I look for a symmetric equilibrium where each firm advertises with probability λ and
chooses intensity Φ (so firms only randomize between two advertising intensities: zero
and Φ). If a firm does not advertise, it optimally selects the price that makes a consumer
just indifferent between searching and not searching (provided it is less than v). Let r
denote that price. Consumers who see an ad from each firm or no ad at all split equally
between the two competitors. Hence a firm’s profit when advertising with intensity Φ
i
and expecting its competitor to play its equilibrium strategy is given by:
λ
Φ
i
Φ +1Φ
i
ðÞ1 ΦðÞ
2
+1ΦðÞΦ
i
+1λðÞΦ
i
+
1 Φ
i
2
1
2
Φ
2
i
, (4.1)
which simplifies to
λ
Φ
2
+
1+Φ
i
2
1
2
Φ
2
i
: (4.2)
This expression is maximized at Φ
i
¼1=2 so the equilibrium value of Φ is 1/2.
I nonetheless go through the equilibrium derivation assuming Φ takes on any value in
0,1=2ð. If a firm does not advertise, its profit is
λ
1 Φ
2
+1λðÞ
1
2
r: (4.3)
In a mixed strategy equilibrium, λ should equate profit expressions
(4.2) and (4.3), which
yields
λ ¼
Φ
2
1 ΦðÞ+ r
Φ r 1ðÞ
: (4.4)
Recall that r is determined by the indifference of a consumer between buying at price r
and searching a firm from which she has received no ad. The probability that a firm is
advertising (and hence charging a low price) conditional on not receiving an ad from that
firm is given from Bayes law by 1 ΦðÞλ= 1 ΦλðÞ. Hence r is a solution to
1 ΦðÞλ
1 Φλ
r 1ðÞ¼s; (4.5)
where the left-hand side is the expected benefit from search given the advertised price is
1. A firm that does not advertise therefore prices at
r ¼1+
1 Φλ
1 ΦðÞλ
s: (4.6)
It is readily verified that, for Φ 1=2, conditions relating λ and r given by
(4.4) and (4.6)
may be depicted as in Figure 4.1, provided that search cost s is not too large and adver-
tising intensity Φ is not too close to 0 (where the equation for the CI curve is derived
132 Handbook of Media Economics
from (4.6) and the equation for the FI curve is derived from (4.4)). Hence, if firms are
constrained to select advertising intensity Φ, the equilibrium values of λ and r are given by
the coordinates of the intersection of the two curves. This is the case as long as the cor-
responding value of r is less than v so consumers are willing to buy at price r. This con-
dition also ensures that consumers who do not receive any ad are willing to incur search
cost s to enter the market.
This equilibrium exhibits price dispersion to the extent that a firm that does not
advertise charges a higher price than a firm that does. This would still be the case if
the advertised price was endogenous. There would, however, be another source of dis-
persion among firms that advertise. Indeed, in our simple framework, if a firm expects its
competitor to advertise a price of 1, in the event that it advertises, it would be better off
undercutting 1 to capture all consumers who receive an ad from both firms. A related
argument rules out any mass point in the distribution of advertised prices.
Robert and
Stahl (1993)
show that, in equilibrium, there is a continuous distribution of advertised
prices. Furthermore, low prices are advertised more. Dispersion of advertised prices is
also found in price advertising settings with no consumer search, such as in
Butters
(1977)
, Stegeman (1991), and Stahl (1994). However, Stahl (1994) finds that, in oligop-
oly, the intensity of advertising does not depend on the advertised price.
I now discuss the comparative statics with respect to search cost s, which is the only
exogenous parameter that has not been set to a specific value. An increase in search costs
results in a shift upward of the CI curve. Recalling that v > 3=2 1+Φ, the mixed strat-
egy survives as long as s < Φ . Then, following an increase in s, the equilibrium point
r
∗
1+s
1+Φ − Φ
2
1+Φ
r
CI curve
λ
∗
1 λ
FI curve
Figure 4.1 Equilibrium for some exogenous value of F. Along the CI curve, a consumer is indifferent
between searching and not searching. Along the FI curve, a firm is indifferent between advertising and
not advertising.
133
Advertising in Markets
moves along the FI curve so that r and λ increase. An increase in search costs therefore
results in an increase in the price charged by a firm that does not advertise, as well as an
increase in the probability that a firm chooses to advertise.
4.2.4 Too Much or Too Little Advertising?
A central question in the literature on price advertising has been the comparison
between the equilibrium and the second-best socially optimal advertising intensity:
second-best here indicates that advertising intensity is adjusted so as to maximize social
surplus, assuming that firms are free to price as they wish. The original work by Butters is
often remembered for establishing that the equilibrium level of advertising is socially
optimal. This, however, is obtained in the model without consumer search. When he
does allow for search, he finds that the equilibrium intensity is excessive.
Stegeman
(1991)
and then Stahl (1994) have shown that the optimality result of Butters is specific
to his demand specification and that, with no consumer search, advertising is typically
insufficient. I first discuss the intuition behind this result and then explain, with the help
of the model of the previous section, why, with consumer search, advertising can be
excessive.
Consider again the model of the previous section, now assuming that consumers may
purchase only if they see an ad from at least one of the firms. Advertising should then be
interpreted as informing consumers about the firm’s existence and location as well as its
price. Still assuming that the advertised price is 1, firm i then choose the advertising inten-
sity Φ
i
that maximizes profit
Φ
i
1
Φ
2
1
2
Φ
2
i
; (4.7)
where Φ is the equilibrium advertising intensity chosen by the competitor. Firm i’s best
response is therefore Φ
i
¼1 Φ=2. The unique equilibrium is symmetric with both firms
choosing advertising intensity Φ ¼2=3. Now for an advertising intensity Φ by each firm,
the corresponding social surplus is given by
2Φ Φ
2
v sðÞΦ
2
; (4.8)
which is maximized at Φ
¼ v sðÞ= v s +1ðÞ. It follows that advertising is excessive for
v s < 2 and insufficient for v s > 2. This ambiguous result reflects the two counter-
vailing external effects associated with a firm’s choice to increase its advertising intensity.
On the one hand, an increase in a firm’s advertising results in an increase in the proportion
of consumers who buy, but for each additional sale, the firm obtains at most the corre-
sponding social surplus (but typically less, if v s > 1): this is what
Tirole (1988, p. 294)
calls the non-appropriation of surplus in the context of entry. On the other hand, the firm
gets to sell to some new customers who, having received an ad from the competitor,
134 Handbook of Media Economics
would have bought in any case: this corresponds to what Tirole (1988, p. 294) calls busi-
ness stealing.
12
The ambiguous result obtained in this fixed price model does not reflect the finding in
the literature. This is because the equilibria that have been obtained in the literature with
endogenous prices typically involve no atom in the price distribution.
13
The welfare
analysis of advertising intensity with no consumer search has been performed in monop-
olistic competition by
Butters (1977) and Stegeman (1991), and in oligopoly by Stahl
(1994)
. I now borrow from Stegeman (1991) the intuition for why these authors find
that advertising intensity cannot be excessive and is typically insufficient. Think of ad
messages that all have the same cost of being sent b> 0asin
Butters (1977). Consider
a firm that would be charging the maximum value in the support of the price distribution.
Because the price distribution is continuous, an ad by that firm steals no business from any
other firm. Hence, at the optimal advertising intensity for that firm, the social surplus
generated by the last ad message sent must be at least the firm’s private benefit, which
is no less than b from profit maximization. Now think of a firm charging a price strictly
below the maximum. The social surplus generated by an ad at that price is at least as large
as that generated by an ad at the maximum. It is therefore at least b. Thus, the advertising
by any firm cannot be excessive. Furthermore, the social surplus from an additional ad at a
price below the maximum is strictly above b if demand is elastic. This argument also
explains why the advertising intensity is socially optimal in
Butters (1977). Indeed, he
considers homogeneous consumers with unit demands. Because the maximum price
is the reservation price, the social surplus at that price coincides with the producer surplus
and advertising is socially optimal at that price. Since demand is inelastic, the social surplus
from an ad is the same at all prices so that the advertising level is socially optimal at all
advertised prices.
In all the studies that do not involve consumer search, the social benefit of advertising
stems solely from the additional sales it generates. By contrast, in the research that allows
for consumer search (
Butters, 1977; Robert and Stahl, 1993), the market is fully covered,
independent of the advertising intensity. This is because all those who do not get any ad
choose to search and buy from the first seller they encounter. From a first-best perspective
(say if we constrain firms to price at marginal cost and consumers are aware of it), adver-
tising has no social value and since it is costly, its socially optimal level is zero.
This is, however, no more the case if firms can set prices freely. Without advertising, if
consumers know their valuations before searching, the market would be in a Diamond-
like situation and, if consumers have unit demand, there would be no market. Hence,
12
See Tirole (1988, p. 288) for how these two effects apply to entry in the model of Spence (1976).
13
See Anderson et al. (2014) for asymmetric equilibria where some price is charged with positive probability
and the equilibrium ad level is socially excessive.
135
Advertising in Markets
firms must be allowed to engage in some advertising activity, so they have some incentive
to offer low prices. Consumers who do not see any ad, expecting that such low prices
might be offered, then have an incentive to participate in the market. As far as I am aware,
the optimal advertising intensity that balances consumer participation with the cost of
advertising has not been investigated.
14
In the setting of Section 4.2.3, it is clear from Figure 4.1 that we may have an equi-
librium with full consumer participation as long as Φ > s so the two curves cross for some
λ < 1. Hence for s < 1=2, the advertising intensity chosen by firms Φ ¼1=2 is clearly
excessive. An analogous result holds in the setting of
Robert and Stahl (1993), where
consumers are homogeneous with unit demand and identical search costs. They find that
for a low enough search cost, there is full participation and the price charged by a firm that
does not advertise is strictly less than the consumers’ valuation. If advertising intensity was
slightly decreased at all advertised prices, the strict inequality between the unadvertised
price and consumer valuation would still hold and consumers would still participate. Pre-
sumably, this result may not generalize for a heterogeneous population of consumers in
terms of search costs or valuations. Advertising may then have a market expansion effect
as in the model with no search. This may be the case, either because it induces search by
high-search-cost consumers or it makes low prices more likely, so more consumers end
up buying.
Welfare results for price advertising with homogeneous products may be summarized
as follows. If advertising does not induce much market expansion, consistently with a
model where consumers may purchase through search, then advertising is likely to be
excessive. If, on the contrary, advertising enhances market participation by consumers
significantly, either because it increases consumer awareness of available sellers or because
consumers are very heterogeneous in their search and purchase behavior, then we may
expect the market provides too little advertising. This suggests that the diagnosis should
be, to a large extent, inferred from an empirical investigation of whether advertising has a
strong market expansion effect or not. Actual markets, however, are characterized by
some degree of product differentiation. Advertising may then contribute to social wel-
fare, even if it only induces a shift of demand from one product to anther. This is because
consumers may be shifting to products with which they have a better match.
I now discuss the analysis of price advertising in markets for horizontally differentiated
products.
14
Although Butters (1977) does find excessive advertising in his model with search, he obtains this result
while assuming that the market is covered independent of the advertising intensity. In his setting, adver-
tising contributes to social welfare by saving consumer search costs because only those consumers who are
not reached by any ad must incur these costs. By contrast, my discussion assumes consumers must incur
search costs before buying whether or not they have received an ad.
136
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