J. Int. Trade & Economic Development
Vol. 14, No. 1, 1 – 18, March 2005
Vertical Pricing and Parallel Imports
YONGMIN CHEN & KEITH E. MASKUS
Department of Economics, University of Colorado at Boulder, Boulder, CO 80309, USA
ABSTRACT We generalize an earlier model of international vertical pricing to explain
key features of parallel imports, or unauthorized trade in legitimate goods. When a
manufacturer (or trademark owner) sells its product through an independent agent in
one country, the agent may find it profitable to engage in parallel trade, selling the
product to another country without the authorization of the manufacturer. Although
parallel imports can be deterred when the manufacturer’s wholesale price is sufficiently
high, there is a trade-off between improving vertical pricing efficiency and reducing
parallel imports. In equilibrium, parallel imports can come from a country with higher
retail prices, which is consistent with some factual data. While countries have varying
interests in such a policy, restricting parallel imports tends to increase global welfare
when trade cost is high, but may reduce welfare when trade cost is low. This finding
suggests that open parallel trading regimes may be most appropriate within regional
trade agreements.
KEY WORDS: Parallel imports, vertical price formation, intellectual property rights
1. Introduction
Parallel imports are goods brought into a country without the authorization
of the original trademark or copyright owner, after those goods have been
placed into circulation legitimately in another market. For example, CocaCola syrup provided by a bottler in Belgium may be authorized for sale only
in Belgium. If the Belgian dealer or an independent agent were to ship the
syrup to Spain without the authorization of Coca-Cola Co., the shipment
would be called parallel imports. Although there are no official statistics on
the volume and nature of parallel imports, parallel trade is considered a
significant phenomenon. According to some recent estimates, parallel
imports account for 5 to 20 per cent of trade within the European Union
for such goods as musical recordings, consumer electronics, cosmetics and
perfumes, and soft drinks (NERA, 1999). Another study found that more
than 50 per cent of certain high-volume brand-name pharmaceutical
Correspondence Address: Keith E. Maskus, Department of Economics, UCB 256, University of
Colorado, Boulder CO 80309-0256, USA. E-mail: Keith.Maskus@colorado.edu
ISSN 0963-8199 Print/1469-9559 Online # 2005 Taylor & Francis Group Ltd
DOI: 10.1080/0963819042000333225
2
Y. Chen & K. E. Maskus
products sold in Sweden come from parallel imports (Ganslandt and
Maskus, 2004).
A country’s policy regarding parallel imports stems from its specification
of the territorial exhaustion of intellectual property rights (IPRs). Under the
doctrine of national exhaustion, rights are exhausted upon first sale within a
nation but the ability of IPRs owners to prevent parallel trade between
countries remains intact. Under the doctrine of international exhaustion,
rights are ended upon first sale anywhere and parallel imports are permitted.
An intermediate policy is regional exhaustion, in which rights are exhausted
within a group of countries, thereby permitting parallel trade among them,
but are not exhausted outside the region.
Policies towards parallel imports are controversial on a number of
grounds (Barfield and Groombridge, 1998; Maskus, 2000; Maskus and
Chen, 2002). Many developing countries prefer to maintain openness to
parallel imports in the belief that this policy permits them to source
goods at lowest cost. This issue is central to the negotiations at the
World Trade Organization over achieving access to essential medicines.
However, the position taken by poor countries in this regard is curious
because standard economic analysis of market segmentation would
suggest that a policy of preventing parallel imports would generate low
prices in those nations (Malueg and Schwarz, 1994; Richardson, 2002). In
Australia, a decision was taken in 1998 to deregulate restrictions on
imports of recorded music in view of the high retail prices in evidence at
that time, while New Zealand partially deregulated its import restraints in
copyrighted goods. The United States government is considering
removing its ban on parallel imports of branded pharmaceuticals from
Canada.
In the European Union, the issue of parallel imports has been raised in
many legal cases, and the European Court of Justice (ECJ) has, through
its rulings, essentially adopted the doctrine of regional exhaustion,
permitting parallel imports within member countries but not from outside
the region. Key rulings were Merck v Stephar, C-187/80; Dior v Evora, C337/95; and EMI v CBS, C-51/75. These decisions often stem from a
competition policy interested in preventing market segmentation by patent
and trademark holders (Ganslandt and Maskus, 2004). For example, in
Rhone-Poulenc Rorer (case C-94/98), the ECJ held that manufacturers
cannot partition the single market by introducing a new variety of a
pharmaceutical product, which could have the effect of replacing market
authorization for the prior variety, where the product is subject to
competition from parallel imports.
Despite significant policy interests in parallel imports, there has been
very limited economic analysis on this issue. Malueg and Schwartz (1994)
were the first to conduct a formal analysis of parallel imports. They
present a model in which parallel imports occur due to international thirddegree price discrimination by a manufacturer (or copyright owner).
Vertical Pricing and Parallel Imports
3
Subsequently, Anderson and Ginsburgh (1999) further considered consumer arbitrage costs in parallel imports, in a framework with both thirddegree and second-degree international price discrimination by a monopoly manufacturer. Less formal literature discussed the problems that
emerge when parallel traders free ride on the marketing and service
investments of authorized distributors (Chard and Mellor, 1989; Barfield
and Groombridge, 1998). In essence, the existing explanations view
parallel trade as arising from international price differences and the
resulting price arbitrage by parallel traders.
While the existing studies have provided important insights, they miss two
important features of such trade. First, frequently a parallel trader either is
an authorized wholesaler himself or obtains the good directly from an
authorized wholesaler.1 Thus, it is the wholesale price, not the retail price,
that determines the profitability of parallel trade. From a theoretical
perspective, it is therefore important to depart from the existing theories’
focus on retail prices and to consider the vertical formation of prices.
Second, there are important empirical regularities that are troublesome for
the existing theories. In particular, it has been noticed that parallel imports
sometimes flow from a country where the retail price is higher to a country
where the price is lower (see, for instance, NERA, 1999; Palia and Keown,
1991). This is inconsistent with parallel trade based on price arbitrage and
calls for the development of a theory based on vertical pricing between a
rights holder and her authorized wholesalers.
Maskus and Chen (2004) addressed these two issues in the study of
parallel imports by incorporating the formation of prices in a vertical
relationship. However, the analysis there was based on the restrictive
assumption of linear demand and relied on a number of special cases. It was
not clear whether similar results exist under general demand conditions.
This is an important question to ask because specific demand assumptions
may not support general conclusions in this literature. Consider, for
example, the central role that demand specification plays in determining
whether third-degree price discrimination generates a welfare-increasing rise
in output (Varian, 1985). The present paper fills this gap by analysing a
model of parallel imports with general demand functions. We generalize the
theoretical results obtained by Maskus and Chen (2004) and provide formal
proofs.
We find that when a manufacturer sells its product through an
independent agent (distributor) in a certain country, its incentive is to
set its wholesale price below what it would be if the manufacturer could
directly set the retail price, in order to reduce the double-markup
distortion. This decision may enable the agent to sell the product
profitably in another country, without the authorization of the manufacturer, even when the retail price in the other country is lower. In a
simple two-country model, we explore the manufacturer’s trade-off
between improving vertical pricing efficiency and preventing parallel
4
Y. Chen & K. E. Maskus
importing,2 and show that parallel imports can flow from a high-price
country to a low-price country. Both industry profits and combined social
surplus in two countries can increase in the cost of conducting parallel
trade. Government restrictions on parallel imports always benefit the
manufacturer, but can either raise or reduce global welfare. Thus, whether
policy should restrict or encourage parallel trade depends on market
circumstances and the degree of trade costs.
Our paper may also be considered an extension into a different market
setting of Brander and Krugman (1983), who developed the seminal theory
of reciprocal dumping. They showed that trade can occur between two
countries with identical demands, by two firms with identical costs. This is
because the two markets are segmented and each firm chooses its outputs in
the two countries separately. Our model has a similar intuition, but in our
case the production cost for the distributor is endogenous, depending on the
wholesale price of the manufacturer. This introduces additional interesting
trade-offs that are the focus of our analysis.3
We set up the model in Section 2, analyse its equilibrium in Section 3, and
consider the effects of restricting parallel imports in Section 4. We conclude
in Section 5.
2. The Model
A manufacturer, M, sells its product in two countries, A and B. In country
A, M sells directly to the consumers, or sells through a wholly-owned
subsidiary whose output is set by M. In country B, M sells its product
through an independent exclusive distributor, L. The inverse demand in A
is p = pA(q), and that in B is p = pB(q), both of which are continuously
differentiable functions. Manufacturer M has a constant marginal cost of
production c 5 0. The retailing cost in both countries is normalized to
zero.4
Suppose that M can offer L any contract in the form of (w,T), where w is
the wholesale price at which L purchases from M and T is a transfer
payment (franchise fee) from L to M.5 However, M cannot prevent L from
selling the product back to A, either directly or through intermediaries. That
is, either M cannot legally limit L’s territory of sales, or it is too costly for M
to enforce any such constraint.6
Suppose that L incurs an additional constant marginal cost t 5 0 in
selling the good back to A. For instance, t could be the additional
transportation cost or transaction cost. Assume that if L sells in Country A,
it will compete with M in a Cournot fashion in that market.
Let the quantities sold in A by M and L be qAM and qAL, respectively, and
the quantity sold in B by L be qB. The timing of the game is as follows: M first
offers contract (w,T) to L, which is either accepted or rejected. If the contract
is rejected, no product is sold in B and M chooses its output in A. Otherwise,
L chooses its outputs in both A and B, and simultaneously M chooses its
Vertical Pricing and Parallel Imports
5
output in A. A subgame-perfect Nash equilibrium is, for any (w,T) accepted
by L, a pair (qAM, qAL) that constitutes a Nash equilibrium in A, together
with an optimal choice of qB by L; and a contract (w,T) that is chosen
optimally by M. As usual, we solve the model by backward induction.
For preliminaries, we first consider equilibrium in Country A, taking as
given any (w,T) that is accepted by L. The profits of M and L through sales
in A are:
pAM ¼ qAM ½pA ðqAM þ qAL Þ c þ ðw cÞqAL
ð1Þ
ð2Þ
pAL ¼ qAL ½pA ðqAM þ qAL Þ w t
For any given t and any (w,T) accepted by L, a Nash equilibrium in A,
denoted as (qAM(w + t), qAL (w + t)), where qAi 5 0, solves the following
first-order conditions:7
0
pA ðqAM þ qAL Þ c þ qAM pA ðqAM þ qAL Þ 0
0
pA ðqAM þ qAL Þ ðw þ tÞ þ qAL pA ðqAM þ qAL Þ 0
ð3Þ
ð4Þ
where equation (3) holds as an equality if qAM (w + t) 4 0 and equation
(4) holds as an equality if qAL (w + t) 4 0.
The equilibrium price in A will be pA (qAM (w + t) + qL (w + t)). For
any given w and t, we shall denote the equilibrium PAM and PAL as
PAM(wjt) and PAL(wjt), where we emphasize that w is a choice variable and
t is a given parameter.
We next consider equilibrium in Country B, again taking as given any
(w,T) that is accepted by L. Distributor L chooses qB to maximize (pB(qB)w)qB. Denote the equilibrium (optimal) choice by qB(w),and let
PB(w) = (pB(qB(w)) – w)qB(w). The equilibrium price in B is pB (qB (w)).
Since firm L’s profit in B, excluding T, is PB(w),the equilibrium choice of T
by M must satisfy
T ¼ TðwjtÞ PAL ðwjtÞ þ PB ðwÞ
Any contract (w,T(w)) is accepted by L in equilibrium. The equilibrium
choice of w therefore maximizes the joint industry profits in two countries,
P(wj(t), where
PðwjtÞ ¼ PAM ðwjtÞ þ PAL ðwjtÞ þ PB ðwÞ þ ðw cÞqB ðw þ tÞ
That is,
PðwjtÞ ¼ PA ðwjtÞ þ PB ðwÞ;
ð5Þ
where
PA ðwjtÞ ½qAM ðÞ þ qAL ðÞ½ðpA ðqAM ðÞ þ qAL ðÞÞ c tqAL ðÞ
ð6Þ
6
Y. Chen & K. E. Maskus
To allow for general results, we do not restrict the demand functions in
either country to a particular form. We instead make the following
assumptions.
Assumption A1
For i = A,B, q[pi(q)-c] is a concave function of q, qi0 = argmaxq 5 0
{q[pi(q) 7 c]} exists uniquely for any given c, and qB(pA0) 4 0, where
pA0 = pA(qA0).
Assumption A2
For any qAM 4 0 and qAL 4 0,
@ 2 pAi
@qAi @qAj
2
2 < 0 and @q@Aip@qAiAj < @@qp2Ai .
Ai
Assumption A3
For any given t 5 pA0 7 c, P(wjt) is continuous and concave in w for w2[c,
pA0 7 t] and is continuously differentiable for w2[c, pA0 7 t).
Notice that qA0 (or pA0) is the profit-maximizing output (or price) for a
monopolist in A. Assumption A1 ensures that profit in country i is
maximized only with output qi0 for i = A,B, and quantity demanded in B is
positive at price pA0. Assumption A2 implies that qAi and qAj are strategic
substitutes and that there is a unique and stable equilibrium in market A.
Assumption A3 imposes additional technical restrictions on P(wjt) that
facilitate our analysis. The concavity of P, in particular, ensures that the
optimal choice of w is unique, but is not essential for the basic insights of the
analysis. Assumptions A1 – A3 can be satisfied by a variety of demand
functions and parameter values. Consider, for instance, the linear-demand
structure used by Maskus and Chen (2004).
Example
pA ¼ a q; pB ¼ 1 q; a 2 ð3=4; 2; c ¼ 0; t 0: Then; p0A ¼ a=2 and
for w 2 ½0; ða=2Þ t;
pA ðwjtÞ ¼
PðwjtÞ ¼
ða þ w þ tÞ2 wða 2w 2tÞ ða 2w 2tÞ2
þ
þ
3
9
9
ða þ w þ tÞ2 wða 2w 2tÞ ða 2w 2tÞ2 ð1 w2 Þ
þ
þ
þ
3
4
9
9
All assumptions A1 – A3 are satisfied for this example.8 We shall use this
example to illustrate our results throughout the paper but certain other
classes of demand functions would satisfy them as well.
Vertical Pricing and Parallel Imports
7
3. Analysis
Lemma 1
p0A t. For any given t 2 [0, pA0 7 c), there exists a unique
Define wðtÞ
> c such that qAL ðwÞ > 0 if w < wðtÞ
and qAL ðwÞ ¼ 0 if w wðtÞ.
wðtÞ
Furthermore, when w < wðtÞ,
qAM (.) increases in w and in t, qAL (.)
decreases in w and in t, and [qAM (.) + qAL(.)] decreases in w and in t; and
when w wðtÞ,
qAM(.) = qA0.
Proof
For the proof see the appendix.
Note that when t 5 pA07 c, qAL(c) = 0. This is the case where t is so high
that parallel imports do not occur even if w = c. We shall say in this case
that parallel trade is blocked. Lemma 1 tells us that if t 5 pA0 7 c, parallel
p0A t. We shall
imports will occur, or be accommodated, when w < wðtÞ
say that parallel trade is deterred if w 4 c and qAL (w) = 0.
Proposition 1
For any given t, the model has a unique subgame perfect Nash equilibrium.
If t 5 pA0 7 c, the equilibrium value of w is w*(t) = c; and if t 5 pA0 7 c,
the equilibrium value of w is
~ 2 ðc; wðtÞÞif
w ðtÞ ¼ w
~
@PðwjtÞ
¼0
@w
w ðtÞ ¼ wðtÞ ¼ p0A t otherwise
ð7Þ
Proof
For the proof see the appendix.
We note that as long as t 5 pA0 7 c, or parallel trade is not blocked, the
wholesale price is not set at the true marginal cost since w*(t) 4 c. This
suggests that either active or deterred parallel trading always causes vertical
price inefficiency.
Proposition 2
There exists some t1 > 0 such that w*(t) 5 wðtÞ
(parallel imports are
accommodated) when t < t1 ; and there exists some t2 2 ½t; p0A cÞ such
that w*(t) = wðtÞ
(parallel
are deterred) when t2 < t < p0A c.
dwðtÞimports
Furthermore, t1 ¼ t2 if
1.
dt
8
Y. Chen & K. E. Maskus
Proof
For the proof see the appendix.
Intuitively, when t is small, parallel imports can be deterred only when w
is much higher than c. Starting from the w that is just high enough to cause
qAL(w + t) = 0, a small decrease in w has small negative effects on the profit
in A and on the value of trade costs incurred,9 but has a large positive effect
on the profit in B. Thus, w*(t) 5 wðtÞ
and parallel imports occur (or are
accommodated) when t is small. When t is large but is still below pA0 7 c, on
the other hand, parallel imports may be deterred with a w that is only
slightly higher than c. Starting from w ¼ c < wðtÞ
and qAL (w + t) 4 0, a
small increase in w has a small negative effect on the profit in B, but has big
positive effects on the profit in A and on lowering trade cost. Thus w*(t) =
and parallel imports will be deterred.
wðtÞ
The optimal change in w caused by a change in t is likely to be a smaller
4 1 and
amount than the change in t itself. Therefore, it is likely that dwðtÞ
dt
3
¼ a2 t, and
a; wðtÞ
thus t1 ¼ t2 . For our linear demand example, t1 ¼ t2 ¼ 14
w ðtÞ ¼
2a þ 8t
13
a
w ðtÞ ¼ t
2
w ðtÞ ¼ 0
if t if
3
a
14
3
a
a<t
14
2
if t a
2
Since qAL(w*(t) + t) 4 0 when w*(t) 5 wðtÞ,
qAL(w*(t)+t) = 0 when
¼ c when t 5 pA0 – c, we
w*(t) = wðtÞ,
t2 < p0A c, and w*(t) = wðtÞ
immediately have the following results concerning equilibrium parallel
imports:
Corollary 1
In equilibrium, there is parallel importing from country B to country A if
t < t1 , parallel trade is deterred if t2 < t < p0A c, and parallel trade is
blocked if t 5 pA0 – c.
When parallel trade occurs, c 5 w*(t) 5 wðtÞ,
qAM (w*(t) + t) + qAL
(w*(t) + t) 4 qA0, and qB (w*(t)) 5 qB0. Thus, if pA (qA0) 4 pB (qB0), which
would be true if demand in A is not higher than in B, we must have
pA ½qAM ðw ðtÞ þ tÞ þ qAL ðw ðtÞ þ tÞ < pB ½qB ðw ðtÞÞ
This condition states that parallel imports originate from the country with
the higher price. Notice that this condition can also hold even if pA (qA0)
4 pB (qB0). We thus have Corollary 2.
Vertical Pricing and Parallel Imports
9
Corollary 2
A sufficient (but not necessary) condition for parallel imports to occur and
to be originated from a country with higher prices is t < t1 and pA (qA0)
4 pB (qB0).
Thus, parallel imports can flow from a country with a higher retail price
to a country with a lower retail price, showing that one of the central points
of Maskus and Chen (2004) survives under general demand conditions.
Indeed, this can happen for countries with similar demands or for countries
with different demands. To see the intuition behind the result more
strikingly, consider a special case of our model where the two countries are
identical. In this case, the usual motive for parallel imports due to monopoly
international price discrimination would not arise. Suppose for a moment
that parallel imports are not legally allowed. Then, the manufacturer, M,
would offer L a two-part tariff contract (w,T) = (c, PB(c)), which would
enable M to receive the same profits from countries A and B and lead to
identical prices in both countries. Now make parallel imports legal.
Consumers would have no incentive to arbitrage between the two countries
since the retail prices are identical. But distributor L may have an incentive
to sell the good back to A, since its marginal cost of acquiring the product
for parallel imports is the wholesale price w, not the retail market price. Of
course, M will anticipate this and raise the wholesale price above c to
decrease L’s incentive for parallel imports. But the increase in w distorts L’s
pricing incentive in market B (causing double marginalization), and hence
M may choose not to raise w to a level that would deter parallel imports. In
equilibrium, the manufacturer balances the needs to improve vertical pricing
efficiency and to limit parallel imports.
It is therefore clear that the reason for parallel imports to occur in this
model is the presence of a vertical relationship and the need to avoid vertical
pricing inefficiency.10 We note that this analytical result does not necessarily
depend on the availability of two-part tariff contracts. Even if M can only
charge w and cannot charge T, parallel imports can still occur and originate
from a country with the higher (retail) price. The availability of two-part
tariff contracts highlights the effects of parallel imports on vertical pricing
efficiency.
Inserting w*(t) into equation (5), we obtain the equilibrium profits for M
as
P ðtÞ ¼ ½qAM ðw ðtÞ þ tÞ þ qAL ðw ðtÞ þ tÞ½pA ðqAM ðw ðtÞ þ tÞþ
qAL ðw ðtÞ þ tÞÞ c
tqAL ðw ðtÞ þ tÞ þ ½pB ðqB ðw ðtÞÞÞ cqB ðw ðtÞÞ
Parallel imports reduce the profits of the manufacturer (or the joint industry
profits in two countries), not only because they create competition in the
10
Y. Chen & K. E. Maskus
country receiving such trade and because they incur additional transaction
(transportation) costs, but also because they prevent the manufacturer from
achieving efficient vertical pricing (setting the wholesale price equal to
marginal cost). An interesting issue is how P* may change as trade cost t
changes. An increase in t increases the trade cost for a given amount of
parallel imports, but it can also cause reductions in both w*(t) and the
amount of parallel imports, with generally ambiguous effects on P*. But if
t2 < t < p0A c, or if parallel trade is deterred in equilibrium, then a
marginal increase in t clearly increases P*. This is because in this case an
increase in t will affect P* only through a reduction in w*(t) =
¼ p0A t, which in turn results in an increase in [pB (qB (w*(t))) – c]
wðtÞ
qB(w*(t)).
We next turn to the joint social surpluses in two countries, which we call
global welfare. The global welfare in equilibrium is
qAM ðwðtÞþtÞþq
Z AL ðwðtÞþtÞ
S ðtÞ ¼
½pA ðqÞ cdq tqAL ðw ðtÞ þ tÞþ
qBZ
ðwðtÞÞ
0
½pB ðqÞ cdq
ð8Þ
0
Similar to the effect on profit, the effect of a change in t on global welfare
tends to be ambiguous in general. However, if t2 < t < p0A c, a marginal
rise in t surely raises S* because, in this case, an increase in t will affect
combined surplus only through a reduction in w*(t) = pA0 – t, which in turn
affects S* only through an increase in the third term,
qBZ
ðwðtÞÞ
½pB ðqÞ cdq
0
When t < t2 it is less clear how P(t) and S*(t) will change as t changes.
For our linear demand example, P*(t) decreases in t when t < a9 but
3
a ¼ t1 ¼ t2
increases in t when a9 < t a2; and S*(t) decreases in t when t < 14
3
a
but increases in t when 14 a < t < 2. Thus, at least in this example, both
global profits and global welfare are U-shaped functions of t, but P*(t)
assumes its minimum at a lower level of t than does S*(t).
4. The Effects of Restricting Parallel Imports
An interesting policy question to analyse is how a ban on parallel imports
would affect pricing and welfare. It should be evident that such a restriction
would support efficient vertical pricing, offering scope for welfare increases.
However, the perfect market segmentation would also prevent competition
11
Vertical Pricing and Parallel Imports
in the manufacturer’s market, raising the possibility of welfare reductions
there.
Thus, suppose L is prevented from selling the product back to A, either
because there exists an effective vertical restraint imposed by M or because
parallel imports are not legally allowed by governments. Permitting again a
contract (w,T), and denoting equilibrium (optimal) variables by adding
superscript v, it is optimal for M to set:
wv ¼ c; and Tv ¼ P0B ¼ qB ðcÞ½pB ðqB ðcÞÞ c
Prices in A and B will then be
pvA ¼ p0A ; pvB ¼ p0B
ð9Þ
When t 5 pA0 7 c, or parallel imports are not blocked, we have w* 4 c
pB ¼ pB ðqB ðw ÞÞ > p0B ; and pA ¼ pA ðqAM ðw Þ þ qAL ðw ÞÞ p0A
with strict inequality if parallel imports occur in equilibrium. We thus have
Proposition 3.
Proposition 3
Assume that t 5 pA0 - c. Then restricting parallel imports reduces prices in
the country where parallel imports originate and may or may not raise prices
in the country receiving parallel imports. Thus, restricting parallel imports
benefits consumers in the country where parallel imports originate but may
or may not hurt consumers in the country receiving parallel imports.
However, restricting parallel imports always benefits the manufacturer.
Turning to global welfare, restricting parallel imports increases welfare of
the country where parallel imports originate, but has ambiguous effects on
the country receiving parallel imports. When t 2 ðt2 ; p0A cÞ, parallel
imports will be deterred through some w*(t) 4 c in equilibrium. In this case,
government restrictions on parallel imports replace the inefficient verticalprice deterrence and thus eliminate the price distortion in B without causing
other losses. When t < t2 , on the other hand, restricting parallel imports
eliminates the inefficiency in vertical pricing for B and avoids the wasteful
additional transaction costs due to parallel imports, but results in higher
prices in A. The policy thus has ambiguous effects on global welfare. For our
linear demand example, we find that the change in global welfare due to
restricting parallel imports is
DS ¼
að5a 4Þ tð12a 23t þ 4Þ
3
þ
if t a
104
26
14
12
Y. Chen & K. E. Maskus
DS ¼
ða 2t þ 4Þða 2tÞ
3
a
if
a<t
32
14
2
3
It is clear here that DS 4 0 when 14
a < t a2 and DS 5 0 if t is sufficiently
small. We thus have Proposition 4.
Proposition 4
Restricting parallel trade may either increase or reduce global welfare. When
t 2 ðt2 ; p0A cÞ, restricting parallel imports increases global welfare but when
t is sufficiently small, restricting parallel imports can reduce global welfare.
We also note that if t 5 pA0 7 c, restricting parallel imports has no
welfare effects.
The result that restricting parallel trade has ambiguous welfare effects
bears resemblance to the finding in the literature that such restriction
facilitates international price discrimination (Malueg and Schwartz, 1994;
Anderson and Ginsburgh, 1999). However, the ambiguity in our model
comes from a different source, which is the elimination of the vertical pricing
inefficiency in one market, combined with reduced competition in the other
market. In general, the welfare effects of restricting parallel import are
ambiguous in this framework, depending on the values of t. Moreover, it is
easy to show in the linear-demand case that this ambiguity does not
disappear when the two countries face identical demands (and hence
restricting parallel imports would have no effect on global welfare if the
motive for parallel imports were international price discrimination).
In Brander and Krugman (1983), restricting reciprocal dumping avoids
resource waste in cross-hauling but results in higher prices in both countries.
Restricting parallel trade in our model also avoids resource waste in crosshauling but results in higher prices in the country receiving parallel imports.
However, here restricting parallel trade actually reduces prices in the
country where parallel imports originate. The reason is that there is the
additional vertical pricing inefficiency caused by parallel trade in our case.
Although, in both cases, restricting trade is (weakly) welfare improving
when trade cost is sufficiently high, the mechanisms for these outcomes are
different. In Brander and Krugman, when t is just at the prohibitive level, a
small decrease in t reduces welfare due to the loss from the replacement of
domestic production with high-cost imports. But here when t is high enough
to deter parallel trade, a marginal decrease in t reduces welfare since it leads
to an even higher w*(t) and thus to more inefficiency in vertical pricing. In
Brander and Krugman, when t is sufficiently small, free trade is welfareimproving since resource waste in cross-hauling is small. In our case,
however, allowing parallel trade may have ambiguous welfare effects even
when t is small, since the inefficiency in vertical pricing does not go away as t
Vertical Pricing and Parallel Imports
13
goes to zero. There are situations, though, where allowing parallel trade is
welfare-improving if t is sufficiently small, as is the case in our linear demand
example.
The question of whether parallel importing should be established as a
global policy has been debated at the WTO. Our analysis can shed light on
this issue in a more general setting than that in Maskus and Chen (2004).
The results suggest that neither a policy that always bans parallel trade nor a
policy that always facilitates it is justified from the perspective of global
economic efficiency.11 Our analysis further suggests that policy choices
concerning parallel imports are closely related to choices on other trade
policies. For instance, if it is desirable that parallel imports be legally
allowed, then it could also be desirable to reduce any trade barrier that
increases the cost of parallel trading. On the other hand, if the cost of
conducting parallel trade is sufficiently high, part of which could be due to
the presence of significant trade barriers, then it might be desirable to ban
parallel imports.12
In considering the welfare effects of our analysis, it is important to
keep in mind the restrictions we have imposed on our model. In
particular, we have assumed that the manufacturer can affect the
retailer’s incentive for parallel imports only through changing wholesale
prices. More generally, a manufacturer may have other instruments to
limit parallel imports and to avoid vertical pricing inefficiency. First, the
manufacturer may restrict the quantity the foreign distributor may
purchase, which could alleviate the problem of parallel imports.13 Second,
the manufacturer may impose (maximum) resale price maintenance on
the distributor in country B, resolving directly the tension between
controlling parallel imports and avoiding double marginalization. However, there may be legal limitations on resale price maintenance, and even
if it is legally allowed, price maintenance may be costly to enforce. Third,
the manufacturer may choose to vertically integrate with the distributor,
eliminating the distributor’s incentive for parallel imports and the
problem of double marginalization. However, if the distributor sells
products of many other manufacturers, vertical integration may not be
practical. Moreover, vertical integration can also introduce well-known
incentive problems of its own. Fourth, the manufacturer may enter the
foreign market directly or contract with several independent distributors
to create retail competition. But these choices may not be economical if
there are fixed costs in running a distribution system; a fact that we have
not considered but can be easily incorporated into our model.
Furthermore, retail competition may alleviate, but need not eliminate,
the double mark-up problem.
The presence of these other instruments implies that the possibility of
parallel imports need not necessarily cause vertical pricing inefficiencies. We
thus need to be cautious in interpreting the welfare results of our analysis
and the policy implications. However, to the extent that these other
14
Y. Chen & K. E. Maskus
instruments have their own costs and limitations, there will be situations
where a manufacturer may still want to sell its product through independent
agents in another country who have certain market power, and our analysis
offers insights in these situations.
5. Conclusion
In this paper we have studied a model of parallel imports incorporating
vertical pricing considerations, generalizing and extending the results of
Maskus and Chen (2004). We find that while the possibility of parallel
imports can increase retail market competition, it can also affect a
manufacturer’s incentive, as the rights owner, in setting the wholesale price
(or royalty payment) and so reduce vertical pricing efficiency. Although
parallel imports can be deterred by the manufacturer through a sufficiently
high wholesale price, they can nevertheless occur in equilibrium and can
even originate from the country with higher retail prices. Both industry
profits and global welfare can increase in trade costs. The possibility of
parallel imports decreases global welfare when trade cost is large, but can
increase welfare when trade cost is low. To the extent that trade cost is likely
to be higher for countries in different regions than for countries within a
region, parallel trade is more likely to increase welfare within a region than
in the entire world trading system.14
To the extent that parallel imports may allow one distributor to free ride
on another distributor’s promotional activities and reduce efficiency of these
activities, a case may be made for the prevention of parallel imports. Our
analysis suggests that there need not be externalities of this type in order to
have welfare-improving restrictions on parallel imports. The need to
improve vertical price efficiency can make it desirable to prevent parallel
imports. Recently, concern about parallel trade has surfaced in pharmaceuticals and biotechnology, as well as in copyright industries including
software, recorded music, videos, and book publishing. These sectors are
characterized by high R&D costs but low marginal costs of production and
distribution. Thus, the differences between retail prices and marginal costs
for these products are often significant. The theory may prove to be
particularly useful in these situations.
Appendix
This appendix contains the proofs for Lemma 1, Proposition 1, and
Proposition 2.
Proof of Lemma 1
¼ p0A t, we must have qAL (w + t) 4 0, since if qAL(w +
When w < wðtÞ
t) = 0, we would have qAM(w + t) = qA0 and
Vertical Pricing and Parallel Imports
15
pA ðqAM ðw þ tÞ þ qAL ðw þ tÞÞ w t þ qAL ðw þ tÞp0A ðqAM ðw þ tÞþ
qAL ðw þ tÞÞ ¼ p0A w t > 0
¼ p0A , qAM
contradicting equilibrium condition (4). When w wðtÞ
0
(.) = qA and qAL (.) = 0 solve equations (3) and (4) and thus constitute
the equilibrium in market A.
When w < wðtÞ,
both equations (3) and (4) hold with equality.
Differentiating these two equations with respect to w and rearranging
terms, we obtain
"
#1
1
@qAL ðw þ tÞ
@ 2 pAM @ 2 pAM
@ 2 pAL
@ 2 pAL
¼
þ
<0
@w
@qAM @qAL @q2AM
@qAM @qAL @q2AL
2
1
@qAM ðw þ tÞ
@ 2 pAM
@ pAM
@qAL ðw þ tÞ
¼
>0
2
@w
@w
@qAM @qAL @qAM
Similarly, @qAL@tðwþtÞ < 0 and
and (4), we have
@qAM ðwþtÞ
@t
> 0. Further, adding up equations (3)
2pA ðqAM ðw þ tÞ þ qAL ðw þ tÞÞ c w t þ ðqAM ðw þ tÞ þ qAL ðw þ tÞÞp0A
ðqAM ðw þ tÞ þ qAL ðw þ tÞÞ ¼ 0
which implies that (qAM(w + t) + qAL (w + t)) decreases in w and t.
Proof of Proposition 1
First, when t 5 pA0 – c, w*(t) = c since this induces the optimal retail price
in B without causing positive parallel imports. Next, suppose that t 5 pA0 –
c. Notice that if w wðtÞ,
then qAL(w + t) = 0, and thus further increases in
w have no effect on PAM (w(t) but reduce PB(wjt). Next, if w 5 c, then
P(wjt) 5 P(cjt). Therefore
the
search for the optimal w can be limited on
the compact interval
c;
wðtÞ
, on which P(wjt) is continuous. Thus w*(t)
exists and w*(t)2 c; wðtÞ
. Moreover, since on this interval P(wjt) is strictly
~ if there is
concave inw by Assumption
A3, w*(t) is unique, where w*(t) = w
~
~ 2 c; wðtÞ
otherwise.
some w
such that @Pð@wwjtÞ
¼ 0, and w*(t) = wðtÞ
By construction, the contract ((w*(t), T(w*(t)) jt), together with (qAM
(w + t), qAL(w + t)) in country A and qB(w) in country B, constitute the
unique subgame perfect Nash equilibrium.
ðwjtÞ
Finally, notice that if t 5 pA0 – c, then @pA@w
is positive at w = c, but
@pB ðwÞ
@pðcjtÞ
is
zero
at
w
=
c.
Therefore
>
0
and
hence
w*(t) 4 c for any
@w
@w
t 5 pA0 – c.
16
Y. Chen & K. E. Maskus
Proof of Proposition 2
First,
@PðwjtÞ
@pA ðwjtÞ
@pB ðwÞ
¼
þ
@w wðtÞ
@w wðtÞ
@w wðtÞ
ðwjtÞ
B ðwÞ
where @pA@w
jwðtÞ
?0 when t?0, but @p@w
jwðtÞ
is a negative constant as
< 0 and hence
t?0. Therefore, when t is sufficiently small, @PðwjtÞ
@w jwðtÞ
when
w*(t) 5 wðtÞ.
That is, there exists some t1 > 0 such that w*(t) 5 wðtÞ
t < t1 .
Next, we show that there exists some t2 , where t1 t2 < p0A c, such that
whenever t > t2 . Suppose this were not true. Then there exists
w*(t) = wðtÞ
and
some t that is arbitrarily close to pA0 7 c, for which w*(t) 5 wðtÞ
@PðwjtÞ
@pB ðwÞ
+
0
j
¼
0.
But
since
w*(t)
?
c
when
t
?
(p
7
c)
,
and
A
w ðtÞ
@w
@w ?0
when w?c + , we have
@PðwjtÞ
@pA ðwjtÞ
!
>0
@w wðtÞ
@w wðtÞ
when w*(t)? c + . This implies that @PðwjtÞ
@w jw ðtÞ > 0 for any t that is lower
than, but sufficiently close to, (pA0 – c), a contradiction.
Finally,
we show that t1 ¼ t2 if j dwdtðtÞ j 1. It suffices to show that if
dw ðtÞ
0 Þ, w*(t) 5 wðtÞ
for
1 dt 1, then for any t’ 4 0 such that w*(t’) 5 wðt
dPðwÞ
0
Þ, dw jw ðtÞ0 ¼ 0. Consider any
t 5 t’.
all t 5 t’. Since w*(t’) 5 wðt
0 Þ þ t0 t. If 0 dwdtðtÞ, then
¼ p0A t ¼ p0A t0 þ t0 t ¼ wðt
Then wðtÞ
0 Þ < wðtÞ.
If 1 dwdtðtÞ < 0, then – dt 4 dw*(t) 5 0,
w ðtÞ w ðt0 Þ < wðt
or dt 5 7 dw*(t). Integrating on both sides, we have
t0 t ðw ðt0 Þ w ðtÞÞ; or w ðtÞ < w ðt0 Þ þ t0 t < wðt0 Þ þ t0 t ¼
wðtÞ:
Notes
We thank Jonathan Eaton, Damien Neven, Marius Schwartz, two anonymous referees, and
participants at numerous seminars for helpful comments. Chen acknowledges research support
from the National Science Foundation under grant # SES 9911229 and Maskus is grateful to
the World Intellectual Property Organization for support.
1
The NERA report (1999) makes this point clearly, noting many sectors in which parallel
trade is a distributor-level phenomenon. In a concrete example, it is estimated that up to 20
per cent of the market for Coca-Cola syrup in UK is served by parallel imports coming from
Vertical Pricing and Parallel Imports
2
3
4
5
6
7
8
9
10
11
12
13
14
17
wholesalers in other European nations. See ‘Coke’s Public-Relations Trouble Was Worsened
by Gray Trade’, The Wall Street Journal, 6 July 1999.
We shall allow the manufacturer to use two-part tariff contracts, so that the double-markup
problem could be avoided if not for the concerns of parallel imports.
The prevention of parallel imports is essentially the enforcement of an exclusive territory in
the international context. As such, our study is also closely related to the literature on
vertical restraints (see, for instance, Katz, 1989). While our analysis is rather different from
this literature, it shares some similar intuition with Chen (1999).
The model can be easily extended to include positive retailing costs in both countries.
Equivalently, we can think of L being a licensee of M in country B. In this case, T will then
be the license fee and w the royalty payment per unit of output. Contracts with a fixed fee
and per-unit royalty are common in international licensing (Contractor, 1981).
However, we assume that M or any agents of M other than L will not sell in B.
For ease of exposition, we shall sometimes suppress the arguments in the functional
expressions for qAM and qAL.
We note that while Assumptions A1 and A2 are fairly standard, Assumption A3 is a stronger
assumption. Since P consists of the profits in market A of a Cournot duopoly and the
monopoly in market B, from the usual monopoly and Cournot analysis, the demand curves
in these two markets may not be too convex to ensure the concavity of P on w. Clearly,
linear demand satisfies this condition but so do other demand specifications.
This comment refers to trade costs tqAL rather than to exogenous ad valorem cost t.
If M could set the retail price in B directly so that vertical pricing efficiency were not a
concern, parallel trade may still occur. But such parallel trade would then only be due to
international price differences. The theory discussed here does not preclude such parallel
imports, but suggests an additional important reason for them.
We note that nations may have conflicting interests in policies towards parallel imports.
When manufacturers are foreign-owned firms, parallel imports are more likely to raise
national welfare in the importing country, which would not count manufacturers’ profits in
its welfare, but this could be at the expense of other countries.
For countries that lack effective control of their borders, a ban on parallel imports is unlikely
to be fully enforced because of smuggling. In that context, t can be interpreted as the cost of
evading controls, or, equivalently, as the level of enforcement of a prohibition. Thus, the best
policy may be to have no prohibition (so that t = 0), which would be preferred to a situation
where parallel imports occur at a higher t.
Suppose L is restricted to purchase no more than qB0, the profit-maximizing output in B. But
at qB0, L may want to divert some of the output back to A, since a marginal diversion has a
second-order effect on L’s profit in B but a first-order effect on L’s profit from A. Thus, if M
wants to deter parallel imports, it will have to limit the purchase of L to less than qB0, which
leads to a trade-off that is somewhat similar to ours: accommodating parallel imports or
having too little output (too high price) in market B. On the other hand, if L is required to
purchase at least qB0, L would have the incentive to engage in parallel imports.
This may suggest an economic rationale for the ECJ’s approach to allow parallel imports
within the Single Market but not across its borders. We also note that the policy implications
of our analysis share similarities with those of Malueg and Schwartz (1994), although for
very different reasons. We mention again that our welfare results need to be qualified, as
discussed at the end of Section 4.
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