Product Match Disclosure in a Distribution Channel ∗
Monic Sun
Boston University
July 9, 2015
Comments are welcome: monic@bu.edu. I would like to thank Yi Luan and Ying Lei for providing
excellent research assistance. I am also grateful to Rajeev Tyagi, Anthony Dukes, Barbara Bickart, Carey
Moorwedge, Sherif Nasser, Shuba Srinivasan, Feng Zhu, participants at the UTD FORMS conference and the
INFORMS marketing science conference, and seminar participants at Boston University, Columbia Business
School and University of Rochester for helpful discussions and comments.
∗
Product Match Disclosure in a Distribution Channel
Abstract
Sellers in today’s marketplace have increasing abilities to facilitate consumers’ learning about their match with her product through prepurchase disclosure. We investigate
how a seller’s incentive to disclose product match information is affected by the structure of her distribution channel. Our model suggests that, while selling through a
monopolistic retailer typically decreases manufacturer disclosure, selling through competitive retailers could increase such disclosure. Furthermore, retailers often have
stronger disclosure incentives than the manufacturer, especially for products with a
strong quality reputation. We collect data on web-only fast-fashion brands in India
and find evidence that is consistent with the model predictions. We also discuss how
product returns and a continuum of product types affect disclosure incentives.
Keywords: Information Disclosure, Product Match, Distribution Channel
1
1
Introduction
With about 250,000 new products launched globally each year, 1 consumers constantly need
to evaluate their potential fit with a product. 2 Sellers, as a result, are adopting many costeffective prepurchase disclosure strategies, such as posting detailed product descriptions online and circulating product pictures and videos. For magazines, books, movies, software
and video games, sellers can also provide a free version online. Warby Parker, a popular
brand of eyeglasses and sunglasses, allows a consumer to virtually try on multiple pairs of
glasses.3 Similarly, Land’s End and Pearle Vision both offer software programs allowing the
consumer to envision himself in their products (Shulman et al. 2009). As prepurchase disclosure becomes popular due to the development of digital technologies, it plays an increasingly
important role in a firm’s overall marketing strategy and may interact with other elements
of the marketing mix.
In particular, manufacturers may have different disclosure incentives depending on how
they distribute their products. Jabong.com, a leading fast-fashion online retailer in India,
posts multiple pictures of each clothing item on their site to help consumers evaluate their potential fit with the item. Many items are from web-only brands with no physical distribution
channels so that pictures are the primary source of product match information. Interestingly, many items have a different number of pictures on Jabong than on their brands’ own
e-commerce sites. When asked why a consumer may not see the same pictures on the retailer
site, a Jabong employee responds that a brand “decides how many pictures to give us.” 4 It
seems that brands are making a conscious decision on what they want consumers to see on
1
http://www.forbes.com/2010/12/03/most-memorable-products-leadership-cmo-network.html,
accessed in July 2014.
2
Recent research at Cisco shows that digital content from the Internet is the most powerful influence in
buying decisions for the majority of shoppers in all channels. See http://newsroom.cisco.com/release/
1128065, accessed in April 2015. The survey suggest that 78% of all shoppers use the Internet to research
and purchase products.
3
https://www.warbyparker.com/virtual-tryon, accessed in April 2015.
4
Interview conducted with Jabong’s customer service on December 4, 2014.
2
their retailers’ websites. Many brands in the U.S. adopt similar strategies. Angela & Roi, an
emerging handbag brand that sells exclusively online, posts multiple pictures for each bag
on the brand’s own website but only offers one picture for each bag on Bluefly, a leading
online retailer that typically displays multiple pictures for each item.
To complicate matters, the disclosure decision is not always up to the manufacturer.
Gilt, for example, has its own in-house photo studio set up in Brooklyn offices where it
shoots models wearing items it carries. 5 Some online retailers offer sales assistance such as
“live chat” to given detailed answers to consumers’ questions about each of their products.
Some incorporate customer reviews into their websites. Casper.com, an online retailer of
mattresses, identifies reviewers with real names, locations, and sleeping habits so that a
potential consumer could evaluate his fit with a mattress by seeking out a like-minded reviewer.6 As retailers often have first-hand knowledge on consumers’ attitudes and behavior,
they can sometimes be in a better position than the manufacturer to disclose product match
information.
To better think about the relationship between product match disclosure and channel
structure, we set up a game theoretic model to answer the following questions. First, how
does a manufacturer’s optimal disclosure strategy change with her distribution channel?
When she distributes through competitive retailers, in particular, how does the intensity of
downstream competition affect upstream disclosure? Second, when retailers are in charge
of digital information disclosure, how would their optimal strategy be different from that of
the manufacturer?
Our model features a monopolist manufacturer who can costlessly disclose truthful information about her product. 7 At the core of the disclosure decision is a seller’s tradeoff
5
http://www.businessinsider.com/gilt-groupe-photo-shoot-2010-7/gilts-brooklyn-office-\
is-in-the-navy-yard-which-is-actually-quite-advantageous-for-photo-shoots-1, accessed in
April 2015.
6
https://casper.com/reviews, accessed in April 2015.
7
See Moorthy (2005) for a general theory of pass-through with multiple manufacturers and retailers.
3
between a product’s margin and demand (e.g., Anderson and Renault 2006, 2009). Disclosure is typically aligned with a margin-driven strategy, as the consumers’ willingness to pay
is more heterogeneous and the product is optimally targeted at well-matched consumers at a
premium price. Nondisclosure, on the other hand, is aligned with a demand-driven strategy,
as the willingness to pay is more homogeneous and the product is optimally targeted at the
mass market at an “average” price.
As the model focuses on an experience good whose match value can only be learned
through prepurchase disclosure or post-purchase consumption, it is more applicable to products that cannot be returned once purchased (e.g., meals, movies, software, spa services,
vacation packages) or products whose price is low when compared to the hassle of a return
so that consumers often keep an ill-matched product rather than returning it (e.g., magazines, books, fast-fashion clothing). A common features of these products is that repeat
purchase is limited so that disclosure plays an important role in the purchase decision.
A baseline result we find is that the manufacturer chooses to disclose product match
information when her quality reputation is weak. 8 Intuitively, when quality reputation is
weak, disclosure helps secure demand from well-matched consumers with a positive margin.
As her quality reputation strengthens, she is attractable to a larger portion of the market.
Serving uninformed consumers is more profitable in this case as she can price to the average,
rather than the marginal, consumer (e.g., Xie and Shugan 2001; Anderson 2002). As a
result, there exists a reputation threshold for nondisclosure: the manufacturer chooses not
to disclose product match information if and only if her quality reputation exceeds this
threshold.
Our key results center around how this reputation threshold changes when a directselling manufacturer switches to distributing her product through retailers. We find that,
if the manufacturer sells through a monopolistic retailer or two differentiated retailers, the
8
To ease exposition, we refer to the consumer as “he” and the manufacturer as “she.”
4
reputation threshold decreases. In other words, she is more likely to practice nondisclosure.
As nondisclosure increases the elasticity of demand, it benefits the manufacturer by putting
downward pressure on the retail markup and final price.
On the other hand, the reputation threshold increases when the manufacturer sells
through highly competitive retailers. As retail competition effectively limits retail markup,
the manufacturer barely loses any demand when compared to the case when she sells directly
to consumers. Therefore, the reduction in her demand is less significant than the reduction
in her margin, and she chooses disclosure in order to restore the margin. Putting the two
scenarios together, we find that although selling through dominant retailers tends to inhibit
upstream disclosure, selling through competitive retailers may increase upstream disclosure.
It is striking that when retailers are in charge of disclosure, they may adopt a nonmonotonic strategy and choose disclosure only if the manufacturer’s quality reputation is
either very low or very high. When the manufacturer’s quality reputation is low, as before,
disclosure helps ensure demand from well-matched consumers. For products with a high
quality reputation, on the other hand, the market is almost fully covered and the profit gain
from quality improvement goes mostly to the manufacturer under nondisclosure: consumers’
willingness to pay is homogeneous and retail markup is limited. By choosing disclosure, the
retailers could obtain a larger share of the profit gain from quality improvement. When
the manufacturer’s quality reputation is mediocre, the dominant effect of disclosure is to
alienate ill-matched consumers, which makes it less preferable to nondisclosure for all channel members. This middle range of quality reputation for nondisclosure shrinks as retailer
competition intensifies: as the downward pressure on retail markup increases, the retailers
can choose disclosure to restore their margins.
To demonstrate the managerial implications of our model, we collect data on 1,434 clothing items from 53 web-only brands in the fast-fashion industry in India. As these brands
sell only through online channels, product pictures and descriptions are the primary source
5
of product match information. We record the number of pictures for these clothing items
across different distribution channels including the brand’s own website and two leading fastfashion online retailers in India, Jabong.com and Myntra.com. Consistent with the model
predictions, if the item is carried by only one retailer, the number of its brand pictures is on
average smaller on the retailer’s site than on its brand site. If the item is carried by both
retailers, however, the number of its brand pictures is greater on a retailer’s site than on its
brand site. When a retailer uses its own pictures for the item, the number of such pictures
is higher than the number of brand pictures on its brand site, regardless of whether it is
carried by one or both of the retailers.
We discuss two extensions of the model. First, we incorporate the possibility of product
returns, which can also help consumers learn their match. Consistent with the literature
(Anderson et al. 2009a), the option to return a product in our model may either increase
or decrease the final demand of a product: the option expands initial demand by putting
a cap on the potential loss from the purchase, while the realized returns from mismatched
consumers reduce the final demand. Based on this intuition, we derive conditions for nondisclosure to be optimal for the manufacturer when returns are relatively easy for consumers.
We find that while there is still a reputation threshold for nondisclosure, the impact of
channel structure on this threshold changes. In particular, the threshold is now the highest
(i.e.,. the manufacturer is the most likely to choose disclosure) when she sells through a
monopoly seller and the lowest when she sells directly to the consumers. The extension
hence highlights the importance of considering the possibility of product returns when the
manufacturer crafts her optimal prepurchase disclosure policies.
We also examine the possibility of a continuum of product types. The analysis becomes
more involved in this case as the privately-informed manufacturer may have an incentive to
pool product types into multiple subsets. A key observation is that a disclosing type should
always make at least the profit of a nondisclosing type, as the latter can always costlessly
6
deviate to choosing disclosure. Using this observation, we characterize the equilibrium in
which the pooling product types all charge the same price and show that the range of nondisclosing types in this equilibrium increases with the quality reputation of the manufacturer.
The finding is consistent with our result that a strong quality reputation suppresses the
manufacturer’s incentive to disclose product match information.
The remainder of the paper is organized as follows. In the next section, we discuss related
literature. Section 3 then presents our main model of costless disclosure of truthful product
match information, Section 4 offers empirical evidence on web-only fast-fashion brands in
India that is consistent with the predictions of our model, Section 5 discusses the implications
of product returns and continuous product types, and Section 6 concludes.
2
Literature Review
The vast literature on product information disclosure starts with a focus on the disclosure
of vertical product quality. In their seminal papers, Grossman (1981) and Milgrom (1981)
establish the unravelling result: all levels of quality will be revealed in equilibrium, as the
highest quality type in any pooling equilibrium would want to separate from the other types
in the pool.
Subsequent studies often characterize a quality threshold above which the
seller would choose to disclose the quality of the product, and document how this threshold
changes with factors such as disclosure costs (Jovanovic 1982; Guo 2009b; Guo and Zhao
2009), consumer’s uncertainty about their preference for quality and asymmetry in firms’
quality levels (Kuksov and Lin 2010), whether disclosure is simultaneous or sequential (Guo
and Zhao 2009), and whether disclosure is made directly to consumers or through downstream retailers (Guo 2009b).9 Rather than focusing on the disclosure of vertical product
There is also an important literature (e.g., Gal-Or et al. 2008; Guo 2009a; Guo and Iyer 2010; Guo et al.
2014) that studies the sharing of information on demand shocks between channel members. Studies in this
literature often assume that retailers and/or manufacturers are privately informed of the real time demand
levels of the product and decide strategically whether to share this information with other members of the
9
7
quality, the current paper assumes that quality of the product is common knowledge and investigates channel members’ incentives to disclose the horizontal match between the product
and individual consumers with heterogeneous tastes. The paper is hence more applicable to
product categories in which a major source of the uncertainty around a consumer’s valuation
of a product comes from the idiosyncratic match.
Following the literature on quality disclosure, research on match disclosure has accumulated quickly in the past decade. Unlike papers on quality disclosure, studies in this literature
typically assume that product quality is common knowledge and focus on the seller’s incentives to disclose product match information. Chen and Xie (2008) explore the relationship
between consumer reviews and seller disclosure, both of which deliver information on consumer’s match with the product, and find that the two forms of disclosure can be either
substitutes or complements depending on the cost of the product and the sophistication of
product users. Sun (2011) models multiple product attributes and shows that the unravelling result may breakdown when disclosure reveals information on both quality and match.
Mayzlin and Shin (2011) and Branco et al. (Forthcoming) explore the interaction between a
seller’s information provision and the consumers’ information search and highlight equilibria
of partial disclosure. Recently, there are also studies that explore the effect of competition on
the disclosure of product match information (e.g., Shaffer and Zettelmeyer 2004; Anderson
and Renault 2009; Gu and Xie 2013).10 While the current paper also focuses on truthful disclosure of product match information, it is the first study in the match-disclosure literature
to investigate the impact of downstream competition on upstream disclosure.
distribution channel. Unlike papers in this literature, the current paper assumes that the manufacturer is
better informed than the manufacturer on the product attributes that would affect how well it matches with
consumers with heterogeneous tastes.
10
Fay and Xie (2008) study probabilistic goods: offers that involve a probability of getting any one of
a set of multiple distinct items. While probabilistic selling (PS) is similar to nondisclosure in that both
make the consumers’ willingness-to-pay more homogeneous and enable the seller to broaden market coverage
by catering to consumers with weak preferences, the two strategies are conceptually different in that the
disclosure decision modeled in the current paper does not require the existence of multiple (component)
products.
8
A key intuition in the literature, shared by the current paper, is that unlike disclosure of
quality information which typically shifts the demand curve up or down, disclosure of match
information tends to rotate the demand curve (Johnson and Myatt 2006).11 Rotation of
demand curve could happen for a variety of reasons and often changes how the total surplus
gets distributed. Anderson (2002), for example, shows in the context of product design that
firms may choose to assemble the product fully even if it is Pareto-efficient for the consumers
to carry out part of the assembly: a fully completed product is associated with a more elastic
demand curve, which allows the seller to capture a greater share of the total surplus. The
current paper goes beyond demand curve rotation, however, by showing that disclosure may
either increase or decrease depending on the intensity of downstream competition.
An important contribution that relates fit revelation to the structure of a distribution
channel is Gu and Liu (2013), who characterize the optimal shelf layout and find that whether
competing products should be displayed together depends on the difference in the products’
ex-ante fit probabilities as well as the intensity of retail competition. While they model
search goods so that consumers always learn the match before making a purchase, we focus on
experience goods with which consumers may not know their match until after the purchase.
Therefore, there is a possibility for consumers in our model to be stuck with an ill-matched
product that is absent from their model.
Another closely related stream of literature is the one on product returns. Prepurchase
disclosure and post-purchase product returns could both serve as effective ways to disclose
product match information. The two strategies differ significantly, however, for two reasons.
First, prepurchase disclosure typically incurs lower marginal cost to firms than product returns, which cost the U.S. companies more than $100 billion annually ( Shulman et al. 2010,
2011). As mentioned above, prepurchase disclosure is often implemented through digital
11
See Renault and Koessler (2012) for a discussion on the necessary and sufficient conditions on consumers’
preference structures in order for the unravelling result to hold.
9
technologies, and the marginal cost of disclosing match information for an additional product is often negligible once the fixed cost of the disclosure technology is incurred. On the
other hand, firms typically have to incur substantial restocking costs for each returned item.
Second, prepurchase disclosure also tends to be less costly to the consumers when compared
with product returns, which are often associated with the hassle of packing and shipping,
and sometimes hefty restocking fees.
Given the significant marginal cost of product returns to both the sellers and consumers,
studies in the returns literature focus on the relationship between the return rate and the
price that consumers paid for the product (Anderson et al. 2009b), the value of returns to
consumers and how sellers can optimally balance it against the operational costs of returns
(Anderson et al. 2009a), the optimal reverse channel structure, including who handles returns
and how much the manufacturer should refund the retailers for returned products ( Shulman
et al. 2010), and the optimal restocking fees in monopoly and duopoly settings ( Shulman
et al. 2011).
Shulman et al. (2009), in a related study where a multi-product manufacturer sells directly to consumers, investigate the interaction of prepurchase disclosure and post-purchase
returns. Consistent with the current paper, they find that the seller has an incentive to
target the well-matched consumers when reservation utility for the category is low. Moreover, it is not always optimal to choose prepurchase disclosure even if it could eliminate all
uncertainty around match. In a more recent paper, Shulman et al. (forthcoming) model
prepurchase information that partially resolves the uncertainty around match and find that
when consumers are reference dependent, such information may increase, rather than decrease, the instances of product returns. While these important studies focus on the effect of
information disclosure on the likelihood of returns, the current paper focuses on the impact
of the channel structure on prepurchase disclosure. Although we exclude the possibility of
product returns in the main model, our extension in Section 5.1 suggests that as an im10
portant form of information disclosure, product returns would indeed change the impact of
channel structure on prepurchase disclosure.
Overall, while there is a large body of literature on information disclosure, we make a
distinct contribution by showcasing the impact of a downstream distribution channel on
costless upstream disclosure of product match information. Our findings that the manufacturer should decrease disclosure when selling through a monopolistic retailer, but increase
disclosure when selling through competitive retailers, and that retailers may have different
disclosure incentives from the manufacturer, all have immediate implications for marketing
managers.
3
The Model
We use an augmented Hotelling model (Hotelling 1929) to capture consumers’ heterogeneous
tastes for the product and the store at which they make a purchase. 12 Formally, suppose a
unit mass of consumers are distributed uniformly in the unit square. The x-axis represents
consumers’ ideal store types, and the y-axis represents their ideal product types.
A consumer’s preference for the product is independent of his preference for the store.
This assumption suits real-world situations in which the store carries a large array of products
and one single product does not have a significant impact on the consumers’ preference for
the store. There are many factors that go into a store “type,” such as product layout, name
of the store, style of service, store ambience and store location. For online stores, store types
can be influenced by factors such as the color theme, page layout and shipping methods.
The two stores in our model are located at xs = 0 and xs = 1, and these locations
are common knowledge. They can be jointly owned by the manufacturer or a monopolistic
We obtain similar results with a circular model (Salop 1979) if consumers’ tastes differ only with respect
to the product. When tastes differ also with respect to the stores, it is more intuitive to incorporate the
second dimension of differentiation with the augmented Hotelling model.
12
11
retailer, or separately owned by two different retailers. The product’s type, captured by its
location, is a random variable that takes the value of yp = 0 or yp = 1 with equal probability.
A consumer located at (x, y) buys at most one unit of the product and gains utility
U (x, y) = v − p − tx ∙ x − ty ∙ y
from the purchase, where v > 0 is the manufacturer’s quality reputation. 13 The consumer
is willing to pay v if his matches with the product and the store are both perfect. One way
to interpret v is to think of it as the product’s quality. An alternative interpretation of v
is the relative weight that a consumer puts on (a fixed level of) product quality. With this
alternative interpretation, a weak reputation does not necessarily come from a low quality
level. Rather, it could be due to other factors such as the newness of the manufacturer.
Other parameters in the utility function above are p, the price of the product, x (resp. y),
the consumer’s store (product) mismatch which equals the distance between the consumer’s
ideal store (product) location and the actual store (product) location, and tx (resp. ty ), the
weight that is placed by the consumer on the store (product) mismatch.
While other variables in the consumer’s utility function are common knowledge, the
product’s type is not known to the consumers without manufacturer or retailer disclosure.
This assumption reflects our observation that it may be harder for consumers to learn their
match with a particular product (e.g., Adobe Photoshop) than to learn the manufacturer’s
general quality reputation, as information on the latter can often be found online. We
assume that if the manufacturer or retailers choose disclosure (e.g., offer a free trial for Adobe
Photoshop), the disclosed information is truthful and all consumers observe the product’s
type.14 Otherwise, the consumers cannot observe the product’s location and keep their prior
In the event that the manufacturer offers multiple product lines that are vertically differentiated, then
v should be thought of as the quality reputation of the product line that includes the focal product that the
consumer is considering.
14
See Shaffer and Zettelmeyer (2004) and Iyer et al. (2005) for in-depth discussions of targeted advertising.
13
12
belief that the product is located at y = 0 or y = 1 with equal probability. 15
As we model preference heterogeneity on two dimensions (store and product) in a continuous framework, certain modelling assumptions are necessary to keep the game well defined
and tractable. For example, the linear mismatch costs along both dimensions enable us to
analyze all possible demand scenarios. With quadratic mismatch costs, for example, optimal
disclosure can only be characterized for the extreme cases of local monopolies and complete
market coverage.16 Also, by fixing the stores at the two ends of the Hotelling line, we can
sidestep discontinuous demand functions that tend to emerge when firms are located inside
the Hotelling interval (d’Aspremont et al. 1979; Tirole 1988). Finally, by restricting the
product’s location to be either 0 or 1, we can avoid getting into the analysis of multiple
equilibria, an issue we discuss further in Section 5.2.
3.1
Equal Weights on Product and Store Mismatch
To highlight the key forces behind disclosure, we first characterize the manufacturer’s optimal
disclosure strategy in a benchmark model where the consumers have equal weights on their
store and product mismatch: tx = ty = 1.
A nondisclosing manufacturer could use her price to signal the product’s location. However, in an
equilibrium where the two types choose nondisclosure and charge different prices, at least one of them can
profitably deviate to disclosure. Therefore, the two types always charge the same price under nondisclosure.
We assume that this price is profit maximizing. An off-equilibrium-path belief that supports this assumption
is that consumers believe that the product is located at 0 when a different price is charged.
16
If demand falls in between these two cases, the shape of demand for each store becomes the area of a
triangle plus a circular sector, making the derivation of optimal prices intractable. For example, if the utility
of consumer (x, y) is v − p − x2 − y 2 , we can obtain that under disclosure (nondisclosure), the two retailers
remain local monopolies in equilibrium if v ≤ 1 (resp. 14 < v ≤ 54 ), in which case the manufacturer’s profit is
1
π
1 2
2
16 πv (resp. 8 (v − 4 ) ). She prefers to choose disclosure if v < 0.85, which is consistent with our intuition
that lower importance of quality triggers disclosure of product match information. On the other hand, the
retailers will compete head to head and cover the entire market under disclosure (nondisclosure) if v ≥ 94
(resp. v ≥ 74 ), in which case the manufacturer’s profit is v − 94 (resp. v − 74 ). She prefers nondisclosure in this
case, consistent with our upcoming result that high importance of quality leads to nondisclosure of product
match information.
15
13
3.1.1
Selling Directly to Consumers
When the manufacturer owns both stores and sells directly to consumers, the game proceeds
as follows: First, the manufacturer learns the product’s location ( yp = 0 or yp = 1) and
decides whether to disclose it to consumers. She then sets a price p and consumers each decide
whether to buy the product. We solve the game backward by comparing the manufacturer’s
profit levels in the disclosure and nondisclosure subgames. As a tie-breaking rule, we assume
throughout the paper that a channel member chooses disclosure when it is indifferent between
disclosure and nondisclosure.
The Disclosure Subgame. Suppose that the manufacturer discloses the product’s location. Without loss of generality, let y = 0. The utility of consumer (x, y) is then
v − p − x − 12 − y, and the three demand scenarios are shown in Figure 1. Correspondingly,
Figure 1: Demand Scenarios in the Disclosure Subgame: Selling Direct
v-p
v-p
Note: The shaded areas indicate demand for the product. The three panels above demonstrate
that as v − p increases, demand also increases.
the manufacturer’s profit is
14
πD =
where g(v) =
√






4 3
v
27
if 0 < v < 34 ,
1
(v − 14 )2
if 34 ≤ v < 74 ,
4


n

o

 1 [−6 + 4v + g(v)] ∙ 1 − 1 − 1 v + 1 g(v) 2
if v ≥ 74 ,
6
2
3
6
21 − 12v + 4v 2 and D stands for disclosure.
It is intuitive that the manufacturer’s profit increases with her quality reputation. Interestingly, however, the market is never fully covered under disclosure: with full market
coverage, the manufacturer would have to charge an extremely low price so that the marginal
consumer who has the worst match with both the product and the store would still purchase,
and this is never profitable in equilibrium. The result is consistent with our intuition that
disclosure is a niche strategy for the manufacturer to target well-matched consumers.
The Nondisclosure Subgame. When the manufacturer does not disclose the product’s
location, expected product mismatch is the same for all consumers:
1
, ∀y
2
1
(y
2
− 0) + 12 (1 − y) =
∈ [0, 1]. Therefore, nondisclosure of product match information tends to make con-
sumer preferences more homogeneous and the demand more elastic. The utility of consumer
(x, y) now becomes v − p − x − 12 − 12 . As a result, there is no demand if v < 12 . For v ≥ 12 ,
the manufacturer’s demand is 2(v − p − 12 ) as consumers’ purchase decisions depend entirely
on their match with the store, and her profit is 2(v − p − 12 )p. In sum, the manufacturer’s
maximum profit is
πN =



0



if 0 ≤ v < 12 ,
1
(2v − 1)2 if 12 ≤ v < 32 ,
8




 v−1
if v ≥ 32 .
Comparing the manufacturer’s profit in the disclosure and nondisclosure subgames, we
obtain the following result (see all proofs in the Appendix).
15
Lemma 1 The manufacturer chooses disclosure iff her quality reputation is low (v ≤ 1.10).
The intuition is the following: disclosure allows the manufacturer to charge a high price
to well matched consumers, while nondisclosure tends to increase demand. When the manufacturer’s quality reputation is weak, targeting a market niche is critical as the average
willingness to pay is too low. As her reputation strengthens, it becomes attractive to sell
across the board and nondisclosure allows the manufacturer to target the average, rather
than the marginal, consumer. As a result, nondisclosure is the preferred strategy when the
manufacturer’s quality reputation is strong.
3.1.2
Selling through a Monopolistic Retailer
Suppose now the manufacturer distributes her product through a monopolistic retailer who
owns both stores. Similar to the consumers, the retailer has to learn the product’s type
through manufacturer disclosure. As before, the manufacturer first decides whether to disclose her product location and then sets a wholesale price w. Next, the retailer sets a final
price p and consumers each decide whether to buy the product. As before, we compare
the manufacturer’s profit levels in the disclosure and nondisclosure subgames to obtain the
reputation threshold for nondisclosure, and then compare this threshold to that under selling
direct.17
Lemma 2 When selling through a monopolistic retailer, a manufacturer discloses her product location less often (v ≤ 1.06) than when she sells direct (v ≤ 1.10).
Lemma 2 suggests that, as before, there exists a reputation threshold for nondisclosure.
This threshold decreases, however, as the manufacturer starts to sell through a monopoly
retailer, making disclosure less likely to occur in equilibrium. Intuitively, when the manufacturer sells through a retailer, she has to share the total margin with the retailer, which
Expressions of the equilibrium price and profit in each subgame an be found in the proof of Lemma 2
in the Appendix.
17
16
makes the margin-driven disclosure strategy less attractive. On the other hand, nondisclosure makes demand more elastic and effectively limits retail markup. As a result, the
manufacturer chooses nondisclosure more often.
3.1.3
Selling through Duopolistic Retailers
Suppose now the manufacturer distributes her product through two retailers, each owning
one of the two stores. Without loss of generality, suppose retailer A owns the store located
at xs = 0 and retailer B owns the one located at xs = 1. The game remains the same as
before except that the two retailers now choose their final prices simultaneously. To keep
the analysis tractable, we focus on the symmetric equilibrium in which they choose the same
price.18
The Disclosure Subgame. Consider first the optimal retail prices in the disclosure subB
game. Denote the wholesale price by w and the two retailers’ prices by pA
D and pD , the
following lemma can be obtained from the retailers’ optimal-response functions.
Lemma 3 In the disclosure subgame, the retailers’ optimal retail prices are
pA
D
=
pB
D
=









v+2w
3
3
4
+
v+w
2

v+w

−

2




 1+w
1
4
−
1
2
if 0 ≤ v − w < 34 ,
q
(v − w − 12 )2 + 3 if
3
4
≤ v − w < 32 ,
if
3
2
≤ v − w < 52 ,
if v − w ≥ 52 .
The retailers’ margin, demand, and profit all increase with the highest potential margin,
v − w.
The two retailers are local monopolies when the highest potential margin, v − w, is low.
As this margin increases, more consumers are served in equilibrium, and the retailers start to
Interesting channel dynamics may occur when one retailer is more dominant than the other ( Geylani
et al. 2007) or when one retailer operates an online arm while the other does not (Ofek et al. 2011).
18
17
compete with each other. When choosing the optimal wholesale price wD , the manufacturer
maximizes her profit given the retailers’ pricing strategies above.
Lemma 4 In the disclosure subgame, the optimal wholesale price is


v


3






v − 34



1
wD =
−0.5 + 0.8v + 3.4(−13.7+v)(2.2+v)
+ 0.01f (v) 3
1
3

f
(v)





v − 32



q


 2 − 5 + v + 1 (v − 5 )2 + 12
3
2
2
2
if 0 < v < 98 ,
if
9
8
if
19
16
if
5
2
Correspondingly, her profit is
M
πD
19
,
16
≤ v < 52 ,
≤ v < 3,
if v ≥ 3,
where f (v) = 976768 − 480768v − 301056v 2 − 8192v 3 + 85134(5 + v)


16 3

v


243




1

(v − 3 )


 4 4
q
1
1 2
D
=
(v
−
w
wD v−w
−
1
+
−
)
+
3
D
2
2
2




3


(v − 32 )

4




 wD ( v−wD − 1 )( 9 − v−wD )
4 4
2
2
≤v<
p
(3 + v)(6 − 2v + v 2 ).
if 0 < v < 98 ,
if
9
8
if
19
16
if
5
2
≤v<
19
,
16
≤ v < 52 ,
≤ v < 3,
if v ≥ 3.
The profit strictly increases with her quality reputation v.
The top portion of Figure 2 demonstrates that retail competition intensifies and the
total demand increases as the manufacturer’s quality reputation strengthens. As before, the
manufacturer never induces full market coverage when she chooses disclosure.
The Nondisclosure Subgame. We now derive the manufacturer’s equilibrium profit under
nondisclosure. There are only two possible demand scenarios here: either the two retailers
are local monopolies or they split and cover the entire market. Given a wholesale price w,
18
Figure 2: Demand Scenarios in the Disclosure and Nondisclosure Subgames
Note: The shaded areas indicate demand for the product. As v increases, more consumers
purchase the product in both the disclosure and nondisclosure subgames.
the optimal retail price is


1

(v −


 2
B
pA
v−1
N = pN =




 1+w
As demand is always zero if v − w <
1
2
1
2
+ w) if
1
2
≤ v − w < 32 ,
if
3
2
≤ v − w < 2,
if v − w ≥ 2.
(consumers’ willingness to pay cannot cover their
expected mismatch), the optimal retail price is not well defined in this region. Given the
optimal retail price above, the manufacturer decides whether to induce retail competition
by charging a low wholesale price.
Lemma 5 The optimal wholesale price is
wN =


 1 (v − 1 ) if
2
2

 v−
3
2
1
2
≤ v < 52 ,
if v ≥ 52 .
19
The manufacturer’s profit is, correspondingly,
M
=
πN



0



if 0 < v < 12 ,
1
(v − 12 )2 if 12 ≤ v < 52 ,
4




 v−3
if v ≥ 52 .
2
Comparing the manufacturer’s profit under disclosure and nondisclosure, we find that
the reputation threshold is the same as before: v = 1.06. This result may appear surprising
at first, but a closer look reveals that it occurs only because the retailers are not competing
at this quality level: they remain local monopolies in both the disclosure and nondisclosure
subgames at v = 1.06. Essentially, as consumers assign the same weight to store and product
mismatch, the powerful retailers find it optimal to stay local monopolies. To identify the
impact of downstream competition on upstream disclosure, we next allow the relatively
weight of store mismatch to decrease.
3.2
Flexible Weights on Product and Store Mismatch
We now consider the general setup in which tx and ty can be different. To ease interpretation,
we rewrite the consumers’ utility function so that results can be discussed in terms of the
relative importance of quality reputation and store mismatch:
u(x, y) ≡
where v 0 =
p0 =
p
ty
v
ty
U (x, y)
v − p − t x ∙ x − ty ∙ y
=
≡ v 0 − p0 − t ∙ x − y,
ty
ty
is the relative importance of quality reputation vis-à-vis product mismatch,
is the normalized price, and t =
tx
ty
is the relative importance of store mismatch.
Without loss of generality, we normalize the importance of product mismatch ty to 1 so that
v 0 = v, p0 = p and t = tx . When ty is different from 1, the consumer’s utility, as well as
the channel members’ margins and profit, can all be obtained by multiplying the current
20
equilibrium outcomes by ty , and results on prepurchase disclosure would remain the same.
One way to interpret t is to think of it as the “transportation cost” parameter in the
industrial organization literature (Tirole 1988), as a higher transportation cost increases the
relative weight that consumers put on their distance from a store. The lower is t, the less
consumers care about the difference between retailers, and the more intense is downstream
competition. We assume t ∈ (0, 1] so that retailers may find it optimal to compete in
equilibrium. As a first step, we examine how manufacturer disclosure changes with t.
Proposition 1 Suppose the manufacturer sells through two retailers. As store mismatch
becomes more important, the manufacturer is more likely to disclose her product type.
Two effects drive this result. First, consumers’ net willingness to pay for the product,
v−t∙x−y, decreases as t increases. As the willingness to pay becomes lower, the manufacturer
has more incentive to use disclosure to increase her margin. Second, consumer preferences
become more homogeneous as t decreases. In the extreme case of t = 0, for example,
all consumers have the same willingness to pay under nondisclosure and the two retailers
enter Bertrand competition. As demand becomes more elastic, nondisclosure becomes more
effective in expanding demand.
To elicit the impact of downstream retailers on manufacturer disclosure, we solve the
game for the other two channel structures and summarize the comparison below.
Proposition 2 The manufacturer’s reputation threshold for nondisclosure is the lowest when
she sells through a monopolistic retailer. When 0 < t ≤ 0.85, reputation threshold is the highest with duopolistic retailers and when 0.85 < t ≤ 1, the threshold is the highest with selling
direct.
The first part of the proposition suggests that exclusive dealing tends to minimize manufacturer disclosure. Across the three channel structures, double marginalization is the most
21
severe when the manufacturer sells through a monopolistic retailer, and the manufacturer
has the strongest incentive in this case to use nondisclosure to limit retail markup.
For an example on the implication of this result, consider a manufacturer of cat food
who sells her product exclusively on Amazon. If she switches to selling directly on her own
website, our result suggests that she is more likely to disclose product match information
(e.g., cats of what breeds, sizes and ages would enjoy her product the most) as without
Amazon, the manufacturer can now fully reap the margin-enhancing benefit of disclosure.
Compared to selling direct, the manufacturer incurs a loss in both her margin and demand when retailers are present. When the transportation cost is low, retailers compete
heavily in price and the manufacturer barely incurs any loss in her demand. As she lowers
the wholesale price to induce better market coverage, the reduction in her margin becomes
more significant than the reduction in her demand, and disclosure in this case could help
restore her margin. As a result, she chooses disclosure more often than when she sells direct.
When the transportation cost is high, the retailers charge a high markup and the reduction
in the manufacturer’s demand becomes more significant. As nondisclosure helps expand
demand, she chooses it more often than when she sells direct. In reality, the magnitude of
transportation cost depends on many factors. The cost may be lower, for example, when
consumers shop online and do not have to physically travel to the store. Under this interpretation, the magnitude of t would depend on the penetration of eCommerce for the particular
product category.
3.3
Retailer Disclosure of Product Match Information
Compared to the manufacturer, sometimes retailers are in a better position to provide product match information. Bestbuy, for example, labels itself “the ultimate showroom” and
offers in-store demonstrations of many electronic products. Car dealers often learn consumers’ preferences on spot and offer individual consultation regarding their match with a
22
particular car. As mentioned before, retailers could also circulate their own pictures of the
products they carry. For situations like these, we are interested in how retailers’ optimal
disclosure strategy may differ from that of the manufacturer.
We set up the retailers’ disclosure game as follows. First, the two retailers 19 learn the
product’s location and choose whether to disclose it to consumers. The manufacturer then
sets the wholesale price. Next, retailers simultaneously set retail prices and consumers decide
whether to purchase one unit of the product. An important feature of the timeline is that the
disclosure decision is made before pricing decisions. The assumption reflects our observation
that retailers often need to commit to a particular disclosure technology (e.g., virtual try-on,
demo versions, professional shooting of product pictures) before wholesale and retail prices
are chosen. To acknowledge the fact that consumers often engage in comparison shopping
across retailers, we also assume that disclosure from a single retailer is sufficient for all
consumers to learn the product’s location.
We start the analysis with the benchmark case of t = 1 and obtain the following result.
Lemma 6 The retailers chooses nondisclosure when the manufacturer’s quality reputation
is in an intermediate range (1.28 < v < 3.77) and disclosure otherwise.
Based on our analysis in Section 3.1.3, the manufacturer in this case chooses disclosure
if and only if 0 < v < 1.10, which contrasts sharply with the retailers’ bell-shaped disclosure
strategy in Lemma 6. We explain the difference in the channel members’ optimal disclosure
strategies by looking at different ranges of the quality reputation.
First, when quality reputation is weak (0 < v ≤ 1.10), all channel members prioritize
the need to secure positive demand from well-matched consumers. As a result, they all
prefer disclosure. As quality reputation increases (1.10 < v ≤ 1.28), the optimal demand
under nondisclosure begins to exceed that under disclosure (see Figure 3). The retailers’
margin is higher under disclosure, while the manufacturer’s wholesale prices are close in the
19
Analysis with a monopolistic retailer yields the same qualitative conclusions.
23
two subgames. As a result, the retailers prefer disclosure while the manufacturer prefers
nondisclosure.
Figure 3: Retailer Margin, Demand and Profit under Disclosure and Nondisclosure
0.5
0.7
0.6
0.4
0.5
0.3
0.4
0.3
0.2
0.2
0.1
1
2
3
4
0.1
v
5
1
2
3
4
5
v
0.30
0.25
0.20
0.15
0.10
0.05
1
2
3
4
5
v
Note: The dashed curves correspond to market outcomes in the nondisclosure subgame, and the
solid curves correspond to those in the disclosure subgame. The kinks in the curves correspond to
corner solutions: the second and fourth demand scenarios under disclosure in Figure 2, and the
third scenario under nondisclosure.
As quality reputation further increases (1.28 < v < 3.77), the manufacturer and retailers
all prefer nondisclosure, as the increase in demand starts to outweigh the loss in their margins.
Finally, when quality reputation is very strong (v ≥ 3.77), the market is almost completely
covered in both subgames. The retailers could obtain a significant margin under disclosure
while the manufacturer has to cut the wholesale price significantly for retailers to compete
for the ill-matched consumers. Under nondisclosure, on the other hand, the manufacturer
24
can extract most of the consumer surplus as retailers compete heavily in price given the
elastic demand curve. As a result, the retailers in this case again prefer disclosure while the
manufacturer prefers nondisclosure.
The following proposition shows that the retailers’ bell-shaped disclosure strategy carries
over to the more general setting with flexible weights on product and store mismatch.
Proposition 3 When t ∈ [0.043, 1], the retailers choose nondisclosure for an intermediate
range of quality reputation, and disclosure otherwise. When t ∈ (0, 0.043), they always
choose disclosure.
Figure 4 illustrates the proposition above. The intuition for the bell-shaped strategy is
similar as before. When the transportation cost is extremely low, retailers compete fiercely
in price and disclosure helps them restore the margin by making demand more inelastic.
Proposition 3 has important implications for mandatory disclosure policies (e.g., labeling
requirements for textile and food) and voluntary word of mouth among consumers (e.g.,
third-party review and discussion forum sites). As channel members have different disclosure incentives, these disclosure initiatives could affect channel members in different ways.
When the manufacturer’s quality reputation is high, they may benefit retailers and hurt the
manufacturer. When her quality reputation is mediocre, they may hurt all channel members.
When her quality reputation is low, they may benefit all channel members.
4
An Application: Web-Only Brands
To demonstrate the managerial implications of the model, we collect data on 1, 434 clothing
items from 53 web-only fast-fashion brands in India, including the price and number of
pictures posted on each item’s brand site and two leading fast-fashion online retailers in India,
Myntra.com and Jabong.com (Myntra and Jabong henceforth). We choose this application
25
Figure 4: Reputation Thresholds for Retailer Disclosure
v
t
Note: The vertical segment in the top curve corresponds to a corner solution (the fourth scenario
in the top panel of Figure 2) in which the manufacturer makes the same profit in both subgames.
for several reasons. First, our main model suits product categories in which individual match
is important and often learned through prepurchase disclosure. The fast-fashion industry,
besides its own economic significance and fast growth, fits our model well. The value of a
clothing item to a consumer depends critically on the match and consumers often rely on
product pictures to estimate this match. The relatively low price point of clothing items in
our data (INR 1,338 or USD 21) also means that consumers would often choose to keep a
product even if the realized match is less than ideal (Anderson et al. 2009b), as they may
26
need to incur significant costs when returning a product. 20
Second, we focus on web-only brands that do not sell in brick-and-mortar stores so that
pictures are the consumers’ primary source of match-related product information. While the
ideal empirical setup would be one in which we can exogenously vary the channel structure
for a brand and see how it would change the number of pictures accordingly, it is impossible
to conduct this experiment in reality. As a second-best alternative, we compare the numbers
of pictures for the same item across different distribution channels. If the manufacturer
offers, for example, 4 pictures on its own site for the item but 6 pictures on the retailer’s site,
we would take this as evidence that the manufacturer has a stronger incentive to disclose
product match information when she sells through the retailer. The ability to conduct the
comparison within an item helps us control for the impact of unobserved brand or item
characteristics on disclosure.
Finally, Myntra and Jabong are leading Indian e-tailers that specialize in fast fashion.
The two companies compete head to head and are similar in many ways. 21 With an annual
revenue of INR 4.42 billion (USD 69.0 million) in 2014, Myntra partners with over 1,000
leading fashion and lifestyle brands in the country to offer a wide range in latest branded
fashion items.22 Its biggest competitor, Jabong, has an annual revenue of INR 4.38 billion
(USD 68.4 million) in 2014 and carries more than 1,500 brands and over 150,000 styles.
While many product pictures on the two retailers’ websites are offered by the product’s
20
A summer dress in a fast-fashion chain store such as Zara or H&M costs INR 2,135 on average, according
to Numbeo (http://www.numbeo.com/cost-of-living/country_result.jsp?country=India, accessed in
June 2015). While both retailers and many brands in our data offer the option to return a product, most
of the time a consumer has to initiate the return by calling the customer service or submitting a request
online, put together a return information sheet with the order number, repack the product with this sheet,
and either schedule a pick up or ship the item back. See Myntra and Jabong’s return policies at https:
//secure.myntra.com/faqs and http://www.jabong.com/support/faq/, both accessed in June 2015. The
option to return a product is also further discussed in Section 5.1.
21
See an interesting article on the competition between the two dominant e-tailers at http://
forbesindia.com/article/cross-border/myntras-big-leap-forward/34871/1, accessed in June 2015.
22
See http://www.livemint.com/Industry/DCpycaGRonulCI2tAXlxaM/Jabong-sales-jump-but-still\
-lag-Myntra.html, accessed in June 2015.
27
manufacturer, there are also some pictures that are taken by the retailers with their own
models. The setting hence offers us a unique opportunity to look at both the manufacturer’s
and retailers’ choices of pictures.
Our model suggests that brands that sell through an exclusive retailer should be less
likely to choose disclosure than when they sell directly to consumers. 23 Therefore, we expect
such brands to post more pictures, on average, for the same item on their own sites than on
the retailer site. Similarly, we expect brands that sell through both retailers to post fewer
pictures for an item on their own sites than on a retailer site. Finally, when the retailers are
using their own pictures, we expect more pictures to be posted for an item on the retailer
sites than on the item’s own brands site, as our model suggests that the retailers should have
strong disclosure incentives given the intense competition (low t). Although our model does
not formally consider the possibility of the manufacturer selling directly and through retailers
at the same time, the predictions should hold as long as there exist consumers who would
shop only on the brands’ own sites. In the extreme case that consumers always comparison
shop across all the sites, no retail margin is possible even when the manufacturer sells only
through one retailer, which is not what we observe from the data. 24
To collect data, we first compile a list of web-only brands by looking at all brands carried
by Myntra or Jabong, and then select brands that meet two conditions: (1) the brand is sold
exclusively through online channels, which can be verified by statements on the brand’s own
e-commerce site or its official social media outlets; (2) the brand sells directly to consumers
on its own website.
For a brand that is carried by only one of the two retailers, we look for items that are
offered on the brand’s own site as well as the retailer site, and search the Internet to make
The range of quality reputation for disclosure in equilibrium is smaller under exclusive dealing than that
under selling direct. Therefore, for each item, the likelihood of disclosure is higher under selling direct.
24
Jabong, Myntra and many brands in our data offer free shipping for purchased merchandise, so a
consumer’s total cost of buying a product is simply its price on the site.
23
28
sure that the item is not carried by e-tailers other than Myntra and Jabong. For each of
these items, we record its price and number of pictures on both the brand’s site and the
retailer site. For brands that are carried by both retailers, we look for items that are offered
on all three sites (brand’s site and the two retailer sites) and record each item’s price and
number of pictures on each site. As there can be many qualified items for certain brands,
we limit our selection to the 50 random items for each brand. This procedure ensures that
our results are not driven by a few dominant brands that offer a huge selection on their own
sites as well as on the retailer sites.
Following this procedure, we are able to identify 7 brands carried only by Jabong, 8
brands carried only by Myntra and 38 brands carried by both retailers. 25 There are a total
of 1,434 items in our data. For each item, we look across all the sites to identify the source
of its pictures on each site.
Table 1: Summary Statistics of Web-Only Brands
Variable
Obs.
Mean
St. Dev.
Min
Max
# Pictures on Brand Site
# Pictures on Myntra
# Pictures on Jabong
1,434
1,236
1,179
4.17
4.42
4.75
1.54
0.97
1.14
1
1
1
15
6
7
Price on Brand Site
Price on Myntraa
Price on Jabong
1,434
1,236
1,179
1,338
1,261
1,425
1,388
1,139
1,587
172
143
200
12,930
12,930
12,930
The average price on Myntra is lower than that on the brand sites because the items
are not the same. For the 1,236 items that are offered on Myntra, the average price on
the brand sites is 1,244 INR, lower than the average price of the same items on Myntra.
a
Table 1 presents summary statistics of clothing items in our data. As one can see, there
are a total of 1,434 items with an average price of INR 1,338 (USD 21) on their brand sites.
The list of brands is available upon request. One brand that is carried by Myntra (Wear Your Opinion)
has items with manufacture pictures as well as items with Myntra pictures. Four brands that are carried by
both retailers (MEIRO, Monte Carlo, Uptown Galeria, Famella) also have items with manufacturer pictures
on both sites and items with retailer pictures on both sites.
25
29
While the average number of pictures and price is similar across the different selling channels,
there is significant variation in both of these variables across items.
We compare an average item’s number of pictures and price across the different sites in
Table 2. Consistent with our observation of the intense competition between Myntra and
Jabong, the two retailers are charging the same price as the brand site for items carried by
both retailers (p > 0.01 for all price comparisons in 2-retailer scenarios in Table 2). On the
other hand, a retailer often charges a higher price than the brand site for items carried by
one retailer (p < 0.01 for three out of the four price comparisons in 1-retailer scenarios in
Table 1). The only exception occurs for Myntra for items with brand pictures. With only
18 observations, the p-value in this case is 0.04 and the average price on Myntra is higher
than that on the brand sites.
Also consistent with the model predictions, Table 2 shows that when an item is carried by
only one retailer and that retailer uses its brand pictures, there are more pictures available
on the brand site (p < 0.01 for both retailers). On the other hand, when an item is carried by
both retailers and they both use pictures from the brand, there are fewer pictures available
on the brand site (p < 0.01 for both retailers). Finally, when retailers use their own pictures,
the item on average has a higher number of pictures on the retailer site, regardless of whether
the brand is carried by one or both of the retailers (p < 0.01 for all four comparisons).
While the results are highly consistent with our predictions, our analysis is not without
limitations. For example, the list of web-only brands comes from the two dominant retailers
so if a web-only brand does not sell through either retailer, we would have missed it. Also,
brands may differ on factors such as their visibility on social media, advertising, and other
factors that are not captured in our data. Nonetheless, our goal here is to demonstrate the
managerial relevance of our model and show that prepurchase disclosure indeed seems to vary
with the structure of the distribution channel. Through this simple application, we hope to
inspire future empirical work that examines prepurchase disclosure more comprehensively.
30
Table 2: Number of Pictures and Product Price on Brand and Retailer Sites
BPicb RPic
p-valuec BPrice
Scenario
R
#Items
#Brands
RPrice
p-value
BP, 1Ra
M
J
237
82
7
3
4.79
3.85
3.85
3.62
0.000
0.004
1031
3164
1092
3290
0.000
0.001
BP, 2R
M
J
840
840
30
30
4.26
4.26
4.40
4.68
0.000
0.000
1327
1327
1327
1307
0.975
0.044
RP, 1R
M
J
18
116
1
5
4.00
3.47
5.11
5.17
0.000
0.000
996
1058
1144
1328
0.040
0.000
RP, 2R
M
J
141
141
13
13
3.43
3.43
5.44
5.48
0.000
0.000
1135
1135
1165
1120
0.115
0.034
BP (RP): brand (retailer) pictures are used on retailer sites. 1R (2R): brand is carried by 1 (2) retailer(s).
BPic (RPic): number of pictures on brand (retailer) site. BPrice (RPrice): price on brand (retailer) site.
c
All p-values are from paired, two-tailed t-tests.
a
b
5
Discussion of Model Assumptions
5.1
Product Returns and Prepurchase Disclosure
While product returns are not allowed in our main model, it is common for sellers to accept
returns for a period of time after the product is purchased. As pointed out in the literature
(e.g., Anderson et al. 2009a; Shulman et al. 2009), consumers often have to incur different
forms of cost when returning a product: they may have to make a trip to the store, pay
for shipping, schedule and wait for pick-up, and in some cases pay a hefty restocking fee.
If return costs are formidable compared to the value of the product itself (e.g., magazines,
fast-fashion clothing) or the product is not returnable (e.g., vacation packages, spa services,
meals), our analysis remains unchanged and the predictions are the same as before.
When returns are easier, it becomes better for consumers to return an ill-matched product
than keeping it. This may occur, for example, with durable products such as furniture,
mattresses and household electronic appliances. One may wonder, in this case, if prepurchase
31
disclosure would still play a significant role in the consumers’ purchase decisions. In theory,
if the cost to return a product is zero, then a consumer could always learn the type of the
product before committing to a final purchase, and even the nondisclosure decision would
become equivalent to the disclosure decision. In reality, however, returns almost always incur
positive costs to consumers. To highlight the impact of product returns on our results, we
analyze below a situation where return costs are small but positive.
To focus on the match-revealing effect of product returns, we abstract away from sellers’
considerations of the operational costs associated with returns and assume that returned
products can be handled efficiently (e.g., a returned product can be easily resold as a new
product). Incorporating positive operational costs of returns would, intuitively, lower the
channel members’ profits under nondisclosure and make disclosure more attractive. 26
Formally, consider the main model with flexible weights on product and store mismatch
in Section 3.2, and suppose that a consumer incurs cost h ≥ 0 when returning a product,
where h captures the cost of “hassle.” The disclosure subgame would remain the same as in
our main model, while the nondisclosure game changes in the following manner.
Consider a consumer with y ≤
1
2
without loss of generality, as demand is symmetric
around y = 12 . A good match is realized if the product type turns out to be yp = 0 , and a
bad match is realized if yp = 1. A consumer in this case falls in one of three scenarios. First,
he would gain positive utility from the purchase even if the product turns out to be a bad
match: v − p − t ∙ x − (1 − y) > 0. In this case he buys the product and never returns it.
Second, the consumer would gain negative utility from the purchase even if the product is
a good match: v − p − t ∙ x − y < 0. in this case, he does not buy the product. Third, the
consumer gains positive utility if the product is a good match, and negative utility otherwise.
Denote his utility upon a bad match by z ≡ v − p − t ∙ x − (1 − y). If z < −h, he returns
26
We also abstract away from exchanges and restocking fees as these factors are specific to product returns
and outside the scope of the current paper.
32
the product, which is consistent with Anderson et al. (2009b) in that a higher price tends
to trigger more returns. Otherwise, he is “stuck” with a product that he has to keep. A
forward-looking consumer can anticipate these decisions and buys the product if and only
if his expected utility from a trial is positive:
1
(v
2
− p − t ∙ x − y) +
1
2
max{z, −h} ≥ 0.
One can easily verify that when h = 0, nondisclosure becomes equivalent to disclosure as all
consumers can costlessly learn the product type before committing to the purchase.
When h > 0.5, we are back to the main model as none of the consumers would ever
return a product. As h decreases, product returns become a real possibility. Consistent with
the product-returns literature (e.g., Anderson et al. 2009a), the option to return a product
in our setting may either increase or decrease final demand.
Lemma 7 Suppose the manufacturer sells directly to consumers and chooses not to disclose
the product’s type. Allowing product returns increases final demand if the demand without
returns is lower than .5.
Essentially, the option to return a product expands initial demand by putting a cap on the
potential loss for consumers, while the realized returns from mismatched consumers decrease
the final demand. When initial demand without returns is low, the manufacturer’s quality
reputation is low and the dominant effect of returns is to expand demand. On the other
hand, when initial demand is already high, the manufacturer’s quality reputation is high
and many consumers would try the product even without the return option. The dominant
effect of returns in this case is to give ill-matched consumers an option to withdraw from
the purchase. Therefore, allowing product returns would increase final demand if and only
if the initial demand level is low.
It is interesting to explore what happens when returns are almost costless to the consumers, as in this case the match-revealing effect of product returns is the strongest. To
answer this question, we allow the consumer’s cost of return to approach zero, and charac33
terize the manufacturer’s optimal disclosure strategy. 27
Proposition 4 Suppose a consumer can return the product at the cost of h → 0+ . (a)
Nondisclosure increase total channel profit if and only if demand under disclosure is higher
than .5. (b) The manufacturer’s reputation threshold for nondisclosure increases with t
under all three channel structures. (c) The threshold is the highest when the manufacturer
sells through a monopoly retailer and the lowest when she sells directly to consumers.
Proposition 4(a) suggests that, when compared to the full disclosure benchmark, having
consumers learn their match through trying the product can be a double-edged sword for
the seller. On one hand, for consumers who decide to try the product, there is a positive
probability for them to be stuck with an ill-matched product, which may help increase final
demand. On the other hand, the uncertainty of match prior to purchase means that the
price needs to be lowered in order to motivate consumers’ initial purchases. When demand
uner disclosure is high (low), the manufacturer’s quality reputation is high (low), many
(few) consumers would be interested in the product, the demand (price) effect dominates
and nondisclosure leads to greater (smaller) total channel profit than disclosure.
Proposition 4(b) suggests that, an increased relative weight on store mismatch (higher
t) induces manufacturer disclosure. As before, consumers’ net willingness to pay for the
product becomes more heterogeneous when retailers are more differentiated, which makes
the demand-expansion effects of nondisclosure less significant.
Proposition 4(c) shows that the effect of channel structure on prepurchase disclosure
changes significantly when product returns are easy. When returns are easy, using a distribution channel always makes disclosure more attractive to the manufacturer, regardless
of the intensity of downstream competition. The difference between the results here and
It would be nice to solve the generalized model with a fully flexible h. However, the model becomes
intractable in this case as consumers are differentiated along two dimensions and demand is not differentiable
everywhere with respect to price.
27
34
those from the main model stems from the fact that when return costs are negligible, the
elasticity of demand barely changes with the disclosure decision. As a result, the manufacturer’s margin stays almost the same and the main effect of disclosure comes from changes
in her demand. Given Proposition 4(a), demand under disclosure has to reach .5 in order
for nondisclosure to be profitable. Due to double marginalization, it is the easiest for the
manufacturer to reach this demand threshold when she is selling direct.
When consumers’ cost of return h is high, on the other hand, the elasticity of demand
is significantly higher under nondisclosure. As a result, the price under nondisclosure is
significantly lower than that under disclosure, and the disclosure decision has to be made by
considering changes in both demand and margin. As the intensity of downstream competition directly affects both of these factors, the impact of channel structure on manufacturer
disclosure becomes more delicate. Overall, Proposition 4 suggests that predictions from our
main model rely on the costs of return being relatively high, and are more applicable to
product categories such as magazines and fast-fashion clothing, or services.
5.2
A Continuum of Product Types
For tractability of the analysis, our main model assumes that there are two symmetric
product types. As a result, the equilibrium disclosure decision is not a function of the actual
product type. In a more general setting with a continuum of product types, the disclosure
decision may become a function of the actual product type.
Formally, suppose that the product’s type yp is uniformly distributed on [0, 1] and keep
other aspects of the baseline model in Section 3.1 unchanged. A first observation of this
new setting is that there may exist multiple Perfect Bayesian Equilibria. In particular, there
always exists a separating equilibrium in which every type of manufacturer discloses her
type and charges the optimal price under disclosure. In this equilibrium, consumers are able
to infer the product type whenever the manufacturer deviates to nondisclosure, making the
35
deviation profit for this type the same as or even lower than its equilibrium profit. There
may exist other equilibria in which some types of the manufacturer pool together by choosing
nondisclosure. Theoretically speaking, a nondisclosing manufacturer could charge different
prices depending on her actual product type, so that the price could serve as a signal of the
product type. All these nondisclosing types, however, must be earning the same profit, as
otherwise a low-profit type could profitably deviate to charging a high-profit type’s price.
Given the equal profit, we focus on the highest-profit equilibrium in which all nondisclosing
types charge the same price, which maximizes their profit given the consumers’ belief.
Given that the profit under disclosure decreases with the distance between the product
and the central location, |y − 0.5|, and that all nondisclosing types earn the same profit,
there exists an f ∈ [0, 0.5] so that the manufacturer chooses disclosure when yp ∈ (f, 1 − f )
and nondisclosure otherwise. 28 While the generalized model is too complex to be analytically
tractable, we can find f through numerical analysis for the case of selling direct. In particular,
for a given level of quality reputation v > 0, we can find f by plotting two profit curves. The
first curve plots how profit under disclosure changes with location l, and the second curve
plots the profit under nondisclosure when firms in [0, l] ∪ [1 − l, 1] choose nondisclosure and
charge the corresponding optimal price. The intersections of these two curves would then
give us the values of f and 1 − f .
We replicate this procedure for different levels of v and see how f changes with v. As
shown in Figure 5, f increases with v, which means that more types choose nondisclosure as
quality reputation increases. As f approaches .5, the manufacturer almost always chooses
nondisclosure in equilibrium. These results are consistent with our main model in that
prepurchase disclosure reduces with the manufacturer’s quality reputation. 29
A similar result is shown in Sun (2011).
When the manufacturer sells through a distribution channel, even the numerical analysis becomes
intractable, although we expect the intuition behind our main results to remain robust.
28
29
36
Figure 5: Equilibrium Disclosure Strategies with a Continuum of Product Types
f
0.5
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
10
v
Note: As the manufacturer’s quality reputation v increases, f also increases, meaning that the
range of nondisclosing types [0, f ) ∪ (1 − f, 1] enlarges in equilibrium.
6
Conclusion
This paper explores truthful, costless prepurchase disclosure of product match information
in the context of a distribution channel. Our model suggests that optimal disclosure indeed depends on whether the manufacturer distributes her products through retailers and
the intensity of downstream competition. When the manufacturer sells through only one
retailer or two differentiated retailers, she is less likely to choose disclosure when compared
with selling direct. On the other hand, when the manufacturer sells through two competitive retailers, she is more likely to choose disclosure when compared with selling direct.
Interestingly, when retailers are in charge, they often choose disclosure for products with
37
either a very high or very low quality reputation. With intense downstream competition, in
particular, the retailers may choose disclosure for all levels of quality reputation. In general,
our results suggest that retailers may benefit more from an informative marketing campaign
than the manufacturer when the product’s quality reputation is high, or when downstream
competition is intense.
We identify a unique setting, Indian web-only fast-fashion brands, and collect primary
data to find evidence for the model. Through comparing the numbers of pictures across
different channels, we find that a brand would provide fewer pictures to a retailer than it
has on its own site if the item is carried only by that retailer. On the other hand, a brand
would provide more pictures to the retailers than it has on its own site if the item is carried
by both retailers. When retailers use their own pictures for an item, they tend to use more
pictures than what is available on its brand site.
Notably, the possibility of easy product returns could change our results qualitatively.
In particular, the manufacturer in this case may have the strongest disclosure incentives
when selling through a monopolistic retailer and the weakest incentives when selling direct.
Our analysis hence suggests that manufacturers should be mindful of both the prevalence of
product returns and the structure of the distribution channel when crafting their prepurchase
disclosure strategies.
38
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40
Appendix
Proof of Lemma 1.
Consider first the disclosure subgame. Start with the case where
demand is lower than 14 . The demand for the product, under price p, is (v − p)2 . Hence, the
profit is maximized at p∗ = v3 , and the equilibrium profit is
4 3
v .
27
The condition on quality
for the demand to fall into this region is v ≤ 34 . Next, consider the case where demand is
in ( 14 , 34 ], the demand in this case is v − p − 14 . The profit is maximized at p∗ = 12 (v − 14 ),
and the equilibrium profit is
1
(v
4
− 14 )2 . The condition on quality is
3
4
< v ≤
7
.
4
When
demand is in ( 34 , 1], the demand can be written as 1 − ( 32 − v + p)2 . The optimal price is
√
1
(−6 + 4v + 21 − 12v + 4v 2 ), and the optimal profit can be obtained by substituting the
6
optimal price into the demand expression. Whenever v > 74 , the equilibrium falls into this
demand scenario. Under nondisclosure, if the market is not completely covered, the demand
is 2(v − p − 12 ), the optimal price is 14 (2v − 1) and the equilibrium profit is 18 (2v − 1)2 . The
condition on quality for is v ≤ 32 . Otherwise, if v > 32 , the market is completely covered, and
the optimal price and profit are both v − 1. Given the profit levels, the manufacturer finds
it optimal to disclose product information if and only if v ≤ 1.10.
Proof of Lemma 2. Consider the disclosure subgame. Start with the case when demand
is strictly lower than 14 . The retailer’s profit function is (p − w)(v − p)2 and the optimal price
is thus p∗ =
v+2w
.
3
Substituting this optimal price into the manufacturer’s profit function,
which becomes w ∙ (v −
v+2w 2
),
3
her equilibrium profit is
16 3
v .
243
we obtain that the manufacturer would charge w∗ =
v
3
and
The condition on quality for demand to fall into this scenario
can be derived, by substituting in the optimal retail and wholesale prices into the demand,
as v < 98 . Similarly, when
9
8
≤ v < 54 , the optimal retail price is v − 12 , the wholesale price
is v − 34 , and the manufacturer’s profit is 14 (v − 34 ). When
price is
When
v+w
2
13
4
− 18 , the wholesale price is
≤ v <
35
,
8
v
2
5
4
≤v <
13
,
4
the optimal retail
− 18 , and the manufacturer’s profit is 18 (v − 14 )2 .
the optimal retail price is v − 1, the wholesale price is v − 74 , and
41
the manufacturer’s profit is 34 (v − 74 ). Finally, when v ≥ 35
, the optimal retail price is
8
q
−1 + 23 v + w3 + 13 (v − w − 32 )2 + 3 and the wholesale price and the manufacturer’s profit
can be obtained by substituting this price into the demand function. The manufacturer never
induces complete market coverage, by a similar logic as that in the proof of Proposition 1.
Consider now the nondisclosure subgame. When the market is not fully covered, demand
is 2(v −
1
2
− p), and the optimal retail price is 12 (v −
1
2
+ w). Plugging this price into the
demand and writing out the manufacturer’s profit, we obtain that the optimal wholesale
price is
1
(v
2
− 12 ). The equilibrium profit for the manufacturer is hence
1
(v
4
− 12 )2 . The
condition for incomplete market coverage is v < 52 . When v ≥ 52 , the market is fully covered,
the retailer’s equilibrium price and profit is v − 1, and the manufacturer’s profit is v − 32 .
Under complete market coverage in the nondisclosure subgame (v > 52 ), we know that
v − wN =
3
,
2
while in the highest demand scenario in the disclosure subgame (v >
v − wD > 32 . Therefore, when v >
35
,
8
35
),
8
wD < wN . Since both wholesale price and demand are
higher under nondisclosure for the manufacturer, her profit is higher under nondisclosure.
We can numerically compare the profit levels under disclosure and nondisclosure for the
other regions of quality. From this comparison, we can see that the manufacturer prefers to
disclose product information if and only if v ≤ 1.06.
Proof of Lemma 3. Consider first the case where the two retailers are local monopolies.
Suppose that, without loss of generality, the product is located at y = 0. A consumer (x, y)
would buy the product from retailer A (located at x = 0) if v − x − y − pA ≥ 0, which is
equivalent to x+y ≤ v−pA . As the density of consumers is one in the unit square, demand for
retailer A is 12 (v − pA )2 . Therefore, retailer A’s profit is 12 (pA − w)(v − pA )2 , and the optimal
1
1
B
retail price is pA
D = 3 (v + 2w). By symmetry, pD = 3 (v + 2w). The corresponding demand
of each retailer, at this optimal price, is 29 (v − w)2 . The resulting profit is
2
(v
27
− w)3 , which
increases with the total potential margin, v −w. To ensure that the two retailers remain local
monopolies, we need the demand for each retailer to be less than 18 , which implies v − w < 34 .
42
Suppose now that the two retailers start to compete and market demand falls into the
second scenario Figure 6.
Figure 6: Retail Market with Wholesale Price wD
v-w
In this scenario, given the retail price of retailer B, the indifferent consumer who expects
B A
B
A
zero utility from a purchase with either retailer is (x, y) = p −p2 +1 , v − pA − p −p2 +1 .
B
A
B
A
Therefore, retailer A’s demand is p −p4 +1 ∙ 2v − 2pA − p −p2 +1 and his profit is (pA − w) ∙
pB −pA +1
pB −pA +1
A
. Equating the first-order derivative of this profit to zero,
∙
2v
−
2p
−
4
2
ensuring a negative second-order derivative, and then equating pA to pB , we obtain that
q
3
v+w
1
B
=
p
=
+
−
(v − w − 12 )2 + 3. At this price, the
the optimal retail prices are pA
D
D
4
2
2
q
1
1
demand for each retailer is v−w
−
+
(v − w − 12 )2 + 3, and the profit is
4
2
4
3 v−w 1
+
−
4
2
2
r
1
(v − w − )2 + 3
2
!
∙
v−w 1 1
− +
4
2 4
!
1 2
(v − w − ) + 3 .
2
r
The retailer’s margin, demand and profit all increase in v − w. For the demand to fall into
this scenario, we need
3
4
≤ v − w < 32 .
When the competition gets more intense and demand falls into the third scenario in
h
i B
B
A
A
∙ p +1−p
− 12 (v − pA − 1)2 .
Figure 6, given pB , retailer A’s demand is 2(v − pA ) − p +1−p
2
4
Multiplying this demand with the retailer’s margin, setting the first-order derivative to zero,
B
and then equating the two retailers’ prices, we find the optimal prices pA
D = pD =
43
v+w
2
− 14 .
5
2 3
A
The corresponding demand of each retailer is − 12 (v−pA
D ) + 2 (v−pD )− 8 , which increases with
v − pA
D and thus with v − w. For the demand to fall into this region, we need
3
2
≤ v − w < 52 .
Since the retailers’ margin also increases with v − w, their profit also increases with v − w.
Finally, when v − w ≥
5
,
2
all consumers purchase a unit of the product and demand
falls into the last scenario of Figure 6. The retailers charge 1 + w to consumers, and have a
demand of
1
2
each. Their profit is also 12 .
Proof of Lemma 4.
Start with a high level of product quality v. The manufacturer
can induce any of the four possible retail market scenarios discussed above. If she decides
to induce complete market coverage, given the retail prices obtained earlier, the wholesale
price must satisfy v − w ≥ 52 . The highest profit the manufacturer can get in this scenario
is hence w4 = v − 52 .
3
2
If the manufacturer induces second scenario in Figure 6, the wholesale price must satisfy
5
2
A
A
≤ v − w < 52 . The manufacturer’s profit is w ∙ −(v − pA
D ) + 3(v − pD ) − 4 , where pD is
given in Lemma 3. There is always an interior w that maximizes this profit when v ≥ 3, which
q
is w3 = 23 − 52 + v + 12 (v − 52 )2 + 12 . Whenever this interior solution exists, it brings the
manufacturer a higher level of profit than under complete market coverage. Therefore, w4
never occurs in equilibrium when v ≥ 3. When
3
2
≤ v < 3, this interior solution does
not exist; instead, there is a corner solution that corresponds to the boundary between the
second and third scenarios in Figure 6, w23 = v − 32 . The corresponding total demand at this
corner solution is 34 , and the manufacturer’s profit is 34 (v − 32 ). The manufacturer’s profit with
this corner solution is higher than that under w4 whenever both solutions can be sustained.
Therefore, w4 and the corresponding complete market coverage never occur in equilibrium.
If the manufacturer induces the second scenario in Figure 6,
3
4
≤ v − w < 32 . The optimal
wholesale price can be obtained by setting the first-order derivative of the manufacturer’s
profit to zero: w2 = −0.5 + 0.8v +
3.4(−13.7+v)(2.2+v)
f (v)
+ 0.01f (v), where f (v) = (976, 768 −
p
1
480, 768v − 301, 056v 2 − 8, 192v 3 + 85, 134(5 + v) (3 + v) (6 − 2v + v 2 )) 3 . The corresponding
44
manufacturer profit is 2w ∙
v−w
4
− 12 +
1
4
q
(v − w − 12 )2 + 3 . By imposing the requirement
above on v − w, we find that the interior solution can be obtained when
19
16
≤ v < 52 . When
v ≥ 52 , manufacturer profit is the highest if she charges the corner solution w23 and when
4
3
≤v<
19
,
16
the manufacturer’s profit is the highest if she induces the boundary case between
the first and second scenarios in Figure 6. In this case, the wholesale price is w12 = v − 34 ,
the total demand is 14 , and the corresponding manufacturer profit is 14 (v − 34 ).
If the manufacturer induces the first demand scenario in Figure 6, in which the two
retailers are local monopolies, the interior solution is w1 =
market demand is
0 < v < 98 . When
16 2
v ,
81
9
8
and profit is
≤v<
19
,
16
16 3
v .
243
v
.
3
The corresponding total
This solution is feasible when the quality is low,
the manufacturer finds it more profitable to charge the corner
solution w12 .
We next compare manufacturer profit at all the attainable, scenario-wise optimal wholesale prices for different ranges of quality. The two regions of quality in which there is more
than one optimal price are
4
3
≤ v <
9
8
and
3
2
≤ v < 52 . In the first region, both w1 and
w12 are feasible but the manufacturer’s profit is higher at w1 . In the second region, both w2
and w23 are feasible but the manufacturer’s profit is higher at w2 . Unsurprisingly, whenever
an interior solution exists, it is more profitable than a corner solution. Putting all quality
ranges together, we obtain Lemma 2.
Proof of Lemma 5.
Consider first the optimal retailer prices. With local monopolies,
the demand for each retailer is v − pA −
1
2
and a retailer’s profit is (pA − w)(v − pA − 12 ).
1
Maximizing this profit, we obtain that the optimal retail price is pA
N = 2 (v −
1
2
+ w). For
the two retailers to remain local monopolies, we need the equilibrium demand to be positive
and less than 12 , which implies
1
2
≤ v − w < 32 .
When the two retailers compete with each other, retailer A’s profit becomes
(pA − w) ∙
1
∙ (1 + pB − pA ),
2
45
and her optimal response is pA = 12 (1 + pB + w). Given pA = pB , the optimal price in this
B
case is pA
N = pN = 1 + w. For the two retailers to compete and cover the entire market,
consumers located right in the middle of the two retail stores need to expect positive utility
from the purchase: v − pA −
1
2
−
1
2
≥ 0. Putting in the optimal retail price above, this
condition reduces to v − w ≥ 2. When
3
2
≤ v − w < 2, there is no interior solution for either
scenario above and we arrive at corner solution where the middle consumers have exactly
B
zero utility: v − pA − 1 = v − pB − 1 = 0, which implies pA
N = pN = v − 1. Taken together,
we can obtain the optimal retailer prices as presented in the text.
Given the optimal retail price, there is no retail competition if v − w <
manufacturer’s profit in this case is w(v −
1
2
3
2
and the
− w). The interior solution for the optimal
wholesale price is wN = 12 (v − 12 ) and the condition on v − w implies v < 52 . At this optimal
price, manufacturer profit is 14 (v− 12 )2 . With complete market coverage, on the other hand, we
can obtain that the optimal wholesale price is wN = v− 32 and the corresponding manufacturer
profit is v − 32 .
Proof of Proposition 1. Consider the first scenario under disclosure in which the two
retailers are local monopolies. Given wholesale price w, a retailers’ demand is
1
(v
2t
− p)2 ,
his margin is p − w, and his optimal price is 13 (v + 2w). The manufacturer maximizes her
profit and charges wD = v3 . For the retailers to remain local monopolies, the demand for
each retailer must be smaller than 4t , which implies v <
9t
.
8
Following the same steps, we
can obtain the other boundaries in the first panel of Figure 7.
To show that the market is never fully covered under manufacturer disclosure, consider,
for any given level of wholesale price w, the manufacturer’s incentive to deviate by increasing
the wholesale price when the market is indeed fully covered. Note that v − wD =
7+3t
4
in
equilibrium under full market coverage. If the manufacturer increases the wholesale price by
a small number, Δw, the retail market would move into the fifth scenario from the bottom
in the first panel of Figure 7. By looking at the first-order condition on the retailer’s profit in
46
Figure 7: Reputation Threshold and Transportation Cost
v
v
v
t
t
t
Note: The manufacturer sells through two retailers in this figure and the shaded areas indicate
demand. The first panel shows how demand changes in the disclosure subgame for different
ranges of v and t. The second panel shows how demand changes in the nondisclosure subgame.
The third panel shows how the reputation threshold for nondisclosure changes with t.
the fifth scenario, p−w =
t−(v−p−1−0.5t)2
,
1−(v−p−1−0.5t)
we can see that the equilibrium retail margin, p−w,
increases with v−p. Therefore, as demand and v−p decrease (i.e., p increases) from complete
market coverage into the fifth scenario, p − w decreases, implying that 0 < Δp < Δw. The
2
2
change in the manufacturer’s profit, (w + Δw)(1 − Δpt ) − w = −(w + Δw) Δpt + Δw, is hence
positive when both Δp and Δw approach 0.
Now consider the nondisclosure subgame. Without retail competition, the optimal retail
price is 12 (v + w − 12 ), the optimal wholesale price is 12 (v − 12 ), and the constraint for noncompetition is given by v < 2t + 12 . When quality is higher than this threshold, the market
47
is completely covered and the optimal wholesale price is v − t − 12 .
Given the manufacturer’s profit functions under both disclosure and nondisclosure, we can
compare the two profits and derive the condition under which she would choose disclosure.
We do this for all scenarios except the top one in the first panel of Figure 7, and obtain the
nonreputation threshold in the third panel.
For the top scenario, the manufacturer induces complete market coverage under nondisclosure and it is sufficient to show that the equilibrium wholesale price under disclosure
is less than or equal to that under nondisclosure. Recall that the optimal wholesale price
under nondisclosure is v − t − 12 . For t ∈ [0, 1], this price is higher than w∗ = v −
4+6t−t2
4+2t
and it is sufficient to show that w∗ is higher than the optimal wholesale price in the top
scenario under disclosure. In the fourth demand scenario under disclosure, w∗ would be the
optimal wholesale price. By continuity, it is sufficient to show that when demand is in the
top scenario, v − w increases with v in equilibrium.
To see this, note that the optimal wholesale price in the fifth scenario is determined by
the first order condition: D(v − p) − wD 0 (v − p) ∙ p0 (w) = 0. Note also that the optimal retail
q
price is p = −1 − 38 t + 34 v + 14 w + 14 (v − w − 4 − 12 t)2 − 8(1 − t). Suppose v − w remains
unchanged in equilibrium as v increases, then w increases but given the retail price above,
v − p and p0 (w) remain unchanged. As a result, the first-order derivative above becomes
negative, and w has to decrease. Therefore, v − w increases with v.
Proof of Proposition 2. It is straightforward to solve for and compare the disclosure and
nondisclosure profits except for the case when v is high (the top scenario in the first panel of
Figure 7). We provide a proof here that the manufacturer’s profit in the disclosure subgame
is lower than that in the nondisclosure subgame for this top scenario.
When the manufacturer sells directly to consumers, she enters the top scenario when
v > 2 − 4t . In this scenario, her profit is p[1 − t( 12 − v−p−1
)2 ]. Suppose that the manufacturer
t
covers the entire market by charging p = v − 1 − 2t , the first-order derivative of the profit
48
is 1 at this price and she finds it profitable to increase the price. That is, the manufacturer
never induces complete market coverage under disclosure.
If v > 2 − 4t , the manufacturer would cover the entire market under nondisclosure and
charge v −
1
2
− 2t . At this price, the first-order derivative of the disclosure profit is negative
and a disclosing manufacturer would find it profitable to decrease the price. Therefore, the
equilibrium price in the disclosure subgame is smaller than v − 12 − 2t . Since both price and
demand are lower under disclosure, the manufacturer chooses nondisclosure.
When the manufacturer sells through a monopolistic retailer, the proof is similar to that
of Proposition 1.
Proof of Lemma 6.
In the disclosure subgame, a retailer’s profit is the product of his
margin and demand:

3

2v 8v 2

∙ 81 = 16v


9
729




1 1
1

∙ = 32

4 8

 q
R
R
3
x
1
1 2
= MDR ∙DD
=
πD
+
−
)
+
3
∙ − 12 +
(x
−
4
2
2
2




1 3
3


∙ = 16

2 8




 h(v) − 1 ∙ − 1 h(v)2 + 3 h(v) − 5
2
2
2
8
if 0 < v < 98 ,
x
4
+
1
4
q
(x − 12 )2 + 3
if
9
8
if
19
16
if
5
2
≤v<
19
,
16
≤ v < 52 ,
≤ v < 3,
if v ≥ 3,
− 0.01f (v),
where MDR = pD − wD , x = v − wD = v + 0.5 − 0.8v − 3.4(−13.7+v)(2.2+v)
f (v)
13
p
2
3
2
f (v) = 976, 768 − 480, 768v − 301, 056v − 8, 192v + 85, 134(5 + v) (3 + v)(6 − 2v + v ) ,
q
v−wD
1
1
1
and h(v) = 2 + 4 = 6 v − 6 (v − 52 )2 + 12 + 13
.
12
A retailer’s profit, in the nondisclosure subgame, is
R
R
πN
= (pN − wN ) ∙ DN
=


 1 (v − 1 ) ∙ 1 (v − 1 ) =
4
2
4
2


1
2
∙
1
2
=
1
4
1
(v
16
− 12 )2
if
1
2
< v < 52 ,
if v ≥ 52 .
By comparing the two profit curves, we find that the retailers’ profits are higher under
49
disclosure if 0 < v ≤ 1.28 or v ≥ 3.77.
Proof of Proposition 3. When demand is in one of the bottom four scenarios in the first
panel of Figure 7, we can simply plot retailer profits under disclosure and nondisclosure and
obtain the reputation thresholds. When demand is in the top scenario, retailer profit equals
t
4
under nondisclosure. Meanwhile, under disclosure, as quality goes to infinity, retailer profit
monotonically increases and approaches
t
2
in the limit. Therefore, there exists v ∗ so that the
retailers would choose disclosure when v > v ∗ .
Proof of Lemma 7. The demand function with the option to return the product at cost
h, under nondisclosure, can be found in the proof of Proposition 4 below. Comparing this
demand with the nondisclosing, direct-selling manufacturer’s demand function without this
option,
DN =
we can obtain the lemma.



0



2
t




 1
if v − p ≤ 12 ,
(v − p − 12 ) if
1
2
<v−p≤
if v − p >
1+t
,
2
1+t
,
2
Proof of Proposition 4. When returns are allowed and consumers’ cost of returning the
product is h > 0, demand under nondisclosure is
DH =



0




2

(v−p−h)2 −(max{v−p−h− 2t ,0})



t


1
if v − p < h,
2(v−p− 2 )+(max{1−h−(v−p),0})2 −(max{v−p−h− 2t ,0})2
t






1−





 1
(1+ 2t −h−v+p)2 −(max{1−h−(v−p),0})2
t
if h ≤ v − p < 12 ,
if
1
2
≤v−p<
if
1
2
+
t
2
1
2
+ 2t ,
≤ v − p < 1 − h + 2t ,
if v − p ≥ 1 − h + 2t .
This demand function is the same as the one under disclosure when h = 0. To show
Proposition 4(a), realize that by the Envelope theorem, the change in the total channel
50
profit when h increases from zero is equal to the change in the total demand. Given the
demand function above, we can obtain Proposition 4(a).
To show (b) and (c), note that again, by the Envelope theorem, the change in the
manufacturer’s profit is equal to the change in her demand when h increases from zero. As
a result, the reputation threshold for nondisclosure is given by the curve in the v-t plane
along which demand under disclosure is .5. This curve is defined by v = 1 +
manufacturer sells direct, v = 2 +
t
4
t
4
when the
when she sells through a monopoly retailer, and an
increasing curve between these two lines when she sells through two retailers.
51