4.2.5 Price Advertising with Product Differentiation
The existing research on this topic (Grossman and Shapiro, 1984; Christou and Vettas,
2008; Sovinsky-Goeree, 2008
) has ignored the possibility of search. It therefore assumes
that a consumer can buy only at firms from which she has received an ad, in which case
she is perfectly informed about that firm’s product and price.
Consider a simple duopoly model of price competition with differentiated products.
If all consumers are perfectly informed, the demand for firm i’s product is given by
e
d
i
p
i
, p
j
> 0, for i ¼1, 2 prices p
i
2IR
+
, for firm i, p
j
2IR
+
for firm j, i ¼1, 2, i 6¼j.
There is a measure one of consumers with unit demand and the perfect information mar-
ket is assumed to be covered so that
e
d
2
p
2
, p
1
ðÞ¼1
e
d
1
p
1
, p
2
ðÞ. Firms simultaneously
select an advertising intensity Φ
i
2 0, 1½and a price p
i
for each firm i ¼1, 2. Advertising
intensity measures the proportion of consumers that are reached by an ad from firm i.It
costs A Φ
i
ðÞ¼a=2ðÞΦ
2
i
, a > 0, for a firm to advertise with intensity Φ
i
. The covered mar-
ket assumption is extended to assume that all consumers who receive an ad only from firm
i (who have measure ϕ
i
1 ϕ
j
) buy from that firm no matter what price it charges.
Furthermore, advertising is not targeted so the demand from consumers who receive
an ad from both firms (who have measure ϕ
i
ϕ
j
)is
^
d
i
p
i
, p
j
. Firm i’s demand with imper-
fect consumer information may therefore be written as
d
i
p
i
, p
j
, Φ
i
, Φ
j
¼Φ
i
1 Φ
j
+ Φ
j
e
d
i
p
i
, p
j
hi
: (4.9)
Assuming firms have constant marginal production costs, c
1
0 and c
2
0, price first-
order conditions are derived in a standard way as
p
i
c
i
¼
d
i
p
i
, p
j
, Φ
i
, Φ
j
@d
i
@p
i
p
i
, p
j
, Φ
i
, Φ
j
¼
1 Φ
j
Φ
j
@
e
d
i
@p
i
p
i
, p
j
e
d
i
p
i
, p
j
@
e
d
i
@p
i
p
i
, p
j
, i ¼1, 2, j 6¼i: (4.10)
Assuming advertising intensities are interior, Φ
i
2 0, 1ðÞ, i ¼1,2, corresponding first-
order conditions are
aΦ
i
¼ p
i
c
i
ðÞ
@d
i
p
i
, p
j
, Φ
i
, Φ
j
@Φ
i
¼
1 Φ
j
+ Φ
j
e
d
i
p
i
, p
j
hi
2
Φ
j
@
e
d
i
@p
i
p
i
, p
j
, i ¼1, 2, j 6¼i; (4.11)
where the second equality is obtained by substituting in the price first-order condition for
firm i.
Let us start by considering the first equalities in
(4.10) and (4.11) and use the notation
D
i
¼d
i
p
i
, p
j
, Φ
i
, Φ
j
, and i’s partial demand derivatives with respect to own price and
advertising, D
ip
and D
iΦ
, respectively. Further define D
iA
¼ D
iΦ
ðÞ= aΦ
i
ðÞ, which is the
demand derivative with respect to advertising expenditures A(Φ
i
). Then substituting
137Advertising in Markets
(4.10) into (4.11) and rearranging, we obtain the well-known Dorfman and Steiner
(1954)
relation:
A Φ
i
ðÞ
p
i
D
i
¼
Φ
i
=2ðÞD
iΦ
D
ip
p
i
¼
D
iA
A Φ
i
ðÞ
D
ip
p
i
¼
η
A
η
p
; (4.12)
where η
A
and η
p
are the demand elasticities with respect to advertising expenditures and
price, respectively.
This simple relation states that the share of revenue devoted to advertising should
equal the ratio of the elasticity of demand with respect to advertising expenditures to
the price elasticity of demand (in absolute value). A simple takeaway is that a firm facing
a demand with lower price elasticity, and hence endowed with more market power,
advertises more. This is the flip side of the persuasive view argument that firms use adver-
tising to enhance their market power.
15
The present setting allows for an analysis of how
advertising relates to market power and how they are jointly determined in equilibrium.
In the framework of
Grossman and Shapiro (1984) and the related literature, the two
sources of variation in market power are the extent of product differentiation and the
number of firms. It is straightforward to discuss the impact of product differentiation
in the duopoly setting above. Assume that there exists a function
d
1
defined on IR, such
that
^
d
1
p
1
, p
2
ðÞ¼
d
1
p
1
p
2
ðÞ, for all p
1
, p
2
ðÞ2IR
2
+
(a property shared by many standard
discrete-choice duopoly models), and marginal costs are identical, c
1
¼c
2
¼c. The full
information covered market condition then implies that
^
d
2
p
2
, p
1
ðÞ¼1
d
1
p
1
p
2
ðÞ.
Further assume that there exists a symmetric equilibrium where both firms charge p
and advertise with intensity Φ
. Let b ¼
d
1
0
0ðÞ¼@
^
d
i
p
, p
ðÞ
=@p
i
, i ¼1, 2.
Then, because
^
d
i
p
, p
ðÞ¼
d
1
0ðÞ¼1=2, first-order conditions (4.10) and (4.11) may
be written as
p
c ¼
1 Φ
Φ
b
+
1
2b
(4.13)
and
aΦ
¼
2 Φ
ðÞ
2
4Φ
b
; (4.14)
so that equilibrium price and advertising intensity are
p
¼c +
ffiffiffiffiffiffiffi
a=b
p
, Φ
¼
2
1+2
ffiffiffiffi
ab
p
: (4.15)
15
See Bagwell (2007) for a detailed discussion of this theme, both from a theoretical and an empirical point
of view.
138
Handbook of Media Economics
In commonly used models, the parameter b may be interpreted as a measure of product
differentiation: it measures how many consumers a firm loses by raising its price slightly
above that of its competitor and is therefore large if there is little product differentiation.
For instance, in the Hotelling duopoly example of
Tirole (1988, pp. 192–294), b ¼1=2t,
where t is the unit transport cost. In a random utility model with i.i.d. valuations for the
two products, f, b ¼
Ð
+ 1
1
f EðÞ
2
dE, where f is the density of the additive random utility
term: it may then be interpreted as the “mass” of consumers who are just indifferent
between the two products at equal prices. For the uniform distribution on [α, β] used
by
Christou and Vettas (2008), b ¼1= β αðÞ. In this uniform case, a broader support
means more heterogeneity in products and tastes.
From the first-order condition,
(4.13) and (4.14), more differentiation, and hence a
lower b, all other things being equal, moves the equilibrium price and the advertising
intensity upward. Note, however, that price is decreasing in advertising intensity. This
is because more advertising by the competitor means less captive consumers who only get
an ad from firm i. For Φ
¼1, the pass-through rate p
c takes its full information value
1/2b. This opens up the possibility that more product differentiation leads to lower prices,
although for the present specification with quadratic costs of advertising, this is not the
case. There is, however, no ambiguity about the impact of an increase in product differ-
entiation on advertising, which is positive.
To discuss the impact of the number of competitors on pricing and advertising, I draw
on the analysis in
Christou and Vettas (2008), who study a variant of the model with a
random utility specification of demand. They find that more firms unambiguously lead to
a decrease in the advertising activity of each firm. Although this seems coherent with the
intuition from
Dorfman and Steiner (1954), it does not reflect a systematic relationship
between market power and advertising. Indeed,
Christou and Vettas (2008) find that an
increased number of competitors does not necessarily lead to lower prices. The intuition
for this is simple and follows from the same strategic interplay between price and adver-
tising that causes a potentially ambiguous impact of product differentiation on pricing.
For a fixed advertising intensity by competitors, an increase in the number of firms
decreases a firm’s price. However, more competition leads to a lower advertising inten-
sity, which increases market power, and hence the price.
Christou and Vettas (2008) find
that this price-augmenting effect may actually dominate in their setting.
The above price comparative statics results suggest that it might be extremely mislead-
ing to ignore the limited access of consumers to information when performing a struc-
tural estimation of market demand. This has been done in numerous studies in the wake
of the groundbreaking work of
Berry et al. (1995) on the automobile industry. Sovinsky-
Goeree (2008)
addresses this issue in her analysis of the US personal computer market in
the late 1990s. She uses data on ad expenditures in various media (magazines, newspapers,
TV, radio) as well as a survey of consumers that includes information about their exposure
139Advertising in Markets
to the various media. This data allows her to simulate the household’s exposure to adver-
tisements, which in turn conditions the household’s choice set (it can choose only among
products it is aware of ). This introduces some heterogeneity among buyers that affects
their purchase decision independent of the product’s characteristics. She jointly estimates
market demand and the firms’ first-order conditions for pricing and advertising.
Her focus is on the measure of market power and how it compares to what it would
have been if the model had been estimated assuming that consumers had full information.
She finds that market power would have been hugely underestimated (and thus demand
price elasticity greatly exaggerated). She estimates a median markup for the industry of
15%, where a standard estimation using the method of
Berry et al. (1995) that assumes
perfect consumer information would yield an estimate of 5%. Note that from pricing
first-order conditions
(4.10) or (4.13), the markup with imperfect consumer information
should clearly exceed what it would be with perfect consumer information. Indeed, the
last term on the right-hand side in
(4.13) is the full information markup and the term that
precedes it is clearly positive. It is also clear that own-price elasticity is larger in absolute
value for the full information setting: with imperfect information, when a firm raises its
price, it only loses to the competitor consumers who were indifferent and who had
received an ad from both firms. Still, there is no clear argument why estimating the full
information model on data generated with imperfect information should necessarily pro-
duce higher or lower estimated markups than would be obtained by estimating the true
model. In any case, the results in
Sovinsky-Goeree (2008) show that the discrepancy can
be very substantial.
16
I now return to the comparison of market-provided advertising with the second-best
socially optimal level. As argued by
Tirole (1988), the main takeaway from the analysis of
informative advertising with product differentiation is that advertising may either be
insufficient or excessive. Again, as
Tirole (1988, p. 294) explains, the two countervailing
forces at work are non-appropriation of social surplus, which suggests advertising might be
insufficient, and the market stealing effect, which induces firms to over-provide advertising.
By contrast with the homogeneous product setting, the positive externality for con-
sumers of an additional ad (associated with the non-appropriation of social surplus effect)
may arise even if the ad reaches a consumer who is also getting some ad from some com-
peting firm. This is because, due to horizontal product differentiation, the additional
product that the consumer is aware of may be a better match for his tastes.
Christou
and Vettas (2008)
find that advertising is inappropriately low with little product
16
As she explains on p. 1053, if three products with identical characteristics and prices are competing, then
the full information model would assume a purely random matching between products and consumers. If,
however, this matching is explained to a large extent by advertisements from different firms reaching dif-
ferent consumers, then the corresponding demand would be much less price elastic. However, she
explains in her online appendix that the inappropriate specification of the model could bias the results
in the opposite direction.
140
Handbook of Media Economics
differentiation and it is excessive when product differentiation is substantial.
17
This does
not mean, however, that there is a systematic relationship between product differentiation
and the welfare properties of market-provided advertising. Indeed, as I have explained
above, it is possible to have excessive advertising with homogeneous products and no
consumer search, as in the asymmetric equilibria studied by
Anderson et al. (2014).
I end this discussion of advertising in differentiated product settings with some con-
siderations on allowing for consumer search. Two preliminary remarks are in order. First,
because the relevant information concerns both a price and a product, and the product
information could involve multiple dimensions, if consumers are allowed to search, a
firm could choose to disclose only part of the relevant information and let the consumer
find out the rest on her own. I discuss this possibility in
Section 4.3.3.2 in a monopoly
setting. Performing such an analysis in oligopoly is non-trivial. Second, as shown by
Wolinsky (1986) and Anderson and Renault (1999), costly sequential search does not
yield the Diamond paradox if consumers search not only for price but also for products
they like.
Consider a simple duopoly with differentiated products where consumers may search
sequentially. If there is no advertising and if, in equilibrium, the two firms charge the
same price, then consumers follow a simple stopping rule when deciding whether they
buy from the first firm encountered or go to the next one: they stop if the utility they
obtain from the first product is above some threshold value. If this is not the case then
they move on to search the second firm and can then make a perfectly informed choice
between the two products. Standard arguments show that this threshold value is decreas-
ing in search costs. I further assume enough symmetry so the threshold does not depend
on which firm is searched first.
Assume now that a firm may use advertising to inform the consumers about its price
and product (it must reveal both) before they start searching. First notice that a consumer
does not benefit from receiving an ad from only one firm (except by saving on search
costs if the first search is costly). The ad merely determines which firm the consumer gets
to see first. Now a consumer who receives an ad from both firms benefits differently
depending on whether her utility with each product is above or below the threshold.
If both her utilities are above the threshold, then she benefits from making a perfectly
informed choice, which would not have been the case if she had received no ad or
one ad. If both her utilities are below the threshold, then she benefits by saving on
the search cost she would have had to incur to make a perfectly informed choice if
she had received at most one ad. If only one of the utility levels exceeds the threshold,
then the nature of the benefit depends on the order in which the consumer uncovers
information.
17
Hamilton (2009) obtains a similar result in the Hotelling duopoly setup.
141
Advertising in Markets
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