the simple economics of brand stretching

The Simple Economics of Brand StretchingAuthor(s): Lynne M. Pepall and Daniel J. RichardsSource: The Journal of Business, Vol. 75, No. 3 (July 2002), pp. 535-552Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/10.1086/339888 .Accessed: 25/03/2011 13:39

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535

(Journal of Business, 2002, vol. 75, no. 3)� 2002 by The University of Chicago. All rights reserved.0021-9398/2002/7503-0006$10.00

Lynne M. PepallDaniel J. RichardsTufts University

The Simple Economics of BrandStretching*

I. Introduction

In January 1999, the Coca-Cola Company announcedits plan to launch a new product line: fashion andsports apparel carrying the Coca-Cola label. In makingthis move, Coca-Cola appears to be following the leadof many other name brand companies that, in recentyears, have launched and marketed new products un-der the original brand name. This phenomenon iscalled “brand stretching”; the term refers to the ex-tension of an established brand name identified witha product in one market to a new product in anothermarket.1 The list of brand stretchers is a long one.Some well-known examples include the Ralph LaurenPolo label from clothing to men’s toiletries, the Virginbrand name from recordings to airlines to beveragesto financial products, the Martha Stewart label froma magazine title to both linen and paint product lines,and the Dr. Martens brand from a well-known U.K.shoe and boot product to a new record label.

Our article is about the phenomenon of brandstretching. This is an important topic for economists

* We thank Luis Cabral, George Norman, two referees, and theeditor of this journal for many valuable comments.

1. See, e.g., “Coke Clothers to Be the Next Real Thing: To BeUnfolded Worldwide” (National Post 1999, p. C12). Examples ofentry via brand extension are numerous and include Disney’s entryinto toys and television, Harley Davidson’s marketing of an after-shave, and Cadbury’s entry into the cream liqueur market. See“These Boots Are Made for Your CD Player” (Independent 1997,p. 9).

We analyze brand stretch-ing—the extension of asuccessful brand labelfrom an initial homemarket to a differentproduct line—using amodel that assumes thatbrand identity is a com-plementary feature thatenhances consumer will-ingness to pay. Our anal-ysis implies a pattern ofbrand-stretching entry inwhich (1) firms withstrong brand identitiesmay prefer to extendtheir brands to marketsthat are “far” from theiroriginal product line, and(2) fragmented or uncon-centrated markets with nostrong incumbent brandsare attractive entry tar-gets for brand extension.

536 Journal of Business

because, fundamentally, brand stretchingis about market entry. Our perspectiveon brand stretching is somewhat different from that taken in previous workin this area, such as that by Wernerfelt (1988), DeGraba and Sullivan (1995),Choi (1998), and Cabral (2000). In these papers, brand stretching is oftenviewed as a way for a monopoly firm to extend its monopoly power into anew market. In that framework, brand stretching is profitable either becauseit confers some sort of scope economies or because it serves as a way tosignal the quality of the new product. The question of how brand stretchingaffects competition in the new product market is not, however, a part of thebrand-stretching story in this earlier work.2

Quality signaling and scope economies may explain why some firms chooseto brand stretch. But many actual cases cannot be understood by these factorsalone. Often the new market into which the brand name is leveraged is, fromthe perspective of production technology or SIC number, “far” from the marketin which the brand name was developed. For example, it seems doubtful thatconsumers will view a sports apparel line as high quality simply because itcarries the Coca-Cola label. Nor is it likely that the Ralph Lauren label enjoyssignificant economies of scope between the production of clothing and after-shave products. Equally important, most actual cases of brand stretching in-volve entry by an established brand name into a market where there are atleast a few, and often many, existing incumbent firms. Hence, the monopolymodels used in most formal analysis are inappropriate. It is for this reasonthat we focus on brand extension as a way to enter existing markets, that is,markets that are already open and have incumbent firms. The widespreadincidence of brand stretching suggests that a strong brand identity can facilitateentry or, more precisely, can enhance an entrant’s ability to compete againstthe incumbent rivals. Supportive evidence on this point is offered by Court,Leiter, and Loch (1999), who find that those firms extending their brandidentities to new markets generate a return to stockholders that averages 5%more than that earned by comparable firms not so leveraging their brands.3

In this article, we model explicitly the brand-name advantage in enteringa new market and then proceed to investigate how brand stretching affectscompetition and profitability in that market. To model the brand-name ad-

2. We say “almost totally” because both Sappington and Wernerfelt (1985) and DeGraba andSullivan (1995) do present a model with duopoly competition. However, Sappington and Wer-nerfelt (1985) have no price competition in their model. DeGraba and Sullivan (1995) considera duopoly model only after focusing on a monopoly setting. Moreover, even in the duopoly case,their analysis considers brand stretching only from the perspective of spillovers to a firm’sreputation for quality on brand versus new name entry. In addition, they set their work in thecontext of entry into a new or just-opening market. The competition they examine is one oftiming, specifically, whether a brand-stretching firm will open a new product market sooner orlater than would a firm entering that market as a new-name product.

3. In Cabral’s (2000) model, for instance, consumers pay their full reservation price, i.e., allsurplus goes to the monopolist. Thus, the equilibrium in that model is such that the entire marketwould move to any rival offering to sell for just one penny less than the price charged by theone firm assumed by the model. The absence of price competition in such a model thereforeseems to be a serious omission.

Brand Stretching 537

vantage, we assume that consumers are willing to pay more for brand-nameproducts because of the complementary consumption effect of a brandname—an effect similar to the one in Becker and Murphy (1993) for the caseof advertising. Simply put, consumers get greater utility or enjoyment fromconsuming products that are well known to other consumers. This is so evenif the brand-name recognition was established in a different product market.For example, a consumer may be willing to pay more for a Coca-Cola T-shirtbecause the brand name Coca-Cola is widely known to others. Wearing theshirt then permits the consumer to talk with others about the shirt or aboutthe label or about Coca-Cola products and, in general, to share and to enhancethe experience of wearing it. Thus, the Coca-Cola brand name in and of itselfhas value to the consumer.

Evidence that consumers value recognition is offered by Grossman andShapiro (1988), who point out that consumers who buy a counterfeit Guccior Coach product from street vendors typically know that the item is not anauthentic Gucci or Coach product (and hence, not of the same quality). Nev-ertheless, such buyers are still willing to pay something for the forged name.Indeed, they would not likely buy the product without the forged brand name.Some formal evidence that a brand name can, like advertising, act as a potentialcomplement in consumption that raises consumer willingness to pay is pro-vided by Smith and Park (1992). They find that firms using brand extensionspend less on advertising per unit of sales than do firms launching unbrandednew products. In other words, brand-name recognition is a substitute foradvertising and therefore should work in much the same manner as promo-tional efforts.

An important preliminary issue is, of course, identifying precisely whatconstitutes a well-known brand name. Here, we follow much of the marketingliterature that centers on market share as a proxy for the strength of a brandin its current market. However, we adjust this measure further in consideringthe extent to which such brand recognition transfers to other markets and thenature of brand competition that will prevail in such potential target markets.Our goal is to identify the various factors that affect the profitability of brandextension into a particular market, as well as the pattern of entry that thisimplies.

Target markets that are relatively easy to enter are likely not only to havemany incumbent firms already in the market but also to attract more than onebrand-stretching entrant. Any firm contemplating extension of its brand intosuch a market must, therefore, consider the potential brand-name competitionfrom another brand-stretching firm entering the same market. Accordingly, inour first model of brand stretching, we examine the entry of two brandedfirms into a new market with many unbranded incumbents. In contrast, ahighly concentrated market is one in which entry is likely to be difficult.4

4. This accords with empirical evidence (see Caves [1998] for a summary) that generally findsentry rates increasing as concentration declines.


Moreover, in this case, the incumbent firm itself is likely to have strong brandrecognition. Therefore, we also offer a second model of entry in which thetarget market is monopolized and so brand competition is between the in-cumbent and just one brand-stretching entrant.

II. Two Simple Models of Brand Stretching

Consider a firm that wishes to extend its brand name into a new market. Thisfirm already has a known brand in some market referred to as the homemarket. Because the firm’s brand has an identity in that market, the firm hasa proprietary name that could enhance its competitive position in other productmarkets, which we call target markets. Again, in keeping with much actualpractice, we assume that the brand stretcher’s recognition in a target marketwill depend on the market share of the firm’s brand in its home market,denoted by S. All else equal, the larger is that share S, the stronger or moreknown is the firm’s brand.5

Of course, market share in the home market is not the only determinant ofthe brand stretcher’s recognition in a target market. To capture how wellidentity in the home market translates into similar recognition in a specifictarget market, we define the parameter a, normalized so that . The0 ! a ! 1greater is a, the more fully does the brand’s home-market recognition transferto the target market. The size of a could be related to some measure of thecommonality between the home and target markets, for example, to the degreeto which they share common consumers or the degree to which the productsin the two markets share similar attributes. For example, the Godiva name inchocolate probably carries over more to ice cream than it does to tires. Hence,the Godiva name would likely have a higher a in the ice cream market thanin the tire market. Alternatively, a could be related to some measure of“closeness,” in terms of fashion or image, between the home market and thetarget market. In the case of Coca-Cola, sportswear is a market that in thissense lies “closer” to the soft drink market than to the market for power tools.

The parameter a is also likely related to the actual size of the home market.This is because in our model brand recognition comes not so much frombeing known for some special feature, for example, quality, as from simplybeing known. A sizable market share in a large or thick market is likely tocarry over as brand strength more effectively than would the same marketshare in a small market. In short, there are a host of factors other than home-market share that determine the potential brand stretcher’s image strength in

5. For example, the marketing firm Interbrand employs a measure of brand strength in itsfrequent ranking of brand identities. Of the four criteria used to measure such strength, the mostimportant by far in their index is market share. Another criterion is how “far” the market examinedwas from the brand’s home market. The two other criteria are “breadth”—as reflected in thenumber of different countries the brand sold in—and a measure of customer loyalty. These lastthree criteria may all be taken as factors influencing our parameter, a, discussed below. See,e.g., “Broad, Deep, Long and Heavy: Assessing Brands” (Economist 1996, pp. 72–73). Court,Leiter, and Loch (1999) also link brand strength to market share.


a specific target market. The parameter a stands in as a proxy for all of thesefactors. The overall brand recognition of a brand-stretching firm in a giventarget market is, therefore, defined as .aS

A. Brand Stretching into a Target Market with Many Incumbents

As noted above, target markets that have many incumbent firms are likely tobe markets that are relatively easy to enter. This feature is likely to make suchmarkets attractive to more than one brand-stretching firm. For this case, then,we will consider the entry of two brand-stretching entrants. They are calledfirm and firm respectively. Because the brand strength of each firm isb b ,1 2

exogenously given by it does not matter whether these two firms entera S ,i i

the target market sequentially or simultaneously. What is important is thateach firm anticipates the entry of the other. That is, in considering brandedentry into a new market, each firm understands that there will be some rivalbrand doing the same thing. It will not necessarily be the same rival in allpotential target markets. Ralph Lauren may expect to confront Calvin Kleinin one market extension but perhaps Coca-Cola in another.

In addition to these two potential entrants, the target market has N identicalincumbent firms, denoted as firm i, , N, where . Each in-i p 1, . . . N ≥ 2cumbent firm has the same unit constant cost of production, c, where 0 !

. In other words, there is no dominant incumbent firm. The incumbentc ! 1firms compete symmetrically for consumers. We assume as well that the brand-stretching firms have the same constant unit production cost as the incumbentfirms. That is, the advantage of the brand-stretching firms is rooted in theirbrand identities and not in any cost advantage.

Firms in the target market compete in prices for consumers, of whom thereare L in total. Each consumer buys at most one product per period. Consumerwillingness to pay for each of the incumbent firms’ substitute products isdetermined by an index v, which is distributed continuously and uniformlybetween 0 and 1. However, consumers value recognition and so are willingto pay more for the products that are more recognized. Accordingly, pricecompetition among the two brand-stretching firms and the incumbent firmswill be affected by consumers’ perception of the differences in their brandstrength.

For the brand-stretching entrants and , brand recognition depends onb b1 2

their market shares in the home market, denoted by and , respectively,S S1 2

and on how well their visibility there translates into the target market, asgiven by the parameters and . Brand recognition, or the factor ofa a a S ,1 2 i i

each entrant’s product, is a highly firm-specific variable, and so it is unlikelythat the two brand stretchers would have exactly the same brand recognitionin the target market. The more likely scenario is that one entrant will havemore brand recognition than the other. Without loss of generality, we willassume here that . That is, brand stretcher has greater branda S 1 a S b1 1 2 2 1

recognition in the target market than does brand stretcher .b2


Because consumers value visibility, they are willing to pay more for aproduct that has a stronger brand image or that is more widely recognizedby others. The increase in consumer willingness to pay for a brand stretcher’sproduct depends, therefore, on the relative difference in brand recognitionbetween the brand stretcher’s product and an incumbent’s product. In keepingwith our basic modeling strategy, we assume that an incumbent firm’s brandstrength in the target market is equal to its market share in that market. Inother words, because an incumbent firm is extending its brand recognition,the parameter a would be equal to one in this case. Because there are N suchincumbents, each identical in the eyes of consumers, the brand strength ofeach is equal to Recall, though, that the brand strength of either brand-(1/N).extending firm is . Accordingly, relating a consumer’s extra willingnessa Si i

to pay to the relative brand strength of a brand-extending firm means linkingthis willingness to pay to . We make this linka S � (1/N), where (i p 1, 2)i i

by assuming that consumer v’s willingness to pay for brand stretcher ’sbi

product is

1v � a S � (1 � v), where 0 ! a ! 1, i p 1, 2. (1)i i i( )N

Relating the willingness to pay for the entrant’s product to the differencebetween and means that consumers are willing to pay more for thea S 1/Ni i

brand stretcher’s product only if it has greater brand strength than an incumbentfirm’s product.

Equation (1) also implies that the value of brand recognition is propor-tionally greater for those consumers with a lower willingness to pay. Thoseconsumers with a relatively high v value the basic product more and brandname recognition less. As v falls, the impact of an entrant’s brand identityon willingness to pay grows. The intuition is that those with a high willingnessto pay or a high v are knowledgeable consumers who understand the basicfunctioning of the product and the essential elements of quality. For example,blue jeans may have initially been bought by those high-v consumers whovalued the pure consumption benefit of such a good. Later, when Calvin Klein,DNKY, and others started to market blue jeans, there were many consumerswho previously had not been a part of the basic blue jean market but whowere then enticed into that market by the prospect of buying designer jeans.In our model, this second group is made up of relatively low-v consumerswhose willingness to pay is so affected by brand names. Consumers whowere already wearing blue jeans before the arrival of designer jeans are thehigh-v consumers who care relatively more about the functionality of the goodand not its brand name.6

6. It could also be the case that brand identity has a larger effect on the intramarginal consumerrather than on the marginal one. That is, the high-v consumers are most affected by brand image.Such an effect is captured by modeling consumer willingness to pay for the entrant’s productas It is easy to show that this alternative specification of consumer preferences[aS � (1/N)]v.E

will lead to the same basic results as those obtained here.


From the consumer’s point of view, the incumbent firms market perfectlysubstitutable products. When there are two or more incumbent firms, pricecompetition among them for consumers is tough, and in equilibrium, this willlead each one to set a price equal to unit cost c. If one incumbent firm set aprice greater than another incumbent firm did, it would serve no customers,and this could not be an equilibrium outcome. Moreover, if some incumbentfirm set a price greater than unit cost c, then another incumbent firm wouldhave an incentive to undercut that firm’s price to serve more customers.Therefore, in the preentry equilibrium we have that each incumbent firm setsa price equal to c.

For any competition among the incumbent firms for consumers willN ≥ 2,exert the same amount of price pressure on the entrants. Nevertheless, con-centration, or the number of rivals N in the target market, is still an importantfactor affecting the profitability of entry via brand stretching. As N gets largerand the target market becomes increasingly competitive, the brand identity

of the incumbent firms becomes ever weaker relative to the identity of1/Neither brand-stretching firm Thus, as N increases, the brand-a S (i p 1, 2).i i

extending firms can enter with an increasingly strong advantage relative tothe initial incumbents in terms of consumer willingness to pay.

A consumer who is willing to pay v for a good marketed by any of theincumbent firms is willing to pay the additional amount [a S � (1/N)](1 �i i

for the brand-stretching entrant’s product . Since price competition amongv) bi

the incumbent firms leads these firms to set a price equal to unit cost c, anecessary condition for the brand stretcher to earn profit by entering thebi

target market is that Otherwise, no consumer will buy thea S � (1/N) 1 0.i i

brand stretcher’s product at a price above cost.Suppose that, for each brand-stretching firm the conditionb , a S �i i i

is satisfied, and so entry into the target market is potentially prof-(1/N) 1 0itable for each firm. Denote by and the prices set by brand-stretchingb bp p1 2

firms and , respectively, and denote by the price of each incumbentIb b p1 2 i

firm’s product. As already noted, in any price equilibrium for allIp p c,i

. Observe as well that, in any price equilibrium in this targeti p 1, . . . , Nmarket, the price of brand stretcher ’s product must be greater than the priceb1

of brand stretcher ’s product, or . If this were not true, then givenb bb p 1 p2 1 2

our assumption that brand stretcher would serve no consumersa S 1 a S , b1 1 2 2 2

in the target market. Clearly, this cannot be a price equilibrium since brand-stretcher firm could always decrease its price and capture some consumers.b2

More specifically, we will assume that, in any price equilibrium,

1⎡ ⎤a S �( )1 1 Nb bp 1 p . (2)1 21⎢ ⎥a S �( )2 2 N⎣ ⎦

Later we will show that condition (2) is satisfied in a price equilibrium.


We begin by describing the firms’ demand functions in the price region forwhich a price equilibrium can exist. Define to be the consumer who isBv12

indifferent between buying from brand stretcher and brand stretcher atb b1 2

prices and . Define to be the consumer who is indifferent betweenb b Ip p v1 2 bi

buying from brand stretcher or an incumbent firm i at prices andbb pi i

where . These definitions imply thatI bp p c, p 1 ci i

b b(p � p )1 2Bv p 1 � ,12 (a S � a S )1 1 2 2

b(p � c)iIv p 1 � . (3)bi 1a S �( )i i N

When condition (2) holds, it is straightforward to show that .B I Iv ! v ! v12 bI b2

This means that consumers with a relatively high v, specifically preferIv 1 v ,b2

to buy an incumbent’s product. Consumers with v such that preferB Iv ! v ! v12 b2

to buy brand stretcher ’s product. Finally, consumers with prefer toBb v ! v2 12

buy brand stretcher ’s product or no product at all. When the price of brandb1

stretcher ’s product, is such that then consumerb bb p , [a S � (1/N)] � p 1 0,1 i 1 1 1

buys a product, and the entire market is served. Otherwise, define byv p 0the consumer who is indifferent between buying brand stretcher ’s productv b1

and buying no product at all. For we have thatv 1 0,

1bv � a S � (1 � v) � p p 0,1 1 1( )N

or

1bp � a S �[ ]( )1 1 1 N

v p . (4)11 � a S �( )1 1 N

The demand for brand stretcher ’s product isb1

B b b bL[v (p , p ) � v(p )] for v 1 0,12 1 2 1b b bq (p , p ) p (5)1 1 2 B b b{Lv (p , p ) otherwise.12 1 2

Demand for brand stretcher ’s product isb2

b b I I b I B b bq (p , p ) p L[v (p , p ) � v (p , p )]. (6)2 2 i 2 2 i 12 1 2

Firms in the target market set prices to maximize profit given the demandsfor their products. For the moment, we will solve for the equilibrium pricesand profits in the postentry target market under the assumption that the unitcost of production . This assumption simplifies the algebra without tooc p 0much loss of generality. By making this assumption, essentially we guaranteethat the entire market is served, both before and after the entry of the brandstretchers. That is, each consumer v buys a product in the target market. If,


on the other hand, the unit cost of production c were high relative to thedistribution of v, then the entire market would not be served in the preentrytarget market. We will discuss the implications of brand stretching in suchhigh-cost target markets later in this section.

We solve for the equilibrium prices (again, assuming that ) in thec p 0appendix, and we report the results here. In equilibrium, each incumbent firmsets a and earns zero profit, whereas the brand-stretching firms setIp p 0i

prices

12(a S � a S ) a S �( )1 1 2 2 1 1 Nbp p ,1 34a S � a S �( )1 1 2 2 N

1(a S � a S ) a S �( )1 1 2 2 2 2 Nbp p , (7)2 34a S � a S �( )1 1 2 2 N

and earn profits

21⎡ ⎤4(a S � a S ) a S �( )1 1 2 2 1 1 Nbp p L ,1 23⎢ ⎥4a S � a S �( )1 1 2 2 N⎣ ⎦

1 1⎡ ⎤(a S � a S ) a S � a S �( ) ( )1 1 2 2 1 1 2 2N Nbp p L . (8)2 23⎢ ⎥4a S � a S �( )1 1 2 2 N⎣ ⎦

Observe that these equilibrium prices satisfy condition (2). Furthermore, weshow in the appendix that firm has no profit incentive to deviate and chargeb1

a price Doing so would only lower its profit.1 1b bp ≤ p (a S � )/(a S � ).1 2 1 1 2 2N N

We can learn several things about brand stretching from the equations above.Consider, first, the brand stretcher with the stronger recognition, firm . Theb1

profit of firm is always increasing in its own brand recognition, bb �p /�a 11 1 1

and 7 This firm’s profit also increases as the number of incumbentb0 �p /�S 1 0.1 1

firms N grows, . However, firm ’s profit is decreasing in the strengthb�p /�N 1 0 b1 1

of the rival brand stretcher, firm , or and In short,b bb �p /�a ! 0 �p /�S ! 0.2 1 2 1 2

for the firm with the strongest brand image, the profitability of brand stretchingincreases as the rival brand stretcher’s identity becomes relatively weaker (eitherbecause this strongest firm’s brand becomes stronger or its rival’s brand becomesweaker) and increases as the target market becomes less concentrated.

Matters are somewhat different for the weaker brand stretcher, firm . First,b2

note that the profitability of brand stretching for firm increases with theb2

brand strength of its rival, firm , or and The weakerb bb �p /�a 1 0 �p /�S 1 0.1 2 1 2 1

7. These derivations and the derivations below are found in the appendix.


brand name is better off competing in a target market with a strong brandname. The intuition behind this result has to do with price competition. Thestronger the brand recognition of firm the higher is the price that it canb ,1

charge to brand-conscious consumers in the target market. This softens pricecompetition and makes it easier for the weaker brand-stretching firm tob2

attract less brand-conscious consumers to its product.Second, the profit of firm is not always increasing in its own brandb2

recognition. Rather, there is an optimal brand recognition for the weaker brandstretcher to have in this target market. Specifically, the most profitable brandstrength for the relatively weaker brand stretcher to have is ∗ ∗a S p2 2

For example, when firm has the optimal brand(4/7)a S � [3/(7N)] ! a S . b1 1 1 1 2

strength in the target market or when , it∗ ∗a S p (4/7)a S � [3/(7N)] ! a S ,2 2 1 1 1 1

earns a profit which is increasing in and N.bp p [a S � (1/N)]/48, a , S ,2 1 1 1 1

Finally, firm ’s profit is—like firm ’s—increasing in the number ofb b2 1

incumbent firms in the target market, . All else (in particular theb�p /�N 1 02

value of a) equal, firm will also prefer a less concentrated market. In sum,b2

the most profitable strategy for the brand-stretcher firm is to seek entryb2

into a nonconcentrated target market in which the rival with the stronger brandhas roughly double the brand strength.

The market shares of the firms in the postentry target market are

12 a S �( )1 1 Nbq p ,1 34a S � a S �( )1 1 2 2 N

1a S �( )1 1 N

bq p , (9)2 34a S � a S �( )1 1 2 2 N

(a S � a S )1 1 2 2IQ p ,34a S � a S �( )1 1 2 2 N

where is the market share of all the incumbent firms. Note that the marketIQshare of the incumbent firms is larger the more differentiated are the twobrand stretchers, or the larger is the difference . Again, the in-a S � a S1 1 2 2

tuition is clear. The greater is the difference between the two brand stretchersin terms of perceived brand strength, the softer is price competition, and softerprice competition benefits the incumbent firms whose low prices then serveto capture more easily the less brand-conscious consumers.

When the unit cost of production is greater, or , then brand-stretchingc 1 0entry increases the number of consumers served in the target market. Beforeentry, the marginal consumer , that is, the one indifferent between buyingv

an incumbent’s product and not buying at all, is . After the brandv p cstretchers enter the market, it is straightforward to show that the marginalconsumer is such that . In other words, brand stretching expands thev ! c


market. Of course, this is not surprising, because it is the lower-v consumerswho care proportionately more about brand names. The size of the targetmarket, both preentry and postentry is, however, smaller the higher is the unitcost of production. Moreover, the higher the unit cost, the less profitable itis to enter this target market. It follows that both brand stretchers will preferto enter large markets, or ones with relatively lower unit costs of production.Increasing market size, as measured by the density of consumers or the pa-rameter L also raises the profitability of brand-stretching entry.

B. Brand Stretching into a Monopolized Target Market

A target market that is monopolized, or highly concentrated, is likely to bea market that is difficult to enter. For this case, therefore, we consider thepotential entry of only one brand-stretching firm. Within the framework usedhere, this implies that this firm enters at a brand name disadvantage relativeto the incumbent. In the preentry market, the incumbent has 100% marketshare or brand recognition equal to one, whereas the entrant has brand rec-ognition equal to . Given the strong brand name recognition of theaS ! 1incumbent, consumers in the target market would not be willing to pay morefor an entrant’s less well-known product. Specifically, a consumer who iswilling to pay v for the good marketed by the incumbent monopolist wouldbe willing to pay only for the brand-stretching entrant’sv � (1 � aS)(1 � v)new product. In contrast with the previous case, it is the relatively low-vconsumers who are more interested in the product of the incumbent firm. Thebrand-stretching entrant in this case would compete for high-v consumers whocare less about brand name recognition.

Denote by and the prices set by the brand-stretcher firm and theb Ip pincumbent monopoly. In a price equilibrium in the postentry market, we musthave that . If the price of the brand stretcher’s product were greaterI bp 1 pthan the price of the incumbent’s well-known brand, then no consumer wouldbuy from the brand stretcher. Clearly, that cannot be an equilibrium, since thebrand stretcher could always decrease its price and capture some less brand-conscious consumers. Define to be the consumer who is indifferent betweenIvb

buying from the brand stretcher and the incumbent at prices and , whereb Ip p. From above, it follows that ConsumersI b Ip 1 p v p 1 � [(p � p )/(1 � aS)].b I b

whose v is such that prefer to buy the brand-stretching entrant’sI1 ≥ v 1 vb

product at its lower price. The consumers who prefer to buy the better-knownincumbent’s product are those with such that , where is theIv v 1 v ≥ v vb

marginal consumer who is just indifferent between buying the incumbent’sproduct and buying no product at all. In this case, the marginal consumer is

. The entire market is never served in a monopolized target market.Iv p p 1 0The demand for the brand stretcher’s product is

b b I I b Iq (p , p ) p L[1 � v (p , p )], (10)b


and the demand for the incumbent’s product is

I b I I b I Iq (p , p ) p L[v (p , p ) � v(p )]. (11)b

Thus, in the postentry target market, the brand stretcher sets to maximizebpprofit,

I b(p � p )Lb b I b b b I bp (p , p ) p (p � c)q (p , p ) p (p � c) , (12)

1 � aS

and the incumbent sets price to maximize its profit,Ip

b Ip � (2 � aS)pI b I I I b I Ip (p , p ) p (p � c)q (p , p ) p (p � c) 1 � L. (13)[ ]

1 � aS

Equations (12) and (13) imply the following best response functions for thebrand stretcher and incumbent, respectively:

Ip � cbp p , (14)

2

b1 � aS � p cIp p � . (15)

2(2 � aS) 2

To solve for the equilibrium prices and profits of the firms, we will, forsymmetry with the previous case, make the same assumption that unit costof production . Given this assumption, equations (14) and (15) yieldc p 0equilibrium prices

1 � aSbp p ,

7 � 4aS

2(1 � aS)Ip p . (16)

7 � 4aS

Equilibrium profits are given by

⎡ ⎤1 � aSbp p L ,⎢ ⎥2(7 � 4aS)⎣ ⎦

⎡ ⎤4(2 � aS)(1 � aS)Ip p L . (17)⎢ ⎥2(7 � 4aS)⎣ ⎦

Observe that these equilibrium prices satisfy the condition that . If theI bp 1 pincumbent firm deviated and charged a price it is easy to show thatI bp ≤ p ,such a deviation would not be profitable.

As was the case with brand-stretching firm in the previous model, theb2

profit of the brand stretcher in equation (17) implies that too strong a brandidentity can be a hindrance rather than a help in entering a monopolizedaStarget market. Both firms face a similar problem, namely, the presence of


another firm with an even stronger brand identity. In the former case, it wasthe other brand-stretching firm, . Here, it is the established monopolist thatb1

already has a clear brand image of its own. As the entrant’s brand imagestrengthens, consumers become willing to pay more for its product. However,it is also the case that the stronger the entrant’s brand image, the closer itsproduct substitutes for that of the incumbent’s—a feature that intensifies pricecompetition. The issue is, of course, to balance these two opposing forces.As it turns out, when the brand-stretching entrant takes on a monopoly in thetarget market, the optimal or profit-maximizing balance is achieved when itsbrand strength is and the entrant’s profit is Entry withbaS p 1/4 p p L/48.a stronger brand image than this will reduce profit. In this light, it shouldperhaps not be surprising that markets dominated by one or a few dominantbrands, such as the cigarette and cereal markets, have been the loci of entryby small or less well-known private labels rather than by equally well-knownbrands from other sectors.

III. Some Lessons from the Model

Our model investigates why a firm with brand recognition in its home markethas an incentive to leverage its asset of a recognized brand name into othermarkets. Abstracting from entry costs, brand stretching is generally profitable.However, it is likely that such entry costs are present and, more important,that they will affect the number of target markets entered. Our analysis servesto illuminate the several factors that influence the choice of the target marketand to make equally clear that there is no “one size fits all” rule for makingthis selection.

One important insight of the model is that the target market that is the mostprofitable to enter is not necessarily the one in which the firm has the greatestbrand recognition, that is, the one for which the term is greatest. TheaSprofitability of brand stretching depends on the nature of the price competitionin the target market, and this, in turn, depends on the brand recognition ofthe brand-stretching entrant relative to that of other firms. A target marketthat is “close” to a firm’s home market, that is, one whose a is high, may beless profitable than one “far” away with a lower a for several reasons. First,it may be that the nearby market is highly concentrated, perhaps even amonopoly, so that the firm’s relative brand strength in that market will beweak in comparison with that of the incumbent firm or firms. Second, a rivalwith an even stronger brand image may be entering the nearby target market,which again will weaken the firm’s relative brand strength. In consideringthis possibility, one should recall as well that a firm that enters as the second-strongest brand really prefers to do so in a market in which the strongestbrand is relatively much stronger. Thus, a firm for whom the choice set oftarget markets is limited to ones in which it knows it will be “second best”may again wish to pursue a somewhat “distant” market in which the loss fromconsumer willingness to pay (as a result of a low a value) is more than offset


by the benefit of softer price competition. In other words, the model helps usto understand the decisions of firms such as Coca-Cola and Dr. Martens toextend their brand names into markets that appear to be somewhat “distant”from their home base.

A related lesson from our model is that it is generally more profitable tostretch a well-known brand into target markets with decreasing concentrationwhether another stronger brand is also entering that market or not. Part of thevalue of this insight is, again, its ability to explain the frequent decision tostretch the brand name to a distant or low-a market. Such a choice may bejustified if it permits entry into such a less concentrated industry that thefirm’s brand advantage is now sufficiently strong that the profitability of entryis increased despite the lower a-value. The attraction of low-concentrationmarkets may also explain the results of Court, Leiter, and Loch (1999) in astudy of brand extension for McKinsey and Company. These authors find that“many strong companies are using their brands to move quickly into industrieswith low brand intensity,” thereby pursuing markets in which “competitionis fragmented” and “where their brand enjoys a competitive advantage” (p.107). Among others, they cite the highly profitable extensions of AmericanExpress into the actual planning and operation of travel packages and of Searsinto such services as pest control and appliance repair.8

IV. Concluding Remarks

We have argued that a firm’s decision to leverage its brand to a new productline is of interest to economists because it is an important manifestation ofthe process of entry, perhaps increasingly so. We have further argued thatboth this perspective and a consideration of actual cases of brand stretchingsuggest that prior analyses of the brand extension phenomenon based on scopeeconomies or quality signaling are unlikely to reveal the entire story of thisentry process. This is because such entry typically occurs in existing marketswith one or more incumbents and, therefore, in markets in which the natureof price competition in the postentry market is crucial. It also occurs in marketsthat seem distant from the home market of the brand-extending firm in whicha reputation or scope economy-based explanation is less plausible.

We have modeled brand recognition as a complement to the product itselfmuch in the way that Becker and Murphy (1993) model advertising. In thisview, consumers prefer to consume a good that is well known by others ratherthan to consume one that is not. A brand name is a measure of this marketrecognition factor. Having a brand name permits a firm to enter an existing

8. One limitation of the above model is that the initial incumbent firms in the target marketare assumed to offer perfect substitutes. There is no differentiation among these initial products.However, in a separate appendix to this article that is available upon request, we consider thisissue by modeling the target market along the lines of the circle model originally pioneered bySalop (1979). Our results suggest that the same basic insights as those obtained herein emergein that context as well.


market where less well-known rivals cannot, primarily because the firm withbrand identity can charge a higher price. However, we show that, if this isthe mechanism by which brand identity works, the entry behavior that followsdepends very much on how price competition is affected by brand namerecognition. While generally brand stretchers will prefer entry into marketsthat are less concentrated, the profitability of such entry will also depend onwhether a rival firm with a well-known brand is also entering the target marketand precisely which firm has the relatively stronger brand recognition. Marketsize is also important. Thus, finding a target market that gives the greatestreturn to the brand-name asset is not clear-cut. Brand-extending firms mayoften seek out markets that are, in some sense, “far” from their initial productline, where their brand strength may not be as great as it would be in a“nearer” market. The reduction in the brand image that the firm can projectin such a market may be offset by the advantages such a market offers interms of lower concentration or the strength of the rival entrant’s brand inthat market.

While the models that we have presented assume no scope economies andhave no consumer uncertainty regarding a product’s quality, we do not meanto imply that such factors are unimportant. Rather, our objective has been toilluminate the entry process beyond the insights that attention to these alter-native factors reveal. At the same time, we find that the rich pattern of entrysuggested by our results is roughly consistent with empirical observation.

Appendix

Post Brand-Stretching Price Equilibrium in the Target Market

In this appendix, we solve for the equilibrium prices (again assuming that ) inc p 0the target market after the brand stretchers have entered. Given the equilibriumconditions

1a S �( )1 1 N

b b(E1) p 1 p , and1 2 1a S �( )2 2 N

I(E2) p p c p 0 for all incumbent firms i p 1,2, . . . , N,i

it is straightforward to show that firm ’s and firm ’s demands are, respectively,b b1 2

(p � p )⎡ ⎤1 2L 1 � ,⎢ ⎥

a S � a S⎣ ⎦1 1 2 2b b bq (p , p ) p (A1)11 1 2 ⎡ ⎤p � a S �1 1 1(p � p ) N1 2

L 1 � � for v 1 0,{ 1⎢ ⎥a S � a S 1 � a S �1 1 2 2 1 1 N⎣ ⎦

p (p � p )⎡ ⎤2 1 2b b bq (p , p ) p L � � . (A2)2 1 2 1⎢ ⎥a S � a Sa S � 1 1 2 22 2 N⎣ ⎦


Firm chooses to maximize and firm chooses tob b b b b b b b bb p p (p , p ) p p q (p , p ), b p1 1 1 1 2 1 1 1 2 2 2

maximize b b b b b b bp (p , p ) p p q (p , p ).2 1 2 2 2 1 2

Suppose that the entire market is served. Later we will show that, for firmis not a profit-maximizing strategy.b , v 1 01

In this case, profit maximization leads to the best response functions,

a S � a S � p1 1 2 2 2bp p ,1 2

1p a S �( )1 2 2 Nbp p , (A3)2 12 a S �( )1 1 N

and to the Nash equilibrium prices,


1(a S � a S ) a S �( )1 1 2 2 2 2 Nbp p . (A4)2 34a S � a S �( )1 1 2 2 N

These prices imply profits


1 1(a S � a S ) a S � a S �( ) ( )1 1 2 2 2 2 1 1N Nbp p . (A5)2 234a S � a S �( )1 1 2 2 N

Next we need to show (i) that firm could not increase its profits by serving fewerb1

customers, that is, have , and (ii) that firm could not increase its profits byv 1 0 b1

deviating from condition (A1) and undercutting firm ’s price so that firm servesb b2 2

no customers:(i) Suppose that and so firm chooses1 1

v p (p � a S � )/(1 � a S � ) 1 0, b1 1 1 1 1 1N N

to maximizep1

1⎡ ⎤(p � a S � )1 1 1(p � p ) N1 2b b bp (p , p ) p p q (p , p ) p p 1 � � , (A6)1 1 2 1 1 1 2 1 1⎢ ⎥(a S � a S ) (1 � a S � )1 1 2 2 1 1 N⎣ ⎦


and firm chooses to maximize as previously defined.b b b b b b b bb p p (p , p ) p p q (p , p ),2 2 2 1 2 2 2 1 2

The candidate equilibrium prices in this case are

12(a S � a S ) a S �( )1 1 2 2 1 1 Nbp̂ p ,1 1 13 a S � 1 � a S � �a S( ) ( )1 1 2 2 1 1N N

1 1(a S � a S ) a S � a S �( ) ( )1 1 2 2 1 1 2 2N Nbp̂ p . (A7)2

1 1 1 ( )a S � 3 a S � 1 � a S � � a S[ ]( ) ( ) ( )1 1 1 1 2 2 1 1N N N

Given these prices, which is a contradiction.v ! 0,(ii) Suppose now that firm deviated and charged a price b b˜b p p p {[a S �1 1 2 1 1

where is defined in (A4). When firm makes such ab(1/N)]/[a S � (1/N)]}, p b2 2 2 1

deviation, it captures all of firm ’s market and serves consumers v, whereb 0 ≤ v ≤2

Firm therefore, earns a profitb˜1 � {(p /[a S � (1/N)]}. b ,1 1 1 1

1ba S �1 1 pN 2b b b˜p̃ (p ) p p 1 � .1 1 2 1 1( ) ( )a S � a S �2 2 2 2N N

Substituting implies thatbp p {(a S � a S )[a S � (1/N)]}/[4a S � a S � (3/N)]2 1 1 2 2 2 2 1 1 2 2

1(a S � a S ) a S �( )1 1 2 2 1 1 N (a S � a S )1 1 2 2bp̃ p 1 �1 3 3[ ]4a S � a S � 4a S � a S �( ) ( )1 1 2 2 1 1 2 2N N

213(a S � a S ) a S �( )1 1 2 2 1 1 N

p ,234a S � a S �( )1 1 2 2 N

which is less than the profit earned in (A5). Such a deviation is not profitable.Given that the two brand stretchers’ prices and profits in (A4) and (A5) characterize

the postentry equilibrium in the target market, we now investigate what factors makea target market more profitable. To simplify the analysis, we define the brand-rec-ognition factor , or for and we consider how increases in and Nb p a S i p 1, 2, bi i i i

affect profitability in the target market. Consider, first, the stronger brand-stretcherfirm, :b1

1 1 32 24 b � (4b � 3b b � 2b ) � (5b � b ) �[ ]( ) 21 1 1 2 2 1 2N N N�p1p 1 0,

3 3�b (4b � b � )1 1 2 N

21 34 b � � 2b � b( ) ( )1 1 2N N�p1p ! 0,

3 3�b (4b � b � )2 1 2 N

1 28 b � (b � b )( )1 1 2N�p1p 1 0.

32 3�N N (4b � b � )1 2 N


For brand-stretcher firm we have thatb ,2

1 3b � 4b � 7b �( )( )1 1 2N N�p 4 32

p p 0 for b p b � ,2 133�b 7 7N2 4b � b �( )1 2 N

21 152 b � � 8b � 7b( ) ( )2 1 1 2N N� p2p ! 0,32 3�b2 4b � b �( )1 2 N

21 3b � 2b � b �( ) ( )2 1 2N N�p2

p 1 0,33�b1 4b � b �( )1 2 N

2�p (b � b ) [N(4b � b ) � 5]2 1 2 1 2p 1 0.3

3�N 3N 4b � b �( )1 2 N

References

Becker, G., and Murphy, K. 1993. A simple theory of advertising as a good or bad. QuarterlyJournal of Economics 15 (November): 498–517.

Cabral, L. 2000. Stretching firm and brand reputation. Rand Journal of Economics 31 (Winter):658–73.

Caves, R. 1998. Industrial concentration and new findings on the turnover and mobility of firms.Journal of Economic Literature 36 (December): 1947–82.

Choi, J. P. 1998. Brand extension and informational leverage. Review of Economic Studies 65(October): 655–69.

Court, D. C.; Leiter, M. G.; and Loch, M. A. 1999. Brand leverage. McKinsey Quarterly, no. 2,pp. 100–109.

DeGraba, P., and Sullivan, M. 1992. Spillover effects, cost savings, R&D and the use of brandextensions. International Journal of Industrial Organization 13 (June): 29–48.

Economist. 1996. Broad, deep, long and heavy: Assessing brands. Economist, November 16,1996.

Grossman, G., and Shapiro, C. 1988. Foreign counterfeiting of status goods. Quarterly Journalof Economics 103 (March): 79–100.

Independent. 1997. These boots are made for your CD player. Independent, March 2.National Post. 1999. Coke clothers to be the next real thing: To be unfolded worldwide. National

Post, January 21.Salop, S. 1979. Monopolistic competition with outside goods. Bell Journal of Economics 10

(Spring): 141–56.Sappington, D., and Wernerfelt, B. 1985. To brand or not to brand? A theoretical and empirical

question. Journal of Business 58 (July): 279–93.Smith, D., and Park, C. 1992. The effect of brand extensions on market share and advertising

efficiency. Journal of Marketing Research 29 (August): 296–313.Wernerfelt, B. 1988. Umbrella branding as a signal of new product quality: An example of

signaling by posting a bond. Rand Journal of Economics 19 (Fall): 458–66.

the simple economics of brand stretching

Documents

brand stretcher bi

incumbent rm sets

specic target market

brand stretcher b1

brand stretchers recognition

weaker brand stretcher

stronger brand image

postentry target market