are also studied. We disuss results in Setion 5 and Setion 6 onludes. 2 The model The industry onsists of an upstream market and a downstream market. In the upstream market, a manufaturer produes a national brand NB) produt with quality at a onstant marginal ost NB. In the downstream market, a monopolisti retailer buys and resells the NB produt. The retailer, meanwhile, has the option of produing and selling a private label PL hereafter) produt with quality s P L. The retailer hooses 6
the quality of the PL produt. The marginal ost of produing a PL does not depend on the quantity, but is inreasing and onvex in the quality level. We assume that the marginal ost of produing s P L is given by C P L s P L ) = s2 L 2. We do not restrit the analysis by having more assumptions on osts. In partiular, we will say that the retailer benefits from a ompetitive advantage when for idential levels of quality the marginal ost of produing a PL is smaller than the marginal ost of produing the NB produt: C P L ) < NB NB < 2 ). On the ontrary, the retailer faes a ompetitive disadvantage when C P L ) > P NB > 2 ). We suppose that there are no barriers to entry to the prodution and sales for the PL produt. Aordingly, there are a large number of upstream firms that an produe the PL produt and the retailer purhases the PL produt at marginal ost C P L s P L ). 9 Consumers have perfet information about the quality of produts. We suppose that the ontrat between the NB manufaturer and the retailer takes the form of a two-part tariff T = w, F ), whih is proposed by the manufaturer, where w and F denote the wholesale prie and the fixed fee harged to the retailer, respetively. The retailer sells the NB produt and the PL produt at p NB and p P L in the event where the retailer aepts the ontrat proposed by the manufaturer). Following the quality-hoie model of Mussa and Rosen 1978), we assume that onsumers are indexed by their preferenes θ, with θ uniformly distributed on an interval [0, a] density, 1 ). There is a unit mass of onsumers. Consumers at different loations a on the interval [0, a] have different tastes for quality. Speifially, the net surplus of a onsumer θ is given by U θ, p k, s k ) = θs k p k k = NB, P L) if he purhases a produt k of quality s k and zero otherwise. By denoting i the good with higher quality and j the other produt, the marginal onsumer who is indifferent about buying the good i and the good j is given by θ ij = p i p j s i s j, while the marginal onsumer who is indifferent about buying the low quality good and not buying at all is determined by θ j = p j s j. We 9 An alternative interpretation would be to onsider that the retailer is vertially integrated and produes PL produt at C P L s P L ). 7
an write the demands as follows: D i p i, p j ) = D j p i, p j ) = 0 if p i p i p j ) or if p i as i a p i p j s i s j if p i p j ) p i < p i p j ) a p i s i if p i < p i p j ) 0 if p j p j p i ) or if p j as j p i p j s i s j p j s j if p j p i ) p j < p j p i ) a p j s j if p j < p j p i ) s with p i p j ) = a s i s j ) + p j and p i p j ) = p i j s j i, j = NB, P L). In the ase where the retailer does not aept the offer of the NB manufaturer, we denote p NB = + the retail prie of the NB produt. It an also be optimal for the retailer to not sell the PL produt in ase PL and NB produts are lose substitutes, and we denote p P L = + the retail prie of PL produt in this ase. We study the following game: - at stage one, the retailer hooses the quality s P L of its PL produt; - at stage two, offers w, F ) are made by the NB manufaturer to the retailer, whih the retailer either aepts or rejets; and - then, at stage three, the retailer sets retail pries p P L and p NB. The timing of the game is not surprising as ontrating deisions present a lower degree of irreversibility than the hoie of quality. In partiular, the development of PL produts is subjet to various stages, suh as the definition of speifiations, a all for tenders to the prodution setor, manufaturing by the hosen supplier, and quality ontrol on the prodution site, whih suggests a long proess and thus onstitutes an irreversible hoie. By ontrast, the terms of a ontrat an be modified more easily and therefore have a lower degree of irreversibility. 10 The retailer owns and ontrols the PL brand whih results in a quality hoie of PL produt s P L made by the retailer. In the next setion, we onsider the situation where the industry is fully vertially integrated and PL positioning maximizes industry surplus. We will use this as a benhmark ase. 10 Other demand side fators may also explain a relative rigidity in produt quality. Consumer quality assessment may involve a ertain degree of subjetivity, thus making the produt quality hange proess relatively long, in omparison with ontrat designing. 8
3 PL positioning in a fully vertially integrated industry Industry surplus involves sales from PL and NB produts, that is, the maximization problem is given by: Max Π I p P L, p NB, s P L, ) = p P L C P L s P L )) D P L p P L, p NB, s P L, ) + p NB NB ) D NB p P L, p NB, s P L, ), whih results in the following first-order onditions in retail pries: p P L C P L s P L )) D P L p P L, p NB, s P L, ) p P L + D P L p P L, p NB, s P L, ) + p NB NB ) D NB p P L, p NB, s P L, ) p P L = 0, p P L C P L s P L )) D P L p P L, p NB, s P L, ) p NB +p NB NB ) D NB p P L, p NB, s P L, ) p NB We obtain p e P L s P L, ) and p e NB s P L, ). 11 First-order ondition in the quality of the PL produt results in: + D NB p P L, p NB, s P L, ) = 0. p P L C P L s P L )) D P L p P L, p NB, s P L, ) s P L +p NB NB ) D NB p P L, p NB, s P L, ) s P L C P L s P L ) D P L p P L, p NB, s P L, ) = 0. Substituting p NB and p P L by, p e P L s P L, ) and p e NB s P L, ), and solving for s P L, we obtain the quality of the PL produt whih is optimal from the point of view of 11 Simple alulations lead to p e P L s P L ) = 1 2 C P L s P L ) + as P L ) and p e NB s P L ) = 1 2 NB + a ) for D P L.) > 0 and D NB.) > 0. 9
industry surplus. Let s P L denote this optimal quality. s P L depends ruially on the size of the market a and the relative prodution ost of the NB produt NB. Without restriting the range of parameter values, three senarios should be distinguished: I, s P L = ŝ P L, II, s P L = s P L and III, s P L = s P L with s P L < ŝ P L < s P L. 12 Figure 1 summarizes the optimal produt line for the different ranges of parameter values a and NB. To failitate the exposition of the different senarios, we will distinguish two ases aording to whih the PL produt faes a ompetitive disadvantage or benefits from a ompetitive advantage with respet to the NB produt. Fig. 1: Optimal produt line in the benhmark ase. 12 Critial values are given by: ŝ P L = 2 3 a, s P L = 3 9s 2 NB 16 NB 4 and s P L = a + 2 + 4s 2 NB + a2 2a 6 NB. 3 Conditions that define these ritial values an be found in Appendix A. 10
In the former ase, NB C P L ) whih translates into P sp s P 2, the PL produt faes a ompetitive disadvantage. If the parameter values fall into region I i.e., if a is relatively low), the vertially integrated struture sells the PL produt only ŝ P L ). As the market size is relatively small a P sp ), the relative prodution ost of the NB produt is too high so as to ensure a positive margin for the NB produt and, only the PL produt is sold. On the other hand, if the market size is very high i.e., in region III ), the vertially integrated struture sells both produts, but the optimal quality of the PL produt is set higher than the quality of the NB produt s P L > s P ). As the market size is high a > ã 1 NB )), there exist opportunities to provide an optimal quality of the PL higher than the quality of the NB produt. Some onsumers will aept paying a very high prie for higher quality. Finally, if the market size falls into an intermediate region i.e., in region II ), the vertially integrated struture sells both produts with the optimal quality of the PL produt smaller than the quality of the NB produt s P L < ). Here i.e., for NB < a ã NB 1 )), the vertially integrated struture uses the PL produt as a tool for market segmentation. Consumers with a high willingness to pay buy the NB produt while onsumers with a lower willingness to pay buy the PL produt. In the latter ase, NB > C P L ) whih translates into NB > 2, the PL produt benefits from a ompetitive advantage with respet to the NB produt. If NB > 9 16, the relative prodution ost of the NB produt is relatively high so that it will be sold only when the market size is relatively high a > ã 2 NB )). In this ase i.e., in region III ), the vertially integrated struture will sell both produts with the optimal quality of the PL produt higher than the quality of the NB produt s P L > ). On the other hand, if the market size is smaller a ã NB 2 )), only the PL produt is sold with s P L = ŝ P L i.e., in region I ). The market size is not large enough to ensure that both produts are sold and it is only the PL produt whih is sold beause it benefits from a ompetitive advantage. Then, we onsider the range of parameters where NB is intermediate 2 < NB 9 s 16 NB), and whereby there may exist opportunities to sell both produts, NB and PL, with the optimal quality of the PL produt smaller than the quality of the NB produt region II: s P L < ). This ase arises, even if the PL produt benefits from a ompetitive advantage. We 11
obtain this ) ase when the market ) size falls into an intermediate region for a suh that ã NB 3 < a Min {ã NB 1, ã NB 4 )}). The vertially integrated struture uses the PL produt as a tool for market segmentation by setting the optimal quality of the ) PL produt smaller than the quality of the NB produt. By ontrast, if a ã NB 3 { ) )} i.e., region I ), only the PL produt is sold ŝ P L ) and if a > Min ã NB 1, ã NB 4 i.e., in region III ), both produts are sold and the optimal quality of the PL produt is set higher than the quality of the NB produt s P L > ). In the former ase, the market size is not large enough to ensure that both produts are sold and, only the PL produt will be sold as the NB produt faes a ompetitive disadvantage. In the latter ase, the vertially integrated struture uses the NB produt as a tool for market segmentation, and the optimal quality of the PL produt is set higher than the quality of the NB produt. 13 The range of produt quality is due to the ompetitive advantage of the PL produt ompared to the NB produt NB > C P L )). We summarize our results in Proposition 1. Proposition 1 Depending on the range of parameter values see Figure 1 for details), the produt line of a fully vertially integrated industry is given by: - Region I, s P L = ŝ P L, the PL produt is sold only; - Region II, s P L = s P L, both PL and NB produts are sold with s P L < ; and - Region III, s P L = s P L, both PL and NB produts are sold, but with s P L >. We have: ŝ P L = 2 3 a, s P L = 3 9s 2 NB 16 NB 4 Proof. See Appendix A. Threshold values in a are detailed in the Appendix. and s P L = a + 2 + 4s 2 NB + a2 2a 6 NB. 3 In the following, we will fous on the set of parameter values orresponding to the region II : the vertially integrated struture uses the PL produt as a tool for market { ) )} 13 An intermediate area also arises in this latter ase, where Min ã NB 1, ã NB 4 < a < ã 2 for whih, PL produt is sold only region I, s P L = ŝ P L ). 12
segmentation by setting the optimal quality of the PL produt smaller than the quality of the NB produt. 14 If the motivation for PL produts is to segment the market, we should expet to have an equilibrium where the quality of the PL produt hosen by the retailer is smaller than the quality of NB produt. However, as we will see, the hoie of the retailer fundamentally hanges the equilibrium produt line. 4 Equilibrium produt line We solve bakwards the previous three-stage game: the retailer hooses the quality level of the PL produt, the supplier of the NB produt proposes a two-part tariff whih is either aepted or rejeted by the retailer and, lastly, the retailer sets the retail pries. At stage three, the maximization problem of the retailer onsists of setting p NB and p P L to maximize its profits: π D p P L, p NB, w, s P L, ) F, where F represents the fixed fee that the retailer pays to the supplier. The maximization problem leads to p e NB w, s P L, ), p e P L w, s P L, ) and the retailer obtains π D p e P L w,.), pe NB w,.), w, s P L, ) F. Then, at stage two, the two-part tariff set by the supplier an be obtained from the following maximization problem: Max w,f w NB ) D NB p e P L w,.), p e NB w,.), s P L, ) + F s.t. π D p e P L w,.), p e NB w,.), w, s P L, ) F π D p e P L s P L ), +, s P L ), where π D p e P L s P L), +, s P L ) represents the disagreement payoff of the retailer. This yields the familiar solution, whereby the partiipation onstraint of the retailer holds 14 We will thus fous on the range of parameters for whih: ) If NB < 2, we have a suh that NB < a ã NB 1 ; If NB 9 16 ). > 2, we have a suh that ã 3 NB ) < a Min { ) )} ã NB 1, ã NB 4 with NB < 13
with equality and the fixed fee that the retailer pays to the supplier is: F = π D p e P L w,.), p e NB w,.), w, s P L, ) π D p e P L s P L ), +, s P L ). The maximization problem beomes: Max w w NB ) D NB p e P L w,.), p e NB w,.), s P L, ) +π D p e P L w,.), p e NB w,.), w, s P L, ) π D p e P L s P L ), +, s P L ), whih is equivalent to maximizing the joint-profits of the NB manufaturer and the retailer beause the retailer s disagreement payoff π D p e P L s P L), +, s P L ) does not depend on the wholesale prie. Using the envelope theorem, the wholesale prie is set to the marginal ost of prodution of the NB produt, that is, w = NB. Finally, at stage one, the retailer hooses the quality of the PL produt to maximize its profits whih is equal to its disagreement payoff: Max sp L π D p e P L s P L ), +, s P L ). Solving the maximization problem above leads to s P L = 2 a. In any ase, the quality 3 s P L of the PL produt is hosen higher than the optimal quality s P L with s P L = s P L, maximizing industry profits). In fat, the retailer hooses the quality of its PL produt in order to strengthen its bargaining power, instead of segmenting the market. We will show that PL positioning struturally hanges the equilibrium produt line. Depending on parameter values, four regions should be distinguished: - Region A, both produts are sold, and the produt line is suh that s P L < : s P L, ) with s P L < ; - Region B, the demand for the PL produt is zero, and only the NB produt is sold:, ); - Region C, both produts are sold, but the produt line is suh that s P L > : s P L, ) with s P L > ; and - Region D, the demand for the NB produt is zero, and only the PL produt is sold: s P L, ). Figure 2 below summarizes the equilibrium produt line for the different ranges of 14
parameter values. We distinguish between the ase where the retailer faes a ompetitive disadvantage NB advantage NB > 2 ). 2 ) and the ase in whih the retailer benefits from a ompetitive Fig. 2: PL positioning and produt line. In the former ase, if the parameter values fall into region A i.e., if a is relatively low: a a NB 2 = 3 NB ), both produts are sold. The quality of the PL produt is loser to the quality of the NB produt ompared to the solution whih maximizes ) industry surplus), but both qualities are sold at the equilibrium. By ontrast, if a is ) ) higher: a > a NB 2 = 3 3 + 9s 2 NB 16 NB, only the NB produt is sold region B, 8 ) ) a NB 2 < a a NB 1 ) or both produts are sold, with s P L > region C, i.e., a > a 1 NB )). In the former region, there will exist opportunities to provide a smaller quality of the PL produt. However, as the retailer does not internalize the joint-profits with the NB manufaturer and only onsiders its disagreement payoff, the demand for the PL produt is zero at the end. This result is related to the finiteness property 15
as mentioned in the Introdution Gabszewiz and Thisse, 1979; Shaked and Sutton, 1983). In vertially differentiated markets, the number of produts with a positive demand depends on the degree of onsumer heterogeneity. When the two qualities are lose, whih is the ase in region B, the more effi ient quality preempts the less effi ient quality. As the retailer faes a ompetitive disadvantage, the less effi ient quality is the PL produt, and the PL produt is not sold at equilibrium. PL positioning struturally hanges the retailer s produt line. 15 In the latter region, the relative ost of the PL produt is lose to the relative ost of the NB produt. At the equilibrium, the demand for the PL produt beomes positive, but now the equilibrium produt line is suh that s P L >. In the latter ase NB > 2, the retailer benefits from a ompetitive advantage, whereby the demand for NB is zero if a is relatively low region D, i.e. a a 2 NB )). As above, this result is due to the finiteness property. The two qualities are lose and the more effi ient quality preempts the less effi ient quality. As the retailer now benefits from a ompetitive advantage, it is the NB produt whih is not sold at equilibrium. The result is that the supplier of the NB produt is denied aess to the retail market, whih was not the ase in the fully integrated vertial industry. PL positioning implies that the NB manufaturer is preempted from the market. On other hand, if the market size is relatively high and the relative ost of the PL produt is lose to the relative ost of the NB produt, the demand for the NB produt now beomes positive. The equilibrium produt line is suh that s P L > s NB region C, i.e. a > a NB 2 )). In this region, the PL produt is a premium brand and the NB produt is used to segment the market. We summarize results in Proposition 2. Proposition 2 Assume parameter values are in region II, depending on the range of parameter values see Figure 2, for details), equilibrium produt line with s P L = 2a > 3 is given by: s P L - Region A, both produts are sold, and the produt line is suh that s P L < : s P L, ) with s P L < ; - Region B, the demand for the PL produt is zero, and only the NB produt is sold:, ); 15 See also Bahiega and Bonroy 2015) for a use of this property in vertial relationships in a different ontext. 16
- Region C, both produts are sold, and the produt line is suh that s P L > : s P L, ) with s P L > ; and - Region D, the demand for the NB produt is zero, and only the PL produt is sold: s P L, ). Proof. See Appendix B. The supplier and the retailer fae a oordination problem. Instead of onsidering industry surplus, the retailer maximizes its outside option so as to strengthen its bargaining position, whih results in a higher quality of the PL produt. Quality ineffi ieny implies that total demand in the ategory is smaller. The ineffi ieny we highlight is due to the timing of the game we have hosen. However, this timing is familiar as ontrating deisions present a lower degree of irreversibility than quality hoies. Another essential feature of PL produts is that their harateristis are fixed by retailers and not by manufaturers. Suppose, instead, that the quality deision is taken by another supplier in stage 1, and the NB manufaturer and this supplier offer two-part tariffs in stage 2 offers are publi and are made simultaneously). The quality hosen by this supplier now maximizes industry surplus. To understand the differene between the two games, it is straightforward to show that ontrats are still effi ient beause of twopart tariffs and the supplier now onsiders the inremental ontribution of its good to the surplus of produt ategory. Let Π I C P L s P L ), NB, s P L, ) Π I +, NB,, ) denotes its inremental ontribution to the produt ategory. In maximizing its inremental ontribution, the supplier maximizes industry surplus as Π I +, NB,, ), whih is the monopoly profit related to the NB produt, independent of s P L. By ontrast, the retailer in positioning its PL produt onsiders Π I C P L s P L ), +, s P L, ) alone, whih is its outside option. 16 The oordination problem we highlight arises as it is the retailer who sets the harateristis of PL produts. As previously seen, PL positioning struturally hanges produt lines. In our setting, total demand at equilibrium dereases due to PL positioning but the retail prie of the NB produt is unhanged. We now turn to the analysis of onsumer surplus and total welfare. Consumer surplus and welfare analysis 16 See also Sott-Morton and Zettelmeyer 2004) for similar point. 17
As there is no double marginalization at the equilibrium of this game, the results in terms of onsumer surplus and welfare will only depend on the omparison of levels of the quality for PL produt between the vertially integrated struture and the situation where the retailer hooses the quality. We denote by CS, s P L ) the onsumer surplus and by W, s P L ) the total welfare. The onsumer surplus with s i < s j ) is given by: CS s i, s j ) = and the total welfare by: pe i pe j s i s j p e j s j ) a θsj p e j dθ + p e i pe j s i s j θs i p e i ) dθ, W s i, s j ) = Π I s i, s j ) + CS s i, s j ), with Π I s i, s j ) representing industry surplus, Π I s i, s j ) = pe i pe j s i s j ) p p e e j j dθ + j s j a p e i pe j s i s j p e i i ) dθ. Simple alulations show that Π I s i, s j ) = 2CS s i, s j ). An impliation of this observation is that the quality of the PL produt, whih maximizes the industry surplus i.e., the vertially integrated struture), maximizes the total welfare. Eventually, the quality of the PL produt hosen by the retailer dereases the total welfare. The analysis above is summarized in the following proposition. Proposition 3 Quality hoie of the PL produt by the retailer is detrimental to the onsumer surplus and the total welfare. Proof. See the text above. As noted in the Introdution, some eonomists have argued that PLs would enhane onsumer surplus and total welfare. While suh an argument may apply when the double marginalization problem between NB produers and retailers applies, our analysis instead shows that the quality hoie of PL produts by the retailer is always detrimental to onsumer surplus and total welfare. Our results are different beause the double marginalization problem is avoided when two-part tariffs are used by suppliers. 18
5 Disussion We have shown that the low differentiation between PL produts and NB produts an be explained by the fat that retailers use PL produts as a bargaining tool with NB manufaturers. Suppliers an adopt several strategies by whih to respond to this situation. In the following subsetion, we disuss these strategies. Moreover, while we have shown that ineffi ient PL positioning arises when the bargaining power of the NB is large, we will show that this ineffi ieny dereases when the bargaining power of the NB manufaturer dereases. This issue is disussed in the latter subsetion. 5.1 PL positioning and manufaturer ounterstrategies It is straightforward to show that the solution to the oordination problem we fous on above is based on the inversion of the order of the steps whih are, on the one hand, PL positioning and, on the other hand, ontrat offers. We now assume the following timing in plae of the previous one. The NB manufaturer proposes a two-part tariff that the retailer aepts or rejets, the retailer hooses the quality of PL produt and, finally, sets the retail pries. The quality hosen by the retailer is thus optimal from the point of view of industry surplus. 17 The objetives of the NB manufaturer and the retailer are now aligned: one the ontrat is aepted, the distributor hooses its PL quality so as to maximize industry surplus. The profit of the retailer is unhanged ompared to the previous game and the profit of the supplier is larger. While the retailer still obtains Π I C P L s P L ), +, s P L, ), the NB manufaturer profits are now: whih are larger than: Π I C P L s P L), NB, s P L, ) Π I C P L s P L), +, s P L, ), Π I C P L s P L), NB, s P L, ) Π I C P L s P L), +, s P L, ), as Π I C P L s P L ), NB, s P L, ) > Π I C P L s P L ), NB, s P L, ) by definition. problem of oordination we disussed earlier is harmful to the supplier alone. The 17 A formal proof of the result is available upon request. 19
While the order of the stages we onsider initially takes into aount the PL proess, the reversal of the steps presented shows ertain partnership poliies that some suppliers have put in plae. In order to reestablish the optimal segmentation of the demand in the produt ategory, some suppliers have developed two types of produts: first, a type of produt that is onsidered innovative and is supported by major advertising ampaigns, and seond, lower quality produts whih have a redued sales potential. The two ategories of produts are sold under two different brands, the first under NB and the seond under PL. Listing the entire produt range implies leaving the retailer its outside option whih is still given by the profit it would make, in the absene of these produts from the NB manufaturer. This supplier-retailer partnership an solve the quality ineffi ieny highlighted above. 18 Other forms of partnerships between suppliers and retailers an be reinterpreted to solve this oordination problem. Retail ategory management for example an be seen as a tool to effi iently segment produt ategory. Depending on its bargaining power, the retailer an adopt suh management to inrease the profits of a given produt ategory and then inrease its profits if its bargaining power is suffi iently large. By leaving one supplier whih has the management of the produt ategory, the retailer segments the market. Another key feature in the retailer s quality hoie of PL produt is the ompetition between NB manufaturers. The following subsetion shows how fiere ompetition between NB manufaturers may in return lead to optimal segmentation in the produt ategory. The retailer will segment the market in positioning PL produt in plae of strengthening its bargaining position vis-à-vi manufaturers. 5.2 PL positioning and NB manufaturers ompetition We take up the initial struture of the game, with the differene that the NB upstream setor is now made up of two homogeneous produers for the NB produt instead of one: P 1 and P 2 with 1 = 1 =. The ost struture onsidered for these manufaturers is as follows: while firm 1, that is, P 1, produes at ost NB1, firm 2, that is, P 2, produes at a higher ost NB2 NB1 ). The ost differene between firms 1 and 2 an be interpreted as the level of ompetition between NB manufaturers. If the 18 Similar insights have been addressed by Bergès and Bouamra-Mehemahe 2012) in another ontext. In the ase of exess prodution apaity, the manufaturer an use its exess apaity by supplying the retailer with a PL produt and thus failitate the entire produt range listing. 20
differene is zero, the firms are in perfet ompetition; by ontrast, when the differene is large, firm 2 does not onstitute an alternative to the effi ient NB manufaturer firm 1). 19 Consider now the following game: in the first stage, the retailer hooses the quality of PL produt to be produed by a ompetitive fringe whose marginal ost of prodution is inreasing and onvex in quality; in stage two, P 1 and P 2 make offers in two-part tariffs, the retailer hooses one of these offers; and finally, in stage three, the retailer sets retail pries. As previously, ontrats proposed by the NB manufaturers are effi ient from the point of view of the vertial struture for a given level of quality for PL produt wholesale pries are respetively equal to marginal osts). 20 The retailer hooses the effi ient manufaturer, the one whose ost is lower i.e. P 1 ). Then, the quality hosen by the retailer orresponds to the quality that maximizes the profits of the vertial struture formed by the retailer and the least effi ient manufaturer P 2 ) in plae of the more effi ient manufaturer P 1 ). Let Π I C P L s P L ), NB2, s P L, ) denote the profits of the vertial struture formed by the retailer and the least effi ient manufaturer P 2 ). The outside option of the retailer is now given by Π I C P L s P L ), NB2, s P L, ) instead of Π I C P L s P L ), +, s P L, ) whih were the profits it would obtain without an alternative NB manufaturer. Simple omparative statis show that the quality hosen by the retailer is an inreasing funtion in the ost of the least effi ient manufaturer P 2 ) and the retailer s profits derease in this. 21 In other words, when the ost differene between NB manufaturers dereases, PL quality dereases, approahing the quality whih is hosen for an optimal segmentation in the produt ategory. The retailer s profits inrease as this ost differene narrows. 22 19 Another possible modeling is to onsider a Generalized Nash Negotiation between the NB manufaturer and the retailer. Both approahes lead to similar results. 20 A formal proof of the result is available upon request. 21 The profits of the retailer are given Π I C P L s P L ), NB2, s P L, ) with s P L whih maximizes s these profits. By using F.O.C in s P L, we have P L NB2 = D NB/ s P L 2 Π I whih is positive with / s 2 P L D NB / s P L < 0, at least if s P L <. Moreover, by totally differentiating retailer s profits, we obtain Π I NB2 = D NB.) < 0. 22 If we have a relationship between NB manufaturers ompetition and differentiation within the produt ategory, we an also address the issue of the introdution of PL produts. Let us now suppose that the introdution deision requires expenditures of a fixed ost, whih is independent of the quality. It is thus possible to show that the retailer s gain in introduing PL produt from whih he will hoose the quality) is an inreasing funtion of the differene in prodution osts between NB manufaturers. 21
6 Conlusion We have studied a model of quality hoie for PL produts. The benhmark ase helps us to determine the environment in whih PL produts ould be used to segment the market. We have shown that the two dimensions whih are the segmentation of the market and strengthening the bargaining power of the retailer play in opposite diretions. More speifially, while the segmentation of the market suggests the differentiation of the NB produt and the PL produt, the quality hoie of the PL produt made by the retailer mimis the quality of the NB produt. The quality differentiation between the PL produt and the NB produt is smaller: the retailer hooses a quality whih raises its disagreement payoff and enables it to reeive a larger share of the joint-profit with the NB supplier. Furthermore, we have determined the equilibrium retailer s produt line in an environment in whih the PL produt would be used to segment the market. We have found that the hoie of the retailer fundamentally hanges the equilibrium produt line. PL produts with higher quality than NB produts may emerge. But, more importantly, we have demonstrated that the result may in some ases be that PL produts are sold only, and that the demand for NB produts is zero. In other ases, we have shown that PL produts are not sold in the ategory. Moreover, while the fous is often on the impat of PL produts on NB produts retail pries, our analysis suggests that the impat is zero. However, total demand is smaller due to less differentiation in quality, whih results in lower onsumer surplus and lower total welfare. The retailer and the NB supplier fae a oordination problem, whih an be avoided if the supplier an propose a ontrat before PL produt positioning. Optimal produt lines an also be restored if NB suppliers are in fiere ompetition. In both ases, the PL produt is thus used to segment the market instead of strengthening the bargaining Let Π I C P L s P L ), NB2, s P L, ) Π I +, NB2,, ) denote the retailer s gain in introduing the PL produt. Simple alulations show that this gain inreases in the differene in prodution osts between NB manufaturers [Π I C P L s P L ),.) Π I +,.)] NB2 = [D NB C P L s P L ),.) D NB +,.)] > 0 with [D NB C P L s P L ),.) D NB +,.)] < 0 beause of imperfet substitution between PL and NB produts. Understanding why PLs are introdued in some produt ategories and not in others ould be related to the degree of ompetition between NB manufaturers. While PLs would be expeted in ategories with little ompetition between NB manufaturers, they would be absent in ategories with fiere ompetition between NB manufaturers. If the reasoning holds in our setting, other dimensions need to be onsidered, a produts are not often homogeneous goods. 22
power of the retailer. One remaining issue not addressed here is that retailers ompete and that the PL produt introdution may play a role in retailers ompetition. As ited in the Introdution, some papers have investigated this question, however, the ompetition between retailers is far from simple. In pratie, many ustomers engage in multi-stop shopping and rely on several retailers in order to fulfill their needs. While some ustomers are onestop shoppers, other ustomers are multi-stop shoppers. PL produts play a role in the shopping behavior of onsumers: for example, we an assume that onsumers who buy PL produts are more often one-stop shoppers than multi-stop shoppers. There is now a literature on ompetitive multi-produt priing using multi-stop shopping and one-stop shopping behavior see for example, Chen and Rey, 2012 and Johnson, 2016). Using these frameworks as building bloks to revisit PL positioning when retailers ompete would be interesting, however, we leave this task for further investigation. 23 23 Some authors have used onsumer shopping osts to revisit vertial relationships issues. See Caprie and von Shlippenbah 2013), Johansen and Nilssen 2016) and Caprie and Shekhar 2017). 23
7 Referenes ACNielsen 2005), "The Power of Private Label: A Review of Growth Trends Around the World", available at http://www.seve.gr/wp-ontent/uploads/2007/07/ 2005_privatelabel.pdf; Avenel, E. and S. Caprie 2006), "Upstream market power and produt line differentiation in retailing", International Journal of Industrial Organization, 24, 319-334; Bahiega, E. and O. Bonroy 2015), "On the benefits of ontratual ineffi ieny in quality-differentiated markets", Oxford Eonomi Papers, 673), 846-863; Bergès-Sennou, F. 2006), "Store loyalty, bargaining power and the private label prodution issue", European Review of Agriultural Eonomis, 333), 315-335; Bergès-Sennou, F., Bontems, P. and V. Réquillart 2004), "Eonomis of private labels: a survey of literature", Journal of Agriultural & Food Industrial Organization, 21), artile 3; Bergès, F. and Z. Bouamra-Mehemahe 2012), "Is produing a private label ounterprodutive for a branded manufaturer?", European Review of Agriultural Eonomis, 392), 213-239; Bergès-Sennou, F. and M. Waterson 2005), "Private labels as experiene goods", Journal of Agriultural and Food Industrial Organization, 32), artile 9; Bonfrer, A. and P. K. Chintagunta 2004), "Store brands: Who buys them and what happens to retail pries when they are introdued?", Review of Industrial Organization, 24, 195-218; Bonnet, C. and P. Dubois 2010), "Inferene on vertial ontrats between manufaturers and retailers allowing for nonlinear priing and resale prie maintenane", RAND Journal of Eonomis, 411), 139-164; Bonroy, O. and S. Lemarié 2012), "Downstream labeling and upstream prie ompetition", European Eonomi Review, 563), 347-360; Bontemps, C., Orozo, V. and V. Réquillart 2008), "Private labels, national brands and food pries", Review of Industrial Organization, 33, 1-22; Bontems, P., Monier S. and V. Réquillart 1999), "Strategi effets of private labels", European Review of Agriultural Eonomis, 26, 147-165; Brander, J. A. and J. Eaton 1984), "Produt line rivalry", Amerian Eonomi 24