4.4.2.2 Repeat Purchase and Money Burning
Tirole (1988, p. 119) gives a simple illustration of how price or advertising can signal the
quality of an experience good that is purchased repeatedly. Assume that the monopolist
considered above faces one consumer with unit demand. The buyer’s willingness to pay is
s independent of how much is spent on advertising. If the consumer buys the product
once, she may choose to purchase it again in a second period after observing s from
her first period experience and observing the second period price charged by the firm.
Since the consumer knows s in the second period, the best the firm can do is to charge a
price of s to extract all the surplus. The firm and the consumer share the same discount
factor δ 2 0, 1ðÞ.
I now study the first period interaction, assuming that s
h
> c
h
c
‘
> s
‘
¼0 (the impor-
tant point is that c
‘
> s
‘
and s
h
> c
h
, so only the high-quality product has a market under
perfect consumer information). I again look for a separating equilibrium. Note that here,
because only a high-quality product will be purchased again in the second period if it is
purchased in the first period, the firm’s quality has a direct impact on its profit even if costs
are equal. If the product is purchased in the first period, the discounted second-period rev-
enue is δs
h
for a high-quality firm and 0 for a low-quality firm. In a separating equilibrium
where it is identified as low quality by the consumer, the ‘ type firm makes zero profit and
we can set its equilibrium price and advertising in the first period at p
‘
¼A
‘
¼0.
I first characterize a separating equilibrium where the high-quality firm only uses adver-
tising expenditure to signal. That is, it charges in the first period its full information price,
p
h
¼s
h
.LettingA
h
* be its equilibrium advertising expenditure, its equilibrium discounted
profit is 1 + δðÞs
h
c
h
ðÞA
h
. If the low-quality firm mimics the high-quality firm, its
profit is s
h
c
‘
ðÞA
h
because it is able to sell at price s
h
in the first period to the consumer
who believes quality is high but cannot earn any profit in the second period. In order to
have an equilibrium, the high-quality firm must be at least breaking even while the low-
quality firm must not find it profitable to pretend it is high quality. So we must have
1+δðÞs
h
c
h
ðÞA
h
0 s
h
c
‘
ðÞA
h
; (4.16)
which requires that δ s
h
c
h
ðÞ> c
h
c
‘
. The left-hand side is the discounted benefit of the
seller of a high-quality product from selling again in the second period, whereas a low
quality seller could not sell again (the Nelson effect in
Tirole, 1988, p. 120). The right-hand
side is the cost saving from selling a low-quality product rather than a high-quality prod-
uct (the Schmalensee effect). As long as the former dominates the latter, there are some
values of A
h
* satisfying (4.1) so that dissipative advertising can be used to signal quality.
In the least cost equilibrium, the amount spent on advertising is A
h
¼s
h
c
‘
(so the ‘ type
is just indifferent between deviating or not).
What changes if price also signals quality? Then the h type firm picks a price p
h
< s
h
.
This can be interpreted as an introductory offer, since the firm moves its price up to s
h
in
the second period. Then condition
(4.16) becomes
171Advertising in Markets
p
h
c
h
+ δ s
h
c
h
ðÞA
h
0 p
h
c
‘
A
h
; (4.17)
which still requires that δ s
h
c
h
ðÞ> c
h
c
‘
Þ. Now in the least cost separating equilibrium,
the high-quality firm’s price and advertising satisfy p
h
¼A
h
+ c
‘
. The corresponding loss
in profit for the h type firm from what it would get under full information is c
‘
c
h
. This
means that, from the point of view of the firm, price signaling and signaling through ad
expenditures are perfect substitutes. In any case, the firm burns an amount of money
c
h
c
‘
off its full information profit to convince the consumer it has high quality.
Although introductory offers and dissipative advertising are perfect substitutes for the
firm, they have very different welfare implications. The former is merely a transfer from
the firm to the consumer. The latter is a purely wasteful activity. Introductory offers are
clearly observed in practice and hence it is unclear from this simple example why firms
should resort to dissipative advertising.
The above example, however, shoots down some important dimensions of the firm’s
problem by assuming perfectly inelastic demand.
Milgrom and Roberts (1986) analyze
the same quality signaling problem while assuming consumers have a heterogeneous will-
ingness to pay. Furthermore, in their setting, a low-quality firm may earn some profit in
both periods in a separating equilibrium. Still it is assumed that more sales in the first
period generate more profit in the second period for the high-quality firm even though
it may have a higher marginal cost. This is due to the Nelson effect: the favorable first period
experience increases the second period demand (there are more repeat purchasers).
Bagwell (2007) offers a characterization of the least cost separating equilibrium in a
reduced form version of the Milgrom and Roberts setting. I now discuss the results
and provide intuition.
It is useful to recall some properties of the pure price signaling analysis in the static
setting. When c
h
> c
‘
, the high-quality firm distorts its price upward because this price
increase is more harmful to the low-quality firm than to itself. For c
h
< c
‘
, it distorts
its price downward because the resulting loss in profit is less for a type h firm than for
a type ‘ firm. In the two-period model, we also need to account for the impact of the
first period price on the second period profit. Under the assumption that more sales in the
first period increase the second period profit more for a high-quality firm, increasing the
first period price is more costly for the high-quality firm. If c
h
< c
‘
, the Nelson effect rein-
forces the h type’s advantage over the ‘ type in reducing its price. By contrast, if c
h
> c
‘
,
the Nelson effect goes against the h type’s advantage over the l type in increasing its price.
Then price signaling involves an upward distortion only if c
h
c
‘
is sufficiently large.
Now if the high-quality firm uses dissipative advertising alone to signal quality, in
order to inflict a $1 loss in profit to a deviating ‘ type, it must incur a $1 loss in its
own profit. If instead it uses a price distortion and c
h
< c
l
, then a drop in price that
decreases the profit of the deviating ‘ type by $1 decreases the h type’s profit by a smaller
amount. For this reason, dissipative advertising is never used in the least cost separating
172 Handbook of Media Economics
equilibrium when high quality is less costly to produce. In the reverse case, however,
because of the Nelson effect it could happen that the price increase needed to decrease
the deviating ‘ type profit by $1 decreases the h type’s profit by a larger amount.
Milgrom
and Roberts (1986)
characterize situations where dissipative advertising is used in that
case along with an upward price distortion.
Although this literature suggests some possible role for dissipative advertising, it does
not necessarily support the view that it should be widely used, given the restriction on
parameters needed for dissipative advertising to be an effective signal, when a distortion in
price can also be used.
51
This suggests the theory of advertising as an indirect transmitter
of information is better supported if it also has a direct demand expansion effect as in the
static framework above and in accordance with the conjectures of
Nelson (1974), who
did not consider dissipative advertising. This is also what is suggested by the empirical
study of
Horstmann and MacDonald (2003) on the compact disk (CD) player market
between 1983 and 1992. They find that new CD players are heavily advertised and sold
at low prices, which is not consistent with the
Milgrom and Roberts’ (1986) results but
could match the prediction of the static analysis where advertising has a direct effect.
52
I now consider an alternative signaling role for advertising.
4.4.3 Advertising and Coordination
Another indirect role of advertising is that it may facilitate coordination. I discuss two
applications.
A first application can be found in
Bagwell and Ramey (1994a, b). Here I present a
simple setup loosely inspired by
Bagwell and Ramey (1994b).
53
A monopoly firm has
three potential customers with an identical price-sensitive demand. There are increasing
returns to scale in production so marginal cost is decreasing in quantity. Thus, for a well-
behaved demand, monopoly price is lower if the firm can sell to more consumers. Let
p
m
(n) be the monopoly price if the number of consumers served is n ¼1, 2, 3. Let
S
n
> 0 be the surplus of a consumer at price p
m
(n) and we have S
1
< S
2
< S
3
. The firm
earns a larger monopoly profit if it sells to more customers and hence faces a higher
demand at any price. Letting π
n
denote monopoly profit when the number of customers
is n, we have π
1
< π
2
< π
3
.
51
See Kihlstrom and Riordan (1984) for a purely competitive setting where prices cannot signal.
52
Arguably, there is not much scope for a Nelson effect for CD players.
53
The example bears several differences with Bagwell and Ramey (1994b). Their main model is a duopoly.
More importantly, advertising is purely dissipative. However, in order for advertising to be used in the
refined equilibria, they assume that the firm has private information about whether it is efficient or not.
Bagwell and Ramey (1994a) present a monopolistic competition model of retailing. The equilibrium with
advertising is in mixed strategy where firms that advertise a lot invest in large-scale operations and attract a
lot of customers. See
Bagwell (2007, section 5.3) for details.
173
Advertising in Markets
Now consider the following game. Initially, only consumer 1 is aware of the firm’s
existence (she is the local consumer base). In a first stage, the firm decides on its capacity
to serve between 1 and 3 customers while charging the corresponding monopoly price. It
may also advertise its existence to consumers 2 and 3. Either it reaches them with personal
flyers, in which case it costs f > 0 to inform each consumer, or it may post a television ad
that is seen by both consumers and that costs T where f < T < 2f (the increasing returns to
using a TV ad are motivated by the idea that the potential population is large). Further
assume that f < π
2
π
1
, f < π
3
π
2
, and T f < π
3
π
2
, so the firm would choose tele-
vision advertising if it was certain both consumers show up. In a second stage, consumer 1,
and other consumers if they have been reached by an ad, decide whether or not to visit the
firm and buy, where a visit costs zero for consumer 1 and γ for consumers 2 and 3. Assume
S
2
< γ < S
3
, so consumers 2 and 3 visit only if they expect the firm to be catering to three
customers. Note that the firm cannot commit to a price in its ad, which is consistent with
Nelson’s assumption that there is no legal restriction on misleading ads. It is also consistent
with the stylized fact that many ads contain no price.
This is a coordination game with three pure strategy equilibria that are Pareto ranked.
In the Pareto-dominated equilibrium, the firm does not advertise and sells only to con-
sumer 1 at price p
m
(1). It is Pareto dominated by an equilibrium where the firm sends
flyers to 2 and 3 and sells to all consumers at price p
m
(3). This equilibrium in turn is less
efficient than the equilibria where the firm posts an ad on TV and also sells to all at price
p
m
(3). In the first equilibrium, non-local consumers, 2 and 3, rationally would not react to
advertising off the equilibrium path. It is then a best response for the firm not to advertise
and to serve consumer 1 alone. By contrast, in the other equilibria, the firm expects con-
sumers to respond to the type of advertising it uses and if it uses flyers it is because non-
local customers would not visit when exposed to a TV ad.
Following
Bagwell and Ramey (1994b), the two least efficient equilibria can easily be
refined away by using equilibrium weak dominance. If consumers see an ad on TV, they
should infer that the firm is set up to sell to three customers and will charge them p
m
(3).
Otherwise, it would not bother expending the resources. If T > 2f , the refinement only
eliminates the no-advertising equilibrium. The equilibrium with flyers survives because it
is the less costly way of reaching non-local consumers and the TV ad survives, because if
the firm deviates to sending flyers, each consumer could believe that only one flyer has
been sent and that the price will be p
m
(2). One interesting property of a TV ad is that,
when one consumer gets to observe it, she may also realize that other consumers are
observing it and that those other consumers themselves realize that other consumers
are exposed to this same ad. In other words, as argued by
Chwe (2001), advertising
may be a way to achieve what game theorists call common knowledge of an event, where
this event may merely be that a group of consumers has observed the same ad.
The second application involves a consumption externality and is inspired by
Pastine
and Pastine (2002)
and Clark and Horstmann (2005). Two firms with zero production
174 Handbook of Media Economics
costs sell to a continuum of identical consumers with mass 1. The utility attached to buy-
ing the product from one firm depends on the extent of the consumption externality
imparted by other consumers buying the same product. The willingness to pay for firm
i’s product is x
i
, where x
i
is the mass of consumers who buy from firm i. This externality
might arise because of fashion or some network externality (among users of the same OS
on a cell phone, for instance). In a first stage, a firm may decide whether or not to spend
some amount A > 0 on dissipative advertising. In a second stage, firms compete in prices.
If the outcome of the first stage is symmetric, then consumers choose the cheapest prod-
uct or split equally if prices are identical. The outcome is then the standard Bertrand equi-
librium with zero profit for each firm. If one and only one firm advertised in the first
stage, then consumers choose that firm when indifferent in the second stage. Hence if
firm a advertised, then consumers buy product b if and only if p
b
x
b
and
x
b
p
b
> x
a
p
a
. Then, there cannot be an equilibrium such that all consumers buy
product b
54
and, if prices must be positive, the only equilibrium is such that firm a charges
1 and firm b charges 0 and all consumers buy from firm a (the situation is analogous to a
Bertrand game with firms having different qualities). The first period game may then be
represented by the following matrix, that shows profits of firms a and b depending on
both firms’ choices to advertise or not.
Firm b
Yes No
Yes A, AðÞ 1 A,0ðÞ
Firm a
No 0,1 AðÞ 0, 0ðÞ
For 0 < A < 1, there are two pure strategy equilibria where only one firm advertises and
serves the entire market in the second stage. The corresponding social surplus, 1 A,is
entirely captured by the advertising firm. This should be compared to the social surplus of
1/2 that accrues to consumers if neither firm advertises. By coordinating consumers on
the same product, advertising raises social surplus by 1/2. This, however, comes at a cost
of A so that, for 1=2 < A < 1, advertising is a wasteful activity.
4.4.4 Concluding Remarks
Advertising that does not contain any direct information may nonetheless inform con-
sumers. As
Nelson (1974) explains, this is the case for experience goods whose quality
cannot be evaluated by consumers prior to purchase. Much theoretical effort has been
devoted to understanding whether and when firms have an incentive to use advertising
in this way. Nelson argues that firms should be expected to spend more on such indirectly
54
Such an equilibrium could exist with a finite price grid, where firm b would charge the highest price below
1 and firm a would charge 0.
175
Advertising in Markets
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