Strategic Competition and Optimal Parallel Import Policy.

Santanu Roy∗

Southern Methodist University, Dallas, TX.

Kamal Saggi†

Vanderbilt University, Nashville, TN.

Abstract

We examine the role of parallel import policy as an instrument of strategic tradepolicy. We consider a duopolistic framework where the home firm enjoys uncontestedmonopoly power in its domestic market and has the option of serving the foreign marketby incurring a fixed investment cost which is observed by the foreign firm prior to pricesetting. When price competition abroad is intense, the parallel import policy of (only) thehome country affects the firm’s decision to export as well as its ability to price discriminateinternationally. Interestingly, when the foreign market is significantly larger than thedomestic one, the home firm gains if it is unable to price discriminate internationally; inan environment where arbitrage induced parallel imports can flow into the home country,the home firm’s desire to not deviate too far from its optimal monopoly price in thedomestic market makes it (credibly) less aggressive in price competition abroad, and thissoftening of price competition raises profits. On the other hand, when the foreign marketis not significantly bigger, it is optimal for the home country to forbid parallel importssince international price discrimination yields higher profits to the home firm. We showthat the home country’s equilibrium parallel import policy is always pro-trade (i.e. itinduces the home firm to export); it is also socially optimal provided that the fixed costsof exporting are not too large. When price competition is weak, the importing country’spolicy determines the market outcome and its unique equilibrium choice is to permitparallel imports. Such openness to parallel imports turns out to be anti-trade and oftenin conflict with social welfare considerations.

Keywords: Parallel Imports, Exports, Oligopoly, Product Differentiation, Market Struc-ture, Welfare. JEL Classifications: F13, F10, F15.

∗Department of Economics, Southern Methodist University, 3300 Dyer Street, Dallas, TX 75275-0496, USA.E-mail: sroy@smu.edu; Tel: (+1) 214 768 2714.

†Department of Economics, Vanderbilt University, Box 1819-Station B, Nashville, TN 37235-1819, USA.E-mail: k.saggi@Vanderbilt.Edu; phone: (+1) 615-322-3237.

1

1 Introduction

The subtle question of whether parallel imports should be permitted or not has been discussed

and debated widely in the academic and policy literature in international trade.1 The fact

that existing multilateral rules on trade and intellectual property have tended to be silent

on the subject suggests that either international agreement on this issue has been difficult to

achieve or the pursuit of nationally optimal parallel import policies does not always generate

significant international externalities. In this paper, to gain some insight into this issue,

we derive nationally optimally parallel import policies and examine their desirability from a

global welfare perspective. Our analysis address several inter-related questions: Under what

circumstances does a country prefer to forbid parallel imports? When does it choose to permit

them? What are the channels via which parallel import policies affects national and global

welfare? An important contribution of the paper is to address these questions in a model

in which the product market is characterized by strategic competition between firms. As

we discuss below, allowing for competition between firms, as opposed to assuming a global

monopoly supplier — as almost the entire literature on parallel imports has tended to do —

brings to light some novel determinants of parallel important policies.2

We develop a two-country duopoly model where only the home firm has the option to

export. This may, in particular, reflect asymmetric protection of intellectual property across

countries or simply differences between the ability of firms to access foreign markets. The

products of the two firms are differentiated horizontally on a Hotelling product space. To

be able to export successfully, the home firm must first incur a fixed investment cost that is

irreversible in nature. The timing of decisions is as follows. First, the two governments (home

and foreign) choose their parallel import policies: each government faces a discrete choice —

to permit or forbid parallel imports. Next, the home firm decides whether or not to bear

the fixed investment cost necessary to export. Finally, firms choose prices — if the home firm

exports, firms compete in prices; otherwise each firm operates as a monopolist in its local

market.1Parallel imports arise when a product protected by some form of intellectual property rights (IPRs) sold

by the rights holder in one country is re-sold in another country without the right holder’s permission. As isclear, the incentive to such trade arises in the presence of significant price differences across countries.

2 It is important to note that the literature does contain several analyses of international oligopoly withintegrated and segmented markets where the underlying pricing regime is assumed to be exogenous: see,among others, Markusen and Venables (1988), Smith and Venables (1988) and Venables (1990). By contrast,in our model, national parallel import policies endogenously determine whether markets are segmented orintegrated.

2

As is clear from above, an important aspect of our approach is that the home firm’s decision

to export is endogenous. This formulation is motivated by a host of empirical evidence which

indicates that pricing regulations (which are another type of policy that affect the ability of

firms to price discriminate internationally) have a strong influence on the entry of firms into

foreign markets — see Danzon and Epstein (2008), Danzon et. al. (2005), Lanjouw (2005),

and the recent overview article by Goldberg (2009). Furthermore, prior theoretical work on

parallel imports has explicitly argued that price regulations and parallel import policies can

lead firms to serve (or not serve) certain markets — see, for example, Malueg and Schwartz

(1994).

An important insight of our analysis is that, when parallel imports are not possible, the

domestic firm can reduce its price in the foreign market without a commensurate reduction

in its domestic price, and as a result, it becomes a more aggressive price competitor in the

foreign market relative to when parallel imports are permitted. While this tends to increase the

domestic firm’s foreign market share, it also tends to increase the intensity of price competition

and therefore, reduces equilibrium market power in the foreign market. If sufficiently strong,

this reduction in market power can reduce the export profitability of the domestic firm and

therefore create a rationale for permitting parallel imports as opposed to restricting them.3 It

should be observed that this insight is novel to the existing literature on parallel imports that

has tended to focus largely on the monopoly case.4 To see why this matters, first note that

if the domestic firm were a global monopolist, then ceteris paribus, a restriction on parallel

imports should (at least weakly) increase its incentive to serve the foreign market — after all, a

monopolist is always free to charge a common price in both markets if it is profit maximizing

to do so. Thus, by creating the possibility of international price discrimination, a prohibition

of parallel imports by a country can only make its monopoly firm better off.

We find that when price competition abroad is intense, the home country is ‘decisive’ in

that only its parallel import policy affects the market outcome. Similarly, when competition

abroad is weak, only the foreign country’s policy is consequential. An important result of

our analysis is that, despite the presence of strategic considerations in our model, a country’s

nationally optimal policy can sometimes be globally optimal, making the need for international

3 In their seminal contribution to optimal strategic trade policy under oligopolistic competition, Grossmanand Eaton (1986) showed that it may be optimal to impose an export tax on the home firm in order to softeninternational price competition; our paper indicates that parallel import policy can play a similar role.

4For example, Malueg and Schwartz (1994), Richardson (2002), Valletti (2006), all assume that the productmarket is monopolistic. Roy and Saggi (2010) do consider an oligopolistic product market but, as we notebelow, their model differs from ours in important ways.

3

coordination over parallel import policies unnecessary. This happens when the home country is

decisive and the fixed costs of exporting are not too large so that inducing exports is nationally

as well as globally optimal. Interestingly, we show that such a pro-trade (i.e. export inducing)

parallel import policy is not unique: underlying parameters determine whether permitting or

prohibiting parallel imports induces exports.

On the other hand, when the foreign country is decisive, it always chooses to permit

parallel imports. Such openness to parallel imports on its part can not only be anti-trade, i.e.

it can deter the home firm from exporting, but can also lower overall world welfare when the

fixed cost of exporting is not too large. By showing that openness to parallel imports is not

necessarily pro-trade and that such openness can create a significant international externality,

the model helps gain some insight into the issue of when and why coordination over parallel

import policies might be useful.

In the current literature on parallel imports, the incentive for individual nations to impose

restrictions on parallel imports primarily takes into account three sets of factors that result

from the increased ability of firms to engage in international price discrimination. First, the

change in domestic consumer welfare resulting from higher domestic retail prices in markets

with more inelastic demand including the possibility that certain markets with very elastic

demands may be served only when firms can price discriminate sufficiently — see Malueg and

Schwarz (1994). Second, the increased ability of manufacturers to engage in vertical controls

such as resale price maintenance and exclusive territories to protect retailers from competi-

tive rent dissipation and free riding by foreign sellers which on the one hand, reduces retail

competition thus increasing retail price, and on the other hand, increases the incentive of

retailers to invest in marketing, advertising and retail infrastructure in the domestic market

that eventually benefits domestic consumers and expands demand — see Maskus and Chen

(2002 and 2004) and Raff and Schmitt (2007). Third, the increased ability of governments

to regulate domestic market power for various purposes and to preserve rent for private in-

vestment in R&D and production of intellectual property without having to contend with the

dissipation of this rent through international arbitrage — see Li and Maskus (2006), Valletti

(2006), Valletti and Szymanski (2006), and Grossman and Lai (2008). The structure of our

model highlights a novel consequence of a restrictive parallel import policy viz., the change

in the competitiveness of the domestic firm in the foreign market arising from its ability to

charge a low price abroad without suffering any erosion in its domestic market power, the

consequent change in the rent earned by the firm abroad and, in the final analysis, its very

4

incentive to export. Finally, Roy and Saggi (2010) analyze parallel import policies in a verti-

cally differentiated international oligopoly where, unlike this paper, there is no asymmetry in

potential market access for firms, and the focus is on relating equilibrium government policies

to differences in the structure of demand between countries.

2 Model

There are two countries: home (H) and foreign (F ). Firm h, the home country’s domestic

firm, has an intellectual property right (IPR) over its product. For the sake of concreteness,

we will suppose that this IPR is a product patent. We will assume that the home firm faces

no competition in the domestic market. The foreign country has its own domestic firm, called

the foreign firm (denoted by f), whose product is horizontally differentiated from the product

of the home firm. Firm f ’s product can be sold legally within the foreign country but is

not exported. Thus, there is asymmetry in potential market access between the two firms.

One way to think about this asymmetry in potential market access is in terms of differences

in IPR protection across countries. The home country offers strong protection and a broad

interpretation of the product patent held by the home firm that, in particular, precludes

any closely related product from being sold within its borders. The foreign country, on the

other hand, offers relatively weak protection and narrow interpretation of the product patent

held by the home firm that, in particular, allows a substitute product to be sold within its

borders. The foreign firm cannot export to the home country because of the strong and broad

enforcement of the home firm’s product patent in the home country. However, the asymmetry

in potential market access can also arise from many other sources such as differences in the

cost of marketing products abroad.

We adopt the Hotelling linear city model of horizontal product differentiation where the

product space is the unit interval [0,1]; the home firm’s product is located at 0 and the

foreign firm’s product is located at 1. Note that here location does not refer to geographical

location but rather a physical characteristic (or type) of the product. The market in each

country consists of a continuum of consumers whose most desired product types are distributed

uniformly on the unit interval. Each consumer buys one or zero unit of a product and earns

gross surplus V from consuming the product. If a consumer consumes a product whose actual

product type is located at a distance d from her "most desired" product type, she incurs a

(psychological) cost t.d, t > 0, in addition to paying the price charged. We assume that V > t

5

which implies that it is socially optimal for all consumers to buy. The total mass of consumers

in country i is given by ni ≥ 0, i = H, F . Without loss of generality, we set

nH = 1, nF = β (1)

where

β >2

3. (2)

The role of restriction (2) is to ensure that when the home firm serves the foreign country, it

always sells a strictly positive quantity in the latter. We assume that production cost is zero

for both firms.

To be able to export to the foreign market, the home firm must first incur the fixed cost

φ ≥ 0. The motivation behind this assumption is simple: selling its good in the foreign marketmay require the home firm to make certain kinds of investment in dissemination of product

information, creation of consumer awareness and establishing access to the retail infrastructure

etc. Further, the firm may need to authorize sales of its product in the foreign market. These

export related decisions have to be made prior to actual selling of goods in the foreign market

and are therefore assumed to be observable by its competitor before market competition

occurs. In particular, if the home firm makes no investment and does not authorize sales

of its product abroad, the foreign firm will know that it has unrestrained monopoly power

in its domestic market. In order to abstract from issues related to vertical relationships, we

will assume that firms sell their products directly to consumers or, equivalently, the retailing

sector in each market is perfectly competitive with zero marginal retailing cost (so consumers

buy at the price set by the manufacturing firm).

Each country chooses between one of two options - to allow parallel imports with no

restrictions (P) or to not allow parallel import at all (N). While one can imagine various

intermediate options, these are the two types of policies that are most commonly observed and,

in fact, correspond exactly to the binary decision on whether to have national or international

exhaustion of the intellectual property rights.

Formally, the game proceeds in three stages. First, the two governments decide whether or

not to allow parallel imports. Next, the home firm decides whether or not to enter the foreign

market. Finally, firms set prices in every market they serve. We determine the subgame

perfect Nash equilibrium outcome of this game.

We begin with some general observations. For i = h, f , we denote the price, the quantity

sold and the profit earned by firm i in its domestic and foreign markets by (pi,qi,πi) and

6

(p∗i ,q∗i ,π

∗i ), respectively.

If firm i is the only firm serving its domestic market, then the domestic demand it faces

is given by:

Di(pi) = ni, pi ≤ V − t (3)

= niV − pi

t, pi ≥ V − t. (4)

The domestic monopoly price pmi and monopoly quantity qmi of firm i that maximize its

domestic profit are given by:

pmi = V − t, qmi = 1, if V ≥ 2t (5)

and

pmi =V

2, qmi =

V

2t, if V ≤ 2t. (6)

If the home firm decides to export to the foreign country, then assuming that all buyers buy,

the demand in the foreign country for the home firm’s product is given by:

dh(p∗h, pf ) = β

∙1

2+

pf − p∗h2t

¸, if (pf − p∗h) ∈ [−t, t] (7)

= 0, if (pf − p∗h) ≤ −t= β, if (pf − p∗h) ≥ −t,

while

df (p∗h, pf ) = β − dh(p

∗h, pf ). (8)

If the home firm can price discriminate across the two markets, it’s reaction function in the

foreign market is given by:

p∗h =t+ pf2

. (9)

The reaction function of the foreign firm is given by:

pf =t+ p∗h2

. (10)

These reaction functions assume that the prices are not too large so that the market is fully

covered. If both firms have the reaction function as indicated above, then the it is easy to

check that there is a unique Nash equilibrium outcome of price competition in country j’s

market given by:

p∗h = p∗f = t, (11)

7

with each firm selling to half the market. Each firm’s profits (gross of any fixed cost of serving

the market) in the foreign country are given by:

π∗f = π∗f = βt

2. (12)

Observe that in the above equilibrium emerging from competition in the foreign country when

the home firm is not restrained by the price it charges in its domestic market and can price

discriminate across the markets, the competitive price ( t2) is lower than the monopoly price

(max{V −t,V2 }) if, and only if, V ≥ 2t. In particular, if V < 2t, then the competitive outcome

generates prices in the foreign country that are higher than the monopoly price. The intuition

here is that with competition, firms split the market and therefore the marginal buyer’s taste

or desired product is closer to the product each firm sells which, in turn, induces the firms to

charge higher prices relative to a monopoly situation (where a firm sells more and therefore,

the marginal buyer’s taste is further away from the actual product type). We shall call this

the niche effect.

In what follows, we refer to the situation where V ≥ 2t as strong competition and the situ-ation where V < 2t as weak competition; this also accords with the standard interpretation of

higher values of t implying greater product differentiation and hence, softer price competition.

As it turns out, there are major differences between the policy and market outcomes between

these two cases. In particular, since only the home firm has the ability to export, only one

country’s parallel import policy ends up mattering. Under strong competition, if the home

country is open to parallel imports then the home firm cannot price discriminate interna-

tionally since the price under competition is lower than its monopoly price and the foreign

country’s parallel import policy is irrelevant. Similarly, when competition is weak, only the

parallel import policy of the foreign country matters whereas the parallel import policy of the

home country is not consequential. We begin with the strong competition case.

3 Parallel import policy under strong competition

In this section, we analyze the policy and market outcomes where V ≥ 2t and competition inthe foreign country is strong. As noted above, we can ignore the parallel import policy of the

foreign country and focus only on the policy choice of the home country.

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3.1 Market outcome

In this subsection, we characterize the market outcome (in stage 3) following each pair of

parallel import policy choices, and the home firm’s decision regarding whether or not to

export.

Independent of the policy choices, if the home firm decides not to export to the foreign

country, then the market outcome in each country is the autarkic monopoly outcome as

indicated in (5). In the rest of this subsection, we focus on the situation where the home firm

chooses to export.

To begin, consider the situation where both countries prohibit parallel trade. This implies

that the pricing decisions in the two markets are independent and, in particular, the home

firm faces no constraint on its ability to price discriminate across the two markets. It follows

then that in the home country, the home firm sets its domestic price at the monopoly level

and sells the monopoly quantity as given by (5). In the foreign country, the equilibrium prices

are as indicated in (11) and firms split the market in the foreign country evenly. In particular,

the prices and quantities sold are given by:

pNh = V − t, p∗Nh = pNf = t, qNh = 1, q∗Nh = qNf =β

2(13)

and the profits (gross of the fixed cost of exporting) are given by:

πNh = V − t, π∗Nh = πNf = βt

2. (14)

Now, observe that V ≥ 2t implies

pNh = V − t ≥ p∗Bh = t

i.e., the domestic price of the home firm exceeds its foreign price. This, in turn, implies that,

as long as the home country prohibits parallel trade, the equilibrium market outcome remains

unchanged even if the foreign country allows parallel imports (thereby preventing the home

firm from charging a lower price in its domestic market). Indeed, this is the unique equilibrium

market outcome when the home country prohibits parallel imports. In particular, if the home

country prohibits parallel imports, the market outcome is independent of the parallel import

policy of the foreign country. We summarize this in the following lemma:

Lemma 1 Assume that V ≥ 2t (strong competition). Suppose the home country prohibits

parallel imports. Then, the home firm charges the autarkic monopoly price V − t and sells

9

to all consumers in its domestic market. If the home firm chooses to export, the market

equilibrium in the foreign country is symmetric where both firms charge price equal to t and

the home firm’s gross export profit is π∗Nh = β t2 .

Next, consider the market outcome when both countries allow parallel trade so that the

home firm is constrained to charge identical prices in both markets, i.e., ph = p∗h. In this case,

the gross total profit of the home firm if it exports to the foreign country is given by:

ph[1 + dh(ph, pf )], for ph ≥ V − t

and

ph

∙V − ph

t+ dh(ph, pf )

¸, for ph ∈ [V − t, V ]

where dh is given by (7). Note that the profit function has a kink at ph = V − t. Maximizing

the two parts of the profit function with respect to ph taking into account the boundary

constraints, we obtain the reaction function of the home firm. Let pfand pf be defined as

follows:

pf= 2V − t

µ3 +

2

β

¶and pf = 2

µ1 +

1

β

¶V − t

µ3 +

4

β

¶.

It is easy to check that pf< pf and that pf and pf are strictly positive if V is large relative

to t, and less than zero if V is close to t.

The reaction function of the home firm is given by:

ph =

µ2 + β

β

¶t

2+

pf2, if p

f> 0 and pf ∈

h0, p

f

i(15)

= V − t, if pf > 0 and pf ∈hmax{0, p

f}, pf

i=

1

2(2 + β)[(2V + βt) + βpf ], if pf ≥ max{0, pf}.

Observe that the above reaction function is flat for a certain range of the rival’s price; this

flat range corresponds to a discontinuity in the marginal revenue of the home firm at the kink

point of its gross revenue function. The first part of the reaction function corresponds to the

situation where the rival’s price is sufficiently low so that the home firm also charges a low

price (below its home monopoly price) to be competitive abroad; at such price, the home

firm sells to all buyers at home. The second part of the reaction function reflects a situation

where the price charged by the foreign firm is moderately high so that the home firm can

10

charge its optimal monopoly price in the home market without losing much market share in

the foreign market. In this range, even when the rival raises its price, the jump discontinuity

in the marginal revenue of the home firm (at the home monopoly price where it sells to all

home consumers) prevents the home firm from altering its best response. The last part of the

reaction function corresponds to the situation where the foreign firm’s price is so high that

the home firm is induced to expropriate more revenue out of foreign buyers that have a closer

taste for its product by raising its home rice above the optimal monopoly price — under such

a situation, the home firm forsakes some profit in the domestic market to increase its profit

in the foreign market.

The foreign firm ’s reaction function is identical to that in (10) i.e.,

pf =1

2(t+ ph). (16)

This reaction function intersects the home firm’s reaction function in either the first or the

second of the three parts in (15). It can be checked that the (unique) Nash equilibrium

outcome is given by:

pPh = t

µ4

3β+ 1

¶and pPf = t

µ2

3β+ 1

¶if V > 2t

µ2

3β+ 1

¶(17)

and

pPh = V − t and pPf =V

2if 2t ≤ V ≤ 2t

µ2

3β+ 1

¶. (18)

Note that if V > 2t³23β + 1

´then

t

µ4

3β+ 1

¶< V − t

so that the equilibrium described in (17) corresponds to a situation where the foreign firm’s

reaction intersects the home firm’s reaction in the first of its three parts described in (15); the

equilibrium described in (18) corresponds to an intersection in the second part of the home

firm’s reaction. In both cases, the home firm charges a price less than or equal to V − t, its

optimal monopoly price at home. The Nash equilibrium outcome described above remains

unperturbed even if the foreign country does not allow parallel imports so that the home firm

is free to charge a lower price in its domestic market in the home country. Indeed, for V ≥ 2t,this is the unique Nash equilibrium outcome when the home country allows parallel imports,

independent of the parallel import policy of the foreign country. The quantities sold in this

11

equilibrium are given by:

qPh = 1, q∗Ph =

β

2− 13, qPf =

β

2+1

3, if V > 2t

µ2

3β+ 1

¶(19)

and

qPh = 1, q∗P1h = β

µ1− V

4t

¶, qPf =

βV

4t, if 2t ≤ V ≤ 2t

µ2

3β+ 1

¶. (20)

Note that assumption (2) ensures that that all quantities are strictly positive. Also, observe

that, pPh > pPf which reflects the fact that the home firm is less aggressive in price competition

than the foreign firm because it loses profit in its home market if it reduces price (below its

monopoly price); this is reflected in the lower market share of the home firm. Since pPh ≤ V −t,all consumers buy in the home country and therefore, the quantity sold in the home country

is identical to that when the home firm is free to price discriminate between the two countries.

Observe that the prices are higher than what the two firms charge in market 2 when the home

firm can price discriminate: in other words, non-discrimination softens price competition.

In the range of parameter values where the equilibrium price of the home firm is strictly

below (V − t), the prices charged by both firms decline with β, the relative size of the market

in the foreign country. If V > 2t³23β + 1

´firm profits (gross of the fixed cost of exporting)

are as follows:

πPh = t

µ4

3β+ 1

¶, π∗Ph = t

µ4

3β+ 1

¶µβ

2− 13

¶, and πPf = t

µ2

3β+ 1

¶µβ

2+1

3

¶(21)

whereas if 2t ≤ V ≤ 2t³23β + 1

´we have

πPh = V − t, π∗Ph = β(V − t)

µ1− V

4t

¶, and πPf =

βV 2

8t(22)

It can be checked that

π∗Ph ≥ π∗Nh ⇐⇒ β ≥ β∗ ≡ 43max

½1,

t

V − 2t¾. (23)

i.e., if the home firm exports, it earns higher profit under non-discriminatory pricing (than

under price discrimination) if, and only if, the size of the foreign market (β) exceeds the critical

threshold β∗. Further, the critical threshold β∗ is (strictly) increasing in t (if V ∈ [2t,3t]).An increase in the size of the foreign market and a reduction in the intensity of competition

makes non-discrimination more attractive to the home firm; the latter follows from the fact

that stronger competition puts the home firm at a greater relative disadvantage under non-

discrimination. We summarize the above discussion in the following lemma.

12

Lemma 2 Suppose that V ≥ 2t (strong competition) and the home country allows parallelimports. Then, the following hold: (i) If the home firm chooses to export to the foreign

country, it charges a common price in both markets that does not exceed the monopoly price in

its domestic market and lies strictly below the latter if competition is very strong (in which case

it sacrifices domestic profit when it serves the foreign market). (ii) All consumers buy in the

home country. (iii) Both firms charge prices that are higher than what they would if the home

firm could price discriminate between the two markets. (iv) The home firm charges a higher

price and has lower market share in the foreign country than the foreign firm and the gross

foreign profit of the home firm is higher than what it earns if it is free to price discriminate

between the two markets if, and only, if β ≥ β∗i.e., the foreign market is relatively large.

3.2 Policy outcome

In this subsection, we outline the implications for parallel import policy that follow from our

analysis of the effect of parallel import policy on market outcomes. Though market outcomes

may, in principle, be affected by the parallel import policy of either country, our results indicate

that given the parameters of the model, only one country’s policy matters. The equilibrium

policy outcome essentially reduces to the optimal policy of the "decisive" country and in the

case of strong competition, it is the home country. Similarly, in the case of weak competition,

the foreign country is decisive.

From Lemma 1 and Lemma 2, it follows that under strong competition, the market out-

come is independent of the parallel import policy of the foreign country. All that matters

is whether or not the home country allows parallel imports. Further, regardless of the home

country’s policy, the home firm sells to all consumers in market 1 so that total domestic sur-

plus generated in the home country is independent of its parallel import policy. Thus, the

only way in which parallel import policy of the home country affects welfare is via its impact

on the net foreign rent acquired by the home firm in the foreign country.

If the home country does not allow parallel imports, then if the home firm serves both

markets, it charges different prices in the two markets and its net foreign profit is given by

π∗Nh − φ = βt

2− φ.

On the other hand, if the home country allows parallel imports, then if the home firm serves

both markets, it cannot price discriminate in equilibrium and its net foreign profit is given by

π∗Ph − φ = t

µ4

3β+ 1

¶µβ

2− 13

¶− φ, if V > 2t

µ2

3β+ 1

¶13

and

π∗Ph − φ = β(V − t)(1− V

4t)− φ, if 2t ≤ V ≤ 2t

µ2

3β+ 1

¶.

from where it follows that

π∗Ph ≥ π∗Nh ⇐⇒ β ≥ β∗. (24)

It follows therefore:

Proposition 3 Suppose V ≥ 2t (strong competition). Then, the following hold:(i) If β ≤ β∗ then it is optimal for the the home country to prohibit parallel imports.

This is the unique optimal policy if β < β∗ and φ < π∗Nh (otherwise the home country is

indifferent between the two policies). Further, for β < β∗ and φ ∈ [π∗Ph ,π∗Nh ], the home

country’s prohibition of parallel imports is pro-trade i.e. it induces the home firm to export.

(ii) If β ≥ β∗ then it is optimal for the home country to allow parallel imports. This is

the unique optimal policy if β > β∗ and φ < π∗Ph (otherwise the home country is indifferent

between the two policies). Further, for β > β∗ and φ ∈ [π∗Nh ,π∗Ph ], the home country’s openness

to parallel imports is pro-trade.

Proposition 3 indicates that when competition in the foreign market is strong, the home

country’s parallel import policy is all that matters for the market outcome and, further, the

home government’s incentive for allowing or not allowing parallel imports is tied exclusively

to the profitability of its firm. When the foreign market is not significantly larger (i.e. β ≤β∗), a home prohibition on parallel imports allows the domestic firm to price discriminate

internationally and thereby creates the most profitable conditions for it in the foreign market

(and therefore provides the most inducement to export). On the other hand, if the foreign

market is significantly larger, allowing parallel imports and preventing the domestic firm from

price discrimination creates the best opportunity for it to profit from the foreign market. This

is because such a policy softens price competition abroad by making the domestic firm less

willing to lower its price and the profit gain from being able to charge higher prices outweighs

the competitive disadvantage that the domestic firm suffers by being constrained to charge the

same price in both markets. The major point to note is that the nationally optimal parallel

import policy under strong competition is always pro-trade; in particular, when the foreign

market is not significantly larger in size and the fixed cost of exporting is moderately large,

it is the prohibition of parallel imports that induces the home firm to export.

14

3.3 Global welfare analysis under strong competition

In this section, we analyze the implications of the optimal policy choice by the decisive country

(the home country in the case of strong competition) for global welfare (which in our model,

reduces to the total net surplus of the two countries).

Proposition 4 Suppose V ≥ 2t (strong competition).Then, the following hold:(i) Suppose φ ≤ min{π∗Ph ,π∗Nh }. If β ≤ β∗ then the home country’s policy decision to

prohibit parallel imports is globally efficient. On the other hand, if β > β∗ then the home

country’s policy decision to permit parallel imports is globally inefficient.

(ii) Suppose min{π∗Ph ,π∗Nh } ≤ φ ≤ max{π∗Ph ,π∗Nh }. Then, the following hold:(ii.a) When β ≤ β∗ the home country’s (pro-trade) policy decision to prohibit parallel

imports is global efficient if φ ≤ tβ4 ; otherwise, it is inefficient.

(ii.b) When β > β∗ the home country’s (pro-trade) policy decision to permit parallel im-

ports is globally efficient if φ ≤ tβ(14 − 19β2); otherwise it is inefficient.

Part (i) of Proposition 4 describes a situation where the fixed costs of exporting are small

and the home firm exports to the foreign country regardless of the parallel import policy of

the home country. When both firms necessarily compete in the foreign country’s market,

the nature of the optimal parallel import policy from the viewpoint of the home country is

determined by how its policy affects the pricing behavior of firms. More to the point, under

such a situation the optimal parallel import policy of the home country depends only on

whether openness to parallel imports helps or hurts its firm. When the foreign market is not

significantly larger in size than the home market (i.e. β ≤ β∗), the home firm earns greater

profit if it can price discriminate internationally than when it cannot and this induces the

home country to forbid parallel imports. On the other hand, when β > β∗ the home firm is

better off if it is forced to charge a common price in both markets and the home country finds

it optimal to permit parallel imports. As mentioned earlier, the latter scenario arises because

the home country’s openness to parallel imports makes the home firm less willing to cut price

in the foreign country’s market. This softening of competition is precisely what makes the

openness to parallel imports globally inefficient when β > β∗.

Parts (ii.a) and (ii.b) refer to a situation where the parallel import policy of the home

country does affect the home firm’s incentive to export. Under such a scenario, the home

country’s optimal policy is one that induces its firm to export to the foreign country, i.e., it

15

is pro-trade. However, this product market outcome is globally efficient only when the fixed

cost of exporting is not large. Intuitively, the home country’s optimal policy does not account

for the loss of profit experienced by the foreign firm and if fixed costs of exporting are large,

the net export profit earned by the home firm is small relative to the loss experienced by the

foreign firm. Furthermore, a comparison of parts (ii.a) and (ii.b) indicates that the pro-trade

decision of the home country is less likely to be globally efficient when the foreign market is

significantly bigger (i.e. when β > β∗) in that the range of fixed costs of exporting for which

the decision is globally optimal is smaller for the case where β > β∗. Once again, this is due

to the fact that the home country’s policy ignores the fate of the foreign firm.

Proposition 4 generally indicates that unless the fixed cost of exporting is large, the home

country’s policy choice is globally optimal. This implies that in markets where fixed costs of

exporting are minor, there may be little reason for international intervention or coordination

over parallel import policies. Note that this conclusion also applies to nations that choose to

prohibit parallel imports from relatively similar sized countries.

4 Weak competition and parallel import policy

In this section, we analyze the policy and market outcomes where V ∈ (t,2t) i.e., competitionin the foreign country is weak. As was noted earlier, under such a scenario only the foreign

country’s parallel import policy affects market outcomes.

4.1 Market outcome with weak competition

In this subsection, we characterize the market outcome following each pair of parallel import

policy choices and the decision of the home firm on whether or not to serve the foreign market.

As before, independent of the policy choices, if the home firm decides not to serve the

foreign market (in the foreign country), then the market outcome in each country is the

autarkic monopoly outcome as indicated in (6). Note that V < 2t implies that (unlike the

case of strong competition) the monopoly outcome now is one where some consumers do not

buy and monopoly power causes domestic distortion. In the rest of this subsection, we focus

on the situation where the home firm does serve its foreign market.

To begin, consider the situation where both countries prohibit parallel trade. This implies

that the home firm faces no constraint on its ability to price discriminate between its domestic

and foreign markets. It follows then that in the home country, the home firm sets its domestic

16

price at the monopoly level and sells the monopoly quantity as given by (6). In the foreign

country, the equilibrium prices are as indicated in (11) and the firms split the market in the

foreign country evenly. In particular, the prices and quantities sold are given by:

pNh =V

2, p∗Nh = pNf = t, qNh =

V

2t, q∗Nh = qNf =

β

2, (25)

and the profits (gross of the fixed cost of serving the foreign market) are given by:

πNh =V 2

4t, π∗Nh = πNf = β

t

2. (26)

Now, observe that V < 2t implies

pNh =V

2< p∗Nh = t

i.e., the domestic price of the home firm is below its competitive foreign price. This equilibrium

market outcome remains unchanged even if the home country allows parallel trade as long

as the foreign country prohibits parallel trade. Indeed, this is the unique equilibrium market

outcome when the foreign country prohibits parallel trade. In other words, when V < 2t, if

the foreign country prohibits parallel trade, the market outcome (and therefore, whether or

not the home firm serves its foreign market) is independent of the parallel import policy of the

home country. Note that that the net welfare generated in the foreign country in the above

market outcome if the home firm serves both markets is given by:

WNF = βV − β

Z q∗Nhβ

0txdx− β

Z qNfβ

0txdx]− π∗Nh

= β

µV − 3t

4

¶.

Lemma 5 Assume that V < 2t (weak competition).Suppose that the foreign country prohibits

parallel imports. Then, the home firm always charges the autarkic monopoly price V2 in the

home country and sells to V2t < 1 consumers. If the home firm chooses to export, it price

discriminates across markets and the market equilibrium in the foreign country is symmetric

where both firms charge price equal to t, the home firm’s gross foreign profit is π∗Nh = β t2 and

the net welfare of the foreign country is

WNF = β

µV − 3t

4

¶

17

Next, suppose that both countries allow parallel imports so that the home firm cannot

price discriminate between home and foreign markets. Recall that in this case the domestic

monopoly price of the home firm is V2 > V − t. Suppose the home firm serves its foreign

market in the foreign country. The reaction functions of the two firms continue to be as given

by (15) and (16) that were derived in the previous section. However, with V ∈ (t,2t), it can bechecked that the (unique) Nash equilibrium outcome is one where the foreign firm’s reaction

function intersects the home firm’s reaction in the third part of the three parts described in

(15). In particular, the equilibrium prices are:

pPh =

µ4V + 3βt

8 + 3β

¶and pPf =

µ2V + (3β + 4)t

8 + 3β

¶. (27)

The quantities sold in this equilibrium are given by:

qPh =1

t

µ4V + 3β(V − t)

8 + 3β

¶, q∗Ph = β

µ1

2+1

t

2t− V

8 + 3β

¶, and qPf = β

µ1

2− 1

t

2t− V

8 + 3β

¶. (28)

The equilibrium common price pPh charged by the home firm satisfies:

pPh >V

2> V − t

and further

pPh < pPf and q∗Ph > qPf .

In other words, in trying to compete with the foreign firm in the foreign market using a

non-discriminatory pricing, the home firm actually ends up raising both its own price (as well

as its rival’s price) above its domestic monopoly price. As the home firm incurs a loss of

domestic profit whenever it raises its price above the domestic monopoly price, it is actually

more reluctant to raise its price than the foreign firm, and hence more aggressive in price

competition (over this range of prices) than the foreign firm, despite the fact that the foreign

firm has no captive market to reckon with. This reflects the niche effect that we discussed

earlier; as competition is weak and consumers care strongly about taste, firms have an incentive

to raise their price sharply when they serve smaller number of consumers whose tastes are

closer to their product type.

The fact that pPh exceeds the home monopoly price (V2 ) that the home firm would like

to charge in its domestic market if it was allowed to price discriminate, also implies that the

above Nash equilibrium outcome remains unperturbed if the home country prohibits parallel

trade i.e., if the home firm is allowed to charge a higher price in its domestic market. Indeed,

18

for V < 2t, this is the unique Nash equilibrium outcome when the foreign country allows

parallel trade, independent of the parallel import policy of the home country.

The gross foreign profit earned by the home firm when it charges a common price in both

markets is given by:

π∗Ph =β(4V + 3βt)

8 + 3β

µ1

2+1

t

2t− V

8 + 3β

¶. (29)

It should be noted that even though the price charged by the home firm is higher than its

domestic monopoly price (i.e. pPf > V2 ), it is lower than what it would charge in the foreign

country if it could price discriminate (wherein it charges t abroad) since V < 2t implies

pPh < t

It is straightforward to check that even though the home firm earns higher market share in

the foreign country than it would if it could price discriminate (where firms split the market

evenly), the profit it earns under non-discriminatory pricing in the foreign country is lower:

π∗Ph < π∗Nh =tβ

2. (30)

The total welfare generated in the foreign country (when V < 2t and the home firm exports)

is given by:

WPF = βV − β

Z q∗Phβ

0txdx− β

Z qPfβ

0txdx− π∗Ph

= βV − t

2

µβ − 2

βq∗Ph qPf

¶− π∗Ph

= q∗Ph

µt

βqPf − pPh

¶+

β

2(2V − t).

It can be checked that:

WPF > WN

F

i.e., the home firm generates higher net welfare in the foreign country when it serves that

market with nondiscriminatory pricing rather than with discrimination. Even though the

home firm holds higher market share under non-discrimination and, in particular, causes loss

of welfare by increasing the taste related "psychological cost" incurred by buyers, it also

expropriates less rent and the latter effect dominates.

We summarize our analysis for the case where V < 2t in the following lemma:

19

Lemma 6 Suppose that V ∈ (t,2t) (weak competition) and the foreign country allows parallelimports. Then, if the home firm serves the foreign market, the following hold: (i) it charges a

common price in both markets that is strictly higher than the monopoly price in its domestic

market; (ii) both firms charge prices that are lower than what they would if the home firm

could price discriminate between the two markets; (iii) the home firm charges a higher price

and has a lower market share abroad than the foreign firm; and (iv) relative to the situation

where the home firm can price discriminate internationally, the home firm earns lower foreign

profit (i.e. π∗Ph < π∗Nh ) but the net welfare of the foreign country is higher.

4.2 Policy outcome with weak competition

In this subsection, we outline the implications for parallel import policy that follow from

our analysis of the effect of parallel import policy on market outcomes for the case of weak

competition.

From Lemma 5 and Lemma 6, it follows that the market outcome is independent of the

parallel import policy of the home country, the exporting nation. All that matters is whether

or not the foreign country, the importing nation, allows parallel imports. If the foreign country

does not allow parallel imports, then if the home firm serves both markets, it charges different

prices in the two markets and the net welfare of the foreign country is given by WNF . On the

other hand, if the foreign country allows parallel imports, then if the home firm serves both

markets, it cannot price discriminate in equilibrium and the net welfare of the foreign country

is given by WPF . As stated in Lemma 6 we have

WPF > WN

F .

However, the gross foreign profit of the home firm under the two parallel import policy options

of the foreign country satisfy:

π∗Ph < π∗Nh .

It follows therefore that if φ ≤ π∗Ph , the home firm serves the foreign market independent

of the parallel import policy of the foreign country and in that case, it is optimal for the

foreign country to allow parallel imports. On the other hand, if φ ∈ [π∗Ph ,π∗Nh ], then the home

firm serves the foreign market only if the foreign country prohibits parallel imports, in which

case the welfare of the foreign country is given by WNF ; if the foreign country allows parallel

imports, the market in the foreign country is monopolized by the foreign firm which then

20

charges the monopoly price V2 , sells to β

V2t buyers and leads to welfare:

cWF = β

ÃV 2

2t−Z V

2t

0txdx

!It can be shown that WN

F < cWF for V ∈ (t,2t) so that it is optimal for the foreign country topermit parallel imports to prevent the home firm from entering its market.5

Proposition 7 Suppose V ∈ (t,2t) (weak competition). If φ ≤ π∗Nh , then it is optimal for the

foreign country to permit parallel imports, while for φ > π∗Nh the parallel import policy of the

foreign country has no impact on the market outcome. In particular, if φ ≤ π∗Ph , if the foreign

country allows parallel imports then the home firm exports to its market charging a non-

discriminatory price in both countries whereas if φ ∈ [π∗Ph ,π∗Nh ], then the foreign country’s

openness to parallel imports deters the home firm from exporting and preserves the foreign

firm’s local monopoly.

Proposition 7 indicates that unlike the case of strong competition, for the range of pa-

rameters for which the choice of parallel import policy matters for the market outcome, the

decisive country under weak competition has a unique nationally optimal policy choice and it

is one of allowing parallel imports. By allowing parallel imports, the foreign country prevents

price discrimination by the home firm that, in turn, actually reduces the rent that the firm

can expropriate via exporting (though it increases the firm’s market share in the foreign coun-

try). With weak competition, reducing rent transfer abroad becomes the driving motive of

the foreign country’s policy. In fact, if the fixed cost of exporting exceeds a certain level, the

optimal policy of allowing parallel imports by the foreign country deters entry by the home

firm and leads to autarky.

Our analysis provides a new insight as to why a developing country with weak intellec-

tual property protection may have an incentive to permit parallel imports: by doing so, it

discourages foreign exporters to enter the local market and this helps protect the local firm

from foreign competition.

4.3 Global welfare under weak competition

We now analyze the global welfare implication when competition is weak. Since the foreign

country is decisive here, it is sufficient to focus on its policy.5 It is straightforward to establish thatWN

2 < W2 if 3V 2+6t2−8tV > 0. Furthermore, we have 3V 2+6t2−8tV= (2t− V )2 + 2t( 2

3V − t) which is positive for V ≥ 3

2t and 3V 2 + 6t2 − 8tV = (V − t)2 + t(t− 2

3V ) which is

positive for V ≤ 32t.

21

Proposition 8 Suppose V < 2t (Weak Competition).Then, the following hold:

(i) If φ ≤ π∗Ph then the foreign country’s decision to permit parallel imports is pro-trade

but globally inefficient.

(ii) If π∗Ph < φ ≤ π∗Nh then the foreign country’s policy to permit parallel imports is not

pro-trade. Furthermore, this policy is globally suboptimal if φ is small whereas it is globally

optimal if φ is large enough i.e. it lies within the interval (π∗Ph ,π∗Nh ].

Thus, under weak competition, not only is the market outcome dependent only on the

parallel import policy of the importing nation (the foreign country), but the nationally optimal

policy choice of the foreign country generates an outcome that is globally inefficient unless the

fixed cost φ of serving the foreign market is very large. In particular, with weak competition

(where the domestic monopoly price of the home firm is lower than the competitive "niche"

price abroad, and the home firm is more aggressive in price competition when it cannot price

discriminate) the foreign country’s optimal policy of allowing parallel imports to prevent price

discrimination is geared towards reducing the rent expropriated by the foreign firm, and this

is what leads to global inefficiency. This suggests that with weak competition (that may be

closely related to weak protection of IPRs available to foreign firms in importing nations),

there is a case for reversing the apparently open parallel import policies of such nations since

such policies can simply driven by the desire to preserve the rents of local firms and may, in

fact, restrict trade if the fixed cost of exporting is moderately large.

5 Conclusion

This paper derives optimal national parallel import policies in an oligopolistic environment

where such policies affect the nature of price competition in international markets as well as

underlying market structure. This is in sharp contrast with existing literature that has tended

to focus almost exclusively on monopoly. By incorporating strategic interaction at the product

market stage, we are able to highlight some hitherto ignored consequences of parallel import

policies: we show that such policies affect the competitiveness of domestic firms in foreign

markets and, therefore, their (prior) incentive to enter such markets. For example, in our two-

country model, when product market competition is intense, a prohibition of parallel imports

by the home country eliminates the threat of arbitrage induced parallel imports and allows

the home firm to charge a low price abroad without suffering any reduction in its domestic

market power. This increased ability to compete abroad without having to lower its domestic

22

price can in turn increase the firm’s incentive to export. In this way, a prohibition on parallel

imports by the home can actually end up acting as a pro-trade policy by making exporting

more attractive to its firm. Our analysis also points out that when market competition is

rather weak, it is openness to parallel imports that is pro-trade: under such a situation,

openness to parallel imports on the part of the home country makes its firm less willing to

lower price abroad thereby softening international price competition and making exporting

more attractive. Thus, whether forbidding parallel imports is in the national interest or not

depends upon whether the home firm is better off having the freedom to price discriminate

internationally or not.

We also investigate the welfare properties of national parallel import policies. An impor-

tant and somewhat surprising result of our analysis is that nationally optimal parallel import

policies can sometimes be globally optimal, eliminating the need for international coordina-

tion over such policies. Such congruence between national and global interests occurs when

the policy chosen is pro-trade (i.e. export inducing) and the fixed costs of exporting small.

On the other hand, openness to parallel imports that results in the preservation of a local

monopoly is not only anti-trade but can also be globally inefficient.

To focus on the novel considerations that arise from strategic interaction between firms, we

have abstracted from aspects of parallel import restrictions related to incentives for investment

in R&D, protection of IPRs, exercise of vertical controls and investment by retailers. Future

research might address to what extent the findings of the literature examining these consid-

erations in the context of parallel imports hold under the type of oligopolistic environment

considered by us.

Appendix

Proof of Proposition 4.

The proof is based on a lemma stated below that evaluates and compares the global welfare

generated when the home country allows parallel imports to that when it does not (for the

case of strong competition). Comparing the globally efficient policy outcome described in

this lemma to the nationally optimal policy outcome (of the home country) described in

Proposition 3 immediately yields Proposition 4.

Lemma 9 Suppose V ≥ 2t (strong competition).Then, the following hold: (a) Suppose φ ≤min{π∗Ph ,π∗Nh } so that the home firm exports to the foreign country regardless of the home

23

country’s parallel import policy. Then, it is globally efficient for the home country to prohibit

parallel imports. (b) Suppose min{π∗Ph ,π∗Nh } ≤ φ ≤ max{π∗Ph ,π∗Nh }. Then, the home firmexports under only one of the two policy choices of the home country and the globally efficient

policy depends on β, the relative size of the foreign country’s market. If β ≤ β∗, then it is

globally efficient for the home country to prohibit parallel imports if φ < tβ4 ; otherwise, it is

globally efficient for the home country to permit parallel imports. On the other hand, if β ≥ β∗

then it is globally efficient for the home country to permit parallel imports if φ < tβ³14 − 1

9β2

´;

otherwise, it is globally efficient for the home country to prohibit parallel imports. (c) Finally,

if φ ≥ max{π∗Ph ,π∗Nh }, global welfare is independent of the policy choice of either country.

Proof. Suppose the home country permits parallel imports. Then, the home firm serves the

foreign market as long as φ ≤ π∗Ph with the market outcome described by (17) - (22) where

π∗Ph = t

µ4

3β+ 1

¶µβ

2− 13

¶, if V > 2t

µ2

3β+ 1

¶(31)

and

π∗Ph = β(V − t)

µ1− V

4t

¶, if 2t ≤ V ≤ 2t

µ2

3β+ 1

¶. (32)

Note that all consumers buy in the home country so that there is no domestic welfare distortion

in that country. The net welfare in the home country is then given by:

V − t

2+ π∗Ph − φ

and that in the foreign country by:

βV − β

Z q∗Phβ

0txdx− β

Z qPfβ

0txdx− π∗Ph

so that for φ ≤ π∗Ph , global welfare is given by (using (19) and (20):

WP = (1 + β)V − t

2− β

Z q∗Phβ

0txdx− β

Z qPfβ

0txdx− φ

= (1 + β)

µV − t

2

¶+

t

βq∗Ph qPf − φ

which implies that

WP = (1 + β)

µV − t

2

¶+ tβ

µ1

4− 1

9β2

¶− φ, if V > 2t

µ2

3β+ 1

¶(33)

24

whereas

WP = (1 + β)

µV − t

2

¶+ tβ

µ1− V

4t

¶V

4t− φ, if V ≤ 2t

µ2

3β+ 1

¶. (34)

If φ > π∗Ph , then the home firm does not serve the market in the foreign country and global

welfare is given by:

WP = (1 + β)

µV − t

2

¶. (35)

Next, suppose that the home country prohibits parallel import. As before, all consumers in

the home country buy so that there is no distortion in the home country. If the home firm

serves the market in the foreign country, it price discriminates between the two markets and

the market in the foreign country is split evenly between the two firms; the market outcome

is described by (13) and (14). The home firm chooses to export as long as φ ≤ π∗Nh where,

π∗Nh =tβ

2(36)

and in that case, global welfare is given by:

WN = (1 + β)V − t

2− β

Z q∗Nhβ

0txdx− β

Z qNfβ

0txdx− φ

= (1 + β)

µV − t

2

¶+

tβ

4− φ. (37)

If φ > π∗Nh , then the home firm does not export to the foreign country and global welfare is

given by:

WN = (1 + β)

µV − t

2

¶. (38)

Observe that for φ ≤ π∗Ph , from (33) and (34), when the home country allows parallel imports

global welfare satisfies:6

WP < (1 + β)

µV − t

2

¶+

tβ

4− φ.

Comparing to the expression in (37), it follows therefore that for φ ≤ min{π∗Ph ,π∗Nh }, it mustbe that

WP < WN

i.e., it is globally efficient for the home country to prohibit parallel imports and thereby permit

international price discrimination.

6For V ≤ 2t( 23β+ 1), β > 2

3implies V

4t< 1 and therefore (1− V

4t) V4t≤ 1

4.

25

Next suppose φ lies betweenmin{π∗Ph ,π∗Nh } andmax{π∗Ph ,π∗Nh }. Recall the critical countrysize β∗ as defined in (23). Using (24), we have that if β ≤ β∗, π∗Nh ≥ π∗Ph and in that case

for φ ∈ [π∗Ph ,π∗Nh ], global welfare is given by (35) when the home country allows parallel

imports and by (37) when it does not which, in turn, implies that it is globally efficient for

the home country to permit parallel imports if max{ tβ4 ,π∗Ph } ≤ φ ≤ π∗Nh and to not permit if

π∗Ph ≤ φ ≤ minntβ4 , π

∗Nh

o.

If β ≥ β∗ then π∗Nh ≤ π∗Ph and in that case, for φ ∈ [π∗Nh ,π∗Ph ], global welfare is given

by (33) when the home country allows parallel imports, and by (38) when the home country

prohibits parallel imports which, in turn, implies that it is globally efficient for the home

country to permit parallel imports if π∗Nh ≤ φ ≤ minntβ³14 − 1

9β2

´, π∗Nh

oand to not permit

if minntβ³14 − 1

9β2

´, π∗Nh

o≤ φ ≤ π∗Ph .

Finally, note that for φ ≥ max{π∗Ph ,π∗Nh }, global welfare is independent of the policy choiceof the home country.

Proof of Proposition 8

The proof is based on a lemma stated below that evaluates and compares the global

welfare generated when the home country allows parallel imports to that when it does not

(for the case of weak competition). Comparing the globally efficient policy outcome described

in this lemma to the nationally optimal policy outcome (of the home country) described in

Proposition 7 immediately yields Proposition 8.

Lemma 10 Suppose V < 2t (weak competition). If the home firm exports, its export profit is

lower if the foreign country allows parallel imports relative to when it does not i.e., π∗Ph < π∗Nh .

Furthermore, the following hold: (a) Suppose φ ≤ π∗Ph i.e., the fixed cost of exporting is such

that the home firm exports regardless of the parallel import policy of the foreign country. Then,

the globally efficient policy is for the foreign country to prohibit parallel imports. (b) Suppose

π∗Ph < φ ≤ π∗Nh . Then, the home firm exports only if the foreign country prohibits parallel

imports. Given the demand parameters, the globally efficient policy depends on the magnitude

of the fixed cost of exporting (φ). If φ is large enough (within the interval (π∗Ph ,π∗Nh ]), then

it is globally efficient for the foreign country to allow parallel imports whereas if φ is small

enough, then as in part (a), it is globally efficient for it to prohibit parallel imports. (c) If φ

> π∗Nh , global welfare is independent of the two countries’ policies.

Proof. Suppose the foreign country permits parallel import. Then, if the home firm serves the

foreign market it charges identical price in both markets and the market outcome described

26

by (27), (28) and (29). The home firm exports as long as φ ≤ π∗Ph where

π∗Ph = β

µ1

2+1

t

2t− V

8 + 3β

¶µ4V + 3βt

8 + 3β

¶(39)

The net welfare of the home country is then given by:

qPh V −Z qPh

0txdx+ π∗Ph − φ

and that in the foreign country by:

βV − β

Z q∗Phβ

0txdx− β

Z qPfβ

0txdx− π∗Ph

so that for φ ≤ π∗Ph , global welfare is given by (using (28)) :

WP = (qPh + β)V −Z qPh

0txdx− β

Z q∗Phβ

0txdx− β

Z qPfβ

0txdx− φ

= β(V − t

2) + qPh (V −

t

2qPh ) +

t

βq∗Ph qPf − φ

= β(V − t

2) + qPh (V −

t

2qPh )

+tβ

µ1

2+1

t

2t− V

8 + 3β

¶µ1

2− 1

t

2t− V

8 + 3β

¶− φ

< β(V − t

2) + qPh (V −

t

2qPh ) +

tβ

4− φ

where (using (28) and V < 2t),

qPh =1

t

µ4V + 3β(V − t)

8 + 3β

¶<

V

2t.

so that t2q

Ph < V

4 and since the function x(V − x) is increasing on£0, V2

¤, we have

qPh (V −t

2qPh ) =

2

t

∙t

2qPh (V −

t

2qPh )

¸≤ 2

t

V

4

3V

4=3V 2

8t.

Thus,

WP < β

µV − t

2

¶+3V 2

8t+

tβ

4− φ, for φ ≤ π∗Ph , (40)

27

If φ > π∗Ph , then the home firm does not serve the market in the foreign country and we have

local monopoly in each country with the monopoly price being V2 . In this case, global welfare

is given by:

WP = (1 + β)

"µV

2t

¶V −

Z V2t

0txdx

#

= (1 + β)3V 2

8t, for φ > π∗Ph . (41)

Next, suppose that the foreign country prohibits parallel imports. If the home firm exports

to the foreign country, it price discriminates between the two markets, sells the monopoly

quantity V2t in its domestic market while the market in the foreign country is split evenly

between the two firms; the market outcome is described by (25) and (26). The home firm

serves the foreign market as long as φ ≤ π∗Nh where,

π∗Nh =tβ

2. (42)

Thus, when the foreign country prohibits parallel imports, global welfare is given by:

WN = (qNh + β)V −Z qNh

0txdx− β

Z q∗Nhβ

0txdx− β

Z qNfβ

0txdx− φ

= β(V − t

2) + β

t

4+3

8tV 2 − φ, for φ ≤ π∗Nh . (43)

If φ > π∗Nh , then the home firm does not export to the foreign country and we have

WN = (1 + β)3V 2

8tfor φ > π∗Nh . (44)

As stated earlier for V < 2t (see Proposition 3), if the home firm exports to the foreign

country, it earns higher export profit when the foreign country does not allow parallel imports

i.e., the home firm is not allowed to price discriminate

π∗Ph = β

µ1

2+1

t

2t− V

8 + 3β

¶µ4V + 3βt

8 + 3β

¶< π∗Nh = β

t

2.

If φ ≤ π∗Ph , then the home firm exports whether or not the foreign country allows parallel

imports, and comparing (40) and (43), we have WP < WN : i.e. it is globally efficient for the

foreign country to prohibit parallel imports.

28

If φ ∈ (π∗Ph ,π∗Nh ], then the home firm exports only if parallel imports are prohibited by

the foreign country. Comparing (41) and (43), we have

WP −WN = (1 + β)3V 2

8t− β(V − t

2)− β

t

4− 3

8tV 2 + φ

= β

µ3V 2

8t− V +

t

4

¶+ φ

which is positive if φ is close to π∗Nh but, depending on the parameters V and t, may be

negative for smaller values of φ.

Finally, if φ > π∗Nh , global welfare is independent of parallel import policy since the home

firm does not export to the foreign country regardless of its parallel import policy.

29

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