WILFRED AMALDOSS and CHUAN HE
In many product categories, consumer tastes are diverse, and firms
use finely targeted advertising to inform consumers about their products.
This article proposes a model of informative advertising that allows for
diverse consumer tastes and multiple competing firms. Using this framework, the authors analyze how diversity in consumers’ tastes, informative
advertising, and improvements in advertising technology may influence
prices. First, informative advertising can lead to lower prices if consumer
valuations are high. However, if consumer valuations are low, informative
advertising can lead to higher prices. Second, when consumer valuations
are high, price increases with greater diversity in tastes, though this result
reverses if consumer valuations are low. Third, improvements in advertising technology lead to higher levels of advertising when consumer valuation is high, but the opposite effect can occur when consumer valuation
is low. The authors relate these theoretical findings to previous empirical
literature on advertising.
Keywords: informative advertising, advertising technology, competition,
game theory
Product Variety, Informative Advertising,
and Price Competition
In several product categories, such as eyeglasses, toys,
apparel, and watches, firms offer a variety of products to
satisfy diverse consumer needs. The competition among
firms offering these products is often nonlocal because consumers can purchase the products easily on the World Wide
Web. Even if firms offer a sufficiently large variety of products, they may not carry the preferred products of some
consumers. It is also conceivable that a consumer’s preferred products are available, but he or she does not receive
information about them. In this article, we investigate how
advertising may influence the prices and profits of firms in
such markets, as well as how improvements in advertising
technology may moderate the effects of advertising.
Advertising can both inform and persuade consumers,
but we focus on that which informs consumers about product characteristics and prices. Considering a market in
which consumers have diverse tastes and seek N different
varieties (e.g., flavors), we investigate three questions: How
does informative advertising influence equilibrium price?
What is the effect of diversity in consumers’ tastes on
equilibrium price? and How do improvements in advertising technology affect equilibrium price? Following Chen
and Riordan (2007) and Grossman and Shapiro (1984), we
develop a model of informative advertising that offers several noteworthy properties. In our formulation, consumers
are distributed on a plane along different taste dimensions
(spokes), each firm competes directly with every other firm
in the market (nonlocal competition), the market can be
partially covered, and competition can occur among a few
or many firms. Our analysis highlights how informative
advertising interacts with market structure and consumer
valuation to shape firm behavior.
First, we show that when many firms compete, prices
are strictly increasing with informative advertising for lowvaluation products, whereas the opposite effect holds when
the products are highly valued. Intuitively, if the base valuation of products is low, some informed consumers can
purchase any product in their consideration set, whereas
others may be able to purchase only one product at best.
Therefore, the price sensitivity of demand varies across
consumers and becomes an important driver of our result.
Specifically, informative advertising increases the relative
importance of consumers who are less sensitive to price
*Wilfred Amaldoss is Associate Professor of Marketing, Fuqua School
of Business, Duke University (e-mail: [email protected]).
Chuan He is Assistant Professor of Marketing, Leeds School of Business,
University of Colorado (e-mail: [email protected]). The authors
thank the anonymous JMR reviewers for their helpful comments. The
authors also thank Jim Bettman, Yongmin Chen, Preyas Desai, Joel Huber,
Sanjay Jain, John Lynch, Carl Mela, Debu Purohit, Ambar Rao, Amnon
Rapoport, Ron Shachar, Richard Staelin, Miguel Villas-Boas, and Ken
Wilbur. Brian Ratchford served as guest editor for this article. Teck Ho
served as associate editor for this article.
© 2010, American Marketing Association
ISSN: 0022-2437 (print), 1547-7193 (electronic)
146
Journal of Marketing Research
Vol. XLVII (February 2010), 146–156
Variety, Advertising, and Price Competition
and thereby encourages firms to charge a higher price.
In contrast, when consumer valuation is sufficiently high,
all informed consumers can gain surplus by buying any
product in their consideration set, so firms cut prices to
attract marginal consumers. Even in the case of oligopolistic competition, the interaction between market structure
and consumer valuation determines whether informative
advertising increases or decreases equilibrium price. We
also identify conditions under which informative advertising has no effect on price.
Second, in markets in which consumers’ tastes are more
diverse, equilibrium prices are lower when consumer valuations are low; this result reverses if consumer valuations
are high. To clarify the intuition behind this finding, we
note that in a market with a constant number of products
available, when consumers’ tastes become more diverse,
fewer consumers have the opportunity to purchase the product that best matches their preferences. This situation creates two opposing forces. On the one hand, firms need to
motivate consumers to purchase their less preferred products, which induces the firms to compete on price. On the
other hand, firms face fewer direct competitors in the market because market coverage declines, which softens price
competition. Overall, when consumer valuations are low,
prices are lower if there is greater diversity in consumer
tastes. The opposite result prevails if consumer valuations
are high.
Third, we find that the influence of advertising technology on equilibrium price depends on consumer valuations
and the convexity of the advertising cost function. When
consumer valuations are low, improvements in advertising
technology lower prices if the convexity of the cost function is below some threshold, but they increase price otherwise. The threshold level is related to the market structure.
However, if consumer valuations are high, improvements
in advertising technology reduce prices. In analyzing the
impact of advertising technology on a firm’s profits, we
observe that improvements in technology always improve
profits when consumer valuations are high but not necessarily in other cases.
A large body of theoretical and empirical literature pertains to advertising (for a review, see Bagwell 2005),
including Grossman and Shapiro’s (1984) extension of
Butters’s (1977) model to analyze the role of informative
advertising in a horizontally differentiated market. A key
result of their analysis is that firms engage in excessive advertising in a monopolistically competitive market. Moreover, improvements in advertising technology
reduce a firm’s profits because of intensified competition. In
Grossman and Shapiro’s model, consumers are distributed
along a circle.
Also using a circle model, Soberman (2004) shows that
price decreases with informative advertising when product
differentiation is modest but increases when product differentiation is high. We extend this analysis to a market
that is partially covered and identify oligopolistic competition conditions in which price may decrease with informative advertising. Although Soberman’s (2004) findings
are tenable for a duopoly, we show that these results may
reverse, depending on the diversity in consumers’ tastes and
the number of competitors. Furthermore, we investigate the
effect of advertising technology on equilibrium advertising
147
and prices. However, we cannot perform this analysis with
a circle model (Soberman 2004).
Competition in a circle model is local, in that a small
change in a firm’s price only affects neighboring firms, not
other, more distant firms in the market. As a major drawback, the symmetry of the circle model requires incumbent
firms to relocate in the product space after the entry of a
new firm (e.g., Grossman and Shapiro 1984; Salop 1979;
Soberman 2004). In our formulation, however, consumers
are distributed on spokes across a network, and competition
is not localized. More generally, the spoke-based model
offers desirable properties that distinguish it from the circle
model and make it appealing as a framework for studying spatial competition. First, the spokes model allows for
symmetric brands and firms but does not require movement
by incumbents when a new firm enters the market. Second,
each firm is in direct competition with all other firms in the
market. Third, this model does not assume that the market is fully covered; rather, market coverage depends on
the number of competing firms and consumer valuations.
Fourth, the spokes model lends itself to the exploration of
the strategic implications of the presence of a sufficiently
large number of firms and diverse consumer tastes (Chen
and Riordan 2007).
Chen and Riordan (2007) use the spokes model to
analyze the effect of nonlocal competition on prices; we
incorporate informative advertising into the model and
investigate a different set of issues. Our research contributes
to literature on informative advertising in several ways. For
example, many product markets contain several segments
of consumers with different tastes, such that their needs
might not be satisfied by the products available in the market. We introduce a model of informative advertising that
reflects these market realities and show how diversity in
consumer tastes and market structure moderates the effect
of informative advertising on prices. These results cannot
be derived from a Hotelling or circular city model.
The rest of this article proceeds as follows: We outline our model in the next section, after which we analyze
the effects of informative advertising on price. We then
investigate the effect of diversity in consumer tastes on
equilibrium prices, the influence of changes in advertising
technology on advertising levels and prices, and the impact
of advertising technology on firms’ profits. Finally, we conclude with a summary of the findings and directions for
further research.
THE MODEL
Consider a product market in which consumers’ tastes
are diverse, so they seek N different varieties (e.g., flavors).
We model the market as a network of spokes on a plane.
Consumers who prefer variety i i = 1 2 N can be
represented by a line li of length 1/2. Each consumer is a
point on the spoke, and we denote the consumer located
on spoke i at a distance x from its proximal end by (li , x),
where x ∈ 0 1/2. At the origin (proximal end) of a spoke,
x = 0, and at the center of the spoke, x = 1/2. We assume
that consumers are distributed uniformly on the spokes network, and we normalize the total mass of consumers to
unity.
148
JOURNAL OF MARKETING RESEARCH, FEBRUARY 2010
Figure 1
MARKET WITH EIGHT SPOKES N = 8 AND FOUR FIRMS
n = 4
li
Notes: N ≥ n ≥ 2, where N and n are integers.
With n firms in the market, we index the firm or product
j = 1 2 n, where 2 ≤ n ≤ N. Each firm produces only
one product and is located at the origin of the spoke for that
particular variety (i.e., at x = 0). In Figure 1, we illustrate
a market with eight spokes N = 8 and four firms n = 4.
The marginal cost of production is a constant, which we
set equal to 0 to facilitate the exposition of the model.
Consumers are completely uninformed about a firm’s
product unless they are exposed to its advertising. As do
Grossman and Shapiro (1984), we assume that advertising
informs consumers about product characteristics and prices
and that each consumer purchases at most one unit of a
product (see also Butters 1977; Soberman 2004). The base
value of all the product varieties is the same, denoted by v.
If the consumer located at (lj x) is aware of the local brand
and chooses to purchase the product, he or she derives the
following indirect utility:
(1)
Ulj x pj = v − tx − pj where t is the consumer’s sensitivity to product characteristics and pj is the price of the product. If the consumer
wants to purchase any other product about which he or she
is informed—such as variety k, such that k = j—the indirect
utility from this nonlocal brand is as follows:
(2)
Ulj x pk = v − t1 − x − pk The consumer located at lj x is 1/2 − x units of distance
away from the center of the spokes network, and brand k
is 1/2 unit of distance farther away. Thus, the total distance between the consumer and the nonlocal brand k is
1/2 − x + 1/2 = 1 − x. The consumer purchases local brand
j if Ulj x pj > Ulj x pk . A marginal consumer who
is indifferent between the two products locates at a distance 1/2 + pk − pj /2t from brand j, and demand for
local brand j is min1/2 + pk − pj /2t 1, which implies
pk − pj /t ≤ 1.
Similar to the assumption in previous informative advertising models (e.g., Butters 1977; Grossman and Shapiro
1984; Soberman 2004), we assume that consumers can
recall the characteristics and prices of the products they
have seen in advertisements when they formulate purchase
decisions. However, they do not engage in any costly information search. This assumption does not imply that consumers are unaware of the underlying market structure
but rather suggests that consumers do not know a priori
which firm sells which product and at what price. We let
(0 ≤ ≤ 1) be the fraction of the target market that a
firm’s advertising reaches.
In Chen and Riordan’s (2007) study, consumers consider
at most two products, and the consideration set consists of a
local brand and a nonlocal brand. Furthermore, consumers
are equally likely to consider the purchase of any available nonlocal brands.1 We include the local brand in the
consumer’s consideration set, such that the probability that
the consumer is aware of the local brand is . In addition,
the consideration set includes at most one nonlocal brand,
which we require to be from among the set of products
whose advertisements the consumer has seen. This restriction is consistent with the notion that consumers remain
uninformed about a product unless they receive exposure to
its advertising. In the limiting case in which consumers are
perfectly informed, our assumption is identical to that of
Chen and Riordan. Furthermore, the assumption that consumers consider at most two brands helps us obtain a pure
strategy equilibrium and reflects the generally small size
of consumers’ consideration sets (Hauser and Wernerfelt
1990; Nedungadi 1990).
We denote the cost of reaching a fraction of the market
by A
, where is a scale parameter that represents
the advertising technology. We assume that A0 = 0,
A
= A/
> 0, and A
= 2 A/
2 > 0; therefore, advertising costs are convex. An inferior advertising technology
increases and makes advertising more costly, such that
A = A/ > 0. When the level of increases, it becomes
increasingly costly to reach additional consumers, often
because the preferred advertising media become saturated.
We capture this aspect of advertising costs by letting A
=
2 A/
> 0. We also assume that advertising technology
is symmetric across all firms.
Consumer Demand
Firm j’s product could be the local or the nonlocal brand
in a consumer’s consideration set. For ease of exposition,
we partition consumers who purchase brand j into four
groups, depending on the composition of their consideration sets (see Figure 2). In Table 1, we summarize demand
from these four groups.
1
An individual consumer may prefer a particular nonlocal brand more
than other nonlocal brands. However, all nonlocal brands varieties have
equal appeal at the aggregate level. We discuss one means to relax this
assumption, by letting the valuation of brands be asymmetric, in the
“Conclusions” section.
Variety, Advertising, and Price Competition
149
Figure 2
Group 2
CONSUMER SEGMENTATION
j is available
and known
L
NL A
NL
NL NA
IBA
NL K
G1a
L NA
LA
G3
NL NK
LK
G2
G1b
L NK
G4
Notes: L = local brand, NL = nonlocal brand, A = available, NA = not
available, K = known to consumer (informed), NK = unknown to consumer (uninformed), G1a = Group 1a, G2 = Group 2, IBA = impossible
by assumption (because N ≥ n ≥ 2), G3 = Group 3, G1b = Group 1b, and
G4 = Group 4. Note that the demand expressions for Groups 1a and 1b
are the same, but we flip the identities of the local and nonlocal brands.
Because a brand cannot simultaneously be both local and nonlocal, we
account for G1a and G1b one time in Group 1’s demand.
Again, for consumers in this group, firm j’s product is
the local brand. However, these consumers lack information
about any nonlocal brand available in the market, so the
probability that a consumer located on spoke lj only considers brand j is 1 − n−1 . We provide the corresponding
demand in Table 1.
We also consider cases in which firm j’s product is the
nonlocal brand in consumers’ consideration sets. Because
the number of brands available in a market is n ≥ 2, and
n − 1 of these brands are equally likely to be the nonlocal brand in the consideration set of a consumer located at
lj x, some nonlocal brand will always be available. However, consumers may be uninformed about these nonlocal
brands.
Group 3
The local brand (variety) k that consumers in this group
prefer is not produced by any of the n firms, and therefore product j is the nonlocal brand in their consideration set. We summarize the demand from this group in
Table 1; the level of demand among this group should grow
in size as consumers’ tastes become more diverse (i.e., as
N increases).
Group 4
Group 1
A consumer in this group considers firm j’s product the
local brand in his or her consideration set. The probability
that a consumer is aware of this local brand j is , and
any nonlocal brand about which the consumer has information can be the second product in the consideration set.
Therefore, the second brand in the consideration set, k = j,
where k ∈ 1 n, comes from the set of products to
which the consumer has been exposed through advertising. The joint probability that the consideration set of a
consumer located on spoke lj includes brands j and k is
1/n − 1
1 − 1 − n−1 (for the proof, see the Web
Appendix at http://www.marketingpower.com/jmrfeb10).
Because the density of such consumers is 2/N, we obtain
the demand level presented in Table 1.
Finally, consumers in this segment are uninformed of
their local brand, and product j is the nonlocal brand in
their consideration set. As Table 1 shows, the demand from
this segment shrinks when consumers’ tastes become more
diverse.
We assume that v − pj /t > 1/2, such that there is some
competition between the local and nonlocal brands. When
1/2 < v − pj /t < 1, all consumers derive a positive surplus
from purchasing their local brand, though for some consumers, the base valuation is not high enough to obtain a
positive surplus from purchasing a nonlocal brand. In contrast, when v − pj /t ≥ 1, every consumer gains a surplus
from purchasing the local or nonlocal brand.
By aggregating the demand across all the four groups
and simplifying the expression, we obtain the following
demand for firm j’s product:
Table 1
DEMAND FROM EACH CONSUMER GROUP
Group
Group 1
Group 2
Group 3
Group 4
Demand
2 1
1 pk − pj
max min
1 − 1 − n−1 +
1 0 .
N n−1
2
2t
k = j k ∈ 1n
v − pj
1
2
1 − n−1 min max 0
.
N
t
2
v − pj 1
1
2 N−n
1 − 1 − n min max 0
−
.
N n
t
2
2
2 1
1 − 1 − 1 − n−1 N n−1
v − pj 1
1
×
.
min max 0
−
2
2
t
k = j k ∈ 1n
(3)


 1 1 − 1 − n−1 1 + pk − pj + 1 1 − n−1



N
t
N








N−n






 v−p 1

1 − 1 − n 

2
j

n

−
+





N
t
2


n−1 


+ 1 − 1 − 1 − 






1 v − pj
<1
for <
qj =
2
t




1
pk − pj
1



1 − 1 − n−1 1 +
+ 1 − n−1


N
t
N






1 N−n

n
n−1

1
−
1
−
+
+
1
−
1
−
1
−



N
n





v − pj


≥1
 for
t
150
JOURNAL OF MARKETING RESEARCH, FEBRUARY 2010
We assume that firms simultaneously choose their prices
to maximize profits. For ease of exposition, we initially
treat the level of advertising reach (
as exogenous to the
model and delineate how advertising and diversity in consumers’ tastes affect price. Subsequently, we endogenize
the level of advertising reach and show how advertising
technology determines advertising reach and thus influences price. We focus on a symmetric, pure strategy Nash
equilibrium to understand optimal firm behavior.
EFFECT OF ADVERTISING REACH ON PRICES
We begin our analysis by examining markets with multiple firms; we subsequently explore markets with only a few
competing firms. Recall that in our formulation, the number
of firms cannot exceed the number of varieties sought by
consumers, such that n ≤ N. In markets with a sufficiently
large number of firms, we find that the effect of informative
advertising (
on equilibrium price p∗ varies with valuation v, as we summarize in the following proposition:
P1 : In markets with a sufficiently large number of firms,
(a) when v1 < v < v2 , the equilibrium price strictly increases
with advertising reach, and (b) when v3 < v ≤ v4 , price
decreases with advertising reach.
v1 =
t
Nt1 − 1 − n + 2 n 2 − 1 − 1 − n−1 + 2/nN − n1 − 1 − n Nt1 − 1 − n v2 = t + n 2 − 1 − 1 − n−1 + 2/nN − n1 − 1 − n Nt1 − 1 − n v3 = t +
n
1 − 1 − n−1 v4 = t +
N2 t1 − 1 − n 2
n
N1 − 1 − n − n
1 − 1 − n−1 1 − 1 − n−1 Proof: See Web Appendix B (http://www.marketingpower.
com/jmrfeb10) for the proof.
To facilitate our exposition, we partition consumer valuation into four regions: t ≤ v ≤ v1 (Region 1), v1 < v < v2
(Region 2), v2 ≤ v ≤ v3 (Region 3), and v3 < v ≤ v4
(Region 4). The first part of the proposition pertains to
the valuation region in which v1 < v < v2 (Region 2).
In this region, demand emanates from two sets of consumers: Group 1 consumers who are aware of both the
products in their consideration sets and consumers who
are aware of only their nonlocal brand (Group 4) or only
their nonlocal brand is available (Group 3). Some Group 1
consumers gain surplus from purchasing either of the products, in which case any reduction in the price of one product makes the competing product less attractive, such that
demand is elastic. The marginal consumer in this group is
located at 1/2 + pk − pj /2t, and a unit reduction in price
shifts the location of the marginal consumer by 1/2t,
with an increase in demand of 1/Nt
1 − 1 − n−1 (see Equation 3). The second set of consumers might at
best purchase the nonlocal brand that appears in their
consideration set. The marginal Group 4 or Group 3 consumer is indifferent between purchasing the nonlocal brand
and not purchasing at all and is located at v − pj /t − 1/2.
Thus, a unit reduction in price increases the location of
the marginal consumer by 1/t. The corresponding effect
on demand from Group 3 and Group 4 consumers is
2/NtN − n/n1 − 1 − n and 2/Nt1 − ×
1 − 1 − n−1 , respectively. Because demand from consumers in Group 1 is less sensitive to price than demand
from consumers in Groups 3 and 4, these latter consumers
tend to pull the price down. As the reach of advertising increases, the importance of consumers in Group 1
increases, which enables the firm to charge a higher price.
If valuation is in the range v3 < v ≤ v4 (Region 4), all
consumers gain positive surplus from buying their local
or nonlocal brand, and the firm can reduce its price and
improve its relative attractiveness to marginal consumers.
This heightens competition for consumers in Group 1, who
are aware of both brands, and reduces price levels. Furthermore, as advertising reach increases, so does the importance of Group 1, which leads to lower prices.
If t ≤ v ≤ v1 (Region 1), consumer valuation for the product falls too low, and the firm acts as a local monopolist.
Therefore, the equilibrium price is v − t/2. Furthermore, if
v2 ≤ v ≤ v3 (Region 3), the marginal consumer must decide
whether to buy the nonlocal brand or not purchase at all,
and the equilibrium price becomes v − t. Thus, it is easy to
show that price will not be affected by consumer reach in
either of these regions.
Proposition 1 refers to the case in which the number
of firms competing in the market is very large. Do the
results still hold when there are only a few firms in the
market, such that n = 2 or n = 3? With such oligopolistic
competition, we find results that are qualitatively consistent
with the predictions in Proposition 1, with the exception
of the case in which v1 < v < v2 (Region 2). In this region,
with many firms, price increases with advertising reach.
With oligopolistic competition, price increases with in
this region until the valuation reaches some threshold level
of v∗ and then declines.
To appreciate why we obtain a different result when only
a few firms compete, consider the situation in which consumer tastes are diverse and N is very large. If a sufficiently
large number of firms compete in the market, most consumers’ preferred local brand will become available. Consequently, the size of Group 1—that is, consumers who are
aware of both their local and nonlocal brands—increases,
whereas the size of Group 3, for which the local variety is
not available, shrinks. As we noted previously, the resulting
decrease in consumers whose demand is more price sensitive (Group 3) and the concomitant increase in consumers
whose demand is less price sensitive (Group 1) should produce higher prices in this region of valuation (Region 2).
As the number of firms declines, however, the number of
product varieties not produced by any firm increases, and
the size of Group 3 grows. These consumers become especially important as the base valuation increases because
more of them can purchase the nonlocal brand. Thus, when
v > v∗ , Group 3 consumers who are more price sensitive
gain more importance, and in circumstances in which n
also is small, we observe lower equilibrium prices as the
advertising reach increases.
More generally, when n is small, as is the case with
oligopolistic competition, the range of valuations for which
p/
> 0 decreases as N increases, and the upper bound of
Variety, Advertising, and Price Competition
the range v1 < v < v∗ declines. For example, when n = 2, we
obtain v∗ = t3N− 2/2N− 1. The value of v∗ reduces from
limN = 2 vn∗ = 2 = 2t to limN → vn∗ = 2 = 3t/2 as N increases. We
also observe a similar shrinkage in v∗ as N increases when
there are three firms in the market.2 Thus, the following
corollary summarizes our finding.
Corollary 1: In oligopolistic competition, if v1 < v < v2 , informative advertising increases firms’ equilibrium
prices for v ∈ v1 v∗ ) but decreases prices for v >
v∗ N n .
According to Proposition 1, it is reasonable to observe
divergent effects of advertising on price. For example, in
Benham’s (1972) natural experiment, the prices of eyeglasses are substantially lower in states that permit advertising than in states that prohibit it.3 Because eyeglasses help
improve vision and affect how a person looks, consumers
attach significant importance to this purchase (Blumenthal
1983). To the extent that eyeglasses represent high valuation goods, Benham’s empirical findings are consistent with
the predictions in Proposition 1. In contrast, heavily advertised, low valuation goods such as cereal generally appear
to be priced higher than their less advertised competitors
(Nickell and Metcalf 1978; see also Farris and Reibstein
1979; Krishnamurthi and Raj 1985). We recognize the need
to exercise caution in interpreting cross-sectional empirical
studies, in that the observed relationship may be related to
unobserved factors. Moreover, we can offer only conjectures about the valuation of goods in these field studies.
These concerns are not an issue for our theoretical model
or laboratory experiments that can control for consumers’
valuation of goods.
For example, using a laboratory experiment, Mitra
and Lynch (1996) show that informative advertising can
improve the match between products and the personal tastes
of consumers and thereby increase prices (see also Mitra
and Lynch 1995). Such advertising also may motivate consumers to engage in product comparisons and pay lower
prices. In their experimental analysis, Mitra and Lynch
(1996) focus on the demand side of the problem, abstracting away from supply-side issues. Our theoretical framework adopts the spirit of their experimental setting, in
that we allow for consumers with diverse tastes and permit the number of products considered to vary endogenously with advertising level. The equilibrium analysis
also goes a step further to understand the net effect of
both supply- and demand-side factors on prices. Specifically, Proposition 1 characterizes the conditions in which
equilibrium price increase (or decrease) with informative
advertising.
Note that when n = 2 and N = 2, the spokes model
reduces to a classic Hotelling model, which enables us
2 ∗
vn = 3 = Nt
2 − 14
+ 18 − 12t1 − /2N
2 − 6
+ 6 − 121 − .
When advertising becomes very small, limN = 2 lim
→ 0 vn∗ = 3 = 2t, and
limN → lim
→ 0 vn∗ = 3 = 3/2t. Likewise, when tends to 1, the range
shrinks.
3
In the 1960s, some U.S. states prohibited all forms of eyeglass advertising, whereas others prohibited only advertising the prices of eyeglasses.
Benham (1972) uses this natural variation in advertising levels across different states to investigate the relationship between retail advertising and
retail price.
151
to compare the results we obtain with Soberman’s (2004)
findings. We agree with Soberman that if n = 2 and
the market is fully covered, the effect of advertising on
prices is positive for 3/2t < v < 2t but negative for v >
2t (for the proof, see the Web Appendix at http://www.
marketingpower.com/jmrfeb10). However, this result is sensitive to the market structure, as we note in Corollary 1.
Specifically, if v > v∗ N n , the results could reverse.
EFFECT OF DIVERSITY IN CONSUMER TASTES
ON PRICES
An important advantage of the spokes model is that it
enables us to study how consumer preferences for numerous distinct varieties N > 2 might affect firm behavior.4
We find that the effect of N on equilibrium price p∗ )
depends on how much consumers value the product, as we
summarize in the following proposition.
P2 : (a) When v1 < v < v2 , p∗ is strictly decreasing in N, but
(b) when v3 < v ≤ v4 , p∗ is strictly increasing in N.
The intuition for the first part of this proposition is as
follows: When consumer valuations fall in the interval v1 ≤
v ≤ v2 (Region 2), some Group 1 consumers can gain a
surplus from purchasing either of the two products in their
consideration set, such that demand from this group is sensitive to prices. The demand from consumers in Group 3
and Group 4 is even more sensitive to price. An increase
in N reduces the number of consumers in Group 1 but
increases that in Group 3. Thus, an increase in N results in
a lower equilibrium price. More formally, for given levels
of and n, the overall effect of N on p∗ is as follows:
(4)
p∗j
N
=
n
1 − 1 − n n
3 + 1 − n−1 − 4N1 − 1 − n 2
× 2v − t 1 − 1 − n−1 − 4t
In this equation, the first term is positive because both its
numerator and denominator are positive. Because v1 < v <
v2 implies that v ∈ t 2t, it also follows that 2v − t ×
1 − 1 − n−1 ∈ t 3t and that the second term is negative.
Thus, the overall expression is negative.
Next, we turn our attention to the second part of the
proposition. If consumer valuation is high, such that v3 <
v ≤ v4 (Region 4), consumers strictly earn a surplus from
purchasing either the local or the nonlocal brand in their
consideration set. This increases price competition among
the firms trying to sell to consumers in Group 1, though
an increase in N still reduces the relative importance of
4
If a consumer’s choice set includes only two varieties, the number of
possible combinations of product varieties that the consumer may prefer
is given by nN − 1/2. Of these different possibilities, the n competing firms may satisfy only nN − 1/2 combinations of brands. Therefore, the fraction of the consumers who can access both their preferred
products is n − 1/N − 1
2 , and the corresponding fraction of consumers who can access only one preferred product is N − n/N − 1
+
n − 1/N − 12
1− . Similarly, the fraction of consumers who would
obtain neither of their preferred products is n − 1/N − 11 − 2 +
N − n/N − 11 − . Thus, diversity in consumer tastes can play an
important role in shaping the competition among firms.
152
JOURNAL OF MARKETING RESEARCH, FEBRUARY 2010
these consumers. Consequently, equilibrium price increases
with N. More precisely,
(5)
p∗j
N
=
t1 − 1 − n > 0
n
1 − 1 − n−1 Recall that when t ≤ v ≤ v1 (Region 1), the equilibrium
price is v − t/2, whereas when v2 ≤ v ≤ v3 , the equilibrium price is v − t. In these two regions, we find that
equilibrium price is unaffected by diversity in consumer
tastes.
Thus, our analysis delineates how diversity in consumers’ tastes affects prices. As a practical implication
of our findings, for very low (Region 1) and moderate
(Region 3) valuation goods, an increase in the diversity
of consumers’ tastes may not affect prices. However, we
may observe a decline in the price for low valuation goods
(Region 2) and an increase in the price for high valuation goods (Region 4) as consumers’ tastes become more
diverse.
EFFECT OF ADVERTISING TECHNOLOGY
ON PRICES
Innovations in Web-based contextual advertising help
firms focus their advertising evermore sharply. Firms can
even selectively advertise their products to consumers on
the basis of the Web pages and information these consumers search. For example, consider the paid advertisements displayed next to the results of a related keyword
search in Google. In essence, these innovations reduce the
randomness associated with traditional mass media advertising and improve its cost efficiency. It is even possible
to customize the messages communicated through these
contextual advertisements and further improve the effectiveness of advertising. We consider the strategic implications of such improvements in advertising technology for
prices.
Specifically, we treat advertising reach as endogenous to
our proposed model. Recall that we previously used a general advertising cost formulation, in which A(
) is the
cost of reaching a fraction of the market when the advertising technology’s scale parameter is . The cost function
is convex, such that A0 = 0, A
= A/
> 0, and A
=
2 A/
2 > 0. Several familiar advertising cost functions
exhibit these properties, including the quadratic advertising
cost function A
= 2 and the logarithmic advertising cost function A
= −/ ln . The constant reach,
independent readership (CRIR) advertising technology proposed by Grossman and Shapiro (1984) also conforms to
this general cost function. That is, CRIR technology recommends that a firm advertise in m magazines with the
same level of readership. If the mass of consumers is normalized to unity and only a fraction of consumers, denoted
r, are exposed to each advertisement, the probability that
a consumer sees none of the advertisements is 1 − rm .
The resulting advertising reach is = 1 − 1 − rm . If each
magazine charges per customer, the advertising cost
function A
= r log1 − /log1 − r. In all these
examples, an increase in raises the cost of advertising,
which implies A = A/ > 0.
We use to denote a firm’s own advertising reach, and
we use to denote the advertising reach chosen by all other
firms. Thus, the demand for firm j equals the following:

pk −pj
1
1

n−1
n−1

1−1−
+ 1− 1+



N
t
N








n−1
 N−n 1−1−
1− 

 v−p 1 


2
j
 +
n

−



N
t
2


n−2 


+
1−
1−1−
1−






1 v−pj
for <
<1
(6) qj =
2
t







pk −pj
1
1

n−1
n−1

1−1−
+ 1− 1+



N
t
N







N−n

n−1






1−1−
1−

v−pj

n
 +1
≥1
for




N
t


n−2 
+ 1− 1−1−
1− Note that Proposition 1 presents the effect of advertising
reach on prices when is exogenous to the model. If
we endogenize advertising reach to understand the impact
of the advertising technology parameter on equilibrium
price, we derive the following proposition.
P3 : (a) When the number of firms is sufficiently large and
v1 < v < v2 , the equilibrium price strictly increases with
the advertising technology parameter if A
> 4N −
3n
/3nA
+ 2v − t/3N; otherwise, price decreases
with . (b) When the number of firms is sufficiently large
and v3 < v ≤ v4 , the equilibrium price increases with .
To appreciate the intuition for the first part of the proposition, we first consider how advertising technology affects
reach, d
/d. When the number of firms is large, is
endogenous, and v1 < v < v2 (Region 2),
(7)
d
/d = N4N − 3n
A
/N4N − 3n
A
+ 2nv − t − 3NnA
Equation 7 is positive if A
> 4N − 3n
/3nA
+
2v− t/3N.5 Note that when the marginal advertising cost
(A
is sufficiently higher than the slope of the marginal
cost (A
, the cost function is not too convex. Thus, when
A
> 4N − 3n
/3nA
+ 2v − t/3N, the cost function is less convex, and firms find it profitable to invest
more in advertising to increase their reach. In contrast,
when the cost function is sufficiently convex, firms restrain
their advertising expenditures, which decreases the level of
advertising reach. Thus, the sign of d
/d depends on the
convexity of the cost function. Turning our attention to the
effect of advertising cost on equilibrium price, we find that
(8)
dp/d = Nn/4N − 3n
2 5t − 2vd
/d
Furthermore, when v1 < v < v2 , as 5t > 2v, equilibrium price increases with advertising cost when d
/d > 0,
5
The detailed derivation appears in the proofs of Proposition 3 and
Corollary 2 in Web Appendix B (see http://www.marketingpower.com/
jmrfeb10).
Variety, Advertising, and Price Competition
which is the case when A
> 4N − 3n
/3nA
+
2v − t/3N. In that situation, the sign of d
/d is consistent with the finding reported in Proposition 1, where
is exogenous to the model. Thus, when v1 < v < v2 , the
overall effect of the advertising technology parameter on
price is moderated by the convexity of the advertising cost
function A
.
To understand the rationale for the second part of
the proposition, note that consumers can gain a surplus
from buying any product in their consideration set when
v3 < v < v4 (Region 4). Furthermore, firms compete head to
head for marginal consumers in Group 1, which leads to
a lower price. In this valuation region, the effect of on
endogenous reach and equilibrium price is
(9)
d
/d = A
/A
+ A
< 0 and
(10)
dp/d = −Nt/n
2 d
/d > 0
respectively. Equation 9 shows that firms reduce the reach
of their advertising as costs increase. Furthermore, the
resulting decrease in advertising reach may help soften
price competition and lead to higher prices, as we show in
Equation 10. Again, we find that Proposition 1 holds when
advertising reach is endogenous to the model.
In the process of clarifying the intuition for Proposition 3, we also unravel how advertising technology influences reach, as we summarize next.
Corollary 2: (a) When the number of firms is large and v1 <
v < v2 , ∗ is strictly increasing in if A
>
4N − 3n
/3nA
+ 2v − t/3N; otherwise ∗
is strictly decreasing in . (b) When the number
of firms is large and v3 < v ≤ v4 , ∗ is strictly
decreasing in .
A practical implication of Corollary 2 is that though
improvements in technology lead to higher levels of
advertising when consumer valuation is high enough
v3 < v ≤ v4 , the opposite may be true if consumer valuation is low (v1 < v < v2 . In particular, better technology can
reduce the level of advertising when the prevailing level
of advertising is high (i.e., A
is large) and when many
brands are available to cater to the diverse tastes of consumers (i.e., n is close to N, which satisfies the condition
in the first part of Corollary 2). For example, consider the
case in which the advertising cost function A
= 11 ,
N = 8, n = 7, t = 1, and v = 1. When = 045, ∗j = 470,
and p∗j = 365. Consistent with the first part of Corollary 2,
we find that if increases to .055, equilibrium advertising and price also increase, such that ∗j = 709, and p∗j =
468. In this case, the inequality in Corollary 2 is satisfied,
and v1 < v < v2 .6 Regarding the advertising cost function,
A
= 2 , the inequality in Corollary 2 clearly cannot
be satisfied. If N = 8, n = 7, t = 1, v = 12, and = 05, then
∗j = 632, and p∗j = 504. When we increase to .1, we
note a reduction in both advertising and price, such that
∗j = 280, and p∗j = 410. Thus, p∗j and ∗j change with ,
as implied by Proposition 3 and Corollary 2.
The preceding discussion helps clarify the empirical findings that Bailey (1998a, b) and Brynjolfsson and Smith
153
(2000) report. Bailey (1998a, b) investigates the prices of
low valuation goods, such as CDs and books, during the
early years of e-commerce, when the reach of Internet
advertising was low and there were few e-tailers in the marketplace. In the context of our model, this scenario could
imply A
> 4N − 3n
/3nA
+ 2v − t/3N, such that
the environment was conducive to increasing prices. In the
late 1990s, firms entered e-tailing at a frenzied pace, and
the business became crowded. The high reach of advertising meant that the advertising cost function likely was more
convex, such that A
< 4N − 3n
/3nA
+ 2v − t/3N.
Therefore, in the years that Brynjolfsson and Smith (2000)
cover, improvements in advertising technology (lower should have led to lower prices, according to Proposition 3.
Our analysis offers a theoretical explanation for the difference in these previous empirical findings.
EFFECT OF ADVERTISING TECHNOLOGY ON
PROFITS
Conventional wisdom suggests that firms should benefit
when they adopt better advertising technology, and recent
research in targeted advertising supports this view (e.g.,
Iyer, Soberman, and Villas-Boas 2005). In this section, we
reveal that an improvement in advertising technology does
not always improve a firm’s profits.
P4 : If the number of firms is large and v3 < v ≤ v4 , any
improvement in advertising technology (reduction in strictly increases the firm’s profits.
To understand the reasoning underlying Proposition 4,
we first abstract away from the effect of advertising technology and examine the impact of advertising reach on
firms’ revenues, such that we treat advertising reach as
exogenous.7 For v3 < v ≤ v4 and n ≥ 2, we have the
following:
(11)
×
2−
+ n1−
n 1−1−
n + 2−2n
2 −1−
n 1−
n −1
n2 2 1−
2 1−1−
n−1 2
Therefore, R∗ /
< 0, and it follows that ∗ /
=
R∗ /
− A
< 0. In essence, in Region 4, increasing advertising reach intensifies competition and lowers profits.
Thus, we can appreciate how advertising technology influences equilibrium profits when reach is endogenous to the
model:
d
d
dq
dp
=p
+q
− A
− A
d
d
d
d
dp
d
− A
− A
=q
d
d
A
A
N
=
− A
qA
+ 1
A
+ A
Recall that dp/d > 0 (Equation 10), d
/d < 0 (Equation 9), and A
A ≥ 0. Therefore, d/d > 0. The intuitions for these results are similar to those we provided for
7
6
1
11
> 4N − 3n
/3n11
−9
+ 4v − t/3N.
R∗
= Nt1 − 1 − n The detailed derivation of firms’ revenues appears in Web Appendix A
(see http://www.marketingpower.com/jmrfeb10).
154
JOURNAL OF MARKETING RESEARCH, FEBRUARY 2010
Proposition 3 and Corollary 2. Consistent with Grossman
and Shapiro (1984), we find that more costly advertising
decreases the amount of advertising but increases prices
and profits.
However, the profit impact of advertising technology
when v1 < v < v2 need not be positive. By treating advertising reach as an exogenous variable and considering cases
with many firms, we can examine the impact of v on revenue in this region of valuations:
(12)
×




2


 +N
1
R∗
=−
Nt4N − 3n
3
12n2 2 4N − n
v − t2
8N3t2 + 4vv − 2t
− n
68v2 − 140vt + 69t2 






For a large N that is sufficiently bigger than n, R∗ /
> 0
for v close to t, but R∗ /
< 0 for v close to 2t. Thus,
in Region 2, when consumer tastes are diverse and the
market is relatively unsaturated, lower consumer valuation
causes firms’ revenues to increase, whereas a higher valuation may lead to the opposite effect. Intuitively, an increase
in advertising reach changes the relative size of the consumer groups catered to by a firm, as well as influencing
the total sales (market share). The net effect of these forces
on firms’ profits could vary.8
In our analysis, we focus on cases in which the number
of competing firms is sufficiently large, which raises the
following question: How do improvements in advertising
technology affect markets in which firms can easily enter
and exit, so that no firm makes any profit in equilibrium?
In the absence of an entry barrier, an increase in the potential to make profits should lure more firms to the market.
Consequently, when v3 < v ≤ v4 , any improvement in advertising technology (i.e., reduction in will increase the
ability of the market to accommodate more firms because
it can potentially cover the entry costs of more firms. However, equilibrium profits remain 0.
CONCLUSIONS
This research attempts to understand how informative
advertising influences the strategic behavior of firms in
markets in which consumers have distinctly different tastes.
Toward this end, we propose a spatial model of informative advertising in which consumers are distributed across
a plane along different taste dimensions (spokes), each firm
can compete with every other firm in the market (nonlocal competition), the market can be partially covered, and
8
By studying how revenue changes with N, we find that under
oligopolistic conditions, Rj∗ /N is negative for low valuations but positive
for high valuations. We also note that the effect of advertising technology on profits could vary. For example, consider the case in which the
advertising cost function is A
= 11 . Let N = 8, n = 7, t = 1, and
v = 1. When = 045, ∗j = 471, p∗j = 365, qj∗ = 081, and j∗ = 010.
However, when = 046, ∗j = 506, p∗j = 377, qj∗ = 083, and j∗ = 009.
Therefore, / < 0. In contrast, when = 06, ∗j = 752, p∗j = 494,
qj∗ = 095, and j∗ = 0029, but when = 061, ∗j = 760, p∗j = 499, qj∗ =
010, and j∗ = 0031. In this case, we observe that / > 0. In both
cases, 11
1 > 4N − 3n
/3n11
−9 + 4v − t/3N, and v1 < v < v2 .
the number of competing firms can be many or few. Our
analysis provides insights into three questions pertaining to
informative advertising.
How Does Informative Advertising Affect Price?
As we show with Proposition 1, if consumer valuations
are low, the equilibrium price increases with the reach of
informative advertising. However, if consumer valuations
are high, we find that price declines with advertising. Our
analysis also characterizes the conditions in which advertising level has no effect on price. To appreciate the driving
force behind these results, we note that price sensitivity
varies across consumer groups. When consumer valuation
is low, informative advertising increases the relative importance of consumers who are less sensitive to price and
thereby motivates firms to charge higher prices. When consumer valuation is sufficiently high, all informed consumers
obtain a surplus by buying any product in their consideration set, which induces firms to cut their prices to attract
the marginal consumer. These findings have a critical practical implication: In some product categories, prices may
increase with advertising, but in other categories, prices
may decrease with advertising. We observe just such a
divergence in empirical literature. For example, heavily
advertised breakfast cereals exhibit high prices (Boulding,
Lee, and Staelin 1994; Farris and Reibstein 1979; Nickell
and Metcalf 1978), whereas the prices of eyeglasses decline
with greater advertising (Benham 1972).
What Is the Effect of Diverse Consumer Tastes on Price?
As consumer tastes become more diverse, firms face
reduced direct competition from other firms, which is conducive to increased prices. However, with diverse consumer
tastes, firms need to reduce their prices to encourage consumers to purchase products that do not match well with
their tastes. The net effect of these countervailing forces
depends on consumer valuations. With Proposition 2, we
show that prices decline with diversity in consumer tastes if
consumer valuations are low, but prices increase with this
diversity if valuations are high.
How Does Advertising Technology Influence Price?
To answer this question, we endogenize the level of
advertising and examine how the advertising technology
parameter influences the advertising level, which in turn
determines the equilibrium price. If consumer valuations
are high, firms compete intensely for the marginal consumer and reduce their prices. Recognizing this competitive situation, firms reduce their advertising level when
advertising costs increase, which softens price competition.
However, if consumer valuations are low, an increase in leads to higher prices when the advertising cost function
is not sufficiently convex, but it decreases price otherwise.
The potentially conflicting predictions of Bailey (1998a, b)
and Brynjolfsson and Smith (2000) regarding low valuation
goods may be consistent with Proposition 3a. That is, the
reach of Internet advertising and the number of e-tailers
both were lesser at the point Bailey considered this market,
Variety, Advertising, and Price Competition
such that the threshold condition for the convexity of the
cost function may not have been satisfied.
Robustness Check
In developing the model, we make a few simplifying
assumptions. Therefore, we assess the robustness of our
model predictions against some of these assumptions and
discuss ways to relax other assumptions to capture new
phenomena. Specifically, we assume that the cost of any
mismatch between a consumer’s taste and product’s feature
is linear. If we relax this assumption, we allow for quadratic
costs. If the consumer located at (lj , x) is aware of the local
brand j and decides to buy it, the indirect utility derived by
this consumer is as follows:
(13)
Ulj x pj = v − tx2 − pj However, if the consumer purchases any other product,
such as variety k for which k = j, the indirect utility
obtained from the nonlocal brand is as follows:
(14)
Ulj x pk = v − t1 − x2 − pk The results of our basic model are generalizable to
this quadratic transportation cost function, and we provide the proof for this claim in the Web Appendix (see
http://www.marketingpower.com/jmrfeb10).
We also assume that a consumer’s consideration set
includes a local brand and a nonlocal brand, such that
the nonlocal brand comes from the set of products to
which the consumer has been exposed through advertising. Thus, informative advertising shapes the composition of the consideration set. For example, for Group 1
consumers, the joint probability that a consumer considers brands j and k is 1/n − 1
1 − 1 − n − 1 . It is
also conceivable that the second product in a consumer’s
consideration set is exogenously fixed a priori, such that
informative advertising only informs consumers about the
prices and characteristics of products. In this situation,
the joint probability that a consumer considers brands j
and k is 2 , and when we assess this alternative formulation, we obtain results that are directionally consistent with
our basic model, as we show in the Web Appendix (see
http://www.marketingpower.com/jmrfeb10).
Limitations and Directions for Further Research
Following Chen and Riordan (2007), we assume that
each consumer’s consideration set has at most two brands,
which helps us investigate nonlocalized competition in a
spatial model and still keep the model tractable.9 To relax
this constraint naturally, further research might assume that
each consumer has heterogeneous valuations for different
9
Hart (1985a, b) also restricts the number of brands a consumer
considers.
155
products. For example, a randomly selected third preferred
brand might be valued at v3 = v − t, a fourth preferred brand
at v4 ≤ v3 , and so forth. This extension would add complexity to the model but also relax the restriction on the
size of the consideration set.
We also consider a market with symmetric firms, but further research might address competition between asymmetric firms. For example, it would be important to understand
the role of informative advertising in a market that consists
of a dominant firm and several subordinate firms. In our
formulation, each firm produces only one product, though
firms often produce more than one. Therefore, additional
research should address both intra- and interfirm issues
related to informative advertising. Furthermore, the motivation for engaging in informative advertising may depend
on whether a firm is a retailer or manufacturer; a manufacturer might release partially informative advertising (e.g.,
nonprice information) and let the retailer advertise prices. It
would be useful for researchers to investigate the strategic
role of different types of informative advertising.
Finally, empirical research indicates that the effect of
advertising on price is divergent. Our analysis provides a
potential theoretical rationale for this divergence, though it
is difficult to define the valuations of the goods that appear
in empirical research precisely, which makes it impossible to develop precise theoretical predictions for the various studies or confirm the predictive power of our model.
A more direct test of our model might take place in a
laboratory setting, in which researchers induce the values
that participants adopt and create markets that parallel the
model structure.
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