Journal of International Economics 100 (2016) 112–119
Contents lists available at ScienceDirect
Journal of International Economics
journal homepage: www.elsevier.com/locate/jie
Markets with untraceable goods of unknown quality: Beyond the
small-country case☆
Timothy McQuade a,⁎, Stephen W. Salant b, Jason Winfree c
a
b
c
Department of Finance, Stanford Graduate School of Business, United States
Department of Agricultural and Resource Economics, University of Maryland, Department of Economics, University of Michigan, Resources for the Future, United States
Department of Agricultural Economics and Rural Sociology, University of Idaho, United States
a r t i c l e
i n f o
Article history:
Received 17 December 2013
Received in revised form 16 January 2016
Accepted 24 February 2016
Available online 2 March 2016
JEL classification:
F12
F13
F61
F68
L15
Keywords:
Collective reputation
Experience goods
International trade
Regulation
a b s t r a c t
When importing durables and nondurables, consumers often cannot discern quality prior to purchase. If they
cannot also identify the individual producer, exporters have diminished incentives to produce high quality
goods. To raise the quality of traded experience goods, previous international literature has proposed consolidation of export firms and the imposition of export quotas, policies that may be appropriate for tiny Taiwan but not
a colossus like China. We contribute to this literature in three ways. First, we explicitly model the way in which
consumers of experience goods rely on the reviews of previous buyers (who in turn rely on the reviews of buyers
before them...) when deciding whether to purchase an experience good. Second, we endogenize the price of any
given quality. Third, we assume that firms may exercise market power. As we show, once the “small country”
assumption is dropped, policies advocated in the literature such as the merger of exporters or the imposition
of export quotas can have adverse consequences on the profits of domestic exporters and on the welfare of all
consumers. On the other hand, the unilateral imposition of minimum quality standards will increase the profits
of domestic exporters while improving the welfare of all consumers.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
Philip Nelson (1970) coined the term “experience goods” to distinguish goods (both nondurable and durable) whose quality can be
ascertained only after purchase. To inform their purchase decisions
about such goods, consumers often utilize what Nelson dubbed “guided
sampling”—sampling guided by the reviews of previous purchasers.1
The economics literature has gone beyond Nelson in distinguishing
two types of experience goods: those produced by firms whose identity
is (1) observable and (2) unobservable. Firms producing the first type of
experience goods can build firm-specific reputations for quality which
consumers remember when deciding whether to buy the good; firms
producing the second type cannot build such reputations since their
☆ We would like to thank Jim Adams, Axel Anderson, Heski Bar-Isaac, Tilman Börgers,
Pierre Fleckinger, Will Fogel, Juan Carlos Hallak, Wenting Hu, Natalia Lazzati, Greg Lewis,
Tom Lyon, Jill McCluskey, Marc Melitz, Ariel Pakes, and Nicola Persico for their helpful
comments and insights.
⁎ Corresponding author.
E-mail addresses: [email protected] (T. McQuade), [email protected]
(S.W. Salant), [email protected] (J. Winfree).
1
Nelson discussed nondurable experience goods on p. 320. His section on “guided
sampling” begins on p. 321.
http://dx.doi.org/10.1016/j.jinteco.2016.02.004
0022-1996/© 2016 Elsevier B.V. All rights reserved.
identities remain unknown to consumers. Hence, an apple orchard in
Washington State cannot build a firm-specific reputation for its Red
Delicious apples since consumers cannot distinguish them from the
same variety grown in other Washington orchards. Washington apples
are not only consumed domestically but are exported to Mexico,
Canada, Taiwan, Dubai, Kuwait, Egypt, China, Indonesia, United
Kingdom, India, Colombia, Venezuela, Russia, Malaysia, Thailand,
Vietnam, and throughout Western Europe.2
Both types of experience goods are discussed in the international
trade literature. Falvey (1989) provides an elegant analysis of the case
where a firm can build a reputation for quality. Chiang and Masson
(1988) and Donnenfeld and Mayer (1987) analyze the case where
building a firm-specific reputation is impossible.3 In the latter case,
firms must share their reputation with their competitors and therefore
have diminished incentive to produce goods or services of high quality.
China provides a striking example of what happens when firms
cannot build firm-specific reputations for quality. Over the last decade,
2
See http://www.bestapples.com/international/international_worldmap.aspx.
In the industrial organization literature, Klein and Leffler (1981) and Shapiro (1983)
initiated discussion of the first type of experience good while Akerlof (1970) pioneered
in discussing the second type. More recent discussions of the second type of good include
Winfree and McCluskey (2005) and Fleckinger (2016).
3
T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
Chinese firms have exported toys, dry wall, infant formula, toothpaste,
cold medicines, blood thinners, pet food ingredients, and other products
laced with lead, antifreeze, and other poisons. According to data from
the Consumer Product Safety Commission (CPSC) and US Census
Bureau, products from the toy and furniture industry accounted for
30% of all imports from China. Recalls by the CPSC affected approximately 10% of monthly Chinese toy imports and 20% of monthly furniture
imports. Coglianese et al. (2009) report that China accounts for half of
CPSC recalls.
As for imported food from China, a report by the Congressional
Research Service (Becker, 2009) reports that, with 70% of total world
production, China is the largest aquaculture producer in the world and
accounts for 14.8% of all seafood imports into the United States. According to the USDA (Gale and Buzby, 2009), “Imports from China accounted
for 60% of the U.S. apple juice supply..., more than 50% of the garlic
supply in 2007..., 10% of the U.S. shrimp supply, 2% of the catfish supply,
and 8% of the base (a type of catfish) supply.” China also accounts for a
disproportionately large share of imports refused entry to the United
States by the Food and Drug Administration (FDA). In fiscal year 2007,
for example, China accounted for 5.8% of all agricultural imports, but
8.6% of FDA refusals.
These quality problems result from what the Congressional Research
Service report terms China's “highly decentralized farm production,
composed of 200 million households typically farming on plots of one
to two noncontiguous acres, which has resulted in a fragmented
marketing system dominated by millions of small firms which handle
small volumes...” Indeed, the FDA reports that China has over 400,000
food or feed manufacturers. Only 12,000 to 15,000 are registered and
hence legally eligible to export. Over one-third of U.S. imports from
China are estimated to come from non-registered establishments.
Coglianese et al. (2009) write, “the complexity and high distributed nature of the Chinese supply chain makes tracking products, and especially imports, to their source exceptionally difficult.” Paul Midler in Forbes
Magazine in 2007 put the matter bluntly: “If Adam Smith were around
today, he would have had to write a separate chapter on global
outsourcing... factories pay little, if any, reputational cost for production
shenanigans. The invisible hand doesn't work well when the manufacturers themselves are unseen.”
Since incentives to improve quality are stronger when fewer
competitors share a collective reputation, the previous literature recommended limiting the number of firms—by consolidation in the case of
Chiang and Masson (1988) and through export licenses in the case of
Donnenfeld and Mayer (1987). The latter authors also propose export
quotas on each firm. These policies make sense in their models because
the exercise of market power is ruled out by assumption. Restricting the
number of export firms by consolidation or other means would not be
appropriate for a country like China whose growing export sector
already dominates world goods trade.
In this paper, we depart from Chiang and Masson (1988) and
Donnenfeld and Mayer (1987) in allowing the quantity choice of firms
to affect the market price. This enables us to discuss the consequences
of remedies for the collective reputation problem, including those
proposed in the literature, when producers have the potential to wield
market power. We also depart from the literature on both types of experience goods by describing concretely how collective reputations are
passed from buyers who have experienced the good to those who are
considering purchasing it.
We consider a variety of potential policy remedies to the collective
reputation problem. One remedy is a multilateral labeling program
which allows consumers to more finely partition all firms operating in
the world market for the good. We find that such a program would
raise the quality of every firm's products and would benefit every
consumer. However, such an effort would likely require considerable international coordination.
More realistic policy measures are those undertaken unilaterally by
a single country. We show that the policy recommendations of the
113
previous literature can have adverse consequences once firms can exercise market power. For example, if export firms consolidate, they have
an incentive to raise prices. The resulting price increases will injure
consumers unless they value quality improvements sufficiently. We
also discuss the consequences of one country undertaking a labeling
program for its own firms, as France has done for its wine producers.4
Such a policy would improve the international competitive position of
that country's exporters at the expense of firms in other countries. Consumers of the experience good again benefit even though price rises
along with quality in the country imposing the regulation. Consumers
importing from other countries also benefit since they pay less for
goods of undiminished quality.
The same effects occur if a country unilaterally imposes a minimum
quality standard on the firms operating within its borders. All consumers would benefit as would the producers in the country imposing
the quality standard; the profits of firms in other countries would fall.5
We proceed as follows. Section 2 introduces the model. Section 3
discusses the collective reputation problem under laissez-faire.
Section 4 investigates both unilateral and multilateral remedies to the
collective reputation problem. Section 5 concludes the paper.
2. Model of international trade
Suppose there are N countries. In country j, nj firms produce an experience good to meet demand for the product by M sequential waves of
consumers.6 The quantity a firm produces for each wave is chosen without collecting additional information and hence can be regarded as
being decided at the outset. The firm's production is uniform in quality.
Consumers cannot observe a product's quality prior to purchase or the
firm (or farm) which produced it. They can, however, observe the
country where the good was produced and, if others have previously
purchased that country's good, can consult their reviews to assess the
average quality of that country's product.
Consumers want at most one unit of the good. When examining a
good known to be from country j, each consumer observes its price.
Consumers arrive sequentially in M waves of equal size. In the first
wave, consumers merely have conjectures about the quality of each
country's good. Subsequent waves of consumers, however, study the reviews of those in the previous wave who purchased the good and base
their purchase decisions in part on their reviews.
If there were only a single wave of consumers, no firm would ever
spend a penny at the outset to enhance quality since any firm that did
so could make strictly higher profits by dropping its quality to the
minimum level. No consumer in that first wave could observe this
deviation prior to purchase. We thus assume MN 1.
However, if there are successive waves of consumers, then such conduct by a firm would be counterproductive. Producing goods of less
than anticipated quality would adversely affect the reviews of that
country's products by the first wave of consumers. Such a deviation
would therefore cause the second price to fall, and the reduced average
quality of that country's product would be reported to the third wave of
consumers. Such a deviation would therefore depress the price all subsequent consumers would be willing to pay for the collective good of
country j. Conversely, the marginal benefit of improving quality at firm
4
The United States often labels its exports. It does not merely export “apples” but
“Washington Red Delicious Apples.” This reduces the number of orchards sharing the
same collective reputation and hence motivates improvements in quality.
5
In February, 2009 China adopted a new food safety law providing mandatory food
safety standards and the mechanisms to enforce these standards. USDA has proposed minimum quality standards for fruits and vegetables grown in specific states but, as discussed
in the concluding section, the Department of Justice has blocked such attempts because
such standards would result in higher prices. As we formalize in Theorem 4.3, however,
the harm consumers would experience from the induced higher prices is always smaller
than the benefit they would enjoy from improved quality.
6
As in the previous literature, we assume that the consumers are not located in the N
countries. We therefore use production and exports interchageably.
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T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
i in country j is the higher price which every wave of consumers after
the first would pay. At the optimum, the firm should equate this marginal benefit to the marginal cost of improving the quality.
Formally, the players in the game are the ∑N
j = 1 nj firms and the
consumers in the M waves. Firm i in country j makes all decisions simultaneously at the beginning of the game, setting unchanging quality (kij)
and setting wave-specific output (qm
ij ) for each wave m = 1 , . . . , M. We
assume that each firm, regardless of country, has the same constant
per-unit (and marginal) cost of expanding output. The per-unit cost of
producing goods of the lowest quality is assumed to be zero. The perunit cost increases at an increasing rate if the firm chooses to produce
higher quality products. In particular, c(0) = 0 , c ′ (0) = 0 but
c ′ (kij) N 0 , c ″(kij) N 0 for kij N 0.7
Consumers in the first wave (m = 1) base their purchase decisions
on their conjecture about the quality and their observation of the
price of each country's goods as well as the reservation utility they
would receive if they did not purchase a unit of the experience good.
Denote the conjecture of these consumers about the quality in country
j as R1j . Members of the first wave who consume one unit of country j’s
product report the quality they experienced and agents in the second
wave base anticipate that the mean quality reported by wave 1 consumers will be the average quality they would experience if they consumed one unit produced in country j. The second wave of consumers
then reports the quality experienced to the third group of consumers,
and so on. Note that the expected quality in any wave m = 2 , . . . , M is
therefore:
Rmj
¼
nj
X
qm−1
ij
m−1
i¼1 Q j
kij ; where
Q m−1
j
¼
nj
X
α , θ N 0 common to all consumers. Given the distribution of reservation
utilities, which is the same for each wave, the experience good must
promise a utility of U(Qm) for it to be optimal for the Qm customers
with the lowest reservation utilities to purchase it. Price adjusts in
each country so consumers are indifferent about the country from
which they import the experience good. That is, every purchaser in
m
wave m expects net utility U(Qm) = α + θRm
j − pj from the experience
goods of every country j. Inframarginal buyers strictly prefer the experience good to their outside option while the marginal buyer is indifferent
between the experience good and the outside option since both yield
net utility U(Qm).10
In a Nash equilibrium, the output and quality choices of each firm i
(i = 1 , … , nj) in country j ( j = 1 , … , N) must maximize the following
payoff function given the strategies of the other players and the conjecture of the early consumers:
h
i
m
m
m
qm
qm
ij α þ θR j −U
ij þ Q −ij −c kij :
M
X
We refer to the second factor in the payoff function as “per-unit
profit.” Whenever firm i in country j is inactive (qm
ij = 0), its profit is
zero.11
In equilibrium, the decisions of firm i in country j must satisfy the
following complementary slackness conditions (denoted c.s.) for m =
1 , . . . , M − 1:
qm
ij ≥0;
qm−1
:
ij
ð1Þ
i¼1
Since consumers cannot distinguish firms within country j, each
firm's merchandise must sell for the same price. Consumers differ in
their outside options. Firms in country j face a sequence of additively sepm
m m
m
arable inverse demand curves denoted Pm
j (Q ,Rj )=α+θRj -U(Q ), for
m
m=1, … ,M and j=1 , … ,N. The function U(Q ), discussed in the next
paragraph, is the highest reservation utility in wave m of the Qm consumers with the least attractive outside options. U(Qm) is assumed to
be strictly increasing, weakly convex, and twice differentiable with
U(0) = 0.8 Therefore, the inverse demand curve of consumers in wave
m is strictly decreasing and weakly concave in quantity.9 Firms in country j can strictly increase the price paid by consumers in waves 2 through
M by producing higher quality for consumers in the first wave, but their
quality choice cannot affect the price paid by consumers in the first wave
since the earliest consumers base their purchase decisions on a
conjecture as no consumers have previously purchased the product
from country j.
Like firms, consumers in each wave are players in the game. They
can choose to purchase one unit of the experience good from some
country j or instead get a reservation utility from their best alternative.
Consumers have different reservation utilities. Every consumer of wave
m who purchases one unit of the experience good of anticipated quality
m
m
m
Rm
j at price pj expects payoff α + θRj - pj for exogenous parameters
7
Given the strict convexity of per-unit cost as a function of quality, our restriction that
the firm provides only one quality rather than a distribution of qualities at each point in
time is without loss of generality.
8
Consumers in every wave differ in the value of their outside options. Let f(x) be the
number of consumers with values in the neighborhood of x. Then the total number of
consumers with a value of their outside option of U or less is Q = ∫U
x = 0 f(x)dx. Hence,
dQ/dU = f(U) and d2Q/dU2 = f ' (U). We assume that (1) f(x)N 0 and (2) f'(x)≤0. Therefore,
Q(U) is strictly increasing and hence invertible. Moreover, it passes through the origin and is
weakly concave. Inverting, we conclude that U(Q) is strictly increasing and weakly convex
with U(0)=0 as assumed in the text. The same restriction on f(⋅) is used to justify weakly
concave inverse demand in the standard Cournot model. See footnote 10.
9
Due to concavity, the inverse demand curve will hit the horizontal axis for sufficiently
large Qm. Price should remain at zero for larger values of Qm. That is, technically
m
P^ j ¼ maxð0; P mj ðQ m ; Rmj ÞÞ:
ð2Þ
m¼1
qM
ij ≥0;
n
∂Rmþ1
m o
j
0
þ θqmþ1
α þ θRmj −U Q m −c kij −qm
≤0; c:s:
ij U Q
ij
∂qm
ij
ð3Þ
n
o
M
M
0
α þ θRM
−c kij −qM
≤0; c:s:
j −U Q
ij U Q
kij ≥0; −q1ij c0 ðki jÞ
þ
M
X
m¼2
"
qm
ij
θ
∂Rmj
∂kij
ð4Þ
#
−c kij ≤0; c:s:
0
We can evaluate the partial derivatives
∂Rmj
∂kij
ð5Þ
¼ q1ij =Q 1j and
∂Rmj
∂qm−1
ij
¼
ðkij −Rmj Þ=Q m−1
j
for m = 2 , . . . , M.
The terms in braces in condition (3) are standard. They reflect the
marginal gain from selling another unit over the marginal cost of producing it. The term following the braces, θqmþ1
ij
∂Rmþ1
j
∂qm
ij
, is novel and captures an
additional consequence (beneficial or adverse) of expanding output marginally. If firm i's quality is greater than the reputed quality of goods from
country j, then increasing output will raise the collective reputation of the
good, which will increase its price in the next wave. On the other hand, if
firm i's quality is below average, then increasing output will lower the collective reputation of goods from country j, which will decrease the price.
The meaning of Eq. (5) is straightforward: if the firm produces no
output, any quality is optimal; if the firm is active (qm
ij N 0) and quality
is set optimally, then a marginal increase in quality must raise the perunit revenue from sales of the goods by as much as it raises their perunit cost of production.
We will focus on symmetric Nash equilibria, those in which every
firm within country j makes the same pair of output and quality choices
m
(kij =kj and qm
ij =qj for all i in country j). In any such Nash equilibrium,
the quality conjecture of the first wave of consumers must be correct (as
10
This micro underpinning of the inverse demand curves facing each firm corresponds
to the standard micro underpinning in the Cournot model where consumers buy at most
one unit and get identical utility from consuming the homogeneous product, but differ in
their reservation utilities. The inverse demand curve is then P(Q)=a-U(Q) where aN 0 is
the gross utility the good provides and U(Q) is the highest reservation utility of the consumers with the Q least attractive outside options.
11
Since Rj is undefined when qij =0 and Q-ij =0, the firm's payoff function is undefined
at that one point. By defining the firm's profit at that point to be zero, we restore continuity
since for qij =0, profit is zero for any Q-ij N 0.
T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
must be the quality anticipated by every successive wave), which implies that, in equilibrium, Rm
j = kj for all m. We then have that:
∂Rmj
∂kij
¼
∂Rmj
∂qm−1
ij
1
nj
ð6Þ
¼ 0:
ð7Þ
The following equations must therefore be satisfied in symmetric
equilibrium:
qmj ≥0; α þ θk j −U Q m −c k j −qmj U 0 Q m ≤0; c:s:
ð8Þ
M
X
1
qmj θ −c0 k j ≤0; c:s:
k j ≥0; −q1j c0 k j þ
nj
m¼2
ð9Þ
where:
Qm ¼
N
X
n j qmj :
ð10Þ
115
nonlocal, unilateral deviation.14 However, a unique Nash equilibrium always exists for sufficiently small θ. This follows since when θ = 0 the
model collapses to the Cournot model with weakly concave inverse demand Pj = α − U(Q). Since consumers do not value quality in this extreme case, firms would not incur the expense of providing it and the
per-unit cost of expanding output would be zero. Such a Cournot
model is known to have a unique nontrivial equilibrium. By continuity
it can be established that our model will continue to have a unique
Nash equilibrium provided θ N 0 is sufficiently small.
3. Properties of equilibrium without intervention
We next record a few basic properties of the equilibrium. We first
detail the quality level chosen by firms as the number of waves
approaches infinity.
Lemma 3.1. If M = 1, all firms in a country j set quality level kj = 0.
Quality level increases monotonically with the number of waves and
approaches the solution to c′(kj) = θ/nj as M approaches infinity.
Proof. Since all firms are active in the equilibrium, we know from
Eq. (12) that the quality choice of a firm in country j is given by:
j¼1
Eqs. (8) and (10) imply that qm
j = qj
for j =1 , … ,N for all m. We can
ðM−1Þθ
c0 k j ¼
:
n jM
ð14Þ
thus simplify the above to:
q j ≥0; α þ θk j −U ðQ Þ−c k j −q j U 0 ðQ Þ≤0; c:s:
ð11Þ
θ
≤0; c:s:
k j ≥0; q j −Mc0 k j þ ðM−1Þ
nj
ð12Þ
where:
Q¼
N
X
n jq j:
ð13Þ
j¼1
Eq. (12) implies the marginal cost of increasing quality unilaterally
at one of the nj firms in country j are the additional production costs
which must be paid to satisfy the demand of consumers in every
wave; the marginal benefit from the increase in quality results from
the higher price paid by the M − 1 groups of consumers following the
first wave.
In the appendix we prove that there exists a single solution to
Eqs. (8)–(10) and that in any such solution all firms are active. Since
any symmetric Nash equilibrium must satisfy these equations, there
can be at most one such equilibrium and in it the firms in every country
must be active. Within country j every firm behaves in the same way in
its quality choice and in the unchanging output it provides to each of the
M waves.12,13 Even if every firm is active in the unique fixed point, firms
in some country may be able to strictly improve their profits with a
12
In footnote 9, we noted that the inverse demand curve is weakly concave until the
horizontal axis is hit and zero for larger Qm. Therefore, there exist trivial Nash equilibria
in which every firm sets its quality, and thus its per-unit cost, to zero and Q is
large enough that the price in country j is zero. As long as output is distributed among
the nj (for j =1, …N) firms so that no firm could raise price in any country j above zero
even if it cut its own output to zero, then every firm would earn zero and no firm could
unilaterally deviate to strict advantage. Note that this only works under the assumption
that producing nothing at the minimum quality is costless and is not robust to small perturbations in the cost function. Trivial Nash equilibria of this kind also exist in the Cournot
model with strictly zero costs. We follow the standard convention of ignoring them.
13
We also exclude solutions to Eqs. (8)–(10) that arise because quality, although the
same for any strictly positive output of the firm, is indeterminate when production is exactly zero. We do so by requiring that the firm choose the same quality when qj =0 as it
would when producing strictly positive output. In the absence of such a requirement, a
firm could produce nothing at a quality so high that the cost of producing anything positive would exceed the revenue which could be gained, thereby satisfying the necessary
conditions. We exclude such solutions.
The result for M = 1 follows from qj N 0 and the assumption that
c(k) is strictly convex and c′(0) = 0. The proof is completed by noting
(M − 1)/M is increasing in M and converges to one. ■
In characterizing the nature of this equilibrium, it turns out that the
intensity of competition within a country is of central importance, even
though all firms compete on the world market and there is a single inverse demand curve faced by all firms.
Theorem 3.1. Countries with a larger number of firms produce lowerquality goods. Every firm within such countries produces less and
earns lower profits than in countries with a smaller number of firms.
Proof. Eq. (12), which holds for firms in each country j, implies that a
country with a larger number of firms exporting the experience good
(the “larger country”) will export lower-quality goods. Since prices adjust so that consumers are indifferent about the source of their imports,
the exports of larger countries must sell for lower prices.
In the equilibrium, any firm offering quality k earns profit per unit of
α + θk − U(Q) − c(k). Since this function is strictly concave in quality
and peaks at k⁎, the implicit solution to θ = c′(k⁎), in equilibrium every
firm will choose a quality kj b k⁎. Therefore, the profit per unit at each
firm in a group rises if the common quality of every firm in that group
increases. It follows that firms in larger countries will have lower profit
per unit. But Eq. (11) implies that any firm with a lower profit per unit
produces less output and hence earns lower total profit.15 ■
This result is intuitive. Since the quality reputation of an individual
firm within a country is linked to the quality choices of its competitors
in that same country, there exists a classic free-riding problem in
which an individual firm has diminished incentive to invest in quality
14
Since the solution satisfies the necessary conditions, no local unilateral deviation will
be profitable.
15
In this model, we follow the rest of the literature in assuming that firms producing in
one country cannot disguise their products as originating in another country where firms
have a better reputation and earn higher profits. Presumably this implicitly requires that
the government identify and prohibit such deceptions since they would be profitable.
“Under EU law, use of the word Champagne on wine labels is intended exclusively for
wines produced in the Champagne region of France under the strict regulations of the
region's Appellation of Controlled Origin... Customs agents and border patrols throughout
Europe have seized and destroyed thousands of bottles in the last four years illegally bearing the Champagne name, including product from the United States, Argentina, Russia,
Armenia, Brazil and Ethiopia.” Castillo (2008).
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T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
provision. A greater number of firms within a country exacerbates the
severity of this collective reputation problem because the perceived
marginal benefit of quality investment is inversely proportional to the
number of firms in the domestic industry (a reflection of the intensity
of competition within that country). A lower collective reputation
makes each firm in that country less competitive on the world market
and therefore less profitable. It earns less per unit and produces less
and hence earns lower profit.
4. Potential remedies
We now investigate potential remedies for the collective reputation
problem. These can be divided into remedies that require international
coordination and remedies that a country can pursue unilaterally. Given
that consumers observe only the country of origin of the experience
good but not the identity of the firm which produced it, we investigate
the effects of giving each consumer the information with which to classify more finely the source of the imported good. Consumers may be
better able to classify every firm in the world or merely better able to
identify the firms from a single country. We also consider the qualitative
impacts of a minimum quality standard on exports imposed by one
country on firms within its borders.
4.1. Multilateral remedies
Suppose consumers receive sufficient information to partition more
finely the source of the imported good, regardless of its country of
origin. Specifically, we have the following result:
Theorem 4.1. Let N denote the worldwide partition of firms.16 Suppose
a labeling program permits consumers to classify firms into a strict refinement N0 ⊂ N so that every firm is now assigned to a smaller
group. Then all firms will produce higher quality products. The output
and profit of at least one firm will increase. The utility of every consumer
of the experience good will increase.
Proof. If every firm is a member of a smaller group, world production
per wave must increase. For, suppose it decreased. Then fewer consumers would buy the good, and it must provide lower utility. But
since each firm shares its collective reputation with fewer competitors,
every firm will increase its quality, and hence the reputed quality of its
group will increase. But since profit per unit is increasing in the common
quality of the group, the sum of the first three terms in Eq. (11) must increase. Since U(⋅) is weakly convex, the second factor of the last term decreases, however. That equation would hold, therefore, only if each
firm's output (qj) increased. But then world output would increase, contradicting our hypothesis.
Consequently, world sales of the experience good must strictly increase. To absorb the increased production, the utility each consumer
receives from the experience good must increase by enough to attract
the requisite number of consumers away from their outside options.
Since each firm belongs to a smaller group, each firm will increase its
quality. Since world output increases, the production of at least one
firm must increase. At such firms, since both factors in the last term of
Eq. (11) increase, net profit per unit (the first four terms of that equation) must increase. Therefore profit at these firms will rise. ■
Hence, consumer welfare would be higher if every consumer recognized not only that a product was imported from a particular country
but also that it was made in a particular region of that country (or, better
yet, by a particular ethnic group within that region). For, the smaller the
number of firms in a category recognized by every consumer, the less
incentive each firm will have to shirk in the provision of quality.17
16
In particular, N has N subsets with the jth subset consisting of nj firms.
In the limit of perfect firm traceability, each firm produces the socially optimal quality
due to additive separability of the inverse demand function. Quantity choices remain suboptimal due to the usual oligopoly considerations.
17
Table 4.1
Firm outputs, qualities, and profits.
Region
Quality
Output
Profit
e1
w1
e2
w2
.5000
.2500
.3333
.3333
.8910
.7348
.7938
.7938
.7939
.5399
.6301
.6301
This table shows the quality, output, and profits of firms in the East and West regions of countries 1 and 2 respectively resulting from the multilateral labeling program. We set α=10, θ=
1, U(Q)=Q, and c(k)=0.5k2 and consider the limiting case M→∞. There are ne1 =2, nw1 =4,
ne2 =3, and nw2 =3 firms in the respective regions. Aggregate output is Q=9.4840.
Note, however, that such a scheme may not be profit-increasing for all
firms, as the following example illustrates.
Example 4.1. Suppose that there are N = 2 countries in the world and
there are initially n1 =n2 =6 firms in each country. We set α=10, θ=
1, U(Q) = Q, and c(k) = 0.5k2. We consider the limiting case of M → ∞.
In equilibrium, all firms produce q1 = q2 = . 7810 at quality level k1 =
k2 = . 1667, and earn profits of Π1 = Π2 = . 6099. Aggregate output is
Q=9.3718.
Now suppose that each country is composed of two regions (the
“East” and the “West”) and that each agent can observe prior to
purchasing not merely the country but the region where the good was
produced. There are now N =4 groupings of firms and we assume that
ne1 =2, nw1 =4, ne2 =3, and nw2 =3. Consistent with the predictions of
Theorem 4.1, aggregate output is now higher at Q=9.4840. The output,
quality, and profits of firms in each region of each country are provided
in Table 4.1. We can see that all firms now produce at a higher quality,
but that firms in the West of country 1 are now producing less and earning less profits than previously. Intuitively, the multilateral labeling program benefits firms in East of country 1 and in both regions of country 2
disproportionately. While the collective reputation problem is indeed alleviated for firms in the West of country 1, their competitive positioning
is now worse, leading to lower equilibrium profits.
4.2. Unilateral remedies
Coordination problems and political differences might make multilateral remedies difficult to implement. Instead a government might pursue
unilateral policies designed to alleviate collective reputation problems
within its own country. Chiang and Masson (1988) recommend consolidation of firms, i.e. mergers, as a potential solution. Donnenfeld and
Mayer (1987) recommend limiting the exports of each firm by export
quotas or taxes. Both sets of authors recommend restricting the number
of exporters by requiring that each of them be licensed. The benefits and
costs of such policies are more nuanced, however, when firms exercise
market power and countries of different sizes adopt trade policies only
if they increase export revenue.
Example 4.2. To illustrate, consider a world in which an experience
good is exported by two countries. Suppose that α = 10, U(Q) = Q,
and c(k) = 0.5k2. Assume country 1 has n1 = 10 firms. We once again
consider the limiting case M → ∞. We investigate the effects of consolidating all firms in country 2 to a single firm (or, equivalently, issuing a
single export license).
We examine the impact of this merger if initially country 2 has 5
firms on the one hand or 50 firms on the other hand and when consumers place a small value on quality (θ = 1) or a larger value (θ = 3).
In Table 4.2, the two numbers of countries are listed in the two columns
and the two valuations of quality are listed in the two rows.
For each of the four cells, we enter a pair of signs (+,−, for example).
The first sign indicates the sign of the profit change experienced by the
exporting firms in country 2 as a result of the merger. The second sign
indicates the sign of the change in the welfare of every consumer as a
T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
Table 4.2
Profits and consumer welfare due to unilateral merger.
θ=1
θ=3
n2 = 50
n2 = 5
(+, −)
(+, −)
(−, −)
(+, +)
This table shows the impact of consolidating all firms in country 2 to a single firm on
the total profits of country 2 and consumer welfare, while varying exogenously θ and
the number of firms in country 2. The first entry in each cell shows the sign of the effect of the merger on country 2's total profits. The second entry in each cell shows the
sign of the effect on consumer welfare. We set n1 =10, α=10, U(Q)=Q, and c(k)=
0.5k2 and consider the limiting case M→∞.
result of the merger. World output increases if and only if consumer
welfare increases.18
In the Salant et al. (1983) model of firm consolidation in Cournot oligopoly, the merger of firms is profitable if they had a sufficiently large
market share before the merger but unprofitable if they had a sufficiently
small market share. The collective reputation model collapses to the
model in Salant et al. (1983) if θ=0 and so it is not surprising that for sufficiently low θ the loss from merger result continues to hold. The mergers
are profitable if prior to the merger, the merging entity has a large number
of firms but they are unprofitable if the number of firms is small. Note that
when θ =1, market share is increasing in the number of firms. This explains the first component in each of the top row of cells of Table 4.2.19
The results when θ=3 are more subtle. First, since collective reputation problems are now more severe, country 2 has a pre-merger market
share of only 27.6% when n2 = 50, but a pre-merger market share of
57.8% when n2 = 5. Intuitively, countries with smaller number of firms
are at such a competitive advantage that they are able to capture a greater fraction of the market. Since collective reputation problems are more
severe in this world, the gains from consolidation are larger. Indeed,
we see from the first entries in the bottom row of Table 4.2 that mergers
lead to increased profits in country 2 when either n2 =50 or n2 =5.
In three of the four cells, the merger injures consumers because it
causes prices to rise and those importing goods from the country with
the unilateral policy benefit less from the improvement in quality than
they lose from the increase in price. In the bottom right cell, however,
consumers importing from country 2 benefit because they value the
quality improvement in the exports of the merging firms more than
any resulting price increase. Consumers importing from country 1 also
benefit because they can buy goods of the same quality for a lower price.
Assume that a country will adopt a trade policy if and only if it increases its export revenue. This example suggests that a country like
China would follow the suggestion to consolidate firms in the export
sector even though consumers everywhere would be injured.
Donnenfeld and Mayer (1987) propose export quotas as a potential
remedy, rather than mergers. In our model, any unilateral policy such as
an export quota or tax that causes the exports of the country imposing it
to contract does nothing to solve the collective reputation problem.
Such a policy will therefore leave quality unchanged, while lowering aggregate output and hence consumer welfare.
18
If world output increases, the buyer who was previously marginal becomes
inframarginal. But since the value of his outside option is unchanged, the value of the good
he is importing must be larger. But then the value of the merged firms exports must be
larger for every other consumer. As for consumers importing goods from another country,
they are indifferent about the country of origin of their imports and hence must also be
better off. But for their welfare to have improved despite the quality of their imports being
unchanged, it must be that the prices of these imports have fallen.
19
The loss from merger seems paradoxical because the merged entity can always mimic
the behavior of its components prior to the merger. But even if it did, its profits would decline
because firms not in the merger would expand their output in anticipation that output of the
merged entity would decline. If this expansion is sufficiently large, the contraction in the
merged firms output in the new equilibrium can result in a loss even if the merger causes
the price to rise. As we see in the bottom right cell, a loss from merger can also occur in
the current model if the merging firms output expands; such a loss occurs because the price
of the exports falls.
117
Such a policy recommendation would be adopted by a country only if
it raised firm profits. In the context of the standard Cournot model,
Gaudet and Salant (1991a) show that whether profits increase depends
on the country's share of world exports of that good before the policy is
imposed. If the share is big, the country's profits would go up; if it is
small, the country's profits would go down. This result extends to our
model for sufficiently small θ.20
An alternative policy to consolidation of firms, export quotas, or
taxes is to classify firms within a country's own borders unilaterally.
We have the following result:
Theorem 4.2. A finer classification of firms within a single country
raises the output and profits of its exporters while lowering the output
and profits of unregulated exporters elsewhere. Overall, world output
per wave expands. Quality rises in the country in which the program
originates and remains unchanged elsewhere. Every consumer of the
experience good benefits from the labeling program.
Proof. The imposition of the labeling program by a single country i must
strictly increase per-wave world production of the experience good. For,
suppose the contrary. Suppose aggregate quantity falls or remains constant. Then the utility which consumers get from the experience good
must weakly decrease. In every country j ≠ i, exporters would maintain
quality since Eq. (12) still holds. So if their exports provide weakly less
net utility, the prices of their exports (P j =a+ θkj − U(Q)) must weakly
increase. Since the per unit profit (P j −c(kj)) would then weakly increase,
Eq. (11) implies that output at each such firm must weakly increase.
As for the firms in country i, their per-unit profit must strictly increase. If the country is able to classify its firms more finely for potential
consumers around the globe, then each firm is a member of a smaller
group and therefore produces a higher quality by Eq. (12). Eq. (11)
then implies that per-wave output at each firm in country i strictly increases. But then we have a contradiction: aggregate output cannot
weakly decrease as we hypothesized since that implies the sum of the
individual firm outputs would strictly increase.
So the imposition of a labeling program by a single country i must
cause per-wave world output of the experience good to strictly increase
and hence must cause the net utility of every consumer of the good to
increase. Since the quality of the firms in countries j ≠i does not change,
their prices, profit per unit, output and total profits must fall. Since aggregate output expands despite the contraction at every such firm, output at every firm in country i must increase. But, as Eq. (11) implies,
such firms would expand output only if their profit per unit also increased. Hence, their total profits would also increase. Since profit per
unit increases at each regulated firm, its price per unit must increase
by more than enough to offset the increased cost per unit of producing
the higher quality. ■
Alternatively, a country may opt to impose a minimum quality standard on the experience good its firms export. We will assume that such
a standard (k) is binding but is not set as high as the one a firm would
choose if it were the only domestic producer. That is, we assume kbk ,
where k⁎ solves θ = c′(k⁎). We establish that:
Theorem 4.3. The imposition of a minimum quality standard by a single country raises the price, output, and profits of its exporters while
lowering the price, output and profits of unregulated exporters elsewhere. Overall, world output per wave expands. Quality rises in the
country in which the program originates and remains unchanged elsewhere. Every consumer of the experience good benefits from the unilateral imposition of the minimum quality standard. Consumers of goods
produced in unregulated countries benefit from lower prices for goods
of unchanged quality. Consumers of goods produced in the country
20
Note that since export quotas or taxes leave quality unchanged, the approach used in
Gaudet and Salant (1991a) can be easily extended to our model where firms in different
countries provide goods of differing quality.
118
T. McQuade et al. / Journal of International Economics 100 (2016) 112–119
with the minimum quality standard would pay more than before but,
even so, benefit from the improved quality.
Theorem A.1. There can be at most one symmetric Nash equilibrium.
Proof. Same as proof of Theorem 4.2. ■
Proof. To exclude the possibility of multiple Nash equilibrium where
firms within each country behave the same, we show there exists a
unique symmetric solution to the conditions necessary for a Nash equilibrium. If firms in country j are active (qj N 0) then condition (12) can be
satisfied only by the unique quality choice making the factor in square
brackets zero. If firms in country j are inactive, we assume that the
firm chooses this same quality (see footnote 13). So we substitute k j ¼
c0 −1 ððM−1Þθ
Mn j Þ N0, for j = 1 , … , N in the N Eqs. of Eq. (11) and seek to solve
Eqs. (11) and (12).
Intuitively, the imposition of the minimum quality standard creates
a competitive advantage for the firms within the country implementing
it and thus, ceteris paribus, disadvantages firms located in other countries. The standard reassures buyers about the quality and safety of
products originating from that country. In effect, the minimum quality
standard eliminates the strategic difficulties caused by collective reputation by force of regulation.
5. Conclusion
In this paper, we considered markets where consumers cannot discern a product's quality prior to purchase and can never identify the
specific firm or farm which produced the good. Hence, it is impossible
for any firm to build a firm-specific reputation for quality.
Consumers can, however, identify the country of origin of the good
and can consult the reviews of those who previously imported the
same type of good from the same country albeit possibly from a
different firm. Since it is costly for any firm to improve the quality of
its exports and since every other exporter in that country can free-ride
on the firm's quality improvement, incentives to improve quality are severely attenuated.
Two articles in the international literature have suggested ways to
rectify the underprovision of quality associated with this collective reputation problem. Both articles assume that the price of a good of any given
quality is exogenously fixed. Given this assumption, Chiang and Masson
(1988) conclude that countries should encourage the merger of firms
exporting the good, Donnenfeld and Mayer (1987) conclude that countries
should restrict exports by means of export quotas or taxes, and both sets of
authors advocate restricting the number of exporters by issuing a limited
number of export licenses. As we show, these policies can be harmful in a
world where prices are endogenous and firms can exert market power.
When buyers can classify imports not only by country of origin but
also by regions within countries, firms have greater incentive to improve
the quality and safety of their merchandise. As a result, both profits and
consumer welfare increase. A minimum quality standard can secure further benefits. If one country imposes such regulations, consumers benefit
not only from the enhanced quality of that country's exports but also from
the opportunity to buy other countries' exports which sell for diminished
prices despite their unchanged quality. The minimum quality standard
imposed by one country raises the profits of the firms compelled to
obey them and reduces the profits of competing exporters with the misfortune to be located in countries without such regulations.
Although we have focused here on international trade, our analysis
of the collective reputation problem also has implications for domestic
antitrust policy. The Department of Agriculture (USDA) has long advocated minimum quality standards for fruit and vegetables in recognition
of the collective reputation problem which farmers face. In the past the
Department of Justice (Bingaman and Litan, 1993) has objected to the
minimum quality standards for oranges, grapefruit, tangerines, and tangelos grown in Florida, for tart cherries grown in Michigan and for oranges and grapefruits grown in Texas. The antitrust authority has
objected out of concern that such standards will injure consumers by
raising prices and limiting volume. However, our Theorem 4.3 can be
reinterpreted as showing that, within the context of our model, unilaterally imposed minimum quality standards always benefit consumers.
Appendix A. Characterization of the symmetric Nash equilibrium
As pointed out in the text, there will exist Nash equilibrium in pure
strategies for sufficiently small θ since the model collapses to the standard Cournot model with a symmetric Nash equilibrium when θ = 0.
Replace Q by X in condition (11). The unique solution to this condition can be written as the continuous function qj(X) ≥ 0. This function
has a strictly positive intercept (qj(0) N 0), strictly decreases until it
reaches zero and remains zero for larger X.
Consider next ∑ j¼1;N n j q j ðXÞ. This function of X must also be continuous with a strictly positive intercept. It must also strictly decline until it
reaches zero and then must remain zero for larger X. It follows that
∑ j¼1;N n j q j ðXÞ must cross the 45 degree line exactly once. At the unique
crossing, ∑ j¼1;N n j q j ðXÞ ¼ X N0. Denote this unique fixed point QN 0. By
construction, given our solution of Eq. (12) there is a unique solution to
Eqs. (11) and (13).21 ■
Therefore, the only candidate for a Nash equilibrium is the unique
fixed point in which all firms within a country make the same quality
and quantity choices. We show now that:
Theorem A.2. In the symmetric Nash equilibrium, if it exists, all firms
are active.
Proof. We confine attention here to the unique equilibrium, if it exists,
in which firms within each country are symmetric. To show here that
all firms must be active in this equilibrium, we establish that whenever
firms in some country j are inactive (qj =0), any of them could unilaterally deviate to strict advantage; hence the unique solution of the firstorder conditions does not constitute a Nash equilibrium. Suppose in
the unique fixed point that qj(Q) = 0 and θkj − U(Q) − c(kj) −
qjU′(Q)≤0 in some country j. We can rule out this solution as a symmetric
Nash equilibrium by the following argument. If this condition were to
hold, then since it is strictly decreasing in qj, there can be no positive
quantity choice that can satisfy the condition with equality for that
same k j ¼ c0 −1 ððM−1Þθ
Mn j Þ N0. Hence, a firm's best reply to the other players'
strategy profile would be zero production. But a firm in country j can
strictly improve on that. Since QN 0 there must be some country h with
strictly positive output and hence with θkh −U(Q)−c(kh)=qhU′(Q)N 0.
A firm in country j could choose the same quality kh, marginally increase
its output above zero, and make a strict profit. Hence, the premise that
there can be a symmetric Nash equilibrium with qj(Q) = 0 must be
false. ■
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21
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