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examines how the extent of (known) vertical quality a¤ects a …rm’s decision to release information
about horizontal attributes. Finally, in related work, Bar-Isaac, Caruana, and Cuñat (2008) explore
a multidimensional good setting in which, as in this paper, consumers also gather information, but
do so attribute by attribute. The study suggests that …rms have strong incentives to in‡uence the
consumers’assessment behavior.
Outside of the literature on branding and advertising, our work is related to Courty and Li (1999,
2000), in which the information that consumers have about their valuation for a good increases
(exogenously) over time.
3
A …rm can exploit this by charging di¤erent prices at di¤erent times or can
o¤er a menu of ref un d contracts. Their work nicely characterizes the impact and the comparative
statics of di¤erent information s tructures for the consu mer types. Our work di¤ers from this and
other work on information disclosure, in a number of respects. First, and most signi…cantly, we
allow no discrimination through prices: There is only one “contract” o¤ered, and all products are
sold at an identical price. Second, our consumers are active in information gathering: They choose
whether or not to incur a cost in learning their valuations, and the …rm chooses this cost directly.
4 ;5
2 Model
We consider a …rm that decides: (i) how much to investment in ensuring quality for a single good;
(ii) the price of the good; and (iii) the ease with which con sume rs can learn their valuations for it.
Consumers have expectations of how much they are likely to value the good based on how much
the …rm has invested or, in the case in which the …rm cannot commit to a given quality provision,
on their inferences of how much the …rm has invested. Consume rs’valuation of the good depends
on their type and an idiosyncratic component. We model investment as leading to a product that
is more likely to appeal to a broader range of consumers of any type. By incurring some e¤ort
that depends on the …rm’s marketing strategy, consumers can learn their realized valuation before
deciding whether or not to buy.
For the time being, we suppose that investment is observed by consumers, and later, in Section
3
See, also, Möller and Watanabe (2008) and Nocke and Peitz (2008).
4
There is a wide literature that has considered information gathe ring and more-general price mechanisms . See
Cremer and Khalil (1992), Lewis and Sappington (1997), Cremer et al. (1998a,b), and Bergemann and Välimäki
(2002) or, in the cont ext of auctions, Ganuza and Penal va (2006) and references therein.
5
Matthews and Persico (2005) study refund policies, but their work is related to this paper inasmuch as they do
so in a framework with infor mation acquis ition, and post ed prices.
5
6, we consider the case in which it is not. The speci…c timing is, therefore, as follows. First, the
…rm decides on marketing, price, and investment strategies. Consumers observe all these choices
and decide whether to acquire more information on the p roduct and, subsequently, whether to buy
it.
2.1 Firm
A monopoly produces a single product incurring a cost c(q) to produce q units. The product can
be a good or a bad match for each consumer, and this is determined stochastically. The …rm can
invest a variable amount x to a¤ect the probability that its p roduct is a good match for a consumer.
In particular, any consumer has a probability of …nding a good match of (x) 2 [0; 1], where is
a non-decreasing function.
6
Where there is no ambiguity, and, in particular, when investment is
observable, we will suppress the argument for (x) and simply write .
In addition to choosing its investment strategy, the …rm posts a price p for the good, and,
costlessly, chooses a marketing strategy A 2 R
+
. Consumers can choose to incur a cost A to learn
the realization of their valuations before buying the good. We will refer to transparency, when
the …rm makes it costless for consumers to learn their valuation (A = 0). When the …rm makes
it prohibitively costly (A = 1 or, equivalently, an A that is high enough so that no consumer
veri…es), we term this opacity. Finally, an intermediate marketing strategy corresponds to those
interior choices of A in which some (but not all) consumers pay to learn the realization of their
valuation. Introducing costs to the …rm for choosing di¤erent marketing strategies would be a
natural extension; however, we abstract from it to highlight the economic forces at work.
7
Summarizing, the …rm in this model is risk-neutral and chooses A, p, and x to maximize its
pro…ts.
2.2 Consumers
There is a mass one of consumers, each of whom is potentially interested in buying one unit of
the good. Consumers have a taste for quality represented by 2 [0; 1], where type is distributed
according to some atomless probability density function f(). Higher values of correspond to
6
Matche s could be independent across consumers (for example, the …rm could introduce additional features that
appeal to some, but not all, consumers) or correlated (in which case the investment improves the probability that
the good will be of high vertical qu ality).
7
It is not clear how these c osts should chan ge. Providing good and accurate information to consumer s is costly;
but it is also costly to deliberately hide and obfuscate information.
6
consumers who have higher valuations, on average.
However, the valuation of the good depends not only on , but also on some ex-ante unknown
idiosyncratic aspect that makes it a good or a bad match for the consumer. The probability that
a match is good is (x).
8
The utility of an agent of type who purchases the good at a price p is
g( ) p if it is a good match and b() p if it is bad. We assume that g() b() for all and
that g() and b() are non-decreasing in .
Before purchasing, the agent may decide to assess the quality of the good by spending A. There
is no point in assessing the quality of the good if the agent plans to buy the good regardless
of the quality level. Thus, assessment will take place only if the subsequent purchase decision
is conditional on …nding high quality.
9
In particular, assessment is valuable only as a form of
protection or insurance against the possibility of buying a bad match. Therefore, there are only
three reasonable strategies for an agent of type and the corresponding expected utilities:
Buy unconditionally without assessing EU
B
() = g() + (1 )b( ) p.
Buy conditionally after assessing EU
A
() = (g() p) A.
Do not buy (do not assess or buy) EU
N
() = 0.
3 A Simple Example
To gain some intuition and to reinforce the description of the model, we brie‡y introduce a simple
example with only two types of consumers (a “high-” and “low-type” one) and no investment
decision.
The …rm prod uce s a good that, with probability
1
2
, becomes a good match and, with probability
1
2
, becomes a bad match. A low-type consumer values a bad realization of the match at 1 and a
good one at 3. The high-type consumer values a bad match at 2 and a good one at 4. Suppose
that half of the population are low-type consumers and that there is a constant marginal cost of
production c.
10
For very high or very low marginal costs, the optimal marketing strategy is going to be extreme.
The intuition is in the spirit of Lewis and Sappington (1994). If c is low enough, extracting as much
8
Note that the probability of a good or bad match is independent of .
9
For expositiona l purposes, and without lo ss of generality, we assume that, when A = 0, those consumers who do
not condition their purchase on what they see, do not assess.
10
In the notation of our model, t his correspond s to b(0) = 1, b(1) = 2, g(0) = 3, g(1) = 4, c(q) = cq, (x) =
1
2
for
all x 0, and there is a de generate type distribution with f(0) =
1
2
and f (1) =
1
2
.
7
pro…t as possible entails choosing an opaque marketing strategy (A = 1) and a price at the low
agent’s average valuation (p =
1+3
2
). The opaque marketing strategy allows the …rm to maximize
the price at which it can sell to all consumers. Instead, if the marginal cost of production is high
enough, then many trades would be ine¢ cient if the …rm sold to all consumers regardless of the
match. The …rm in this case achieves maximum pro…ts by making it costless for consumers to learn
their valuation (A = 0) and charging a price equal to the high-type consumer’s valuation when he
has a good match (p = 4).
Finally, consider an intermediate value of the marginal cost. If the …rm could price discriminate,
it would prefer to keep both consumer-types in the dark (by setting A = 1) and extract the full
surplus from each, or to make it costless for them to learn their ex-post valuation and charge a
di¤erent high-valuation price according to the consumer’s type. Howe ver, without the ability to
price discriminate, the …rm’s optimal strategy may be di¤erent from the extreme strategies studied
above. It can set the smallest positive A and highest price p in a way that a high-type consumer
(just) prefers buying the good without assessing (to buying conditionally after assessing), and a
low-type consumer (just) prefers buying conditionally (to not buying the good at all). Here, this
entails p =
5
2
and A =
1
4
. This allows the …rm to extract much of the surplus f rom a high-type
consumer regardless of the match, and from a low-type consumer who has a good match.
11
This is
a form of discriminating: low-types pay a price p bu t only half of the time.
1
2
3
4
Denotes profits Denotes costs incurred
Opaque Marketing
Intermediate Marketing Transparent Marketing
1
2
3
4
1
2
3
4
1
2
3
4
Denotes profits Denotes costs incurred
Opaque Marketing
Intermediate Marketing Transparent Marketing
1
2
3
4
1
2
3
4
Figure 1: Ex-post demands and pro…ts for di¤erent marketing strategies (c = 1).
Figure 1 illustrates the di¤erent induced demand functions (that is, after consumers have chosen
11
Note that the …rm cannot extract all this surplus, since it chooses its marketing and pricing to deter the high-type
from assessing and must provide enough surplus to induce th e low-type con sumer to assess.
8
whether or not to assess) depending on the marketing strategy chosen. Given that the marginal cost
in the …gure is set at an intermediate value, c = 1, an intermediate marketing strategy outperforms
the other two options. It is also easy to verify on the graph that, if the marginal cost is su¢ ciently
lower (higher), an opaque (transparent) strategy becomes optimal. Note that, at c = 1 if the two
types of markets were segmented, the …rm would choose an opaque strategy in both of them. This
apparently paradoxical result in terms of marketing strategies is not surprising once one recognizes
that marketing and pricing are an integrated strategy.
12
Concluding, intermediate marketing may be a valuable tool to extract surplus f rom consumers.
It is most appealing when: (i) there is a good mix of consumer types and where, (ii) the induced
valuations (after low-types choose to assess and high-types do not) are “relatively”close; and (iii)
the surplus that is not captured (the di¤erence between the value of bad matches for the low types
and the marginal cost of production) is not too high.
4 General Results
We turn back to the general model set up in Section 2. First, we focus on consumer strategies,
taking the …rm’s strategy as given.
4.1 Characterizing Consumer Behavior
We begin by introducing two lemmas that allow the behavior of every consumer to be described in
a simple way.
Lemma 1 If an agent of type prefers assessing to buying unconditionally, then so do all agents
of ty pe .
Proof. prefers assessing to buying unconditionally, and so
(g() p) A > g() + (1 )b() p, (1)
which holds if and only if
p
A
1
> b(). (2)
12
Under an opaque strategy, the …rm would char ge prices equal to 3 for the high-type co nsumers and 2 for the
low-type ones. In this particular example, the …rm would be indi¤erent between an opaque and a transparent strategy
for the low-type consumers, but marginal changes to their va luations would make opaque strictly preferred while
keeping the intermediate strategy as t he optimal one for the integrated market.
9
Since b() is non-decreasing in , then condition (2) h olds f or all .
Lemma 2 If a consumer of type prefers not to buy, then all consumers with also prefer
not to buy.
Proof. prefers not to buy when
0 > max f(g( ) p) A; g() + (1 )b() pg . (3)
Both arguments of the max are non-decreasing in , and so condition (3) holds for all .
As a consequence of Lemmas 1 and 2, to characterize consumer behavior, it is su¢ cient to
identify the consumers who are indi¤erent between buying unconditionally and assessing, between
buying unconditionally and not buying, and between assessing and not buying. Consumer strategies
are homogeneous within the intervals determined by such consumers.
13
Let T
BA
denote the consumer indi¤erent between buying un cond itionally and assessing. Then,
T
BA
is implicitly de…ned by EU
B
(T
BA
) = EU
A
(T
BA
). By Lemmas 1 and 2, there can be, at most,
one solution. If there is no solution, it is because all consumers prefer one option over the other.
If EU
B
() > EU
A
() holds for all , we de…ne T
BA
= 0: This is with some abuse, but has no
consequences, as the mass of consumers with = 0 is zero. When EU
B
() < EU
A
() holds for all
, we de…ne in a similar fashion T
BA
= 1.
Similarly, we de…ne T
BN
as the consumer who is indi¤erent between buying without assess ment
and not buying. T
BN
is implicitly de…ned by the equation EU
B
(T
BN
) = 0. Again, if EU
B
() > 0
for all denote T
BN
= 0; and if EU
B
() < 0, then T
BN
= 1. Finally, let T
AN
denote the consumer
indi¤erent between assessing and not buying, implicitly de…ned by EU
A
(T
AN
) = 0, and if no
solution exists, denote T
AN
= 0 if EU
A
() > 0 and T
AN
= 1 otherwise.
Note that T
BN
, T
BA
and T
AN
depend on the …rm’s choice of price, p, marketing, A, and
investment (which appears indirectly through ), as well as all exogenous parameters of the model;
however, we of ten suppress these arguments for notational simplicity. In the case that T
BN
, T
BA
13
Note that, in some circumstances, all consumers may have the same strict preferences over some (or all ) of these
assessment strategies, so that no consumer is indi¤erent between two of these strategies.
10
and T
AN
are interior they are implicitly de…ned as follows:
g(T
BN
) + (1 )b(T
BN
) = p, (4)
b(T
BA
) = p
A
1
, (5)
g(T
AN
) = p +
A
. (6)
4.2 The Firm’s Problem
With these de…nitions and preliminary results, the …rm’s sales can be simply written down as:
S =
Z
1
maxfT
BN
;T
BA
g
f()d + 1
T
BA
>T
AN
Z
T
BA
T
AN
f()d, (7)
where 1
T
BA
>T
AN
is an indicator function that takes the value 1 if T
BA
> T
AN
and 0 otherwise. The
…rst integral in (7) corresponds to sales to consumers who buy without assessment, and the second
expression correspon ds to those who assess and buy only when they …nd high quality, which occurs
with probability .
The …rm’s problem, then, is to choose (A; p; x) in order to maximize pro…ts:
= pS c(S) x. (8)
Note that sales S depend on T
BN
, T
BA
and T
AN
and, therefore, on (A; p; x).
Proposition 1 highlights implications for consumer behavior when the …rm optimally chooses an
intermediate marketing strategy— that is, 0 < A < 1 with some consumers assessing, rather than
either an opaque (A = 1) or a transparent (A = 0) one.
Proposition 1 If intermediate marketing is strictly optimal in equilibrium, there are both con-
sumers who assess, and consumers who buy without assessment.
Proof. Suppose that the …rm’s optimal strategy is to choose some intermediate A 2 (0; 1). If all
consumers assess, then the …rm can do better by increasing the price, and reducing A accordingly
(thereby inducing identical assessment and purchase behavior). If no one assesses, then the …rm
can do no worse by choosing the same price and A = 1.
11
Proposition 1 illustrates one of the two mechanisms outlined in the introduction. It is at the
heart of the idea of using the marketing strategy as a non-price means of discriminating between
di¤erent consumer types. Proposition 1 suggests (and this is veri…ed below) that the marketing
strategy can be pro…tably used as a means of inducing di¤erent consumer types to behave di¤erently.
All of the above has the following implications.
Corollary 1 If intermediate marketing is strictly optimal, there is some interior threshold T
BA
above which all types buy without assessment and lower types assess and, possibly, another threshold
T
AN
below which consumers do not buy.
Proof. Immediate consequence of Lemmas 1 and 2, and Proposition 1.
Corollary 2 If intermediate marketing is optimal for the …rm, there must be variation in the value
of a bad match— i.e., b() cannot be constant. In particular, agents must be heterogeneous.
Proof. By Proposition 1, it is necessary that some agents prefer to assess and others buy without
assessment. Suppose that some type prefers to buy without assessment and some type prefers to
assess. Then, as in (2), it must be that p
A
1
b() and p
A
1
> b(), which would contradict
that b() is constant in .
Another necessary condition for intermediate marketing to be optimal is that b(1) > min
q
c(q)
q
.
Indeed, if this condition fails, the optimal marketing strategy is either transparency or simply to
make no sales. The intuition is clear: Intermediate or opaque marketing strategies allow the …rm to
make sales even when matches are bad. However, if bad matches unambiguously destroy surplus,
there is no advantage to making such sales.
Corollaries 1 and 2 contain the main intuition for why intermediate marketing can be used as
a means of non-price discrimination. When intermediate marketing is optimal, there is a mass of
consumers with high ex-ante valuations of the good (consumers with high ) that buys without
assessment. There is also a mass of consumers with lower ex-ante valuations for the good (lower )
that assesses and buys only upon …nding a good match. Finally, there may be a group that has very
low ex-ante valuations and decides not to assess or buy. The …rm is, therefore, using the marketing
strategy as a way to induce consumers with low ex-ante valuations to base their consumption
decision on their ex-post valuations. The …rm can sell to those with a good idiosyncratic match
12
even if their ex-ante expected valuation is below the price. At the same time, consumers with
high ex-ante valuations remain “in the dark” and base their purchase on their ex-ante average
valuations.
14
Just as in Section 3, the valuations after the information-gathering decisions might
end up relatively less-dispersed and allow, the monopolist to extract relatively more of the consumer
surplus.
15
However, the …rm cannot directly discriminate between consumers in terms of information pro-
vision, so di¤erent assessment behaviors have to be achieved indirectly through the right marketing
policy A. Assessment can be seen as paying a premium A that insures against a bad match.
Therefore, for some consumers to assess and for some not to, there must be heterogeneity in their
valuations of a bad match. Given that low valuations are increasing in the type, the …rm can select
an A such that high consumers do not verify, while s ome low ones do.
It is important to stress that the results, so far, are fairly general, as they do not depend on the
particular choice of consumer utility functions or the type distribution. In the following section,
we focus on the family of linear utility functions with uniformly distributed types. This allows us
to write explicit expressions for p and A to gain additional intuition about when each marketing
strategy is optimal. In particular, we show that there exist a range of parameters for which an
intermediate marketing policy becomes optimal.
5 The Linear-Uniform Case
In this section, we make some more-speci…c assumptions on the model to fully characterize the
equilibrium. We demonstrate that intermediate marketing and discrimination can arise, and we
explore the role of consumers’ preferences for these phenomena to happen. Speci…cally, suppose
that c(q) = cq, the distributions of consume rs is uniform on [0; 1], and valuations are linear in type
so that b() = b + s and g() = g + (s + ). Suppose, also, that investment is a b inary decision
and (abusing our notation slightly) that the probability of a good match is if the …rm makes an
investment at cost k and 0 otherwise. Note that our earlier assumptions on b() and g() require
that g b, s 0, > (b g) and s + 0.
14
In other words, intermediate marketing acts a s a broad market strategy with high ex-ante valuation consumers,
while it acts as a niche strategy with low ex-ante valuation ones.
15
A similar desire to induce ex-post similar valuations is familiar from the literatu re on bundling, as in Adams and
Yellen (1 976), in which negative correlation in valuations of di ¤erent bundle components leads to rela tively similar
valuations of the bundle, and so allows the seller to, in e¤ect, more accurately assess the c onsumer’s valuation and,
thus, extract more surplus.
13
The …rm wants to maximize pro…ts by choosing (A; p; x). From Equations (7) and (8), we can
write down the …rm’s pro…t function (using the assumption that is uniformly distributed) as:
= (p c) [(1 maxfT
BN
; T
BA
g) + (T
BA
T
AN
) 1
T
BA
>T
AN
] k 1
invest
, (9)
where 1
T
BA
>T
AN
is an indicator function that takes the value 1 when T
BA
> T
AN
and 0 otherwise,
and 1
invest
is an indicator function that takes the value 1 when the …rm invests and 0 otherwise.
Given that the investment decision is binary, we treat each case separately. First, we consider
the (less interesting) case in which the …rm makes no investment. Then, the marketing strategy
is irrelevant: Consumers never consider assessing as they have no doubts that the match will be
bad. Thus, we can conclud e that T
BA
= T
AN
= 0. Using Equation (4), we obtain T
BN
=
max(min(
pb
s
; 1); 0) and pro…ts simplify to = (p c)(1 T
BN
). Depending on the values of the
parameters, the optimal price results in either an interior solution with p
NI
=
b+c+s
2
and pro…ts
of
NI
=
(bc+s)
2
4s
, or a corner solution of either p
NI
= b and
NI
= b c, or p
NI
b + s and
NI
= 0 (which is equivalent to not operating and no s ales).
Now, we analyze the more interesting case in which the …rm invests in quality. We can charac-
terize consumer behavior in terms of the parameters using Equations (4), (5), and (6), as follows:
T
BN
= max(min(
p g (1 )b
s +
; 1); 0), (10)
T
BA
= max(min(
(p b)(1 ) A
s(1 )
; 1); 0), and (11)
T
AN
= max(min(
A (g p)
(s + )
; 1); 0). (12)
These are illustrated in Figure 2 below for the intermediate case. Note that by assessing rather
than always buying, an agent saves the cost of paying a price p that is above his valuation (in
case of a low realization). He gains this bene…t (equal to p b + s) with probability 1 , but
must pay a cost A. Similarly, in assessing rather than never buying, a consumer gains a surplus
(g + (s + ) p) (by buying the well-matched product with probability ), which must outweigh
the cost of assessment A (which is always paid) for assessment to be worthwhile.
14
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