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How do advertised brands benefit from private labels?An application of rational expectations modelsG. R. Chena

a Department of Finance, I-Shou University, Kasohsiung, TaiwanPublished online: 08 May 2014.

To cite this article: G. R. Chen (2014) How do advertised brands benefit from private labels? An application of rationalexpectations models, Applied Economics, 46:24, 2891-2902, DOI: 10.1080/00036846.2014.916388

To link to this article: http://dx.doi.org/10.1080/00036846.2014.916388

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How do advertised brands benefit

fromprivate labels? An application of

rational expectations modelsG. R. Chen

Department of Finance, I-Shou University, Kasohsiung, TaiwanE-mail: dionysiac@isu.edu.tw

Private labels have traditionally been viewed as a threat to advertised brands.Contrary to traditional wisdom, this study uses a two-asset rational expectationsmodel to show that advertised brands could benefit from private labels. While themanufacturer’s advertising creates product differentiation, the retailer’s synchro-nous pricing strategy further enhances the product differentiation and raisesprofits as well as the efficiency of price discounts for the advertised brand. Inaddition, the existence of private labels improves the advertising efficiency,especially for newly introduced brands. The economic role of private labels isnot limited to taking a free ride on the manufacturer’s advertising efforts, and thisrole cannot be replaced by another advertised brand.

Keywords: rational expectations model; product differentiation; Cournotmodel; advertising

JEL Classification: C68; D84; M21; M37

I. Introduction

Private labels have grown substantially since the 1950sand currently represent a significant proportion of theretail market. Quelch and Harding (1996) concluded thatprivate-label competition will remain a serious threat tonational brands. In the US, private labels held a 17.4%market share in 2010, reflecting a 2% increase over 5 years(Nielsen, 2011). In the UK, the market share of privatelabels in the groceries segment grew from 39% of the salesin 2008 to 41% in 2010 (Marian, 2011). Private labelshave been steadily gaining market shares in the fast-moving consumer goods segment over the last few dec-ades and now account for one-third of sales(Szymanowski, 2013). Arguments on how private labelsinfluence advertised brands can be divided into twoschools of thought. The first perspective considers privatelabels to be copycats of familiar products, requiring muchsmaller advertising budgets than national brands do,and taking free rides on larger manufacturers’ product

development efforts (Quelch and Harding, 1996).Retailers position their private labels to imitate leadingnational brands; these labels often match national brandsin appearance and are placed next to each other on storeshelves (Scott-Morton and Zettelmeyer, 2004). Nationalbrands find it difficult to build entry barriers against pri-vate labels, because such labels are launched by distribu-tion channels in direct control of the allocation of shelfspace. Since retailers tend to take a free ride on manufac-turers’ advertising efforts by projecting a brand image onretailer products, national brands thus effectively sharetheir advertising budgets with private labels. Post theintroduction of private labels, it therefore appears irra-tional for national brands to maintain the same advertisingbudget. Experts subscribing to the second school ofthought, however, contend that manufacturer brands canbenefit from private labels. Kim and Parker (1999) demon-strate how advertising allows the retailer to set collusiveprices and to better price discriminate across brand seekersversus product seekers, while gradually increasing the

Applied Economics, 2014Vol. 46, No. 24, 2891–2902, http://dx.doi.org/10.1080/00036846.2014.916388

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prices for both segments. Pauwels and Srinivasan (2004)showed that the introduction of private labels benefitspremium-brand manufacturers but not second-tier brandmanufacturers. Soberman and Parker (2006) present amodel in which a manufacturer colludes with a retailer tosimultaneously supply both a national brand and a storebrand. When only the national brand is available, themanufacturer ignores product seekers and simply concen-trates on brand seekers. The production of private labelsallows the manufacturer to discriminate between brandseekers and product seekers (Soberman and Parker, 2006).

In contrast to prior literature, this study aims to answerthe question: Could advertised brands benefit from privatelabels even in the absence of differences in consumers’preferences, which divided them into brand seekers andproduct seekers? This study develops a risk reductiontheory in which retailers manoeuvre price synchronousstrategies to enhance brand differentiation based on iden-tical quality preference across consumers. While the col-lusive argument predicts that retailers will eventuallystock only the most premium brand in each category, thisstudy’s results can be applied to retailers stocking variousgoods with different levels of brand awareness. Choi(2007) suggests that studies on the association betweenprivate labels and national brands would benefit fromincluding variables such as advertising and promotions.We present a rational expectations model in which con-sumers can use the equilibrium price to judge productquality. According to this model, private labels do notmerely exploit advertising but can also serve to mediatebetween advertising information and retailers’ promotionstrategies. Unlike previous studies, we investigate the roleof private labels from associations among price covar-iance, product differentiation and risk perception. Wedemonstrate that under the assumption of identical con-sumer preferences, private labels could still serve theinterests of manufacturers by enhancing consumer confi-dence in product quality.

This study is organized as follows: Section II postulatesa conceptual framework for the entire economic model.Section III presents a rational expectations model thatincludes both an advertised brand and a private label.Section IV derives the consumer demand functions forthe advertised brand and the private label and showshow two standardized products are differentiated byadvertising information. Section V shows how a privatelabel can improve the efficiency of an advertised brand’sprice promotions. Section VI presents the effects of pricesynchronization in a cooperative model that demonstratedhow the profits on advertised brands are higher in thepresence of private labels. Section VII shows that privatelabels could raise the advertising efficiency for newlyintroduced national brands. Section VII shows that thestandardized effect of price synchronization might out-weigh the risk reduction effect while two products have

comparable advertising coverage, suggesting that the rolethat private labels play in this regard cannot be played byanother advertised brand. Finally, Section X explains themanagerial implications of the model and outlines thelimitations of this study.

II. Conceptual Framework

This study aims to investigate the interactions betweenadvertising information and price promotions. Serving asa mechanism of differentiation, advertising can be used tocreate market power by relaxing price competition (Tirole,1990; Boulding et al., 1994). Advertising could also raisethe consumer tendency to purchase a promoted productbecause it reduces risk perceived by consumers (Byzalovand Shachar, 2004). First, we construct a rational expecta-tions model to show that advertising creates the productdifferentiation that benefits both advertised brands andprivate labels. Although advertising can make price pro-motions more efficient (Erdem et al., 2008), various mod-els indicate that price variations can leave negative effectson brands (Klein and Leffler, 1981; Bagwell and Riordan,1991; Kirmani and Rao, 2000). In addition, empiricalstudies have provided evidence of a robust price–qualityeffect (Rao and Monroe, 1989; Dodds et al., 1991; Erdemet al., 2008). If a product is over-promoted, consumerswill then buy less of the product at the regular price, whichin turn results in a loss of brand equity and brand aware-ness (Mayhew and Winer, 1992; Yoo et al., 2000).

This study shows that retailers could play the role of riskreduction, lowering the adverse effects of price promo-tions by manoeuvring the consistency of price move-ments. Although there are price differences betweennational brands and private labels, prices appear to syn-chronize perfectly over time across advertised brands andprivate labels (Deneckere and Davidson, 1985; Cotterilland Putsis, 2000), with correlations mostly exceeding 0.95(Parker and Kim, 1997; Kim and Parker, 1999). Bothprivate label and national brand reaction functions aresignificantly positive sloped and asymmetric (Putsis,1997; Cotterill and Putsis, 2000). This study aims toshow that advertised brands could benefit from the pricesynchronization identified by empirical findings; the exis-tence of private labels thus helps maintain the long-termrelationship between manufacturers and retailers. We con-struct a rational expectations model in which consumersuse retail prices and advertising to infer product quality.When an advertised brand launches a price promotion, theaccompanying price reductions by private labels makeconsumers realize that price promotions are regular eventsrather than a consequence of quality downgrading. Thisrelaxes consumers’ concern over product quality. Formanufacturers, promoting with retailers generates better

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sales performance than promoting alone. Althoughadvertised brands have to share advertising efforts withprivate labels, private labels could improve advertisingefficiency, especially for newly introduced brands. Whilethe risk reduction effect improves the sales performanceof advertised goods, it could be offset by a homogeneouseffect when two brands with comparable advertisingcoverage are promoted simultaneously, suggesting thatthe role of private labels cannot be replaced by an adver-tised brand. Contrary to previous literature, this studyinvestigates the role of private labels from associationsamong price covariance, product differentiation and riskperception.

This study uses a two-asset rational expectations modelto illustrate how price covariance between advertisedbrands and private labels influences the level of risk per-ceived by consumers. The rational expectations equili-brium (REE) formally specifies how equilibrium price isendogenously related to agents’ private information.Grossman (1976) shows that the private informationrevealed by price implies that equilibrium cannot havebeen arrived at if information acquisition is costly.Hellwig (1980) argues that since noise comes from thesupply side, the price cannot provide sufficient informa-tion; therefore, simply observing the price cannot provideenough information to predict an asset’s return. Admati(1985) considers the interplay between private informa-tion and equilibrium prices in a multi-asset extension ofHellwig (1980). Easley and O’Hara (2004) show thatinformation asymmetry has a substantial effect on pricesand demands, affecting assets through a liquidity channel.An increase in information asymmetry leads to a fall inasset prices and a reduction in uninformed investors’demand for the asset (Wang, 1993; Kelly andLjungqvist, 2012). Under REE, price is both endogenousand exogenous; this enables us to explore the associationbetween information asymmetry, product differentiationand co-promoting.

III. Rational Expectations Model

Assume that a retailer carries two products: an advertisedbrand and a private label. These two products are identicalin every aspect, except for the fact that the private labeldoes not make use of advertising. The product qualityvector is Q ¼ q1 q2½ �0, where qi is the true quality ofproduct i, the subscript i ¼ 1; 2 signifying advertisedbrand and private label, respectively. Suppose that Qfollows a normal distribution, where the mean and var-iance are expressed as:

Q , Nð�Q;VÞ; �Q ¼ �q�q

� �;V ¼ v11 v12

v12 v22

� �:

Suppose that the value of the quality conveyed by aproduct’s advertising is

A ¼ Qþ ε (1)

whereA ¼ a1 a2½ �0 and ai is the advertising informationfor product i received by consumers. As advertising infor-mation imprecisely reflects true quality, the noise con-tained in the advertising information is denoted byε ¼ ε1 ε2½ �0. Suppose that ε follows a normal distribu-tion, where the mean and variance are expressed as:

ε , Nð0; SÞ; S ¼ s11 s12s12 s22

� �

Advertising information with a lower sii is more precisewhen communicating quality, so s�1

ii denotes advertisingprecision. Since private labels do not use advertising, it isequivalent to assume the following:

s22 ! 1 (2)

The consumer utility function is uðQÞ ¼ � expð�γ�1QÞ.As previously noted, Q is normally distributed so that thedemand function for consumers who infer quality usingonly price can be derived as

ZdðPÞ ¼ γVarðQ PÞ�1 EðQ PÞ � Pjð Þ�� (3)

where EðQ Pj Þ denotes the product quality matrix pre-dicted by consumers based on retail price matrixP ¼ p1 p2½ �0, VarðQ Pj Þ represents the variance of pro-duct quality conditional on retail prices and γ > 0 is thelevel of risk tolerance. The demand function for consu-mers who infer quality using both advertising and pricecan be derived as:

ZdðA;PÞ ¼ γVarðQ A;PÞ�1 EðQ A;PÞ � Pjð Þ�� (4)

where EðQ A;Pj Þ represents the product quality matrixpredicted by consumers based on advertising informationand retail prices, and VarðQ A;Pj Þ is the variancematrix ofproduct quality conditional on both advertising informa-tion and retail prices. Equations 3 and 4 show that con-sumer demand becomes stronger with higher expectedquality and lower quality variance. Consumers can useendogenous variables P as a quality indicator, whichmatches the scenario of reality; this property gives arational expectations model an advantage over traditionalWalrasian equilibriums. Suppose that ðQ;A;PÞ follow ajoint normal distribution. The mean and variance of qual-ity in Equation 4 can be expressed by

EðQ A;PÞ ¼ H0 þ H1j A þ H2P (5)

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VarðQ A;PÞ ¼ J0j (6)

The mean and variance of quality in Equation 3 can beexpressed by

EðQ PÞ ¼ C0þC1j P (7)

VarðQ PÞ ¼ D0j (8)

The property of treating prices as endogenous as well asexogenous variables allows us to analyse consumers’reactions when they face price variations. In the following,we need to introduce sources of variations. Zs denotes thesupply quantity, which is normally distributed with themean and variance of

Zs , Nð�Z;UÞ; �Z ¼ �z1�z2

� �;U ¼ u11 u12

u12 u22

� �:

Assume that a change in supply quantity is a necessarycondition for price promotions; each firm launches pricepromotions by altering its supply quantity. Supply var-iances u11 and u22 represent the price promotion intensityfor advertised brands and private labels, respectively. Thismeans that the manufacturer can accumulate goods andthen release them when offering a discount. In addition,u12 represents the covariance between the national brandand the private label’s price promotions; a higher u12indicates that the two products have a higher degree ofprice synchronization and launch simultaneous price pro-motions more frequently.

IV. Consumer Demand in the RationalExpectations Model

Let λ 2 ð0; 1Þ be the fraction of consumers whose qualityexpectations are based on product advertising and price,and let 1� λ be the fraction of consumers whose qualityexpectations are based only on price, where a positive λcan generate product differentiation for two homogeneousgoods in this model. �Zd denotes the average demandquantity, which is the weighted average of informed (canobserve advertising) and uninformed (cannot observeadvertising) consumer demand.

�Zd ¼ λγEðQ A;PÞ � Pj½ �VarðQ A;PÞj þ ð1� λÞγ EðQ PÞ � Pj½ �

VarðQ PÞj(9)

Let �Zd ¼ Zs, this produces an equilibrium price matrixthat is a function of the advertising and supply quantity(Kao, 1992; Chen, 2015 forthcoming):

P ¼ B0 þ B1A�B2Zs (10)

Given that ðQ;A;PÞ has a joint normal distribution, wecan obtain the variance matrix S for the three:

S ¼V V VB0

1

V Vþ S VB01

B1V B1V B1ðVþ SÞB01þB2UB0

2

24

35

(11)

Using the techniques of least-square method, togetherwith the variance matrix, we can obtain the H1;H2;C1 inEquations 5 and 7 by solving the following equations:

H1ðVþ SÞþH2B1V ¼ V (12)

H1VB01þH2 B1ðVþ SÞB0

1þB2UB02ð Þ ¼ V (13)

C1 B1ðVþ SÞB01þB2UB

02ð Þ ¼ B1V (14)

Substituting H1;H2;C1 into Equation 9, we can obtain thecoefficients for Equation 10 as follows:

B0 ¼ W0 γ�1ðλþ λ�1γ�2USÞ�1�Zþ V�1 �Qh i

(10a)

B1 ¼ W0 λS�1 þ ðSþ λ�2γ�2SUSÞ�1h i

: (10b)

B2 ¼ γ�1W0 Iþ ðλþ λ�1γ�2USÞ�1h i

: (10c)

W0 ¼ λS�1þV�1þðSþλ�2γ�2SUSÞ�1h i�1

: (10d)

The expected value of Equation 10 represents the averageprice that consumers are willing to pay at a given supply,which can be used as demand functions in the duopolymodel.

Lemma 1: The demand functions pei ðz1; z2Þ, i ¼ 1; 2, forthe advertised brand and private label are representedbelow:

pe1 ¼ �q� b11z1 � b12z2 (15)

pe2 ¼ �q� b12z1 � b22z2 (16)

where

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b11 ¼ v11γ

ðv11v22 � v212Þ"�λγ

s11þ u22γ

s11u22 þ ðλγÞ�2s211ðu11u22 � u212Þ

þ v22γ

v11v22 � v212

��v11γ

v11v22 � v212

�� v212γ

2

v11v22 � v212

#�1

b12 ¼ v12γ

ðv11v22 � v212Þ"�λγ

s11þ u22γ

s11u22 þ ðλγÞ�2s211ðu11u22 � u212Þ

þ v22γ

v11v22 � v212

��v11γ

v11v22 � v212

�� v212γ

2

v11v22 � v212

#�1

b22 ¼"

v11γ

v11v22 � v212� v212γ

2

v11v22 � v212

�λγ

s11

þ u22γ

s11u22 þ ðλγÞ�2s211ðu11u22 � u212Þ

þ v22γ

v11v22 � v212

��1#�1

:

Proof: The expected value of Equation 10 is

EðPÞ ¼ EðB0Þ þ EðB1AÞ � EðB2ZsÞ¼ W0 γ�1ðλþ λ�1γ�2USÞ�1�ZþV�1 �Q

h iþW0 λS�1 þ ðSþ λ�2γ�2SUSÞ�1

h i�Q

þW0γ�1 Iþ ðλþ λ�1γ�2USÞ�1h i

�Z

¼ W0 V�1 þ λS�1 þ ðSþ λ�2γ�2SUSÞ�1h i

�Q

þW0γ�1hIþ ðλþ λ�1γ�2USÞ�1

� ðλþ λ�1γ�2USÞ�1i

¼ W0W�10

�QþW0γ�1�Z ¼ �QþW0γ

�1�Z:

Let s22 ! 1 and expand W0γ�1, we can obtain b11,b12and b22.

Q.E.D.

In Equations 15 and 16, two identical products becomedifferentiated because one product is advertised, whereD ¼ b212=b11b22 expresses the degree of product differen-tiation, ranging from 0 when the goods are independent ofone another to 1 when the goods are perfect substitutes(Singh and Vives, 1984).

Proposition 1: Given that the two products have identicalquality variances (v11 ¼ v22 ¼ v12), as λ ! 0, the pro-ducts become homogeneous. As λ increases, the two pro-ducts become more differentiated.

Proof: Substituting b11, b12, b22 in Equations 15 and 16into D ¼ b212=b11b22, we have the degree of product dif-ferentiation as follows:

D ¼v12

v11v22 � v212

� �2

v11v11v22 � v212

� �λs11

þ ðλγÞ2u22s211ðu11u22 � u212Þ

þ v22v11v22 � v212

!

(17)

As λ ! 0, we have D ¼ 1; given that v11 ¼ v22 ¼ v12, thetwo products become homogeneous. Because λ is thedenominator of D, an increase in λ causes a decline in D;therefore, we can conclude that a greater λ leads to a higherdegree of product differentiation.

Q.E.D.

Proposition 1 indicates that without advertising, the twoproducts are perfect substitutes for each other. The intro-duction of advertising by one of the products makes themmore independent of each other; this corresponds withTirole’s (1990) argument that firms can use advertisingto differentiate themselves, resulting in a lower pricecompetition. Kim and Parker (1999) showed that advertis-ing allows the retailer to better price discriminate acrosstwo segments (brand seekers versus private-label seekers)while gradually increasing the prices for both segments.That study reveals that retailers can react to the heavyadvertising amongst national brands by increasing prices,revenues and profits generated from both national brandsand private-label brands.

V. Synchronous Pricing Strategies and PriceDiscounts

Although price reductions could increase sales quantitiesowing to the downward sloping demand function, theycould also make consumers suspicious about productquality (Klein and Leffler, 1981; Bagwell and Riordan,1991; Kirmani and Rao, 2000; Erdem et al., 2008). Whileempirical findings indicate that national brand prices havea significant positive relation to private-label prices(Deneckere and Davidson, 1985; Cotterill and Putsis,2000), another set of studies concludes that the emergenceof private labels actually increased total revenues for allbrands, including advertised brands (Connor andPeterson, 1992; Pauwels and Srinivasan, 2004;

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Soberman and Parker, 2006). If a retailer carries both anadvertised brand and a private label, the price synchroni-zation between them makes consumers realize that pricepromotions are regular events rather than a consequenceof quality reduction; reduced uncertainty over productquality thus makes price promotions more attractive. Toinvestigate the efficiency of price promotions, we areinterested in the demand functions as they have the choicevariables on the right-hand side. Solving the demandfunctions in Equations 15 and 16 produces the followingdemand functions:

z1 ¼ �qðb22 � b12Þb11b22 � b212

� b22b11b22 � b212

pe1 þb12

b11b22 � b212pe2

(18)

z2 ¼ �qðb11 � b12Þb11b22 � b212

þ b12b11b22 � b212

pe1 �b11

b11b22 � b212pe2

(19)

where b11, b12 andb22 are given in Equations 15 and 16.The first-order derivative of national brand quantity z1

with respect to national brand price p1 denotes the effi-ciency of price reduction for the advertised brand. Ahigher value of first-order derivative means that pricepromotions can generate more sales quantities.

Proposition 2: Suppose that a retailer carries an adver-tised brand and a private label, and the demand functionsare Equations 18 and 19, respectively. A higher degree ofprice synchronization can make price promotions gener-ate more sales quantities.

Proof: The efficiency of price promotions is expressed asfollows:

� dz1dp1

¼ b22b11b22 � b212

¼ λγs11

þ u22γ

s11u22 þ ðλγÞ�2s211ðu11u22 � u212Þþ v22γ

v11v22 � v212

(20)

To investigate how price synchronization affects the effi-ciency of price promotion, Equation 20 must be differen-tiated with respect to the degree of price synchronization:

dðdz1=dp1Þdu12

¼ 2λ�2γ�1s211u22u12

ðs11u22 þ ðλγÞ�2s211ðu11u22 � u212ÞÞ2 > 0:

.Q.E.D.

Proposition 2 indicates that when an advertised brand anda private label cut prices independently, the sales quanti-ties generated will be less than when the same two pro-ducts are promoted jointly. If a price reduction represents aquality reduction for consumers, it might not stimulate thesales expected by retailers as well as manufacturers. Apositive price covariance reverses the possible adverseeffect by letting consumers realize that price promotionsare not a result of quality downgrades, but regular eventsthat are not related to product quality.

VI. Synchronous Pricing Strategies in aCooperative Model

Suppose that a retailer selects optimal sale quantities thatmaximize the collective profits for an advertised brand aswell as a private label. Assume also that the two productsare identical in quality and cost; the only difference is thatone is advertised while the other is not. The optimalquantities can be obtained from Equations 15 and 16.

Lemma 2: A retailer sells an advertised brand and aprivate label with demand functions in the form ofEquations 15 and 16, respectively. The purchase costs ofthe two products are TCi ¼ czi and i ¼ 1; 2, where i ¼ 1 isthe advertised brand and i ¼ 2 is the private label. Theretailer’s optimal purchase quantities for the advertisedbrand and private label are

z�1 ¼ð�q� cÞðb22 � b12Þ2ðb11b22 � b212Þ

(21)

z�2 ¼ð�q� cÞðb11 � b12Þ2ðb11b22 � b212Þ

(22)

Proof: By using Equations 15 and 16, a retailer’s profitcan be expressed as the sum of the profit of both products.

π ¼ π1 þ π2 ¼ ðpe1 � cÞ � z1 þ ðpe2 � cÞ � z2¼ ð�q� cÞðz1 þ z2Þ � w11z

21 � w12z1z2

� w12z1z2 � w22z22

(23)

By setting the first-order derivative with respect to zi equalto 0 and solving these two equations simultaneously, wehave Equations 21 and 22.

The following proposition shows how price variationsimpact the profit on the advertised brand. Section IIassumes that an increase in u11 and u22 leads to pricevariations. Considering the price–quality relationship,although price promotions might generate more salesbecause of the downward sloping demand curve, it alsocauses an adverse effect on product evaluation, which

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decreases sales because of consumer misinterpretations ofprice reductions as quality reductions (Kalyanaram andWiner, 1995; Mela et al., 1998; Jedidi et al., 1999; Erdemet al., 2008; Valette-Florence et al., 2011).

Proposition 3: Ceteris paribus, an increase in price pro-motion intensity leads to a decrease in the profits on theadvertised brand.

Proof: Substituting b11, b12 and b22 defined in Lemma 1into Equations 15 and 16 yields the profit function ofadvertised brand:

π1 ¼ ð�q� cÞ2ðα� θÞ4

(24)

where

α ¼ λγs11

þ u22γ

s11u22 þ ðλγÞ�2s211ðu11u22 � u212Þþ v22γ

v11v22 � v212

(25)

θ ¼ v12γ

ðv11v22 � v212Þ(26)

Differentiating α with respect to u11 and u12 yields

@α@u11

¼ �λ�2γ�1s211u222

ðs11u22 þ ðλγÞ�2s211ðu11u22 � u212ÞÞ2 < 0

(27)

@α@u22

¼ �λ�2γ�1s211u212

ðs11u22 þ ðλγÞ�2s211ðu11u22 � u212ÞÞ2 < 0

(28)

Differentiating Equation 24 with respect to u11 and u12yields

@π1@uii

¼ ðq� cÞ24

@α@uii

; i ¼ 1; 2 (29)

From Equations 27 and 28, we can conclude that Equation29 is negative.

Q.E.D.

When a retailer offers a price discount, consumerscannot determine whether this reflects low quality oran increase in quantity. As national brand price varia-tion (u11) increases, the uncertainty that consumers face

with respect to the quality of the advertised goods alsoincreases because the price is not sufficiently reliablefor predicting quality. Consumers who observe theseprice promotions may wonder why the prices wouldfluctuate if the quality of a product is as high as it isclaimed to be. The following proposition shows that theprofit for the advertised brand could increase with pricesynchronization between the advertised brand and theprivate label.

Proposition 4: Ceteris paribus, the higher the degree ofprice synchronization between the advertised brand andthe private label, the greater is the profit on the advertisedbrand.

Proof: Differentiating Equation 23 with respect to u12yields:

@α@u12

¼ 2λ�2γ�1s211u22u12

ðs11u22 þ ðλγÞ�2s211ðu11u22 � u212ÞÞ2 > 0

(30)

As in Equation 29, differentiating the profit of an adver-tised brand with respect to u12 yields:

@π1@u12

¼ ðq� cÞ24

@α@u12

> 0 (31)

Q.E.D.

In contrast to Proposition 3, Proposition 4 explains thereason behind price synchronization, a phenomenonobserved by Parker and Kim (1997), Deneckere andDavidson (1985) and Cotterill and Putsis (2000). Whileprice promotions confuse consumers with respect towhether the price variations reflect quality variations orare just a result of an increase in supply, price co-move-ments convince consumers that price variation is notrelated to quality. Thus, we see that the greater the degreeof price synchronization, the lower the adverse effects ofprice promotions. This result explains the empirical find-ings that a private label could increase the profitability of anational brand manufacturer (Connor and Peterson, 1992;Kim and Parker, 1999).

Proposition 5: Ceteris paribus, the product differentia-tion in Equation 17 would increase with the frequency ofprice promotions and decrease with the degree of pricesynchronization.

Proof: The first-order differentiations of Equation 17 withrespect to price variation are as follows:

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@D

@u11¼ � @D

@fðλγÞ2u222

s211ðu11u22 � u212Þ2> 0

@D

@u22¼ � @D

@fðλγÞ2s211u212

s411ðu11u22 � u212Þ2> 0

where f ¼ λs11

þ ðλγÞ2u22s211ðu11u22�u212Þ

þ v22v11v22�v212

. Since a higher D

represents a lower degree of product differentiation (asexplained in Proposition 1), we can conclude that pricepromotions decrease product differentiation. Then, wedifferentiate D with respect to the degree of pricesynchronization:

@D

@u12¼ @D

@f2ðλγÞ2u12

s211ðu11u22 � u212Þ2<0:

This indicates that price synchronization makes two pro-ducts more differentiated.

Q.E.D.

Proposition 5 indicates that price promotions maketwo players more homogeneous, because the pricevariations offset the advertising strength due to anincrease in the risk perceived by consumers.However, a synchronous pricing strategy enhancesthe advertising strength that makes two productsmore differentiated, indicating that product differentia-tion is negatively associated with the risk perceived byconsumers.

VII. Synchronous Pricing Strategies andAdvertising Efficiency

In this section, we define advertising efficiency as thedifferentiation of a brand’s profit with respect to its adver-tising coverage:

@π1@λ

¼ ðq� cÞ24

@α@λ

¼ 1

s11þ 2λγ3u22s211ðu11u22 � u212Þ

s11u22ðλγÞ2 þ s211ðu11u22 � u212Þ� �2

(32)

Based on Equation 32, we can investigate whetherprice synchronization can raise the advertisingefficiency.

Proposition 6: Ceteris paribus, an increase in the degreeof price synchronization results in an increase in the

advertising efficiency when advertising coverage

λ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu12s11ðu11u22�u212Þ

u11u22γ2

q.

Proof: Differentiating the advertising efficiency inEquation 32 with respect to the degree of price synchro-nization yields:

@2π1@λ@u12

¼ ðq� cÞ24

@2α@λ@u12

¼ ðq� cÞ24

2λγ3u22s311 u12s11ðu11u22 � u212Þ � λ2γ2u22u11 �

s11u22ðλγÞ2 þ s211ðu11u22 � u212Þ� �4 :

As λ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu12s11ðu11u22�u212Þ

u11u22γ2

q, one has @2π1

@λ@u12� 0:

Q.E.D.

For a newly introduced brand, advertising informationmay not be sufficient for consumers as a sole qualityindicator; retail prices still play an important role in qualityjudgment. While the retail prices with supply noises makeconsumers cautious about the product with low level ofadvertising, the synchronous pricing strategies can helpadvertising information to be communicated by retailprices in a more efficient manner. Proposition 6 corre-sponds with the Varadarajan et al. (1986), which indicatedthat the synchronous price promotions can enhance theimage of the new brand and lower the risk consumersperceived in trying new brands. However, as advertisinghas been widely observed and serves as a reliable qualityindicator for consumers, the demand for synchronous pri-cing strategies to raise advertising efficiency could disap-pear. Therefore, a heavily advertised good is more likely tobe promoted independently because it has consumers withless suspicions about price variations. This result corre-sponds with the findings of Krishna (1991), who referredto a similar situation where Pepsi and Coca-Cola, whichare national brands with heavily advertising, launchedpromotions in alternating weeks over a period of 3months.

VIII. Two-Asset Model with Advertising forBoth Products

If we replace the private label with an advertised brand, thepropositions in the previous sections might not hold. Thearguments that synchronous pricing strategies could ben-efit advertised brands are not valid for two products withcomparable advertising coverage. This is because syn-chronous pricing strategies have two divergent effects.The first effect is of risk reduction, which we have dis-cussed in the previous sections. The second is the

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standardization effect, which could make two productsmore homogeneous. When two products have similarbrand recognition, the standardization effect would dom-inate so that synchronous pricing strategies cause negativeeffects on both products. Suppose that the private label isreplaced by another advertised brand, Equation 9 thenbecomes

�Zd ¼ λ1γEðQ A1;PÞ � Pj½ �VarðQ A1;PÞj þ λ2γ

EðQ A2;PÞ � Pj½ �VarðQ A2;PÞj

þ ð1� λ1 � λ2Þγ EðQ PÞ � Pj½ �VarðQ PÞj

(33)

where λ1 and λ2 denote the weight of advertising cover-age for the products of firm 1 and firm 2, respectively,and 1� λ1 � λ2 represents the weight of consumerdependence on price for those who cannot see anyadvertising. Suppose, in order to judge quality, 80%of the consumers rely on the advertising of firm 1,and 80% on that of firm 2, whereas 20% rely onneither; we set λ1 ¼ λ2 ¼ 0:8=ð0:8þ 0:8þ 0:2Þ ¼0:444 and λ3 ¼ 0:2=ð0:8þ 0:8þ 0:2Þ ¼ 0:112. Therelationship between product quality and product i’sadvertising is

Ai¼ Qþεi; i ¼ 1; 2: (34)

Suppose that ε follows a normal distribution where themean and variance can be expressed as follows:

εi , Nð0;SiÞ; Si ¼ si11 si12si12 si22

� �; i ¼ 1; 2: (35)

Because the advertising of firm 1 and firm 2 cannot reflectthe quality of each other’s products, it is equivalent toassume

s122 ! 1; s211 ! 1:

Under these assumptions, Equation 10 becomes

P ¼K0þK1Q�K2Zs; (36)

where

K0 ¼ W0 NU�1�Zþ V�1 �Q�

;

K1 ¼ W0 λ1S�11 þλ2S

�12 þ NU�1N

� ;

K2 ¼ γ�1W0 Iþ γNU�1�

;

W0 ¼ λ1S�11 þλ2S

�12 þ V�1þNU�1N

� �1;

N ¼ λ1γS�11 þ λ2γS

�12 :

Equations 15 and 16 become

pe1 ¼ �q� k11z1 � k12z2 (37)

pe2 ¼ �q� k12z1 � k22z2 (38)

where

k11 ¼hv11ðv11v22 � v212Þ

�1 þ λ2ðs222Þ�1

þ ðλ2γÞ2u11ðs222Þ�2ðu11u22 � u212Þ

�1i��1

k12 ¼hv12ðv11v22 � v212Þ

�1 þ λ1λ2γ2u12ðs111s222Þ

�1

ðu11u22 � u212Þ�1i��1

k22 ¼hv22ðv11v22 � v212Þ

�1 þ λ1ðs111Þ�1

þ ðλ1γÞ2u22ðs111Þ�2ðu11u22 � u212Þ

�1i��1

� ¼ γhv11ðv11v22 � v212Þ

�1 þ λ2ðs222Þ�1

þ ðλ2γÞ2u11ðs222Þ�2ðu11u22 � u212Þ

�1i

hv22ðv11v22 � v212Þ

�1 þ λ1ðs111Þ�1

þ ðλ1γÞ2u22ðs111Þ�2ðu11u22 � u212Þ

�1i

� γhv12ðv11v22 � v212Þ

�1 þ λ1λ2γ2u12ðs111s222Þ

�1

ðu11u22 � u212Þ�1i2

Given the demand curves in Equations 37 and 38, theoptimal output of firm i in a cooperative model is similarto the forms in Equations 21 and 22, except thatb11; b12; b22 are replaced by k11; k12; k22. The effect ofprice synchronization cannot be analysed by differentia-tion techniques when both products are advertised due tothe complication, so we use a numerical analysis instead.Figure 1 shows the effect of price synchronization on theprofit of the advertised brand, which is not unidirectional.When the other product is a private label without advertis-ing coverage (λ1 ¼ 0:5; λ2 ¼ 0), the profit of the adver-tised brand is positive related to the price synchronizationdue to the risk reduction effect. This is consistent with theargument made by Varadarajan et al. (1986) that jointpromotions could lower consumers’ perceived risk.When another product has comparable advertising cover-age (λ1 ¼ 0:5; λ2 ¼ 0:5), both players’ profits decreasewith price synchronization due to the standardizationeffect. This is consistent with the empirical finding that

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two dominant firms, such as Pepsi and Coke, tend to avoidsimultaneous promotions (Krishna, 1991).

Figure 1 indicates that the advantage of synchronouspricing strategies only accentuates when one product isprivate label. Therefore, the role of private label is notmerely limited to exploiting brand advertising. Further,this role cannot be replaced by another advertised brand.

IX. Conclusions

Consumers use retail prices to infer the quality of a pro-duct; therefore, price variations caused by promotionsnegatively affect perceived quality. This study constructsa rational expectations model with two homogeneousproducts where the manufacturer’s product is advertisedand the retailer’s is not. While the existence of advertisedbrands generates product differentiation between adver-tised brands and private labels, the existence of privatelabels further increases the product differentiation by gen-erating price synchronization between the two products.Although price promotions reduce an advertised brand’sprofits, synchronous pricing strategies increase the brand’sprofits by lowering the risk perceived by consumers.

This study makes four contributions. First, it shows thatadvertising can create product differentiation for twohomogeneous products, and this product differentiationcan be further enhanced by synchronous pricing strate-gies. The product differentiation could be negativelyaffected by consumers’ perceived risk. A decrease inperceived risk, whether caused by advertising or synchro-nized pricing, could lead to a higher degree of productdifferentiation. Second, the study shows that the existenceof private labels can improve the performance of pricepromotions on advertised brands. Third, the model con-structed here proves that a higher degree of price

synchronization between the advertised brand and theprivate label raises the profit of the advertised brand.Fourth, the model also indicates that price synchronizationmanoeuvred by retailers enhances advertising efficiency,especially for a newly introduced brand. The risk reduc-tion arguments explain why advertised brands can coexistwith private labels in spite of retailers taking a free ride ona manufacturer’s advertising efforts. The price correla-tions organized by retailers could bring about risk reduc-tion for advertised brands, which stabilizes the long-termrelationship between manufacturers and retailers. Thisstudy also explains the reason behind various types ofsimultaneous price promotions within categories. Whileprice promotions have adverse effects on consumers’ riskperception, synchronous pricing strategies could reduceconsumer uncertainty over product quality. However, thisstudy also suggests that, due to the effect of homogeneity,the risk reduction effect is not evident when two productshave comparable advertising coverage. In summary, amass retailer can act on behalf of manufacturers under itsstores by coordinating the timing of price promotions forvarious brands. Therefore, in contrast to the Quelch andHarding’s (1996) view that advertised brands must ‘fightto win’, manufacturers’ battles against private labels mayultimately result in an alliance with private labels.

This study suggests that the role of contemporaneouspromotions in the rational expectations model deservesmore attention, both from a theoretical and from anempirical perspective. On a theoretical level, the researchlimitation of this model is that the static property of REEmight simplify the dynamic reality. It would be interestingto examine how many of the results in this study areaffected by the assumption of dynamic price movementsor repeated games. Finally, this study opens the door forempirically differentiating independent promotions andsynchronous promotions and their implications in applied

11.40

11.45

11.50

11.55

11.60

11.65

0.01 0.06 0.11 0.16 0.21 0.26

u12

π1 λ1 = 0.5, λ2 = 0.5

λ1 = 0.5, λ2 = 0

Fig. 1. The vertical axis is the profit for the advertised brand; it increases with the degree of price synchronization when there isa great distance in the weights of advertising coverage between two products and decreases when two products have comparableweights of advertising coverageNote: Parameter value: v11 ¼ v22 ¼ 0:2; v12 ¼ 0:15; u11 ¼ u22 ¼ 0:3; s111 ¼ s222 ¼ 0:3; γ ¼ 0:1; �q ¼ 200; c ¼ 190:

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areas. Extending this work into dynamic settings would bethe next logical step in terms of fitting the data to rationalexpectations models.

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