private label positioning: quality versus feature ... · journal of retailing 82 (2, 2006) 79–93...

Journal of Retailing 82 (2, 2006) 79–93

Private label positioning: Quality versus featuredifferentiation from the national brand

S. Chan Choi a,∗, Anne T. Coughlan b,1

a Marketing Department, Rutgers Business School, 180 University Avenue, Newark, NJ 07102, USAb Marketing Department, Kellogg School of Management, Northwestern University, Evanston, IL 60208-2008, USA

Abstract

This paper investigates the retailer’s problem of positioning her private label against two national brands in terms of both product quality andproduct features. Using a demand function derived from consumer utility, we show that the private label’s best positioning strategy dependson the nature of the national brands’ competition and its own quality. When the national brands are differentiated, a high quality private labelshould position closer to a stronger national brand, and a low quality private label should position closer to a weaker national brand. Whenthe national brands are undifferentiated, the private label should differentiate from both national brands.© 2006 New York University. Published by Elsevier Inc. All rights reserved.

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eywords: Private label; National brand—private label competition; Private label positioning; Product quality; Product features; Vertical and horizontalifferentiation

Introduction

By 1999, private label products (or equivalently, storerands) accounted for over 20 percent of supermarket unitales and 15.7 percent of dollar sales (Williams 2000). In 77f 250 supermarket product categories, private labels in the.S. collectively have higher unit market shares than their

trongest nationally branded competitor, while they are sec-nd or third in 100 of those categories (Quelch and Harding996). Among other retailer benefits, private labels add diver-ity to the product line in a retail category (Raju et al. 1995;oberman and Parker in press). This product differentiationan reflect quality differences or just differences in features.1

∗ Corresponding author. Tel.: +1 973 353 5635; fax: +1 973 353 1325.E-mail addresses: [email protected] (S. Chan Choi),

[email protected] (A.T. Coughlan).1 Tel.: +1 847 491 2719; fax: +1 847 491 2498.1 The analytic modeling literature refers to quality differentiation as verti-al differentiation and to feature differentiation as horizontal differentiation.quality attribute is one for which a consumer’s ideal point is infinite (more

s always better). A feature attribute is one for which a consumer’s ideal

Improvements in both packaging/features as well as qualityhave been partially responsible for private label sales growthin U.S. grocery retailing in the late 1980s (Wellman 1997).How to position a private label product in competition withnational brands is thus an extremely important managerialquestion. However, it is still not well understood how theprobable relationship between quality and feature position-ing affects the profitability of private labels, nor how varyingdegrees of feature differentiation between national brandsaffect the optimal positioning of the private label. We attackthese questions in the present research and show that enrich-ing our analytic understanding of these issues affects thepredictions about how retailers can optimally position theirprivate labels in competition with national brands.

Quality differentiation usually exhibits itself through theperception that private labels are of lower quality than thecorresponding national brands (e.g., Ann Page canned soups– the A&P grocery chain’s former private label – were widelyviewed as lower quality than Campbell’s canned soups).2

2 One of the authors met and interviewed the son of the flavor chemist
oint is finite (e.g., color, package size, labeling, flavor). The legal liter-ture’s discussion of “trade dress” is a reference to feature differentiationor the lack thereof) through such attributes as packaging and labeling.
for A&P’s private label products. This unfortunate man was forced to eatAnn Page private label products, including canned soups, throughout hischildhood. He readily admitted that the Ann Page brand was significantly

022-4359/$ – see front matter © 2006 New York University. Published by Elsevier Inc. All rights reserved.
oi:10.1016/j.jretai.2006.02.005
mailto:[email protected]

mailto:[email protected]

dx.doi.org/10.1016/j.jretai.2006.02.005

80 S. Chan Choi, A.T. Coughlan / Journal of Retailing 82 (2, 2006) 79–93

Quality differentiation is based on the notion that the char-acteristic on which differentiation occurs is one for whichall consumers value the highest possible level (all else heldconstant – such as price). A superior quality national brandmay lose its quality differentiation from the private labelif private-label retailers are eventually able to match thenational brand’s technology and perception (e.g., President’sChoice cookies compared to the national brand Chips Ahoy).However, the quality differentiation literature predicts that asecond product – a private label in our context – in the marketwould find it optimal to differentiate itself by offering a lowerquality product than that of the market leader (Shaked andSutton 1982; Moorthy 1988). For instance, Moorthy obtainsa quality-price equilibrium where two brands are positivelybut finitely separated in their quality levels. Likewise, Desai(2001) shows that, in a competitive scenario, firms optimallyoffer different quality products respectively for different mar-ket segments.

In contrast, feature differentiation refers to the degree towhich products have different forms, sizes, or packaging.Different brands in a category may exhibit little feature dif-ferentiation (e.g., McCormick and Spice Islands spices bothcome in jars that fit the standard kitchen spice rack, andboth brands sell a broad range of commonly-used spices),or more significant feature differentiation (e.g., Progressocanned soup comes in a pop-top can while Campbell’srlPatt“vpheuofs(teibmna(n

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independence between the two dimensions of differentia-tion.

Many private label retailers have purposely sought to min-imize feature differentiation from national brands, by mak-ing their packaging, sizes, typeface, and labeling extremelysimilar to their respective target brands. In a mid-1990s law-suit against Venture Stores, Inc., Unilever alleged trademarkinfringement of Venture’s lotion for mimicking its VaselineIntensive Care Lotion (Harvey et al. 1998). However, thecourt ruled in Venture’s favor, stating that the Venture storebrand’s label explicitly invited the consumer to compare Ven-ture’s product with its target brand.

Two interesting features of this case deserve mention inour context. First, the principle upheld was the legality ofminimum feature differentiation (or horizontal differentia-tion, in economic and legal terms); but one of the basicinsights of location modeling is the optimality of maximumfeature differentiation. Second, while the apparent issue isthe lack of pure feature differentiation through trade dressimitation, it would seem intuitively that Venture was also try-ing to signal a product of similar quality to its consumers.This suggests that in many real-world cases, the retailer’spositioning of the private label inherently involves bothfeature and quality positioning messages to its consumers.The concept of differentiation of the private label from thenational brand is thus not a unidimensional concept. Theoipvipd

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equires a can opener; Kleenex brand facial tissues inter-ock, enabling a special top-of-box dispensing feature, whileuffs brand dispenses out of a larger hole spanning the topnd side of the box, and can dispense multiple tissues at aime). Unlike a “quality” characteristic, a “feature” charac-eristic of a product is one for which “more” is not alwaysbetter,” and can include characteristics where variety isalued by the consumer. For example, the consumer mayrefer full-sized facial tissue boxes in some rooms of theouse, versus the “boutique” size in other rooms; differ-nt flavors of jam, yogurt, or other food products; or liq-id versus powder plant fertilizer for different sized plantsr for indoor versus outdoor use. When products are dif-erentiated only through feature differences, the literatureometimes finds that minimum differentiation is optimalHotelling 1929), and other times that maximum differen-iation is the equilibrium (d’Aspremont et al. 1979). Saymant al. (2002) add a third brand (a private label) in their model,n which the two incumbent national brands are assumed toe maximally feature-differentiated. They find that it is opti-al for the private label to imitate the stronger of the two

ational brands. Their empirical study reveals that althoughstore brand is often made to look like a national brand

i.e., minimizes feature differentiation), an imitation mayot have much impact on its quality perceptions, indicating

orse than the national brand competitors. This depiction of the privateabel as lower quality than the national brand is consistent with standardepresentations in the literature as well; see, for example, Soberman andarker (in press).

verall interchangeability or substitutability between thems a function of both quality and feature differences acrossroducts, and the retailer’s positioning choice for its pri-ate label will naturally reflect both dimensions.3 Our modelnvestigates the nature of national brand-private label com-etition in a market characterized by both quality and featureifferentiation.

In sum, this paper moves beyond the existing literaturen several dimensions. It allows for the purchase of multi-le brands within a product category, a phenomenon thats seen in many commonly purchased categories but notxplicitly considered in the modeling literature. It allows theegree of feature differentiation between the private labelnd competing national brands to vary, and the results showhat this has a substantive effect on the private label’s opti-

al position in the marketplace. It examines the interactionetween feature and quality differentiation, considering thatne may be correlated with the other, and shows that this

3 The inclusion of more than one dimension of differentiation has beenonsidered in the location-modeling literature. One such model was pro-osed by Vandenbosch and Weinberg (1995), who assume that the productseing sold are characterized by two quality dimensions. Their equilibriumolution is “max-min” differentiation in which the strong brand locates athe best position (i.e., high quality on both product dimensions) and the sec-nd brand chooses maximum differentiation in one dimension and minimumifferentiation in the other in a large part of the parameter space. While theirodel does consider two dimensions, they do not consider the differences

etween quality differentiation and feature differentiation; further, theirs is aocation model with fixed total category demand, as opposed to our flexibleemand utility-based model.

S. Chan Choi, A.T. Coughlan / Journal of Retailing 82 (2, 2006) 79–93 81

affects the profitability of optimal positioning of the privatelabel. And finally, this work is grounded in consumer util-ity theory, and does not rely on ad hoc specifications of thedemand function; we show that this affects the interpretationof the effect of demand parameters on optimal position-ing of the private label in a way that prior work has notdone.

In what follows, we first introduce a model of two compet-ing national brands and one private label. Although closed-form solutions can be derived for the private label’s optimalstrategy, they are too complex for meaningful interpretation.Therefore, we resort to numerical methods to investigate theirproperties in the following section. One of our key find-ings is that, when the two national brands are significantlydifferentiated in their features, the private label’s optimalstrategy is to minimize feature differentiation from one of thenational brands. Further, its target brand to imitate dependson its own quality level: when its quality is high, the pri-vate label should imitate the stronger brand; otherwise, theweaker one. But when two incumbent national brands arefeature-undifferentiated (e.g., offer similar flavors and pack-aging), the retailer is better off maximally differentiating herprivate label from the national brands in the feature dimen-sion. In addition, we investigate the impact of private labelpositioning on national brand profits. The last section sum-marizes of our results and delineates directions for futurer

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Feature differentiation can be a profitable strategy in cat-egories where consumers buy just one unit if they are seg-mented into groups with different valuations placed on thefeature dimension of the product. But it can also be usefulin a market where individual consumers value variety, androutinely buy and hold multiple different brands in a productcategory. This is an extremely common occurrence: we polleda convenience sample of nine (9) respondents to ask in whatcategories they hold both private labels and national brands.The sample revealed that joint holdings of private labels andnational brands were present in 10.8 product categories perhousehold on average. Categories mentioned by more thanone respondent include (in alphabetical order, with numbersof respondents mentioning the category): butter/margarine(three), cereal (three), cheese (three), cookies (two), cook-ing oil (three), soaps (five), jam (three), juice (three), lunchmeat (two), milk (two), paper towels (four), pasta (three),plastic storage bags (six), spices (two), sugar (two), tea bags(four), and tomato sauce (two). Table 1 reports more detailon the findings, including reasons given for holding both anational brand and a private label; for example, in the papertowel category, it was common for the respondent to say thatshe puts national brand paper towels in the kitchen, typicallyfor texture or form (one household has half-size paper towelsheets in the kitchen, available only as a national brand, tominimize waste), and to stock private label paper towels withht

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esearch.

The model

In this section, we present a triopoly (three-product)emand model derived from a consumer utility framework.he three products are two national brands and one private

abel. The two national brands can have various degrees ofeature and/or quality differentiation. In some product cate-ories (such as teabags), two leading national brands (Liptonnd Twining’s) are not highly differentiated in features (e.g.,avors, nature of the teabag). On the other hand, in a cat-gory like copy paper, products are differentiated in theireatures (e.g., paper suitable for black-and-white printing ver-us color printing), and the retailer would typically decideo position its private label between the different featuresffered by the national brands. This is in fact what Officeepot does, offering private label copy paper for black-

nd-white copying but not for color copying.4 However, inhe teabags case, the private label tea may have anotherption than imitating the two similar national brands—it mayifferentiate “outside the space” between the two nationalrands. Indeed, in the author’s kitchen, the private labeleabag is peppermint flavored tea, which is not available in the

ajor national brands, but is valued for its different (flavor)eature.

4 Source: Office Depot catalog, issue valid through 10/19/2004.

ousehold cleaning supplies, where it was felt that any paperowel would be satisfactory.

This very common type of response indicates clearly thatonsumers routinely do buy and hold both national brandsnd private labels, and do so for various reasons, some basedn form differentiation (e.g., flavor [teabags, jams, cookies,nd lunchmeat], package sizes [rice, potato chips], or formpowder and liquid fertilizer]), and some based on qual-ty needs (e.g., national brand stewed tomatoes are higheruality, but the higher quality is not needed in all recipes;ome respondents reported using private label teabags foreveryday,” saving national brand teabags for special occa-ions or visitors). Brands can of course differ in both qualitynd features (e.g., Ziploc storage bags are viewed as bothigher quality than the store brand, and different in formecause they come in different sizes and with different “zip-er” technologies). Finally, note that our research focus isn the strategic question of how a private label should beositioned against national brand competition; at this levelf inquiry, it is important to take account of actual holdingf products in the home, to understand the position that pri-ate labels serve in the household’s consumption and henceurchase patterns. Given the broad set of products men-ioned by respondents, it is therefore reasonable to expand thecope of inquiry to explicitly consider multi-unit, multi-brandurchases in a category. We capture this in our demand func-ions, which are derived from a consumer utility-maximizingramework.

Our representative consumer utility function takes the fol-owing standard quadratic form widely used in economics


Table 1Summary of consumer survey of holding/usage of both national brand and private label products in the household

Respondent Categories in which household holds bothnational brand and private label

Reasons for holding both national brand andprivate label in the household

One (married couple with oneteenager at home)

Bathroom cleaners, coffee, facial tissue, jam,juice, light bulbs, lotion, pain relievers, papertowels, plastic storage bags, shampoo, tea bags,vitamins

Taste/sensory differentiation (coffee, jam, juice,tea bags); different forms fit different uses forsame product category (bathroom cleaner, lightbulbs, plastic storage bags, vitamins), everydayversus “special” use (facial tissue, lotion, papertowels), stocking up but no perceiveddifferentiation (pain relievers), different familymembers have different favored products(shampoo)

Two (married couple with oneteenager at home)

Cereal, cheese, flour, garbage bags, jam,ketchup, oatmeal, paper towels, plastic storagebags, rice, soap, soda, spices, tea bags

Taste/sensory differentiation (cheese, jam, soap,soda, spices); different forms fit different usesfor same product category (flour, garbage bags,oatmeal, paper towels, plastic storage bags,rice), everyday versus “special” use (tea bags),different family members have different favoredproducts (cereal, ketchup)

Three (married couple, no kids,husband’s job is out of town)

Coffee creamer, cooking oil, milk, soap, socks,soup/broth, spices, sweetener, yogurt

Taste/sensory differentiation (milk, spices,yogurt); different forms fit different uses forsame product category (soap, soup/broth,sweetener), stocking up but no perceiveddifferentiation (coffee creamer, cooking oil,socks), different family members have differentfavored products (milk)

Four (married couple, five youngchildren, kitchen is beingremodeled)

Bacon, butter, cookies, creme rinse (for hair),frozen vegetables, lunch meat, paper plates,plastic storage bags, soap, sugar

Taste/sensory differentiation (butter, cookies);different forms fit different uses for sameproduct category (bacon, lunch meat, paperplates, plastic storage bags, sugar), everydayversus “special” use (soap), different familymembers have different favored products (cremerinse, frozen vegetables)

Five (married couple with four boys) Aluminum foil, butter, cereal, granola bars,juice, lotion, mustard, pancake mix, pasta,pickles, plastic storage bags, salsa, seafood sauce

Taste/sensory differentiation (cereal, salsa);different forms fit different uses for sameproduct category (granola bars, juice, pancakemix, pickles), stocking up but no perceiveddifferentiation (aluminum foil, butter, lotion,mustard, pasta, plastic storage bags, seafoodsauce)

Six (married couple, “emptynesters”)

Cheese, cooking oils, milk, paper towels, pasta,plastic storage bags, popping corn

Taste/sensory differentiation (cooking oils);different forms fit different uses for sameproduct category (milk, pasta, plastic storagebags, popping corn), everyday versus “special”use (cheese, paper towels)

Seven (married couple with two kids) Bread, butter/margarine, cheese, dog treats,olives, paper towels, pasta

Taste/sensory differentiation (olives); differentforms fit different uses for same productcategory (bread, butter/margarine, dog treats,paper towels), everyday versus “special” use(cheese),stocking up but no perceiveddifferentiation (pasta)

Eight (married couple with two kids) Bread crumbs, canned tuna, cereal, dried fruits,dried beans, nuts, tea bags, tomato sauce, vinegar

Taste/sensory differentiation (bread crumbs,dried fruits, nuts, tea bags, vinegar); differentforms fit different uses for same productcategory (canned tuna, dried beans, tomatosauce), different family members have differentfavored products (cereal)

Nine (married couple with two kids) Ballpoint pens, canned baked beans, cookies,cooking oil, hot dog buns, jam, juice, laundrydetergent, lunch meat, plant fertilizer, plasticstorage bags, potato chips, reams of printingpaper, stewed tomatoes, tea bags

Taste/sensory differentiation (cookies, cookingoil, jam, lunch meat, stewed tomatoes, tea bags);different forms fit different uses for same productcategory (ballpoint pens, canned baked beans,laundry detergent, plant fertilizer, plastic storagebags, potato chips), everyday versus “special”use (reams of printing paper),stocking up but noperceived differentiation (hot dog buns, juice)


(Dixit and Stiglitz 1977; Singh and Vives 1984; Hackner2000):

U(q1, q2, qp) = (α1 − p1)q1 + (α2 − p2)q2 + (αp − pp)qp

− 12 (β1q

21 + β2q

22 + βpq2

p + 2γ12q1q2

+ 2γ1pq1qp + 2γ2pq2qp), (1)

where qi is the quantity of product i consumed and pi is theprice of product i (i = 1, p), and the subscript p represents theprivate label. The other parameters have standard interpreta-tions in utility theory, which can be seen by examining themarginal utility of consumption for the three products:

∂U

∂qi

= αi − βiqi − γijqj − γipqp − pi, i = 1, 2,

j = 3 − i;∂U

∂qp

= αp − βpqp − γ1pq1 − γ2pq2 − pp.

Clearly, the higher is any product’s α parameter, thehigher is the marginal utility of consumption of that product(whether national brand or private label); thus, α1, α2, andαp represent the intrinsic quality of each product. We assumethat min{α1, α2}> αp. The difference between αi and αp istherefore a measure of the quality differentiation between anational brand and the private label. The parameter βi (or βp)

following demand system:

q1 = 1

T[B1 − (β2βp − γ2

2p)p1 + (βpγ12 − γ1pγ2p)p2

+ (β2γ1p − γ12γ2p)pp], (2)

q2 = 1

T[B2 + (βpγ12 − γ1pγ2p)p1 − (β1βp − γ2

1p)p2

+ (β1γ2p − γ12γ1p)pp], (3)

and

qp = 1

T[B3 + (β2γ1p − γ12γ2p)p1 + (β1γ2p − γ12γ1p)p2

− (β1β2 − γ212)pp], (4)

where

T = β1β2βp + 2γ12γ1pγ2p − β1γ22p − β2γ

21p − βpγ2

12,

B1 = α1(β2βp − γ21p) − α2(βpγ12 − γ1pγ2p)

− αp(β2γ1p − γ12γ2p),

B2 = −α1(βpγ12 − γ1pγ2p) + α2(β1βp − γ21p)

− αp(β1γ2p − γ12γ1p),

B

tfttcb

tduoeevuahl

wionγ

al

measures the rate at which the marginal utility of consump-tion for product i (or p) declines with units of the productconsumed, or equivalently, the rate at which the consumerbecomes satiated with consumption of the product. It is nat-ural to assume that min{β1, β2}> βp, reflecting a steepermarginal utility decline for the less valued private label. Notethat this representative utility approach embodies aggregatepreference for diversity via parameters in the utility function.

Finally, the γ∈[0,β] parameters measure the rate of declineof marginal utility of consumption for one product withrespect to the consumption of one of the other products.For example, γ1p represents the interchangeability or sub-stitutability between products 1 and p. More specifically,γ2

1p/(β1βp)expresses the degree of feature differentiation,ranging from zero when the goods are independent to onewhen the goods are perfect substitutes (Singh and Vives1984).5 Therefore, the utility function (1) captures both qual-ity and feature differentiation between the national and storebrands.

The utility-maximizing consumer will optimally allocatethe quantities consumed by solving the first-order conditions:(∂U/∂q1) = 0, (∂U/∂q2) = 0, and (∂U/∂qp) = 0. Solving thesethree first-order conditions for q1, q2, and qp, we obtain the

5 Several papers including Blattberg and Wisniewski (1989) andSethuraman et al. (1999) document the existence of this asymmetric priceeffects between the two quality tier products. Actual modeling of this asym-metry requires a nondifferentiable demand function that is kinked at everyprice point, and developing such a model is beyond the scope of the currentstudy.

3 = −α1(β2γ1p − γ12γ2p) − α2(β1γ2p − γ12γ1p)

+ αp(β1β2 − γ212).

For the demand coefficients to have sensible signs and forhe second order conditions to be satisfied, we require βi ≥ γ ikor any {i,k}∈{1,2,p}, k �= i, and βp ≥ βi for i = 1,2. That is,he rates of decrease in own-marginal utilities are greaterhan cross-marginal utilities, and satiation occurs faster whenonsuming the private label than when consuming a nationalrand.

Note that these demand functions are in the same form ashat of the most popular linear demand function. However, ouremand coefficients are explicitly expressed in terms of thenderlying utility parameters. It is easy to see that changingne of the γ substitutability parameters, for example, nonlin-arly affects the intercept as well as all price coefficients ofach demand function. Therefore, our demand structure pro-ides clear insights into the effects of changes in underlyingtility parameters on market outcomes rather than postulatingd hoc own-price and cross-price effects on demand, whichas been much criticized as a major limitation of traditionalinear demand functions.

While national brand manufacturer i determines theholesale price (wi) for his product i whose quality level

s αi, the retailer’s decision is to choose the optimal levelf quality differentiation (αp) of her store brand from theational brands, the degree of feature differentiation (γ1p,2p) between its store brand and each of the national brands,nd the retail prices for the national brands and the privateabel (p1, p2, pp). Since the focus of our paper is on the


retailer’s decisions, we assume that α1 and α2 are alreadygiven.6 Observing the quality levels of the national brandsand anticipating subsequent price equilibrium, the retailerpositions her private label product in the quality and featuredimensions. Thus, our equilibrium is sub-game perfect, inwhich the second-stage price equilibrium is reached imme-diately after the differentiation decisions. Price competitionis modeled as a manufacturer-Stackelberg game, in whichmanufacturer i sets the national brand’s wholesale price(wi) anticipating the retailer’s pricing reaction in all threebrands.

The retailer is assumed to use product-line pricing aspart of category management. The manufacturer-Stackelbergpricing game is solved recursively, starting from the retailer’spricing decision. The retailer thus maximizes her combinedprofit:

Maximizep1,p2,ppΠR = (p1 − w1)q1 + (p2 − w2)q2

+(pp − νp)qp, (5)

where νp is the unit variable cost of the private label, whichis assumed to be an increasing function of αp (that is, creat-ing a higher-quality private label product results in a highermarginal cost of production). Solving the first-order condi-tions ((∂

∏R/∂p1) = 0, (∂

∏R/∂p2) = 0, (∂

∏R/∂pp) = 0) for p1,

p2, and pp, we obtain the following retailer reaction func-t

p

ttppchii

nnfilbtttn

moufHs

private label’s price to the level of the national brand’s whole-sale price.

Result 1. Suppose the demand is represented by a lin-ear function with symmetric cross price effects. When theretailer employs product-line pricing, the private label’s opti-mal price is independent of the national brands’ wholesaleprices.

However, as shown in Hall et al. (2004), a linear demandwith asymmetric cross-price effects produces interdependentreaction functions in category pricing. On the other hand,Moorthy (2005) shows that, when there is no retailer compe-tition (such as in our model), a linear demand function tendsto produce “balanced” retail pass-through rates where bothpositive and negative effects of the other brand’s cost changeare roughly cancelled out.

Given the retailer’s reaction functions (6), each manufac-turer’s pricing decision is to choose his wholesale price so asto maximize his short-term profit:

MaximizewiΠMi = (wi − vi)qi[pi(wi), pj(wj), pp],

(7)

where ν1 is his unit variable cost (w1 ≥ νi). Solving its first-oolcnlnfs

aβ

ctaqtnWtfnFa

ions:

1 = w1 + α1

2, p2 = w2 + α2

2, pp = αp + νp

2.

(6)

To guarantee that the retail margin is positive, we requirehat α1 ≥ w1. It is interesting to note that pp is independent ofhe national brands’ wholesale prices, even though the threeroducts are interrelated in demand. The retailer chooses therivate label’s price based only on its own quality and variableost. We found that this is a property of any linear demand thatas symmetric cross-price effects (i.e., (∂qi/∂pj) = (∂qj/∂pi),�= j).7 Under such a demand function, product-line pricingmplies that it is in the retailer’s best interest not to link the

6 Clearly, over a longer time frame the national brands’ quality levels areot given parametrically, but can be altered through product innovation by theational brand manufacturers. In the short run, however, national brands arexed in quality and indeed, the branding effort most manufacturers undertake

ocks them in to a specified quality range for their products, a key part of therand’s image. Given these considerations, we proceed with the assumptionhat the quality levels of the two national brands are fixed at �1 and �2. Notehat Sayman et al. (2002) also make this assumption, saying: “We assumehat NB positions are fixed. Although NBs may prefer to reposition, it doesot happen often even over the long run.”7 Symmetric cross-price effects emerge from any general utility maxi-ization framework. Asymmetric cross-price effects, which are sometimes

bserved in grocery scanner panel data, could arise in some non-standardtility circumstances: for example, where the consumer gets utility not justrom consuming product, but from getting a “good deal” on price as well.owever, such departures from standard utility formulations are beyond the

cope of the present work.

rder condition, we can derive closed-form solution of theptimal wholesale prices. Also, by substituting these equi-ibrium wholesale prices into the reaction functions (6), wean derive closed-form equilibrium retail prices for the twoational brands and the store brand as well as all other equi-ibrium quantities. However, these solutions are complex andot amenable to immediate analytic interpretation.8 We there-ore investigate their properties numerically in the followingections.

Investigating the equilibrium solution’s properties

The closed-form equilibrium quantities are very messynd are functions of the nine utility parameters (α1, α2, αp,1, β2, βp, γ12, γ1p, γ2p) and the manufacturers’ variableosts (ν1, ν2, νp). Moreover, with the parameter restric-ions imposed in the previous section, the solutions are notmenable to analytical analysis, because the equilibriumuantities are discontinuous and highly nonlinear outsidehe parameter ranges. Therefore, we resort to an extensiveumerical analysis to examine the equilibrium properties.e first present the results from our full model in which

he two national brands are significantly differentiated ineatures, and then discuss a special case in which the twoational brands are not significantly feature-differentiated.or simplicity, we assume all variable manufacturing costsre normalized to zero.

8 The solutions are presented in Appendix A.


Case 1: The two national brands are differentiated in thefeature dimension

To examine a case where the two national brands arefeature-differentiated, we start by denoting γ12 = γ > 0 forease of exposition. The feature-positioning decision for theretailer involves deciding where to place the private labelin the range of features represented by the national brands’differentiation. Suppose that the private label “perfectly” imi-tates national brand 1: i.e., γ2

1p/(β1βp) = 1. Since βp ≥ β1,perfect substitution would occur at γ1p ≥ β1, beyond theallowable range. That is, as long as βp > β1, the private labelcannot be a perfect substitute (in the feature dimension) forthe national brand. In this case, we let γ1p = β1 and γ2p = γ

(that is, the private label and national brand 1 are equallyfeature-differentiated from national brand 2). The conversestatements are true when the private label imitates nationalbrand 2.9

We make some assumptions to improve the tractability ofthe analysis:

• β1 = β2 = β (that is, the marginal utility parameter fornational brand 1 equals that for national brand 2).

• We normalize by setting β = 1 without loss of generality,but retain a key assumption that βp ≥ β = 1.

• α1 ≥ α2 ≥ αp (with full generality, we designate national

•

eavktae(tunqo

β

svriglaf

γ

Fig. 1. Retailer profit in vertical and horizontal differentiations. (Parametervalues used: α1 = 1.1, α2 = 1.0, β = 1, βp = 1.5, γ = 0.5.).

shape. A typical shape of the retailer profit function, lettingαp and k both vary, and given a set of specific utility parame-ters (α1 = 1.1, α2 = 1.0, βp = 1.5, γ = 0.5), is shown in Fig. 1.The key reason we care about these convexity characteris-tics of the retail profit function is its immediate implicationthat the retailer will make the most profit by choosing eitherminimum or maximum values of both feature and quality dif-ferentiation from the national brand; some intermediate levelof differentiation is less profitable. In the following, we firstexamine the retailer’s profit function with specific parametervalues, and then employ an extensive sensitivity analysis toshow that the properties can be generalized to all values inthe feasible parameter domain.

Effects of quality differentiationFig. 1 shows that the retailer’s profit initially decreases as

the private label’s quality (αp) increases, and then increasesas it approaches that of the second national brand (α2 = 1).As defined above, this means equivalently that retail profit isconvex in αp. This convexity can be verified by checking thesign of the second order derivative of ΠR with respect to αp inall feasible utility parameter domains. The result of this sen-sitivity analysis is presented in Appendix A (Fig. A1), whichresults from a numerical computation of the minimum valuesof ∂2ΠR/∂α2

p with respect to αp and k for a set of 16 even-ictrpirio(

It

brand 1 as the higher-quality brand).νp = 0 (the variable cost of private label production is nor-malized to zero).

Our assumption that β1 = β2 = β implies the following lin-ar rule for the feature position of the private label:γ1p = β − knd γ2p = γ + k, where k∈[0,(β − �)]. When k = 0, the pri-ate label horizontally imitates national brand 1; and when= β − γ , it imitates national brand 2. With these specifica-

ions, equilibrium prices, quantities, and profits in the channelre thus functions of α1, α2, αp, βp, γ , and k. We can thenxamine the retailer’s decisions on its private label’s quality0 ≤ αp ≤ α2) and its feature differentiation (0 ≤ k ≤ (β − γ))hat maximize her total profit, as functions of the fundamentaltility parameters: γ (the feature differentiation between theational brands), βp (the private label’s unattractiveness asuantity consumed increases), and the relative quality levelsf the two national brands (α1 and α2).

For any specific values of the utility parameters (α1, α2, αp,p, and γ) that satisfy the conditions discussed in the previousection, we numerically show that the retailer’s profit is a con-ex function of k as well as αp. This means that as k increases,etail profit first falls, and then eventually rises with furtherncreases in k; and similarly for increases in αp. In short, araph of profit as a function of k (holding αp constant) wouldook like a “U” shape, with the highest values at the minimumnd maximum value of k, and similarly, a graph of profit as aunction of αp (holding k constant) would also look like a “U”

9 For numerical exploration, we examine the parameter range up to

1p = β1.

nterval sample values of βp∈[1.2, 2] and γ∈[0, 0.7], whichover the reasonable parameter domain. The Figure showshat the second order derivative of the retailer’s profit withespect to the quality parameter (αp) is nonnegative for allotential values of βp and γ (for any fixed α1 and α2), imply-ng that retailer profit is convex in its private label’s qualityegardless of the utility parameter values. This immediatelymplies that maximum retailer profit occurs where αp takesn either its minimum value (of zero) or its maximum valueof α2).

To establish which of these is optimal, consider next Fig. 2.n Fig. 2, the lower curve shows a set of points for whichhe retailer’s profit is invariant with respect to a change in


Fig. 2. Parameter region for feasible differentiation. (Parameter values used:α1 = 1.1, α2 = 1.0, β = 1, βp = 1.5, γ = 0.5.). Note: The feasible region (wherethe private labels demand is positive) is completely within the region inwhich the retailer’s category profit increases as the private label’s qualityincreases. Suppose the private label’s quality is 0.85. Due to the convexityof the profit function with respect to the feature differentiation parameter k,the optimal differentiation is the corner solution within the feasible region:i.e., either point A or B. Our numerical solution in Table 2 shows that pointA (k = 0.0396) provides higher retailer profit than point B (k = 0.5).

αp. Below this curve (in the white area of the Figure), theretailer’s profit decreases in αp; above the curve (in both thelight gray and dark gray regions of the Figure), it increasesin αp.

However, not all pairs of (αp, k) are feasible strategies forthe retailer. When the private label’s quality is below a certainlevel (αp), its demand becomes negative, and this defines thefeasible quality range for the private label. This minimumquality level depends on the degree of feature differentiationof the private label (k). That is, for demand to be nonnegative,the private label’s quality cannot be lower than the mini-mum quality αp(k). In Fig. 2, the upper curve (the boundarybetween the light gray and dark gray regions) represents theminimum quality function αp(k).

Now we are interested in finding the properties of theretailer’s profit within this feasible region. We note in Fig. 2that the feasible strategy region is contained within the regionwhere quality increases lead to profitability increases. There-fore, the retailer finds it in her best interest to increase thequality of the private label up to that of the second nationalbrand, as long as the quality cost is negligible. These insightstogether lead to Result 2.

Result 2. For a fixed value of the feature substitutabilityparameter γ and costless private label quality (αp) improve-ment, it is optimal for the retailer to seek minimum qualitydm

w

a strategic motive for private label positioning. When higherquality implies a higher cost, our results more closely matchthose from some location models in the economics litera-ture (e.g., Shaked and Sutton 1982; Tirole 1989) which usequadratic cost functions to obtain interior quality solutions.When it is costly to increase private label quality, minimumquality differentiation will not always be the best decision(for example, private-label liquid laundry detergent is notwidely viewed as having a quality level equal to that of thenational brands). The functional form of the cost functionthen tempers the incentive to increase private-label quality,but does not invalidate the quality-increasing incentive weuncover here.

We move next to a discussion of the effects of featuredifferentiation, in which we assume that the private label’squality has already been set at certain feasible level.

Effects of feature differentiationFocusing now on feature differentiation of the private

label, we establish in this section that due to the convex-ity of the retailer profit in feature differentiation (k), it isnever optimal for the retailer to position her private labelbetween two national brands that are themselves significantlyfeature-differentiated. Instead, given national brand featuredifferentiation, it is optimal for the private label to minimallydanftfitfhtwg

(futeci(tuifptA“ia

ifferentiation from the second national brand (i.e., to maxi-ize the private label’s quality level).

Note that our minimum quality differentiation result holdshen quality choices can be freely made and it hence reflects

ifferentiate from one of the two national brands. Raju etl. (1995) and Sayman et al. (2002) find that when the twoational brands are of different quality, it is always optimalor the store brand to imitate the stronger national brand. Butheir interpretations of what we call feature and quality dif-erentiation are not derived from utility fundamentals as ourss and do not therefore fully represent the interaction amonghe national brands and the store brand.10 In our utility-basedormulation, we do show that if the store brand’s quality isigh enough, it is optimal to feature-position it closest tohe higher-quality national brand, as these authors do. Buthen the private label’s quality is sufficiently low, it cannotenerate positive sales volume when feature-imitating the

10 The demand functions posited by Raju et al. (1995) and Sayman et al.2002) are essentially the same. The reason our finding concerning optimaleature positioning differs from theirs lies in our derivation of demand fromtility fundamentals. Raju et al. acknowledge the “assumed linearity” ofheir demand function but do not consider utility-derived demand functionsxplicitly. Sayman et al. (2002) say “we assume that positioning affects onlyross-price sensitivity and not other attributes such as quality. This is a lim-tation of our model . . .” Both sets of authors assume cross-price sensitivitythe derivative of private-label demand with respect to the price of one ofhe national brands) to be represented by a single parameter �i, while ourtility-based formulation (see Eqs. (2) through (4) above) shows that it isn fact a much richer function of all of the marginal-utility variables. Ourormulation indeed does show that a change in feature positioning – our γ

arameter – affects both the cross-price demand effect and the intercept ofhe demand function (what Sayman et al. call the “base level of demand”).lthough Sayman et al. argue that their simpler model formulation gives

clean” results, our analysis shows that the results are not fully general-zeable, and that optimal feature positioning does indeed have to take intoccount the quality of the private label relative to the national brands.


higher-quality national brand; we show that when this is so,imitating the feature positioning of the lower-quality nationalbrand is the most profitable retailer strategy.

As a basis for these results, we first examine the general-ity of the convexity of retail profits with respect to k withinthe parameter region. Convexity of a function means that thefunction is shaped like a “U” with respect to the variable ofinterest: thus, the function takes on its highest values whenthe variable is either very low or very high. In our context,we establish that the retailer’s profit function is convex withrespect to k, that is, that minimal or maximal feature dif-ferentiation of the private label produces the highest profits– not some intermediate level of feature differentiation. Weshow this convexity in Appendix A (Fig. A2) for all utilityparameter values, not just the ones used to create Fig. 1. Thus,the retailer’s optimal feature positioning for the private labelis either as close as possible to the higher-quality nationalbrand, or to the lower-quality national brand.

Given the convexity of the profit function, the retailer’soptimal feature position might seem to be to imitate thestronger national brand as in Sayman et al. (2002).11 How-ever, given our utility function specification, we are able toshow that national brand 1 can be of so much greater qual-ity that a private label trying to imitate it in features simplycannot sell a positive quantity. In Fig. 2, for example, wenote that the feasible (i.e., positive-demand) range of fea-tnu1pα

tbl1tlα

tatttrqoebqα

t

d

Lastly, we note that in order to guarantee a nonnegativedemand for the private label (given the other parameter val-ues in this example), the minimum possible quality for theprivate label is αp = 0.7475, in which case the only feasiblefeature differentiation is k = 0.2898 (as seen in the bottom rowof Table 2). Bold numbers in the profit columns in Table 2indicate the optimal feature positioning of the private labelat various quality levels. At a “high” intrinsic quality level(i.e., 1.000 ≥ αp ≥ 0.900), the private label’s optimal feature-position is closer to the stronger national brand. When itsintrinsic quality is relatively lower (i.e., 0.900 ≥ αp ≥ 0.850),the private label still optimally imitates the stronger brand,but not up to the “maximum” level. Within the range of0.850 ≥ αp ≥ 0.7475, however, the optimal feature-positionof the private label is to move closer to the weaker nationalbrand. We formalize this in Result 3 below.

Result 3. A higher-quality private label is better off posi-tioning closer to the stronger national brand, while a lower-quality private label is better off positioning closer to theweaker national brand.

Combining insights from the above two subsections, wefind that it is optimal for the retailer to position the pri-vate label (a) with minimum quality differentiation from thenational brands, and (b) with minimum feature differentiationfbTtpwaqlonpftiittnifib

isifwd

ure differentiation (k) of the private label between the twoational brands depends on its quality level (αp). In this Fig-re, national brand 1 has a quality parameter α1 equal to.1, while the lower-quality national brand 2 has a qualityarameter α2 equal to 1.0. Then consider an example wherep = 0.95, that is, where the private label’s quality is close

o, but not quite equal, to that of the lower-quality nationalrand. In the example in Fig. 2, it is optimal for the privateabel to maximally imitate the higher-quality national brand. However, as discussed above, it cannot be a perfect substi-ute for the national brand because its β parameter is strictlyower. When the private label’s quality drops further to, sayp = 0.85, the closest possible (or “maximum”) imitation of

he stronger brand is k = 0.0396 (Point A), which produceshigher total retailer profit than the maximum imitation of

he weaker brand k = 0.4936 (Point B). Any closer imitationhan this (any value of k less than 0.0396) results in nega-ive demand for the private label product (see Table 2 for allelated numerical quantities). Thus, when the private label’suality is not “high enough,” pretending to be a knock-offf the stronger brand may not be convincing enough to gen-rate positive demand. The private label’s quality needs toe sufficiently high if it is to be positioned against a high-uality national brand. At an even lower quality level (belowp = 0.85), however, it is optimal for the private label to imi-

ate the weaker brand.

11 Raju et al. (1995) do not consider the possibility of national brands withifferent quality levels.

rom one of the two national brands, with the targeted nationalrand depending on the private label’s given quality level.he minimum quality differentiation result intuitively means

hat the private label’s quality should be improved as far asossible; this is because quality is a product characteristic forhich more is always better than less, in the consumer’s eyes,

nd therefore the private label does best at the highest possibleuality level. The feature differentiation result, given a qualityevel for the private label, is an interesting and non-obviousne. Given the already-existing feature differentiation of theational brands, and consumers’ utility placed on variety, therivate label intuitively does best maximizing its differencerom one of the national brands. This is only possible by imi-ating the feature positioning of the other national brand. Thenteresting question is then which national brand to imitaten features? The private label is best off imitating the fea-ure positioning of the lower-quality national brand becausehis positions it head-to-head against the least threateningational brand (from a quality perspective)—thus maximiz-ng its sales potential. If the private label were to imitate theeature position of the higher-quality national brand instead,ts sales would suffer more, due to the greater discrepancyetween its quality and that of the stronger national brand.

An example of minimum feature differentiation is Pres-dent’s Choice chocolate chip cookies, which mimics thetronger national brand Chips Ahoy rather than another lead-ng national brand like Pepperidge Farm. Pepperidge Farmeature-differentiates by offering larger individual cookies,ith fewer cookies per package and different packagingesigns and materials. It is perceived as being a higher-


Table 2Optimal private label differentiationa

quality cookie than Chips Ahoy. President’s Choice cook-ies physically resemble the Chips Ahoy cookie in texture,taste, and packaging (dimensions of feature differentiation),and are generally viewed as being of comparable qualityto Chips Ahoy. Another example, focused on quality posi-tioning, occurs with paper towels. A&P’s store brand papertowel ($1.29 per roll) resembles the weaker brand Marcal($1.69) in package colors and “look-quality” more than itdoes the market leader Scott ($1.89). The Marcal brand ismade from recycled paper, which generally implies a lowerquality, whereas the store brand’s quality is perceived to besignificantly lower than that of the market leader’s.

These results characterize the optimal positioning strat-egy of the private label when competing with two feature-differentiated national brands. In the next section, we con-sider the private label’s positioning strategy when facing twonon-feature-differentiated national brands.

Case 2: The two national brands are undifferentiated inthe feature dimension

When the two national brands lack feature differentia-tion, the private label can have another option for its featurepositioning—to differentiate from both national brands. Theteabag example mentioned above exemplifies this choice; thenational brands offer similar flavor choices, and the storebA

on Jewel Food Stores’ shelves are Smuckers and Welch’s.While both are high-quality brands, Smuckers is more asso-ciated with jams, while Welch’s is more associated with grapejuice, and therefore might exhibit a lower quality (α) parame-ter. Both national brands offer an array of jam flavors, but theJewel brand offers flavors that neither national brand does(blueberry preserves, cherry preserves, and blackberry jamwere stocked on the store shelf in the Jewel brand but not ineither of the national brands). In a category like this whereconsumers value variety and routinely buy and stock multipleflavors in their homes, feature-differentiation through flavoris chosen by the store managing its private label. While theteabag and jam categories do exhibit some feature differen-tiation between the national brands, we analyze this sort ofbehavior by simplifying to assume the feature differentiationis absent. A small degree of feature differentiation will notalter the model’s results.

In our demand functions (2)–(4), having undifferentiatednational brands would mean that γ1p = γ2p = γp from our pri-vate label’s point of view: that is, the private label is equallydifferentiated from both national brands in the feature dimen-sion. Further, a lack of feature differentiation between the twonational brands means that consuming a unit of either one hasan equal effect on the marginal utility of consuming an incre-mental unit of one of the brands. Mathematically, this impliesthat the cross-price demand parameter (γ12) is essentially thest

rand offers a completely different choice: peppermint tea.nother example is the jam category. Two national brands

ame as the own-price demand parameter (β1 = β2 = β); buto insure that the problem has an interior solution, we need to


introduce a small number ε such that γ12 = β − ε, where werecollect that γ12 is the cross-product substitutability param-eter between the two national brands.

We can derive closed-form solutions for the equilibriumprofits of the retailer and manufacturer, as well as equi-librium prices and quantities.12 To improve interpretabilityof the results, we make the same assumptions as above inthe case of feature-differentiated national brands. By nor-malizing β = 1, we have γ12 = 1 − ε. For simplicity, we firstexamine the case where the two national brands are charac-terized by the same quality: α1 = α2 = α ≥ αp. Let x ∈ [0,1]denote the level of quality differentiation such that αp = xα.With these specifications, equilibrium prices, quantities, andprofits in the channel are thus functions of x, γp, βp, and α.We can then examine the quality (x) and feature (γp) valuesthat maximize retailer profit, as functions of the fundamentalutility parameters: βp (the private label’s marginal unattrac-tiveness as quantity consumed increases) and α (the qualitylevel of the two national brands). An analysis of the equi-librium demand for the store brand shows that store-brandsales are positive only when γp < x, which is analogous toFig. 2’s upper curve. Intuitively, this condition implies thatif the store brand is “too inferior” in quality to the nationalbrands (i.e., if x < γp), store-brand demand will be negative.Alternatively, the condition implies that the relative quality ofthe store brand as compared to national brands places a limitontc

ai(dnvttotsmbsaroAf

Ri

i

feature-differentiate from the national brands. The higher theprivate label’s quality, the more it can differentiate.

Intuitively, feature differentiation of the private labelis optimal when the national brands are not feature-differentiated because of the value consumers place on vari-ety, as represented in our utility function specification. Forexample, one consumer we interviewed buys national brandpasta for herself and her husband, which is available onlyin small package sizes; when her college-age son entertainsfriends at home, however, she provides store-brand mostac-cioli because it comes in a much larger package size thatis unavailable in any of the national brands. In this case, itis package size that is the feature differentiator between thenational brands and the private label.

We can also extend our results to a case where the twonational brands, while undifferentiated in feature, are qual-ity differentiated (i.e., α1 > α2 ≥ αp). We show a numericalexample of this more complicated case in Appendix A to illus-trate that (a) the more quality differences there are betweenthe two national brands, the more stringent is the conditionon minimum quality of the store brand to guarantee positivestore-brand sales; and (b) it is still optimal for the retailerto maximize the feature differentiation of the store brandfrom the national brands (subject to positive sales of the storebrand), as above. Thus, our results on the optimality of maxi-mbq

S

itctf(niciadblidb

cifta

n how feature-differentiated the store brand can be from theational brands, and still garner positive sales; the higher ishe store brand’s quality, the more differentiated in feature itan be and still survive in the market.

Without loss of generality, we therefore restate γp

s γp = y·x, with y ∈ [0,1]. Equilibrium retailer profitn this situation, as � approaches zero, is given byα2[βp + x2(1 − 2y)])/4(βp − x2y2. The choice of the optimalegree of feature differentiation of the store brand from theational brands translates in this context to a choice of thealue of y (in the permitted range of 0 ≤ y ≤ 1) that maximizeshese equilibrium retailer profits. It is straightforward to showhat this profit expression is decreasing in y: the optimal valuef y is thus zero, implying maximal feature differentiation ofhe store brand from the national brands. We can also easilyhow that (if it were costless) the retailer would choose mini-al quality differentiation of the store brand from the nationalrands, that is, x = 1. Finally, it is also easy to show that in thisituation, maximal feature differentiation of the store brandlso maximizes unit sales of the store brand. However, theange of the parameter y implies that the relative quality levelf the private label limits the degree of feature differentiation.higher private label’s quality allows it to more differentiate

rom the national brands, as formalized in Result 4.

esult 4. When the two national brands are undifferentiatedn the feature dimension, it is optimal for the private label to

12 The solutions for a simplified setting where the two national brands aredentical are presented in Appendix A.

um feature differentiation of the store brand, given nationalrands that lack feature differentiation, holds regardless of theuality differences between the national brands.

ummary

Interestingly, therefore, the nature of competitive position-ng between the national brands affects the relative positionhe retailer wishes to establish for its store brand. In thease of feature differentiation between the national brands,he retailer optimally positions the store brand at the sameeature position as one or the other of the national brandsconsistent with Sayman et al. 2002). But here, when theational brands themselves are essentially undifferentiatedn features, it is no longer in the retailer’s best interest tohoose a feature position equal to those of the national brands;nstead, retail profit is maximized by maximally differenti-ting the store brand from the national brands in the featureimension. Sayman et al. (2002) do not derive this result,ecause they do not consider the possibility that the privateabel feature-differentiates from two national brands. Thus,n a multiple-national-brand world, private-label positioningecisions optimally take account of the existing national-rand competition.

In sum, our analysis of the case of two national brandsompeting with the private label shows that optimal position-ng of the private label should take into account the relativeeature positions of the national brands as well as the rela-ive quality of the private label itself. When national brandsre significantly differentiated only in the feature dimension,


the private label can choose a feature position equivalent toone of the national brands. A relatively high quality privatelabel should position closer to the stronger brand, but a lowerquality private label should position toward the weaker brand.But when national brands are not differentiated in the fea-ture dimension, the results are quite different: the retaileroptimally maximizes the feature differentiation between theprivate label and the national brands. But the degree of possi-ble differentiation is proportional to its relative quality level.

Impact of private-label positioning on national brandprofits

Our main focus in this paper is on the retailer’s decisionof how to position the private label versus the national brand.However, it is interesting to examine the impact of these deci-sions on the national-brand manufacturer as well. One canimagine a longer time horizon than we model here, wherea national-brand manufacturer, knowing the retailer’s strate-gic and tactical incentives to position the private label and toprice both products, would optimally invest in its own fea-ture and/or quality differentiation efforts through time. Whilemodeling this more extensive game is beyond the scope ofthis paper, it is instructive to think about the impact on themanufacturer of these retailer actions.

eviobutbsh(mfbbp

btbtbbsuht

m

its quality and to increase its feature differentiation from theprivate label through time. A case in point would be the phar-maceutical industry’s strategy of developing an “improved”version of a prescription drug as its patent expires. The newdrug typically tries to distance itself from the old one inboth its efficacy (e.g., strength) and feature (e.g., purple pill)dimensions. In the differentiated national brands case, onthe other hand, a higher quality private label is more likelyto imitate the stronger brand in both feature and qualitydimensions and share the segment revenue. Depending onthe comparative strength and feature differentiation possibil-ities, therefore, it is conceivable that a national brand mightactively seek the position of the second quality brand, ratherthan the top quality position.

Discussion of results and future research directions

The majority of the location theory literature suggests thatmaximum differentiation in both quality and feature dimen-sions is the optimal positioning strategy for a rival brandsuch as a private label. However, the push to make privatelabel products “better,” which decreases differentiation, isnot surprising, given our analysis. Even when a success-ful private label attacks the national brand by creating anoffering of virtually equal quality, a retailer’s profitabilitycaNpqAfp

bWfgiTbqtdp

iaNttoqdf

It can be shown that the manufacturer’s equilibrium profitxpression in the single national brand case is convex in thealue of γ: decreasing in γ initially, then eventually increas-ng with further increases in γ . The same convexity can bebserved in the case of two feature-undifferentiated nationalrands. Further analysis reveals that the national brand man-facturer, like the retailer, benefits from facing a private labelhat is maximally feature-differentiated from the nationalrand. The manufacturer’s equilibrium profit can also behown to be decreasing in αp, the quality of the private label,olding the manufacturers’ national brand quality constantwhether there are two or just one national brands in thearketplace). Thus, like the retailer, the national brand manu-

acturer benefits from products that are feature-differentiated;ut unlike the retailer, the national brand manufacturer alsoenefits from competing with a lower-quality private labelroduct.

The implications are somewhat daunting for the nationalrand manufacturer, particularly when we take into accounthe likely positive correlation (rather than independence)etween increases in private label quality and increases inhe γ parameter (that is, decreases in feature differentiationetween the private label and national brand). The nationalrand manufacturer is harmed by a strategic retailer thateeks to increase the quality of the private label— partic-larly if this quality increase also comes at the expense of aigher level of γ . Such a situation implies a double penaltyo manufacturer-level profits.

Recognizing these implications, a strategically orientedanufacturer is likely to persist in efforts to both increase

an increase if this product improvement is not too costlynd/or is accompanied by persistent feature differentiation.evertheless, there are hints that retailers perceive extensiverivate-label marketing campaigns – that could increase theuality perception of their store brands – to be very expensive.

costly campaign, combined with an initially reasonablyavorable private label product position, may not in fact be arofitable move by the retailer.

Our analysis shows that optimal differentiation strategiesy the private label depend on several underlying factors.hen the national brands are substantially differentiated in

eatures, the private label, if its quality is relatively high, isenerally better off imitating the stronger national brand (asn the example of a store brand of liquid detergent imitatingide rather than Woolite) or one of two parity-quality nationalrands (as with Office Depot copy paper). However, a loweruality private label would be better off positioning towardshe weaker brand. When the national brands lack clear featureifferentiation, the private label is better off taking a distinctosition (as in the peppermint tea or jam examples).

The national-brand manufacturer, meanwhile, does bestn a retail environment where his brand is “king” in quality,nd is highly feature-differentiated from the private label.ational brands thus stand to be hurt by strategic moves on

he part of retailers to improve the quality of private labels andheir close positioning. On a larger level, the rational responsef national brand manufacturers is to continually increase theuality of their national brands, find new methods of featureifferentiation (such as novel packaging, sizes, and productorms), or both.


Finally, our research shows that the nature of differenti-ation matters in private label—national brand competition.Product substitutability is not a unidimensional concept; afocus on quality investments alone obscures the importanceof feature differentiation in maintaining a vibrant productcategory. Our utility-based demand model, allowing for thepossibility of natural market expansion with greater prod-uct variety as well as greater product quality, highlights themultiple positioning opportunities open to retailers as theyseek to optimize their investments in private labels, as wellas to manufacturers seeking to preserve their national-branddominance in the market.

This paper thus contributes to the private label—nationalbrand competition and positioning dialogue on multiplefronts. The purchase of multiple brands in a product category,commonly seen in real consumer behavior but not consideredin prior work, is considered here. Our work expands on pre-vious work in the area by also allowing the degree of featuredifferentiation between the private label and national brandsto vary, and by combining a consideration of feature and qual-ity positioning of the private label versus its national brand

cntltalp

o

vate label from an analytic and predictive point of view.Our research results suggest testable implications for futureresearch, regarding the most likely combinations of posi-tioning one might observe in national brand-private labelcompetition, and the most likely conditions under whichone would observe investments in improving the privatelabel’s quality. We also focus on a manufacturer-retailerinteraction where the retailer is assumed to be a categorymanager. A different, but interesting, research questionis what incentives such a retailer has to use categorymanagement rather than individual product managementwithin the category to position and price its products.This research question could provide some interestinginsights not only into the retailer’s decisions, but also intothe manufacturer’s optimal defensive national brand posi-tioning strategies, given that it sells through a retailerthat either does or does not practice category manage-ment.

Appendix A. Technical appendix

Solution for the two national brand case

α2(β1βp − γ21p)(βpγ12 − γ1pγ2p) + α1[β2

pγ212 − γ2

1pγ22p + 2βpγ1p(β2γ1p − γ12γ2p) − 2β1βp(β2βp − γ2

2p)]2 2 β 2

βp

pγ2

−βp

γ21p

−pγ

γ21p

−pγ

p∗p = αp

2.

ounterparts. These additions to the modeling structure are

w∗1 = − (αp − νp)[γpβpγ12 + γp(2β2γ1p − 3γ12γ2p) −

β2pγ2

12 − 3γ21pγ2

2p + 4β1βpγ22p − 2

w∗2 =

α1(β2βp − γ22p)(βpγ12 − γ1pγ2p) + α2[β2

pγ212 − γ2

1

− (αp − νp)[γ2pβpγ212 + γ2

2p(2β1γ2p − 3γ12γ1p)

β2pγ2

12 − 3γ21pγ2

2p + 4β1βpγ22p − 2

p∗1 =

α2(β1βp − γ21p)(βpγ12 − γ1pγ2p) + α1[2β2

pγ212 − 4

− (αp − νp)[γ1pβpγ212 + γ2

1p(2β2γ1p − 3γ12γ2p)

2(β2pγ2

12 − 3γ21pγ2

2p + 4β1βpγ22p + 4β2β

p∗2 =

α1(β2βp − γ21p)(βpγ12 − γ1pγ2p) + α2[2β2

pγ212 − 4

− (αp − νp)[γ2pβpγ212 + γ2

2p(2β2γ2p − 3γ12γ1p)

2(β2pγ2

12 − 3γ21pγ2

2p + 4β1βpγ22p + 4β2β

ot just complications added on to prior work; we show thathey have significant impacts on the profitability of privateabel positioning decisions. Finally, we consider these fac-ors in a fully consistent consumer utility-based model thatllows us to examine the true fundamental effects of under-ying utility factors on retailers’ optimal positioning of theirrivate label products.

The focus of this research is on the positioning decisionf the retailer that manages both a national brand and a pri-

1(2β2βpγ1p − βpγ12γ2p − γ1pγ2p)]

γ12γ1pγ2p − 4β1β2β2p + 4β2βpγ2

1p

2p + 2βpγ1p(β2γ1p − γ12γ2p) − 2β1βp(β2βp − γ2

2p)]

β2(2β1βpγ2p − βpγ12γ1p − γ2pγ21p)]

γ12γ2pγ1p − 4β1β2β2p + 4β2βpγ2

1p

γ22p + 2βpγ1p(3β2γ1p − 2γ12γ2p) − 6β1βp(β2βp − γ2

2p)]


21p − 2βpγ12γ1pγ2p − 4β1β2β2

p + 4β1βpγ21p)

γ22p + 2βpγ1p(3β2γ1p − 4γ12γ2p) − 6β1βp(β2βp − γ2

2p)]


21p − 2βpγ12γ1pγ2p − 4β1β2β2

p + 4β1βpγ21p)

.See Table A1.

A.1. A special case: vertically differentiated, buthorizontally undifferentiated national brands—anumerical example

For simplicity, assume that β1 = β2 = 1, γ1p = γ2p, and�12 = β1 − �. The second equality comes from the fact that


Table A1Equilibrium values (assuming the two national brands are identical)

Results for manufacturer and/ornational brand

Results for retailer and/or private label

Wholesale price, w∗1 and retail margin, m∗

1 for the NBβp(α1 + ν1) − γ(αp − νp)

2βp

βp(α1 − ν1) + γ(αp − νp)

4βp

Retail prices, p∗1 and p∗

p

βp(3α1 + ν1) − γ(αp − νp)

4βp

αp+νp

2

Quantities, q∗1 and q∗

p

βp(α1 − ν1) − γ(αp − νp)

4(β1βp − γ2)

2β1βp(αp − νp) − γ2(αp − νp) − βpγ(α1 − ν1)

4βp(β1βp − γ2)

Profits of NB mfgr., Π∗M , and retailer, Π∗

R

(βp(α1 − ν1) − γ(αp − νp))2

8βp(β1βp − γ2)

4β1βp(αp − νp)2 + Y

16βp(β1βp − γ2)a

a Y = [βp(α1 − �1) + γ(αp − �p)][βp(α1 − �1) − 3�(αp − �p)]; retailer profit function is the sum of retail profits across the private label and the national brand.

Fig. A1. Sensitivity analysis to check convexity of the retailer profit withrespect to αp. Note: The vertical axis represents the value of the second orderderivative minimized with respect to the two differentiation parameters (αp

and k) at any given pair of values of the two non-decision parameters (βp

and γ). Since all minimum values of the second order derivatives are positivewithin the plausible parameter range, this numerically demonstrates that theretailer profit function is convex in αp.

Fig. A2. Sensitivity analysis to check convexity of the retailer profit withrespect to k. Note: The vertical axis represents the value of the second orderderivative minimized with respect to the two differentiation parameters (αp

and k) at any given pair of values of the two non-decision parameters (βp

and �). Since all minimum values of the second order derivatives are positivewithin the plausible parameter range, this numerically demonstrates that theretailer profit function is convex in k.

the two national brands are horizontally undifferentiated. Theundifferentiated two national brands can be represented bysetting ε → 0. Further, assume that the national brand 1’sintrinsic quality is k ≥ 1 times that of the national brand 2(α1 = kα2), and that the store brand’s intrinsic quality is afraction (0 < x ≤ 1) of that of the national brand 2 (αp = xα2).For the store brand to have a positive demand, we requireγ1p < (2x/(1 + k)). By setting y < 2/(1 + k) this inequality canbe converted to γ1p = yx. Therefore, for a given value of x, yis a surrogate for the horizontal differentiation parameter γ1p

(i.e., the smaller is y, the more differentiated the store brandis from the national brands). Although the profit function isunwieldy, its surface graph shows that smaller y increases theretailer’s total profit.

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