HIAS-E-56

Parallel Imports and Repair Services
Jota Ishikawa
Hitotsubashi University and RIETI

Hodaka Morita
University of New South Wales

Hiroshi Mukunoki
Gakushuin University

October 2017

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8604
http://hias.ad.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:http://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

All rights reserved.

Parallel imports and repair services⇤
Jota Ishikawa†

Hodaka Morita

Hitotsubashi University and RIETI

University of New South Wales

Hiroshi Mukunoki
Gakushuin University
October 13, 2017

Abstract
This study explores the e↵ect of parallel imports on both domestic and foreign countries when
the producer may refuse to provide repair and maintenance services for parallel imported units, or
charge higher prices for those services. This service discrimination makes it possible for the producer
to weaken intra-brand competition and reduce the degree of price convergence between countries. If
this is the case, both the positive e↵ect of parallel imports on consumers in the destination country
and the negative e↵ect on the producer and consumers in the source country become weaker. If
the quality of the good depends on the producer’s investment, permitting parallel imports in thepresence of the service discrimination could lower the quality, because lower quality leads to a larger
price gap between countries. As a result, it is possible that prices increase, consumers lose, andwelfare deteriorates in both countries. This negative welfare e↵ect is more likely to emerge as the⇤ We wish to thank Yasuhiro Arai, Richard Baldwin, Taiji Furusawa, Tadashi Ito, Tomohiro Kuroda, Keisuke Hattori,

Kazunobu Hayakawa, Keisaku Higashida, Toshiyuki Matsuura, Yoichi Sugita, Arijit Mukherjee, Jee-Hyeong Park andparticipants at the conferences and workshops held at Aalto University, Hitotsubashi University, Kochi University, National
Taiwan University, Nova School of Business and Economics, Peking University, and RIETI for their helpful comments andsuggestions. Jota Ishikawa acknowledges financial support from the Japan Society for the Promotion of Science throughthe Grant-in-Aid for Scientific Research (S) Grant Number 26220503, Hodaka Morita acknowledges financial support
from the Australian Research Council, and Hiroshi Mukunoki acknowledges financial support from the Japan Society for
the Promotion of Science through the Grant-in-Aid for Scientific Research (A) and (C) Grant Numbers 24243034 and26380310. The usual disclaimer applies.
† Corresponding author : Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan; Fax: +8142-580-8882; E-mail: jota@econ.hit-u.ac.jp

1liberalization of trade in goods proceeds. The prohibition of service discrimination recovers the
positive welfare e↵ect.
Key words: parallel imports, service discrimination, goods quality, welfare, trade liberalization

1

Introduction

When consumers purchase imported goods, these may be products imported in parallel through distributors not authorized by the original producers, who hold the property rights of those products. These
goods are called “parallel imported goods” (PI goods) or “gray market goods.” PI goods are not counterfeit goods. They are genuine goods purchased from authorized distributors in the source countries andtransported to the destination countries without the consent of the property holders. The unauthorized
distributors, or parallel traders, engage in such trade to profit from price di↵erences of the same good
between markets in di↵erent countries. Specifically, parallel traders earn profits by purchasing the goodin a country where the price of the authorized good is low, and reselling it to consumers in a country
where the price of the same good is high. The end user of a good might also be a parallel trader if
he/she purchases a good in a foreign country and transports it to a di↵erent country.
Because there are no multilateral rules regarding the permission of parallel imports (PIs, henceforth),each country can choose whether to permit or prohibit them.1,2 PIs are mostly permitted in Japan. In the
United States, however, they are only permitted for trademarked goods as long as the US and foreign
trademarks are held by the same owner, or di↵erent owners are in a parent-subsidiary relationship(Maskus, 2000). The EU members only allow PIs from other EU members. Russia has not liberalized
PIs. Although parallel trade is typically observed for pharmaceutical products (e.g., Ganslandt andMaskus, 2004), it also occurs for many other products. NERA (1999) reported that PI goods within
the European Union (EU) include footwear and leather goods, musical recordings, motorcars, consumer
electronics, domestic appliances, cosmetics and perfumes, clothing, and so on. Yeung and Mok (2013)
reported that the market share of parallel imported automobiles in Hong Kong and Singapore was
1 More specifically, countries choose between adopting national exhaustion and international exhaustion of intellectual

property rights. Under national exhaustion, property rights expire only in the market where goods are initially sold. Thus,
the trademark holders can legally prevent PIs. Under international exhaustion, parallel trade is allowed because property
rights expire globally, irrespective of where goods are originally sold by the trademark holders.
2 A few studies have investigated countries’ choices of parallel import policies. In a monopoly model, Richardson (2002)
showed that all countries permit parallel imports in a global Nash equilibrium if they can choose whether to permit orprohibit parallel imports. Roy and Saggi (2012a) investigated strategic interdependence between countries’ PI policies ina North-South model of international oligopoly.

2

15%-25%, and is 15%-17% in the US and the UK.
PIs encourage international price arbitrages and promote international market integration. Fromthe viewpoint of original producers, parallel trade is usually harmful because it limits their abilities todiscriminate prices among countries.3 Basically, permitting PIs reduces prices in destination countries
and raises prices in the source country. If parallel traders are competitive, the price gaps between
countries are reduced to the marginal costs of parallel trade that include tari↵s. The price convergence,
which is often called the full market integration, benefits consumers in the countries that receive PIs
and hurts consumers in the country that originates them.

1.1

PIs and service discrimination

Even if PIs are allowed and parallel traders are competitive, this does not always mean that it leads tothe full market integration. This is because producers might use instruments to mitigate the negativee↵ect of PIs. One possible way is to reduce the substitutability between the authorized units and the
PI units by providing after-sales services, such as repair and maintenance services, only to authorized
products. For instance, Nikon Inc. USA, a subsidiary of the Japanese company of optical instruments,
Nikon, does not provide support or a warranty service on parallel imported items, including fee-based
repair work.4 Samsonite, the US luggage manufacturer, employs the same policy in Japan. World
Commerce Corp, the Japanese authorized distributor of the Swiss watch company, Franck Muller,
refuses to repair parallel imported watches. Firms also discriminate prices in after-sales services and set
higher maintenance and repair prices for PI units, while they provide free repairs or charge a lower fee
for authorized units. An empirical analysis supports the view that discrimination in after-sales services
weakens intra-brand competition between authorized goods and parallel imported goods. Chen, Lai, and3 Some analyses have suggested that permitting parallel trade may increase the profit of the producer.

Anderson and

Ginsburgh (1999) suggest that a monopolist might use consumers’ arbitrage activities through parallel importation toundertake second-degree price discrimination, if arbitrage costs di↵er across consumers. Knox and Richardson (2002)
show that parallel imports may benefit the producer because they reduce the optimal tari↵ of the destination country.
Ra↵ and Schmitt (2007) found that, in the presence of demand uncertainty, parallel imports lead to larger orders fromretailers because they enable retailers to ship unsold inventories to countries where demand turns out to be unexpectedly
high. In a duopoly model, Matsushima and Matsumura (2010) found that permitting parallel imports increases profits ofall firms because it serves as a commitment device to soften price competition in the destination country. Roy and Saggi(2012b) also showed a similar commitment e↵ect of parallel imports in a di↵erent setting. Mukherjee and Zhao (2012)
pointed out that parallel imports have the wage reducing e↵ect in unionized markets.
4 Nikon Inc. USA declares in its website: “Nikon Inc. USA cannot provide any technical support or warranty service
on Gray Market items. Additionally Nikon Inc. USA cannot perform any fee-based repair work on Gray Market items.
Please do not contact Nikon Inc. USA for help with any Gray Market products.”3

Yu (2013) investigated Taiwan’s Yahoo! auctions of Nikon cameras and showed that authorized goods
with a longer duration of warranty and that are repaired by the official dealers have higher transaction
prices than PI goods.
Given this background, this study theoretically examines the e↵ect of PIs when a producing firm
may refuse to provide repair and maintenance services or may set a higher repair price for a PI good.
In this study, refusal of repairs and price discrimination in repair services are together referred to as“discrimination in repair services” or simply “service discrimination.” Specifically, we investigate a firm’s
incentive to discriminate repair services, and how the welfare e↵ect of permitting PIs is associated withsuch a business practice. In our model, the di↵erence in the demands for the good induces the firm to
set di↵erent prices in di↵erent countries. There are many parallel traders, and the competition among
them reduces the price of the PI good by an amount equal to the sum of the price of the authorized
good in a low-priced country and a tari↵. This implies that, in the absence of service discrimination, theprice di↵erence between the two countries reduces to the level of tari↵s. We call this price convergence
full market integration.
We find that service discrimination works as a tool to weaken the intra-brand competition and makes
the domestic and foreign markets only “partially” integrated. Partial market integration means that thefirm cannot fully discriminate prices, but can still charge a higher price in a high-demand country thanin a low-demand country. By discriminating services, the firm intentionally decreases the attractivenessof the PI good and makes the authorized good and the PI good vertically di↵erentiated. The servicebased product di↵erentiation reduces the degree of price convergence and the firm can partially recover
its loss from its inability of discriminating prices between countries. Therefore, the firm always prefers
discrimination in terms of repair services for the PI good. It is worth noting that the firm is willingto discriminate services only if it faces PIs. In other words, the firm has no incentive to sell the goodthat is not subject to repair services in the absence of PIs (see Section ?? for details). We should take
into account service discrimination to discuss the economic impacts of parallel trade, because they are
inseparably related.

1.2

Service discrimination and welfare e↵ects of PIs

With regard to the welfare e↵ects of PIs, they critically depend on whether repair services are discriminated against the PI good, and also on whether the likelihood of the product’s breakdown, referred toas the quality in our model, is exogenously given or endogenously determined. The purchased goods
may break down for a variety of reasons including inappropriate quality control and inspections in the4

production process, careless handling of the goods during their storage and distribution, and consumers’
inadequate ways of using the goods. The producer can reduce the likelihood of breakdown (or increase
the quality of the product) by undertaking costly activities such as intensive quality control and inspections, provision of training to workers involved in storage and distribution of the goods, and developmentof user-friendly manual for consumers. Higher quality product is less likely to break down and lower
quality product is more likely to break down. If the repair services are not provided, the consumer’s
expected utility is increasing in the product quality, whereas, if the repair services are provided, theconsumer’s utility is not directly a↵ected by the product quality in our model. The quality of the product, however, indirectly a↵ects the consumer’s utility because consumers may pay more to bear the costof repairs.
Let us first summarize the welfare e↵ects of service discrimination given the level of the productquality. Compared to the case of full market integration, the price in a high-demand country becomes
higher and consumers in the destination country su↵ers from service discrimination, given the level ofproduct quality. The service discrimination, however, decreases the prices and benefits consumers in thesource country. Thus, given the level of product quality, service discrimination worsens the welfare of
the destination country and world welfare, while it benefits consumers and the producer, and improves
the welfare of the source country. Nevertheless, permitting PIs with service discrimination realize lower
price in a high demand country compared with the price under market segmentation. With the fixed
quality of the product, permitting PIs always benefits consumers, improves the welfare in the destination
country, and improves world welfare, while it hurts both consumers and producers and also worsens thewelfare in the source country.
The producer’s endogenous choice of the product quality substantially changes the welfare e↵ects ofpermitting PIs. Specifically, permitting PIs may worsen consumer surplus and welfare in all countries
in the presence of service discrimination, while it has the same directions of welfare changes as thosewhen the quality is fixed in the absence of service discrimination.
Not only PIs a↵ect prices, but also they a↵ect innovation activities. For example, PIs may lead toless cost-reducing R&D, or a deterioration of the quality of products and/or the quality of before- andafter-sales services. This is because the inability to discriminate prices between markets may reduce thegains from producers’ investments in improving the quality of their products and services (Grigoriadis,2014). Then, an intriguing question is that whether those incentives depend on service discrimination.
Among others, we focus on how PIs a↵ect the quality of the product, when the firm engages in costly
activities to improve it.

5

We show that the e↵ect of parallel imports on the quality depends on whether the firm discriminates
repair services. Our findings show that if the firm does not discriminate services and parallel imports
realize full market integration, permitting PIs has no e↵ect on the quality of the good that the firm
determines. Without service discrimination, the price gap between the two countries is independentof the quality. Besides that, irrespective of whether parallel trade is permitted or not, changes in thequality have the same e↵ect on prices and sales in each market. Then, permitting PIs does not change
the e↵ect of an increase in the quality on the firm’s profit and the firm chooses the same level of quality
in equilibrium.
In contrast, PIs with service discrimination may lower the quality of the good that the firm chooses.
This is because a lower quality reduces the substitutability between the authorized good and the PI
good, which weakens intra-brand competition or generates a greater profit opportunity in the repair
market of the PI good. The lower quality hurts consumers who purchase the PI good in the destination
country, because their expected utilities decline. The lower quality also hurts consumers who purchase
the authorized good in both countries. This is because a lower quality increases the firm’s expected costfor repairs and this cost increase is passed through to the price of the authorized good, at least partly.
If this e↵ect is large enough to exceed the price-reducing e↵ect of (partial) market integration in thedestination country, permitting parallel imports may increase the prices of the good in all countries,
hurt consumers in all countries, and worsen welfare of all countries.
The e↵ect of trade liberalization on the optimal quality also depends on the firm’s service discrimination. Trade liberalization basically reduces the firm’s cost of exporting and increases the firm’s gains
from improving the quality and reducing the expected unit cost for repairs. Hence, trade liberalization
leads to higher quality if parallel trade is prohibited or parallel trade does not come with service discrimination. With service discrimination, however, trade liberalization may induce the firm to set lower
quality. Because trade liberalization reduces the cost of conducting parallel trade, it gives the firm more
incentive to di↵erentiate the authorized good and the PI good by setting lower quality. If this additional e↵ect is large enough, the firm has a stronger incentive to lower the quality as the tari↵ becomes
lower. Thus, permitting PIs with service discrimination can hurt consumers and worsen the welfare in
the destination country, and this becomes more likely as tari↵s fall. These results suggest that, in thepresence of service discrimination, the progress of trade liberalization may transform welfare-improving
parallel imports into welfare-worsening parallel imports.
These contrasting results provide novel policy implications (see Section 4.3). To evaluate the welfaree↵ects of permitting PIs, it is important to take into account the firm’s service discrimination and its

6

e↵ects on the firm’s choice of the product quality.

1.3

Relationship to the Literature

In our model, service discrimination allows the firm to increase its overall profit by vertically di↵erentiating the quality of authorized good and the PI good. The idea that parallel importation allows the
manufacturer to vertically price discriminate between the authorized good and the PI good has beenpreviously studied by Ahmadi and Yang (2000). In their model, consumers discount their valuationon the PI goods compared to the authorized goods because of the inconvenience due to market-specificproduct di↵erentiation or due to service di↵erentiation (e.g., the lack of technical support and warranty). Hence Ahmadi and Yang’s (2000) model is not designed to compare cases in which services
are discriminated and they are not discriminated, whereas such a comparison is a key element of ouranalysis. We compare welfare e↵ects of permitting parallel imports under service discrimination andnon-discrimination, and show that the comparison result becomes di↵erent in an important way when
we endogenize the determination of product quality. Furthermore, we show that the e↵ect of trade liberalization on the optimal product quality also depends on whether or not the service is discriminated.
In contrast, Ahmadi and Yang (2000) focus on the e↵ect of parallel imports on the firm’s profitability
and they do not study the welfare e↵ects of parallel imports or the endogenous determination of productquality.
This paper has considered the repair services in the context of international trade. Ishikawa, Morita,
and Mukunoki (2016) investigate how the welfare e↵ects of trade liberalization depend on whether andby whom repair services are provided. They show that trade liberalization may hurt the consumers of
the importing country and world welfare, if it is not accompanied by FDI in repair services. However,their paper does not consider the e↵ects of parallel imports.
In both Ahmadi and Yang (2000) and Ishikawa, Morita, and Mukunoki (2016), the quality of thegood is exogenously given. However, parallel imports and repair services could a↵ect the quality of thegood a producer chooses. The distinctive feature of this paper is that it takes into account the firm’s
choice of the product quality that changes the likelihood of the product’s breakdown, and discusses
how the discrimination in repair services a↵ects the quality choice and the welfare e↵ects of permitting
PIs. The paper also provides a new result with respect to how the e↵ects of PIs are connected to thedegree of trade liberalization. We will show that, in the presence of service discrimination, the welfare
consequence of permitting PIs is more likely to be negative as trade liberalization proceeds.
There have been some analyses which investigate how permitting PIs a↵ects firms’ incentives to7engage in R&D activities. Li and Maskus (2006) explore how PIs inhibit the firm’s cost-reducing
R&D activities. Valletti (2006) shows that parallel imports reduce the quality of the product whendi↵erential pricing is demand based but raise the quality when it is cost based. In a North-South model,
Grossman and Lai (2008) show that parallel trade promotes product innovation because it induces theSouthern government to change their price control in favor of Northern firms. Matteucci and Reverberi(2014) suggest there is a case where PIs enhance a quality-enhancing R&D, when the quality a↵ects
the consumers’ willingness to pay di↵erently between the source and the destination countries. Hwang,Peng, and Shih (2014) suggest whether PIs promote product innovation depends on the market structureof the destination country and the number of the distributors that engage in parallel trade. However,none of these papers has considered how PIs a↵ect the quality of the product when a lower quality
means a higher failure rate of the product and the broken units become reusable by repair services.
Quality of the product in our paper has similarity to durability of the product, which has beenstudied in the industrial organization literature. And several papers in the literature have shown thatdurable-goods producers may intentionally reduce durability of their products. For instance, Bulow(1986) showed that a durable goods monopolist may reduce the durability of its output to reduce its
time inconsistency problem. Waldman (1996a,b) claimed that the monopolist has incentive to reducethe durability to reduce the competition between the new units and the old units. More recent papers
such as Choi (2001), Fethke and Jaganatthan (2002), Goering and Pippenger (2002), Goering (2007)
and Strausz (2009) also considered endogenous determinations of durability. None of them, however,considered the e↵ect of PIs on the firm’s choice of durability, let alone how they are related with service
discrimination.
The existing studies show that welfare e↵ects of PIs are much more complicated than it seems.
Malueg and Schwartz (1994) investigated how uniform pricing induced by parallel importation a↵ects
global welfare. They showed that permitting PIs yields lower global welfare if many markets become
unserved by the monopolist. Ishikawa (2004) examined a move from segmented to integrated markets
in a monopoly model. Generally speaking, permitting PIs promotes price arbitrages and makes markets
more integrated. The analysis showed that the welfare e↵ects of the integration crucially depend on theextent of arbitrage and the shape of the marginal cost curve. Maskus and Chen (2004) and MuellerLanger (2012) used a model of vertical control to show that allowing PIs improves global welfare if thecost of undertaking parallel trade is low, but reduces global welfare if the cost is high. In this paper,
we show that welfare e↵ect depends on whether the producer discriminates repair services against the
PI good, and also whether it optimally chooses the level of the product quality.

8

The remainder of the paper is organized as follows. Section 2 develops a monopoly model in whicha purchased good may need repair services, and derives the equilibrium without PIs and that underPIs without service discrimination. Section 3 investigates the equilibrium the equilibrium under PIs
with service discrimination. Section 4 compares the equilibrium outcomes, discusses the welfare e↵ects
of parallel imports, investigates how the endogenous determination of the quality changes them, andprovides some policy implications. Section 5 relaxes some assumptions of the basic model and discusses
the robustness of the results. Section 6 summarizes the paper and o↵ers concluding remarks. Lastly,
the appendix contains the proofs of some propositions in the paper.

2

Model

We consider a two-country model with a single firm in the foreign country (country F ) that produces
good x, which it supplies locally and to the domestic country (country D). An import tari↵, t, is
imposed on good x by the domestic country. Each consumer purchases at most one unit of good x.
Consumers in country i (i = D, F ) are identical except in their willingness to pay for the good. If
consumer j in country i purchases the good at price pi , its utility is given by Uji = vj

pi , where vj is

the consumer j’s willing to pay for the good. We assume each consumer’s utility under no purchase isnormalized to zero. The population in each country is identical and given by n, though the distributionof the willingness to pay is di↵erent across the two countries. In this model, only the distribution of vj
in each country matters for the equilibrium outcomes. Therefore, we henceforth omit the subscript jfrom Uji and vj and each consumer’s utility is denoted by Ui = v
distributed over the interval [0, b] with density fD = 1b .

pi . In country D, v is uniformly

In country F , v is uniformly distributed over1
the interval [0, kb] with density fF = kb
, where k is positive and k < 1. This means that consumers incountry D, on average, attach a higher value to good x.
If parallel trade is allowed, consumers in each country can purchase the good from either authorized
distributors controlled by the firm or other distributors who purchase the good in the other country
and resell it through parallel trade without authorization. We call the good purchased from authorized
distributors “the authorized good” and that purchased from parallel importers “the PI good.”
After consumers purchase the goods, they may break down because of imperfect quality control. The
probability of the good working correctly is q 2 (0, 1) , which is referred to as quality (see Section 1.2
for a discussion) and it is common to both the authorized good and the PI good. Hence, the probabilityof the good breaking down is (1q). If the consumers utilize repair services provided by the producing

firm, the broken good becomes consumable. However, without repair services, broken goods are useless9and have zero scrap values. We assume if a consumer purchases the authorized good, the good is subject
to free repairs.5 However, the firm may refuse to repair the PI good or charge a fee for the repair. The
unit cost of production for the firm is given by c (> 0), and the unit cost of repairs is given by m, whichshould be lower than c.
If parallel trade is allowed, many competitive parallel traders can purchase the good in the country
where the price is low and sell it to the country where the price is high. For simplicity, we assume
parallel traders incur no additional cost other than the tari↵. We only focus on the situation where thefirm always provides the good in both countries.
We consider the following three situations: (i) Regime N in which parallel imports are banned incountry D; (ii) Regime I in which PIs are allowed and the firm provides the same repair services to theconsumers purchasing the PI good as those provided to the consumers of the authorized good; and (iii)
Regime R in which PIs are allowed and the firm discriminates the repair services against the PI goodby either refusing to repair the PI good or charging a fee for the repair. We show that refusing repairs
and charging for repairs of the PI good have the same e↵ect on the equilibrium prices and welfare (seeSection 5.1 for details). These firms’ behaviors are referred to collectively as service discrimination.
The model has four stages. In the first stage, the firm sets authorized prices in country D andcountry F in all three regimes. In the second stage, consumers in each country purchase the authorized
product in all three regimes. If parallel trade is permitted (Regime I and Regime R), parallel traders
may also purchase the authorized product in this stage. In the third stage, nothing happens in Regime
N . In Regime I and Regime R, however, parallel traders export the purchased good to other countries
and sell it to consumers who purchase the PI good, if parallel traders earn non-negative profits. Thereis no time discounting between the second stage and the third stage. Thus, consumers always wait until
the third stage if they anticipate that purchasing the PI good will generate higher utility. In the fourthstage, consumers find whether the purchased unit is broken. In Regime N and Regime I, any purchasedunit is subject to free repairs and consumers always utilize repair services. In Regime R, however, only
the broken units of the authorized product are subject to free repairs and the broken units of the PI
product remain unrepaired if the original producer refuses to repair the PI units. If the purchased unitsof PI product are subject to fee-based repair services, consumers choose whether they pay for them.
5 We confirm that the firm is willing to o↵er a full warranty for the authorized good. See Section 5.1.

10

2.1

No parallel imports

As a benchmark, we start with Regime N , where PIs are prohibited. In this case, the markets of the twocountries are completely segmented (full segmentation). The monopolist is able to make independent
decisions in setting the prices in each country. Let pi denote the price the consumer pays. A consumer
in country i purchases the good if Ui = v

pi

0 holds. Under market segmentation, all consumers

purchase the authorized good if they buy. Therefore, pi coincides with the price of the authorized goodin country i. The consumers whose willingness to pay for quality satisfies v

pi purchase the good.

The demand for good x in each country is given byxD (pD )=xF (pF )=⇣pD ⌘pD ) = n 1
,
b ⌘
⇣
pF
nfF (kb pF ) = n 1.
kb
nfD (b(1)(2)

Let p = fF pF + fD pD = (pF + kpD )/bk denote the average price of the good weighted by the densitiesof the preference distribution. Then, the total consumption of the good becomesX(p) = xD (pD ) + xF (pF ) = n (2

p) .

(3)

The firm’s profit is given by⇧ (pD , pF ) = (pDt)xD (pD ) + pF xF (pF ){c + (1q) m}X(p).

(4)

The first two terms represents the tari↵-exclusive revenues from selling in the two countries, and thelast term represents the sum of the firm’s total cost of production and the expected total cost of repairs.
The firm maximizes this profit with respect to pD and pF . By solving the first-order conditions, theequilibrium prices are given by
peN
D
peN
F

=
=

b + c + t + (1 q) m,2
kb + c + (1 q) m
.
2

(5)
(6)

Note that these prices are decreasing in q, because higher quality means a lower failure rate of the
product and thereby decreases the firm’s expected cost of repairs, reducing the optimal prices of theauthorized good.6 To ensure positive sales in each market, xD peN
eN
D > 0 and xF p
F > 0, we assumeb > max[{c + (1by pNq) m}/k, c + t + (1q) m] holds. The equilibrium average price of the good is given

= (e
pN
pN
F + keD )/bk.

6 Section 5.5 discusses what happens if the production cost is positively related to the quality.

11

By comparing the equilibrium prices, we havepN ⌘ peND

peN
F = {(1k) b + t}/2 > 0. This implies

that the firm sets a higher price in the domestic country where consumers’ willingness to pay for thegood is, on average, higher than in the foreign country.7

The equilibrium cut-o↵ level of v, above which consumers purchase the good in each country, becomesN
veiN = peNeNeN
i . The equilibrium profits are given by ⇧ = ⇧ p
D, p
F and the equilibrium consumer surplus

in country F and country D are, respectively, given by
N
CSD

=

n
b
b

CSFN

=

nF f F

N
veD

Z kb



(v

N
v
eF

N
b + veD
2

peN
D =

peN
F )dv =

n b

peN
D
2b

n kb peN
F
2kb

2

,

(7)

2

.

(8)

N
N
N
N
N
The equilibrium welfare of each country is given by WD= CSD+ txD peN
D and WF = CSF + ⇧ ,Nand the equilibrium world welfare becomes W W N = WD
+ WFN .

2.2

Parallel imports without service discrimination

If parallel trade is allowed, the price di↵erence of good x between the two countries creates an opportunity
for parallel trade. Since there are many competitive parallel traders, the price of the PI good in country
D becomes pF + t.
The firm is able to choose whether it provides free repair services for the good sold by unauthorized,
parallel traders. Suppose it does do so (Regime I). Then, the good sold directly by the authorized
distributors and the good sold by parallel importers are perfect substitutes. This means that if the priceof the authorized good, pD , is higher than pF + t, all consumers purchase the PI good. Each consumer’sutility in country D is given by UD = v

min[pD , pF + t].

By (5) and (6), if the producer sets the same prices of the authorized goods as those without PIs,
then the price gap between the authorized good and the parallel imported good becomesIf (1k)b  t holds, we have

peN
D

(e
pN
F + t) =

pN

t=

(1

k)b
2

t

.

(9)

pN  t, implying that the price of the PI good, peN
F + t, is higher than theprice of the authorized good, peN
D . In this case, no consumers in country D purchase the PI good even if

the producer charges peNeNeNeN
D and pF . Then, the producer will set p
D and pF in equilibrium and permitting
7 For simplicity, we only focus on the case with k < 1 where p
eN
eN
D > p
F

an oligopoly model (see Section 5.4), when peND
antidumping policy against the foreign firm.

< peN
F

holds in this paper. Note that if we consider

holds, the government in the domestic country may implement

12PIs has no e↵ects on the equilibrium prices and welfare.8 To explore the e↵ects of permitting PIs, we
put the following assumption throughout the paper.
Assumption 1 (1k)b > t holds.
pN > t holds, with which all consumers buy the PI good if the firm

Assumption 1 ensures thatsets the same prices as those charged under full market segmentation. We can confirm that the firm
has no incentive to set pD lower than pF + t given
pD

pN > t holds. This implies that the firm sets

pF + t and consumers in country D always pay pF + t if they purchased the good. If the firm sells

the authorized good by setting the price pD = pF +t and consumers purchase it, it receives pD but needs
to incur the tari↵, t. If pD > pF + t holds and consumers purchased the PI good, the firm receive pF
from selling the good to parallel traders and it doesn’t need to incur t. In either case, the producer pricethat the firm receives from serving the good in country D becomes pF . In other words, the threat ofparallel trade makes the two markets completely integrated and the equilibrium price di↵erence between
the two markets is always equal to the tari↵ level.
Consumers purchase the good if Ui

0 holds, and the demand in country F is given by (2) and thedemand in country D is obtained by substituting pF + t for pD in (1). The firm’s profit is obtained bysubstituting pF + t for pD in (4), which is given by⇧ (pD , pF ) = [pF{c + (1q) m}]X(p).

(10)

The weighted average price, p, is now given by p = (kpD + pF )/bk = {(1 + t)k + 1}pF /(bk).
The firm maximizes (10) with respect to pF . Then, the respective equilibrium prices that consumers
pay, peID and peIF , become:

peID
peIF

=
=

peIF + t = peN
D
peN
F +

k
(1 + k)1( pN(1 + k)

pN

t ,

t).

(11)
(12)

Note that the equilibrium prices are the weighted average of the equilibrium prices under market segmentation. The equilibrium cut-o↵ level of v in each country becomes veiI = peIi . We have peID < peN
D andpeIF > peN
F implying that PIs without service discrimination increase price in country F and decrease theprice in country D. The price gap of the authorized good between countries becomesApparently,

pI <pI ⌘ peID peIF = t.

pN is satisfied and allowing parallel imports decreases the price gap between the

countries. The equilibrium average price of the good is given by pI = (epIF + kepID )/bk, and pI = pN

8 As we will see in the following analysis, the producer’s profit is maximized when it charges the prices under Regime

N . Therefore, the producer has no incentive to discriminate services if (113k)b  t holds.

holds. Given the uniform distribution of v in each country, the price gap under PIs without service
discrimination becomes a mean-preserving contraction of the price gap without PIs. Since the total
consumption of the good, which is given by (3), depends only on the average price, permitting PIs
without service discrimination has no e↵ect on the total consumption of the good.
Figure 1 depicts the equilibrium prices without PIs and PIs without service discrimination. In the
figure, the dd curve and the f f curve represent the demand curve for the good in country D and thatin country F , respectively.
[Insert Figure 1 around here]
The equilibrium profit becomes ⇧I = ⇧ peID , peIF

and the respective equilibrium consumer surplus

in each country is given by

I
CSD

=

CSFI

=

nfD
nfF

Z b

(v

I
v
eD

Z kb

(v

peID )dv =Iv
eF

peIF )dv =n{b(epIF + t)}2,2bn kb peIF
2kb

(13)

2

.

(14)

I
I
The equilibrium welfare of each country is given by WD= CSD+txD peID and WFI = CSFI +⇧I peID , peIF ,I
and the equilibrium world welfare becomes W W I = WD
+ WFI .

2.3

Parallel imports with service discrimination

We now investigate Regime R, where the firm discriminates repair services by either (i) refusing to repair
the PI good or (ii) charging a positive fee for the repair. Let peR
i denote the equilibrium price of theauthorized good in country i and ⇧R and CSiR are the equilibrium profit of the firm and the equilibrium

consumer surplus in country i, respectively. We can show that both (i) and (ii) qualitatively yields thesame equilibrium outcomes and welfare. The detailed analysis is provided in Section 5.1. Here, wechoose the case with the refusal of repairs to derive the equilibrium under service discrimination.
Suppose the firm refuses to repair the PI good (Regime I). The equilibrium prices, profit, andconsumer surplus are respectively given by peIi , ⇧I , and CSiI . However, if q < 1, the authorized good
and the PI good generate di↵erent expected utilities, even if they are sold at the same price. Specifically,
if a consumer in country D buys an authorized good at price pD , his/her utility becomes
A
UD
=v

pD .

(15)

Suppose that consumers are risk neutral. If the consumer buys a PI good at price pF + t, then his/her
expected utility becomes
PI
UD
= qv

(pF + t) .
14

(16)

A
Let vDbe the preference parameter of the consumer who is indi↵erent between buying an authorizedA
PI
PI
good and a PI good (UD= UD), and vD
be the parameter for the consumer who is indi↵erent between
Ubuying a PI good and no purchase (UD= 0). We have
A
vD

=

PI
vD

=

pD

(pF + t),1 q
pF + t
.
q

(17)
(18)

A
PI
By comparing vDand vD, we have
A
vD

PI
vD
=

qpD (pF + t).
(1 q)q(19)This means that if pD > (pF + t) /q holds, which means that the “quality-adjusted price” of the PI goodAis lower than the price of the authorized good, consumers with preference parameter v 2 [vD, b] buy thePIAauthorized good and consumers with parameter v 2 [vD, vD] buy the PI good. Even if the price of the

PI good is lower than that of the authorized good, the consumers with high v buy the authorized good
because the price di↵erence is insufficient for them to compensate for the risk of the good being broken
down and not being repaired. The consumers with low v buy the PI good because they value the goodless and are more sensitive to the price of the good.
A
PI
If vD
> vD
holds, both the authorized good and the PI good are purchased in equilibrium. If
A
PI
A
vD
 vD
holds, all consumers purchase the authorized good. The equilibrium ranking between vD
and
PI
vD
and the firm’s optimal pricing depend on the quality of the product, q.

There exist threshold values qH and qL , 0 < qL < qH  1.9 The equilibrium pattern of consumption
depends on the level of q: (i) high quality (q 2 (qH , 1)), (ii) middle quality (q 2 (qL , qH )), and (iii) low
quality (q 2 [0, qL )). This implies that the functional forms of consumer surplus and the firm’s profit
may take di↵erent forms. Specifically, in all three cases, the equilibrium consumer surplus in country F
is given by
CSFR =

n bk peR
F
2kb

2

.

(20)

However, the equilibrium profit and the equilibrium consumer surplus take the di↵erent forms dependingon the level of q. In the following, we elaborate the equilibrium prices, the equilibrium profit, and theequilibrium consumer surplus in the three cases.
9 Note that q

H is strictly smaller than 1 if b and m are large and c and t are small. See the proof of Lemma 2.

15

2.3.1High quality

Suppose q 2 (qH , 1) holds, then the demand for the authorized good and the demand for the PI goodin country D are, respectively, given byxA
D (pD , pF )=I
xP
D (pD , pF )

=

⇥
nfD b

⇥ A
nfD vD


⇤
A
vD
=n 1

pD

(pF + t),q)b⇤qpD (pF + t)
PI
vD
=n
,
(1 q)qb
(1

(21)
(22)

while the demand in country F is given by (2). An increase in pF not only raises the price of the goodin country F , but also the price of the PI good in country D. These price changes increase the demand
for the authorized good and decrease the demand for the PI good. An increase in pD , on the other
hand, has the opposite e↵ects. The sum of the consumption of the authorized good and that of the PI
good in country D becomes

PI
xA
(p
,
p
)
+
x
(p
,
p
)
=
n
1
D
F
D
F
D
D

(pF + t)
.
bq

(23)

It depends on the quality-adjusted price of the PI good. The total consumption of the good is given byPI
X + (p, pF ) = xF (pF ) + xA
D (pD , pF ) + xD (pD , pF ) = X(p)n(1q) (pF + t)
·
bq

(24)

We have confirmed in Section 2.1 that, without service discrimination, the total consumption is independent of q. Here, the total consumption depends on q. Given the prices, an increase in the quality
increases the total consumption because it decreases the e↵ective price of the PI good. The firm’s profit
is given by⇧+ (pD , pF )=PI
pD x AD (pD , pF ) + pF xF (pF ) + pF xD (pD , pF )(1q) m{xF (pF ) + xA
D (pD , pF )}cX + (p, pF ).

(25)

The third term of this equation is the revenue earned from selling the good to the parallel traders. By
solving @⇧+ (pD , pF )/@pF = 0 and @⇧+ (pD , pF ) /@pD = 0, the equilibrium prices of this case become:
peR
D

peR
F

=
=

peR
F +t+
peN
F +

(1

k[b (qq)(b + m)⌘ pbD ,
2k) {t + (1 q) m}]⌘ pbF .
2 (q + k)

The price gap of authorized good between the countries becomespR ⌘ peR
D

(26)
(27)
peR
F . It is apparent thatpR > t holds and the price di↵erence between the two markets does not reduce to the level of thetari↵. In other words, the two markets are not fully integrated, but only partially integrated. The extra
price di↵erence over the tari↵ level is due to the “quality premium” of the authorized good, because16the authorized good is subject to free repair services and its expected quality is higher than that of the
PI good. Here, the quality premium is given by peRD(epR
F + t) =pR

t = (1q)(b + m)/2 > 0. As

q decreases, consumers in country D regard the authorized good and the PI good as becoming morevertically di↵erentiated, and the firm is able to discriminate more on pricing. The equilibrium averageRprice of the authorized good, pR = (epR
> pN = pI and permitting PIs withpR
F + keD )/bk, satisfies p

service discrimination reduces the total consumption of the good.10 By (3) and (24),Figure 2 depicts the equilibrium prices in this case. Here, the dd curve represent the overall demand
curve for the authorized good and the PI good, which is given by (23). The quality-adjusted price of the
PI good, (epR
F + t)/q, determines the total sales. Then, the aa curve in the figure represents the demand
for the authorized good, which is given by (21). Given the price of the authorized good, peR
D , the salesof the authorized good is determined on the aa curve. The total sales minus the sales of the authorized
good corresponds to the sales of the PI good.
[Insert Figure 2 around here]
The equilibrium profit of this case is given by ⇧R = ⇧0 peReRD, p
F , and the equilibrium consumer

surplus in each country is given by
R
CSD

=
=

nfD
n b

"Z

b

(v
A
v
eD

peR
D
2b

2

+

peR
D )dv +

A
Z veD
PI
v
eD

{qv

(e
pR
F + t)}dv

#

2
n{qe
pR
peR
D
F +t }.
2bq (1 q)(28)

The first term of (28) represents the surplus that would have been obtained if all consumers purchased theauthorized good given peReR
D . In equilibrium, some consumers purchase the PI good at p
F +t. Consumers of
the PI good include those who would have purchased the authorized good if the PI good is unavailable.
They also include new consumers who did not purchase the authorized good at peR
D . These demand shifts

and new purchases generates the consumers’ gains from purchasing the PI good.11 The second term of(28) represents this additional consumer surplus.
2.3.2

Middle quality

Suppose q 2 (qL , qH ] holds. In this case, the firm opts to block PIs by setting pD = (pF + t) /q, rather
than accommodating them. In this case, the firm maximizes (4) subject to pD = (pF + t) /q. The
10 We can calculate that pR

X(pR )}

n(1

q)

peR
F +t

pN = (1/(bq) < 0.

q) (e
pR
F

0 R eR )peNF ) > 0. By (3) and (24), X (p , p
F

X(pN ) ={X(pN )

11 More specifically, if the PI good is unavailable, consumers of the PI good with v 2 [eA ) would have purchased the
pR
eD
D, v

PI, p
authorized good while those with v 2 [evDeRD ) would not have purchased the authorized good.

17

optimal prices become:
peR
D

peR
F

=
=

ke
pN
pN
D + q(eF + t)⌘ p̀D ,
k + q2k(qepNt) + q 2 peN
DF⌘ p̀F .
k + q2

Because peR
eR
eR
D = p
F + t /q > p
F + t holds, we have

(29)
(30)

pR > t. The firm is able to make the pricedi↵erential between the two countries more than the tari↵ level. The quality premium of the pricedi↵erence is
peR
D

(e
pR
F + t) =

pR

t=

(1

q)
q

(e
pR
F + t) > 0.

(31)

R
N
I
12
The equilibrium average price of the good is given by pR = (epRpR
F + keD )/bk, and p > p = p holds.

Since the total consumption of the good is given by (3) in this range of q, PIs with service discrimination
decreases the total consumption of the good.
Figure 3 depicts the equilibrium prices in this case. Since peRpR
D = (eF + t)/q holds, consumers purchase

only the authorized good in equilibrium.

[Insert Figure 3 around here]
The equilibrium profit is given by ⇧R = ⇧(e
pR
eR
D, p
F ) and the equilibrium consumer surplus in countryR
D becomes CSD
= n(b

2.3.3

Low quality2peRD ) /2b.

Finally, suppose q 2 (0, qL ] holds, all consumers in country D prefer the authorized good, if they buy
one. In this case, peNpN
D < (eF + t)/q holds. This implies that the firm is able to block PIs, even if itcompletely discriminates the prices between the two countries. Therefore, the firm charges peR
eN
F =p
F and

peR
eN
D = p
D in equilibrium. Here, the firm’s refusal to repair by itself blocks PIs, making the two markets
completely segmented. The equilibrium price gap satisfies

pR =

pN .

The equilibrium profit and the equilibrium consumer surplus in country D are respectively given byRN⇧R = ⇧N and CSD= CSD.

In summary, the equilibrium price in country i, peReR
bi if qH 6= 1 and q 2 (qH , 1),
i , becomes p
i = p

peR
eR
eN
i = p̀i if q 2 (qL , qH ], and pi = pi if q 2 (0, qL ]. In all three cases, the equilibrium welfare of

R
R
PI R
R
R
R
each country is given by WD= CSD+ t{xApReR
pD , peRD (eD, pF ) + xD (eF )} and WF = CSF + ⇧ , where
I R
R
R
xP
pD , peR= WD+ WFR .
D (eF ) = 0 for q  qH . The equilibrium world welfare becomes W W
12 We have pR

pN = k(1

q){qe
pN
D

2
(e
pN
F + t)}/(k + q ) > 0.

18

3Price e↵ects of permitting parallel imports

In Section 2, we have derived the equilibrium prices under three regimes (N , I, an R). Here, we compare
the equilibrium prices given the level of the quality to explore the price e↵ects of parallel imports.
If there is no service discrimination, permitting PIs changes the regime from Regime N to Regime
I. We have the following lemma.
Lemma 1 Given the level of q, peNeIF < peID < peN
eIF + t = peID hold.
F <p
D and pWithout service discrimination, parallel imports make the two markets completely integrated, andthe producer price of selling the good is given by pF = pDt, no matter where the firm sells the good.

Then, the profit-maximizing prices becomes the weighted average of the equilibrium prices under market
segmentation. As a result, the firm increases the price in the foreign country and decreases the price inthe domestic country such thatpI = peID

peIF = t is realized. As is shown in section 2.2, peID < peN
D andpeIF > peN
F hold and the consumers in foreign country are indi↵erent between purchasing the authorized
good and the PI good.

Service discrimination makes the quality of the authorized good higher than that of the PI goodwhen the firm refuses to repair the PI good. As a result, the firm is able to sustain the price di↵erence
between the two countries above the tari↵ level. We have the following lemma.
Lemma 2 Under regime R, there exist threshold values qH and qL , 0 < qL < qH  1 with the following
properties.
(i) Suppose q 2 (qH , 1). Then (epReReN
F + t)/q < p
D <p
D hold. In the equilibrium, some consumers purchase
the PI good whereas some other consumers purchase the authorized good in country D.

(ii) Suppose q 2 (qL , qH ]. Then (epReReN
F + t)/q = p
D <p
D hold. In the equilibrium, all consumers purchase
the authorized good and no consumers purchase the PI good in country F.

(iii) Suppose q 2 (0, qL ]. Then peR
eN
pR
D = p
D  (eF + t)/q hold. In the equilibrium, all consumers purchase
the authorized good and no consumers purchase the PI good in country F.

Lemma 2 suggests that, depending on the level of q, we have three cases regarding the firm’s pricing.
The logic behind Lemma 2 can be explained as follows. Recall the equilibrium under Regime N in which
consumers in country i (i = D, F ) with v

veiN = peNeNi purchase the authorized good at the price of pi .

Now let us turn to Regime R that we consider here, and suppose for the moment that the monopolist

sets pi = peNi , the same prices as in the equilibrium of Regime N . In country D, consumers have an
option of purchasing the PI good at the price of peN
F + t and leave it unrepaired should the good break19

N
down. Consider the consumer with the cut-o↵ v = veD. The consumer purchases the authorized goodNrather than the PI good if and only if veD

peN
D

N
qe
vD

(e
pN
eN
eN
F + t) , p
D p
F + t + (1

N
q)e
vD
. We findthat this condition holds when q is small enough satisfying q 2 [0, qL ]. That is, when the probability of
the good breaking down (1q) is relatively high, the attractiveness of the PI good without repair is too

low to impose a binding constraint on the monopolist’s profitability. The result is that the monopolist
can make the same profit as in Regime N by charging the same prices as in Regime N in both countries.
Let us turn to the case of q > qL . The PI good without repair services is now sufficiently attractive
so that, if the monopolist continues to choose pi = peNi (i = D, F ), some consumers in country D withrelatively small v (but still v

NveD) purchase the PI good rather than the authorized good. Thatis, the attractiveness of the PI good is now sufficiently high so that it imposes a binding constraint

on the monopolist’s profitability. When q is in an intermediate range (satisfying q 2 (qL , qH ]), theattractiveness of the PI good is moderate in the sense that, in equilibrium, the monopolist chooses pD
and pF such that all consumers who purchase the good in country D purchase the authorized good at
pD and no consumers purchase the PI good. However, when q is higher than qH , the attractiveness of
the PI good becomes substantially high so that the monopolist’s profit-maximizing choice is to induce
some consumers with intermediate value of v to purchase the PI good, selling the authorized good tohigh-v consumers only.
By combining Lemmas 1 and 2, we can compare the equilibrium prices under the three regimes.
Because the service discrimination reduces the degree of market integration, peID < peReReIF
D and pF < palways hold.

Proposition 1 Compare equilibrium prices under the three regimes. We have (i) - (iii).
(i) Suppose q 2 (qH , 1). Then peID < (e
pR
eR
eN
eN
eR
eIF hold.
F + t)/q < p
D <p
D and pF <pF <p(ii) Suppose q 2 (qL , qH ]. Then peID < (e
pR
eR
eN
eN
eR
eIF hold.
F + t)/q = p
D <p
D and pF <pF <p(iii) Suppose q 2 (0, qL ]. Then peID < peR
eN
pR
eN
eR
eIF hold.
D =p
D  (eF + t)/q and p
F =p
F <p

Thus, PIs with service discrimination lead to the same direction of price changes as PIs without

service discrimination do if q > qL holds, but has no e↵ect if q  qL holds. Service discrimination,
however, reduces the extent of the price changes. This implies that, given PIs are permitted, prohibiting
service discrimination decreases the price in the destination country and increases the price in the source
country.

20

4

Welfare e↵ects of permitting parallel imports

In Section 3, we have investigated how parallel imports change the consumer prices in each country.
These price changes a↵ect consumers in each country, the firm, and the welfare of each country. Here,we compare welfare under the three regimes to explore the welfare e↵ects of permitting PIs and how
the firm’s service discrimination changes the e↵ects. This section also discusses policy implications of
the results.
In the following analysis, we first discuss the welfare e↵ects of PIs in the baseline model, where thelevel of the quality of the product, q, is exogenously given. Then, we extend the analysis to the situationin which q is endogenously determined by the firm, and re-examine the welfare e↵ects of permitting PIs.
As we will see below, endogenous choice of quality complicates the welfare e↵ects of permitting PIs in
the presence of service discrimination, while it does not qualitatively change the welfare e↵ects in theabsence of service discrimination.

4.1

Exogenous quality

Let us start with the case with exogenous quality of the product. Without service discrimination,
permitting PIs change the regime from Regime N to Regime I. In Regime I, the firm must sell theauthorized good with the constraint that the consumer prices satisfy pF = pD + t. PIs fully integrate
the two markets and the firm’s per-unit profit is always given by peIF

c = peID(c + t) no matter

where it sells the good.13 We have ⇧I < ⇧N because the inability to discriminate prices due to PIs
hurt the domestic firm. PIs a↵ect consumers in each country di↵erently. Because the authorized good
and the PI good are homogeneous in Regime I, the price decrease from peNeID benefits consumers in
D to pN
I
country D and the price increase from peNeIF hurts consumers in country F . Therefore, CSD< CSD
F to pand CSFI < CSFN hold. Because the price decrease increases the imports of country D, permitting PIs

increases the tari↵ revenue of country D, given the tari↵ level. Since both consumer surplus and theNItari↵ revenue increase, we have WD< WD. In contrast, WFI < WFN holds because consumer surplus

and the firm’s profit decreases in country F .
Let us next investigate how service discrimination changes the welfare e↵ect of permitting PIs. With
service discrimination, in order to block consumers from purchasing the PI good in country D, the firm
13 If the firm supplies the good in country F

Hence, its per-unit profit is peIF

through its own distributors, it receives peIF but t is incurred by the firm.

(c + t). If the firm supplies the good in country F through (competitive) parallel traders,

it receive peID but t is incurred by parallel traders. In this case, its per-unit profit becomes peID
holds, we have peIDc = peIF(c + t).

21c. Since peIF

peID = tmust set the prices such that they satisfy pD  (pF + t)/q. If the quality of the product is low enoughto satisfy q 2 (0, qL ], even if the firm charges the same prices as those without PIs, peNeN
D and pF , theseprices satisfy peNpN
D  (eF + t)/q and the firm does not need to adjust prices to block the PI good. In thiscase, permitting PIs has no e↵ect and the same equilibrium outcomes as those in Regime N are realizedR
NR
Nin Regime R: ⇧R = ⇧N , CSD= CSD, CSFR = CSFN , WD
= WD
, and WFR = WFN .

For q 2 (qL , 1), however, the quality di↵erence between the authorized good and the PI good is not
so large and all consumers will buy the PI good if the firm continues to change peN
eN
D and pF . Then, theprice constraint is binding and the firm sets the prices such that pD = (pF + t)/q holds to block the
PI good, if q is not so high such that q 2 (qL , qH ] holds. If q is high such that q 2 (qH , 1) holds, thefirm earns higher profit by setting pD > (pF + t)/q and letting some consumers purchase the PI goodin country D than the profit with blocking the PI good. Note that the firm always has an option toblock the PI good by manipulating the level of prices to satisfy peRpR
D = (eF + t)/q. This means that if thefirm sets the prices such that some consumers purchase the PI good (or some consumers of the PI good
are refrain from paying the repair price), the firm earns a higher profit than if it blocks the PI. Morespecifically, the firm accommodates parallel trade because it can earn an additional profit from selling
the good to parallel traders and the (overall) price in each country becomes closer to the price undermarket segmentation. However, if q is small, the prices that accommodate PIs substantially reduce theprofits from selling the authorized good. Thus, the firm chooses to block them.
In either case, the constraint is less strict than the constraint under Regime I as long as q < 1.
Therefore, the firm’s profit, consumer surplus in each country, and the welfare of each country lie
between their respective level under Regime N and the level under Regime I.14 We have the following
proposition.
Proposition 2 Compare equilibrium profit of the firm, consumer surplus and welfare of each country
under the three regimes. We have (i) and (ii).
NR
IN(i) Suppose q 2 (qL , 1). Then ⇧I < ⇧R < ⇧N , CSD
< CSD
< CSD
, CSFI < CSFR < CSFN , WD
<
R
I
WD
< WD
and WFI < WFR < WFN hold.
14 With q 2 (qH , 1), PIs create a new market in country D for consumers with lower willingness to pay.

Nevertheless,PIs always lower the profit because they decrease the profits from selling the authorized good in both countries, and thisnegative e↵ect always dominates the positive profits from selling the PI good to new consumers in country D. Although
the consumers of the PI good faces a lower price with service discrimination (epR
eIF + t), (epR
F + t  p
F + t)/q(epR
F + t)/q

peID =(epIF + t) > 0 holds, implying that the quality adjusted price of the PI good becomes higher and the total

R < CS I and W R < W I hold, even if some consumers
imports becomes lower with service discrimination. Therefore, CSD
D
D
D

purchase the PI good in this range of q.

22

N
R
I
(ii) Suppose q 2 (0, qL ]. Then ⇧I < ⇧R = ⇧N , CSD
= CSD
< CSD
, CSFI < CSFR = CSFN ,
N
R
I
WD
= WD
< WD
and WFI < WFR = WFN hold.

We can also compare the world welfare. Because parallel imports reduces the firm’s monopoly power
to set the prices and reduces the efficiency loss caused by the price discrimination, permitting PIs always
improves world welfare, given the level of q.
Proposition 3 Compare equilibrium world welfare under the three regimes. We have (i) and (ii).
(i) Suppose q 2 (qL , 1). Then W W N < W W R < W W I holds.
(ii) Suppose q 2 (0, qL ]. Then W W N = W W R < W W I holds.
It has been a controversial issue whether governments should apply antitrust laws to service discrimination against parallel imported goods. Given that PIs are permitted and given the level of q,
Proposition 2 suggests that there is a strong conflict of interest between the source country (country F )and the destination country (country D) in allowing service discrimination. The source country supports
service discrimination while the destination country opposes it. From the standpoint of world welfare,PIs should be permitted irrespective of whether services are discriminated. However, prohibiting service
discrimination realizes higher world welfare.

4.2

Endogenous quality

Up to this point, we have discussed the welfare e↵ects of PIs and service discrimination when q is
exogenously given. As explained in the Introduction, one concern over allowing PIs is that the reduced
profits of firms owing to market integration will decrease the gains from firms’ innovation activities andwill lead to a deterioration of product quality. Here, we investigate how PIs a↵ect the firm’s incentive
to provide better product quality that increases the “quality” of the good in the sense that consumers
worry less about breaking down. We will show that the firm is able to use service discrimination moree↵ectively as a tool to discriminate prices, if it can choose the level of the quality.
To this end, we add a new stage before the first-stage (i.e., stage zero) in which the firm chooses thequality of the product. Existing studies that have examined the quality e↵ect of PIs have not explicitly
considered the possibility that the good breaks down. We examine endogenous determinations of thequality, when higher quality means less probability of the good being broken down.
We suppose the firm must incur the fixed cost, K(q), to produce the good with the quality, q. The
fixed cost reflects the costs of making R&D activities to develop a product with a lower failure rate,
the costs of introducing instruments that provide a more precise quality inspection, the costs of seeking
23

suppliers that provide more durable parts and components in the manufacturing process, and so on.
It is natural to suppose that this fixed cost increases as the quality of the product increases. Hence,
it is assumed that K(0) = 0, K 0 (q) > 0 and K 00 (q)is quadratic in q and given by K(q) =2

q /2, where

0. Specifically, we assume that the fixed costis positive and constant. Let qeN , qeI , and qeR

respectively represent the profit-maximizing levels of q under Regime N , R, and I.
4.2.1

Welfare worsening parallel imports with service discrimination

Let us now investigate how the firm’s endogenous choice of the quality changes the welfare e↵ects ofNRI
permitting PIs. Recall that, when the level of q is exogenously given, we have that CSD
 CSD
< CSD
,
N
R
I
CSFI < CSFR  CSFN , ⇧I < ⇧R  ⇧N , WD
 WD
< WD
, WFI < WFR  WFN , and W W N  W W R <W W I hold, with equality if and only if q 2 (0, qL ] (see Propositions 2 and 3). Although service
discrimination diminishes the impact of PIs, PIs with service discrimination neither reduce consumer
surplus and the welfare in the importing country nor worsen world welfare, compared with the casewhere PIs are prohibited. When the firm endogenously determines the quality of the product and it
discriminates services, permitting parallel imports can hurt consumers and the welfare in the importing
country, and also can worsen world welfare.
Let us start with the welfare e↵ects of permitting PIs without service discrimination. Under both
Regime N and Regime I, the presence of the repair cost means the increased probability of breaking
down raises the firm’s expected cost of undertaking the repairs, (1q)m. We call this e↵ect the cost-

increasing e↵ect of the lower quality. Since consumers always utilize repair services for free without
PIs or PIs without service discrimination, the decrease in q does not a↵ect the eventual quality of thegood and thereby has no e↵ect on the price gaps between the countries,pN andpI . Therefore,

only the cost-increasing e↵ect matters and ⇧N and ⇧I (which do not include the fixed cost, K(q),to realize quality q) are always increasing in q, implying that a decline in the quality always reduces
the firm’s profitability, if PIs are banned or the firm cannot discriminate the repair services. Because
consumers’ willingness to pay for the good is uniformly distributed in each country, the reduction in
the international price gap from Regime N to Regime I does not a↵ect the total consumption of thegood (see Section 2.2). The increase in the cost of undertaking repairs also raises the equilibrium pricesof the good, but the magnitudes of the price changes is the same between Regime N and Regime I.
Therefore, the magnitudes of the cost-increasing e↵ect also become the same and we have qeN = qeI since@⇧I /@q = @⇧N /@q > 0 always hold.15 Since PIs without service discrimination do not change the level
15 We have @⇧N /@q = @⇧I /@q = N [(1 + k) [bk{c+(1 q)m}]+{(1 k)b t}k]m/(2bk) > 0, because b > {c+(1 q)m}/k

24

of the product quality, the directions of the changes in consumer surplus and welfare are the same as
those with exogenous q.16
N
I
N
I
Proposition 4 Even when q is endogenously determined, CSD< CSD, CSFI < CSFN , WD
< WD,

WFI < WFN and W W N < W W I always hold.
Note that both the price gap without PIs,

pN , and the price gap without service discrimination,

pI , are independent of q.17 With service discrimination, a decrease in q not only increases the expected
cost of undertaking the repairs but also decreases the quality of the PI good and thereby widens theequilibrium price gap,

pR for q 2 (qL , 1).18 Therefore, a decrease in q increases the firm’s ability

to discriminate prices in the presence of service discrimination. The e↵ect is called the marketsegmentation e↵ect of a decline in quality. Because of the market-segmentation e↵ect, an increase inq not only increases K(q) but also makes the price constraint stricter and reduces the price gap.
Since PIs with service discrimination decrease the total consumption of the good for q 2 (qL , 1) (seeSections 2.3.1 and 2.3.2), they definitely reduce the sales of the good that are subject to repair services.
Hence, PIs with service discrimination reduce the cost-increasing e↵ect of a decrease in q on the firm’s
profitability, making the firm less willing to improve the quality of the good.19
Because of the presence of the market-segmentation e↵ect and the lesser cost-increasing e↵ect, PIs
with service discrimination can lower the equilibrium level of the quality. Specifically, if the marginal
cost for improving quality (i.e. K 0 (q)) is small enough such that qeN = qeI > qL holds, qeR < qeN = qeI canand (1 k)b > t hold.
16 As Schwarts (1990) and Malueg and Schwarts (1994) have suggested, PIs without service discrimination (i.e., RegimeI) improve world welfare compared to the case with the monopolistic third-price discrimination (i.e., Regime N ), as
long as all markets are served and PIs weakly increase the total consumption of the good. If we consider a non-uniform
distribution of v and PIs strictly increase the total sales, the cost-increasing e↵ect is larger under Regime I and we will
have qeN < qeI . However, the higher quality enhances the positive welfare e↵ect of PIs without service discrimination and

it does not qualitatively a↵ect the results of Proposition 4.
17 In Regime N ,pN is independent of q because an increase in q reduces peNeN
D and pF by the same degree. In Regime
I,

pI = t always holds.
L , 1), the firm needs to satisfy pD = (pF + t)/q to block the PI good. Even if q becomes sufficiently high18 For q 2 (qsuch that the firm let some consumers to buy the PI good by setting pD > (pF + t)/q, the analysis in Section 2.3.1 suggeststhat an increase in q decreases the price di↵erence of the authorized good between the countries, pR .
19 If we consider the non-uniform distribution of v and the price convergence by permitting PIs has an e↵ect to increase
the total consumption of the good, the total consumption of the good under Regime R may be larger than that under
Regime N . In this case, the larger cost-increasing e↵ect gives the firm more incentive to increase q under Regime R. Evenso, qeR < qeN can hold because of the market segmentation e↵ect and qeR < qeI always holds. Therefore, the main resultsof the paper remain unchanged. See also footnote 16.

25

hold.20 Alternatively, if K 0 (q) is large enough such that qeN = qeI  qL holds, then we have qeR = qeN = qeI
and permitting PIs has no e↵ect on the optimal quality, irrespective of service discrimination.

Figure 4 depicts an example of the determination of the optimal level of the quality in each regime.
In this example, the optimal level of q satisfy qeR < qeN = qeI .21[Insert Figure 4 around here]

As mentioned above, a lower quality increases the cost of repairs. The increased cost is passed
through to the prices of the good. Given that qeR < qeN holds, this cost-increasing e↵ect of a decline in q

increases both pD and pF , hurting consumers in both countries and causing an efficiency loss. Because
pF increases, the e↵ect also increases the quality-adjusted price of the PI good (i.e., (pF + t)/q). As
Proposition 2 suggests, a decline in the quality raises the price in the importing country within Regime
R. Therefore, if the price-increase due to a decline in q dominates the direct e↵ect of price arbitrages that
decreases pD , permitting PIs with service discrimination hurts consumers and worsens the welfare in theimporting country. Since permitting parallel imports with service discrimination still hurts consumers
and the welfare of exporting country, it worsens world welfare in this situation.
R
Proposition 5 When q is endogenously determined, there is a set of parameterization where CSD
<
N
R
N
CSD
, WD
< WD
, and W W R < W W N hold.

When the product quality is endogenously determined, there is a case where PIs with service discrimination decrease consumer surplus, the welfare in the importing country, and worsens world welfare,
while PIs without service discrimination increase them by Proposition 4.
Thus, the producer’s service discrimination may transform welfare-improving PIs into welfare-worsening
ones. In the short run, where the firm does not change the quality of the product, PIs conventionally
improves consumer surplus and the welfare in the initially high-priced, destination country. It also
improves world welfare. In the long run, where the firm optimally chooses the quality of the product,
20 Parallel imports with service discrimination do not necessarily reduce q. If K 0 (q) is small enough such that qeR 2 (qH , 1)

holds, the market for the authorized good and the market for the PI good coexist in country D. Under Regime R withq 2 (qH , 1), a decline in q a↵ects the firm’s profit from selling the good to parallel traders since it changes the relative
demand for the PI good. We call this e↵ect the PI-market e↵ect. The PI-market e↵ect is either positive or negative
because the demand for the PI good is an inverted-U shaped in q, which complicates the ranking between qeR and qeN = qeI .
If qeR 2 (qL , qH ] holds, the PI-market e↵ect is absent and qeR < qeN always holds.
21 The parameters other than q are set as follows: n = 100, b = 40, k = 1/3, c = 5, m = 1, t = 3, and= 100. In

this case, the cut-o↵ levels of q become qH = 0.68758 and qL = 0.51191. In the numerical example, we have qeN = qeI =0.69737 > qeR = 0.51538.

26

allowing PIs to promote price arbitrages is backfiring for the destination country. In other words, blocking PIs may benefit the destination country, because consumers can buy the good with a better quality
in the absence of parallel imports. In this case, prohibiting service discrimination not only decreases
the price in the destination country given the level of quality (see Proposition 1) but also increases thequality of the good, improving the welfare of the destination country and world welfare. To recover thewelfare-improving nature of PIs, service discrimination should be prohibited.
4.2.2

Trade liberalization and welfare-worsening parallel imports

We have shown that PIs can be welfare-worsening for all countries when q is endogenously determined,
but the likelihood of the case depends on parameter values. Here, we focus on the tari↵ level, t, andhow the reduction of t changes the welfare e↵ects of allowing PIs.
When the firm optimally chooses q, t a↵ects the equilibrium level of q. On the one hand, tradeliberalization enhances the firm’s incentive to increase q by increasing the profit from exporting and,
thereby, the marginal gains from increasing the quality.22 Thus, without service discrimination or
without PIs, the former e↵ect always dominates the latter, and trade liberalization leads to a higher
level of qeN and qeI .

However, in Regime R, trade liberalization may reduce qeR . Even if trade liberalization increases qeR ,the extent of the increase in qeR may be less than those of qeN and qeI . Recall that, in Regime R, a decline
in q may increase the firm’s profitability due to the market-segmentation e↵ect. Then, since lower t
increases the attractiveness of the PI good, it may also increase the firm’s incentive to choose lower q
to o↵set partly the damage from the increased arbitrage pressure. Because of this extra incentive, tradeliberalization may decrease qeR or widen the gap between qeR and qeN even if it increases qeR .23 Figure 5
depicts a case where trade liberalization decreases qeR .24[Insert Figure 5 around here]

As the gap between qeR and qeN increases, permitting PIs is more likely to decrease the consumer

surplus and welfare in country D and worsens world welfare in the presence of service discrimination.
This in turn suggests that trade liberalization may make PIs with service discrimination more likely to
be welfare-worsening. We have the following proposition.
22 We have @ 2 ⇧N / (@t@q) = @ 2 ⇧I / (@t@q) =23 When qeR 2 (qN m/2b < 0.

L , qH ] holds, the PI-market e↵ect is absent and only the market-segmentation e↵ect works under service

discrimination. In this case, qeR < qeN = qeI always holds, and we can show that trade liberalization always widens the gap
between qeR and qeN = qeI .
24 See the proof of Proposition 6.

27

Proposition 6 Consider a tari↵ reduction from t0 to t1 (< t0 ). When q is endogenously determined,
N
R
N
R
there is a set of parameterization where CSD
< CSD
, WD
< WD
, and W W N < W W R hold at t = t0 ,R
NRNbut CSD
< CSD
, WD
< WD
, and W W R < W W N hold at t = t1 .
R
NR
NWhen q is fixed, CSD> CSD
and WD> WD
always hold (see Proposition 2). However, when q

is endogenously determined, the choice of lower q induced by PIs may result in lower consumer surplus
and lower welfare in country D. It may also worsen world welfare. And, if lower t increases the firm’s
incentive to reduce q or diminishes its incentive to increase q, trade liberalization makes PIs more likely
to be welfare-worsening.

4.3

Policy implication

We have seen that the welfare e↵ects of PIs depend on whether repair services are discriminated against
the PI good and whether the quality of the product is fixed or endogenously determined. The resultsof the paper provide some useful policy implications.
>From the viewpoint of the importing country (country D), prohibiting the discrimination in repair
services benefits the domestic consumers and improves the domestic welfare. As is shown in Section 1.1,
however, the service discrimination are prevalent in the real world. Even if governments recognize service
discrimination, they may not require the original producer to support PI goods.25 The governments of
the importing countries should introduce a more rigid regulation to prevent the service discrimination
if they permit PIs.
Even if the importing country has a regulation to ban the discrimination in repair services, the original
producers may not be able to provide the repair services for PI goods due to technical reasons. For
instance, they may lack physical and human resources to provide the services for PI goods. Japan Fair
Trade commission basically bans producers’ refusals to repair PI goods if the producers intentionallydiscriminate against the PI goods, but the commission takes the position that the refusals do not
automatically violate the antitrust laws if the producers face difficulties in providing the repair services.26
Under the situation, the consumers in the importing country cannot avoid the discrimination in repair
services and permitting PIs always changes the regime from Regime N to Regime R. If the quality of the
25 For instance, although Australian Competition and Competition Commission cautions that consumers of PI goods“may not get assistance such as product/technical support or repair/spare part facilities from the local manufacturer ortheir representative,” it says that “the local manufacturer is not required to help you if the product develops a fault.” See
https://www.accc.gov.au/consumers/sales-delivery/buying-parallel-imports (accessed on March 5, 2017).
26 See http://www.jftc.go.jp/dk/soudanjirei/ryutsutorihiki/sonota/seigen1.html (accessed on March 5, 2017, written in
Japanese).

28

product is fixed, the government of the importing country should still permit PIs because Propositions
2 and 3 suggest that PIs still decrease the consumer price and increase the amount of imports, which
in turn increase consumer surplus and the welfare of the importing country, and also improve world
welfare. If the quality is endogenously determined, however, Proposition 5 suggests that PIs with service
discrimination could increase the consumer price, decrease the amount of imports in the importing
countries, worsen consumer surplus, the domestic welfare, and world welfare. In the latter case, theimporting country should rather prohibit PIs.
With regard to the relationship between parallel-import policy and trade policy of the importing
country, Proposition 6 tells us that, in the presence of discrimination in repair services, a reduction ofimport tari↵ may turn welfare-improving PIs into welfare-worsening ones. Recently, many developing
countries newly joined the WTO and have committed to lower tari↵s, and the proliferation of free
trade agreements enhance trade liberalization all over the world. The result implies that, unless service
discrimination are prohibited, attempts to integrate markets by permitting PIs may fail in a world with
low tari↵s. Prohibiting service discrimination becomes more important as trade liberalization proceeds.
Besides that, when a tari↵ reduction decreases the optimal level of quality in the presence of service
discrimination, service discrimination can increase the optimal tari↵ of the importing country that is
set to maximizes its welfare. This is because a higher tari↵ leads to higher quality. In contrast, a tari↵
reduction always increases the optimal quality in the absence of service discrimination, which decreases
the optimal tari↵. This implies that service discrimination can decrease the importing country’s incentive
to lower tari↵s and undermine the progress of trade liberalization in goods.

5

Discussion

In this section, we explore the robustness of these results by relaxing some assumptions made in thebasic model.

5.1

Price discrimination in repair services

Here, we consider an alternative situation where the monopolist may provide repair services for the PI
good, but a repair price is charged against the PI good. Let r denote the repair price the firm charges
for the PI good in country D. We find that the equilibrium in this case is economically equivalent to
the equilibrium in the case where the firm refuses to repair the PI good. To see the logic, suppose thatthe firm chooses pF to sell the authorized good in country F , and that, in country D, the firm wishes to29sell the good without repair services to consumers with v 2 [v + , v ++ ) and the good with repair services
to consumers with v 2 [v ++ , b], where v + = (pF + t)/q < v ++ < b. In the case of repair refusal, the firm
can achieve this outcome by choosing pD = pF + t + (1if and only if v 2 [v++q)v ++ so that v

pD

qv(pF + t) holds, b]. Whereas, in the case of price discrimination in repair services, the firm canq)r and r = v ++ . If pD > pF + t + (1q)r,

consumers with v 2 [v ++ , b] purchase the PI good and repair services, whereas, if pD = pF + t + (1q)r,achieve the same outcome by choosing pD

pF + t + (1they are indi↵erent between purchasing the PI good and repair services, and the authorized good. In
any case, the firm’s overall profit is identical between the case of refusal to repair and the case of pricediscrimination in repair services. This in turn implies that, for q 2 (qH , 1), the equilibrium outcome
is economically equivalent between the two cases; besides the analogous logic applies to establish theequivalence between the two cases for all q < qH as well. We have the following proposition.
Proposition 7 In equilibrium, the overall price of the PI good under the fee-based repair service is thesame as the price of the authorized good under the refusal of repairs.
Therefore, the refusal of repairs and the fee-based repair services for the PI good are qualitativelyindi↵erent for the firm and consumers, and their e↵ect on the quality of the product discussed in thenext session is also indi↵erent. In other words, the equilibrium in the case of the fee-based repairs of
the PI good practically coincides with the equilibrium under the refusal of repairs.
The equilibrium pricing of the firm is summarized as follows (see the proof of Proposition 7 fordetails): the firm sets (i) the prices such that some consumers of the PI good are unwilling to repair the
broken units for q 2 (qH , 1); (ii) the prices such that all consumers of the authorized good and the PI
good repair the broken units for q 2 (qL , qH ); and (iii) the same overall prices as those without PIs andall consumers repair the broken units for q 2 [0, qL ).

5.2

Fee-based repairs for the authorized good

We have assumed that the firm o↵ers a full warranty to the buyers of the authorized good. Here, weshow that this assumption does not a↵ect the qualitative results of our basic model and the firm actually
prefers the full warranty in some cases. Suppose parallel importation is prohibited and let si denote
the repair price that the firm sets for repairing the authorized unit in country i. Consumers repair the
broken units of the authorized good if vi

si holds. That is, the utility gain from the repair exceeds therepair price. Consumers primarily purchase the authorized good if qvi

pi . These inequalities suggestthat there exist consumers who buy the authorized good, but never purchase the repair services if andonly if si > pi /q holds. Without loss of generality, we set t = 0 for expositional convenience.
30

Given that si > pi /q holds, the profit of the firm in country i is given by⇡ i (pi , si ) = [pi + (1where xsF (pF ) = nfF (kbq)si{c + (1q) m}]xsi (pi ) + nfi (pisF ) and xsD (pD ) = nfD (b

c)

✓

qsi

pi
q

◆

,

(32)

sD ). By maximizing ⇡ i (pi , si ) with respect

to pi and si , the optimal prices become psF = (c + bkq)/2, psD = (c + bq)/2, sbF = (bk + m)/2, andsbD = (b + m)/2. However, these prices fail to satisfy the supposition that si > pi /q holds.

Therefore, the firm sets the repair prices such that every consumer of the authorized good prefers to

pay for the repair services. In this case, consumers whose willingness to pay satisfies vi
buy the good and all of them purchase the repair services. Let Pi = pi + (1pi + (1q)siq)si denote the overall

price of the authorized good. Then, the firm’s overall profit becomes⇧s (PD , PF ) =X⇡ i (Pi ) = [Pii=D,F{c + (1q) m}]xi (Pi ),(33)

where xi (·) is defined in (1) and (2). Because (33) has the same functional form as (4), the profitmaximizing level of each price also coincides (Pei = pei ), as does the equilibrium profit: ⇧s (PeD , PeF ) =
⇧ peN
eN
D, p
F .

Because the firm’s profit is larger when all consumers utilize the repair services, the combination of

the good’s price and the repair prices does not matter to the firm, as long as the overall price is equal topei and they are consistent with si  pi /q. If the firm set a higher repair price, the good’s price becomes
lower. If the firm provides a full warranty, it means that the firm sets a higher price to cover the costof the repairs.
In the presence of PIs, the firm becomes more willing to provide the full warranty in country F
to keep the price of the authorized good high and to mitigate the arbitrage pressure. If the firm does
not provide a full warranty in country D, the authorized good and the PI good becomes perfectly
substitutable and the firm captures the quality premium of the authorized good by setting a high repair
price. After all, the overall price of the authorized good in country D becomes the same as the price of
the authorized good with the full warranty.

5.3

Repair services by ISOs

Until now, we have restricted our attention to the case where only the original firm can provide therepair services. Here, we consider the case in which independent service organizations (ISOs) are alsoable to provide the repair services for the PI good. We assume there are many ISOs and the competition
among them reduces the repair prices to their marginal cost.

31

The original firm of the good should have more technical information about the good than the ISOs,
and will stock more parts and components that are necessary to repair the good. Hence, it is natural
to assume that the quality of the repair services performed by the firm is not lower than the quality
performed by the ISOs. Let µ 2 (0, 1] represents how well a repair recovers the original quality of good
x. As µ approaches one, the quality gap between the unbroken unit and the repaired unit narrows, andthe quality is fully recovered when µ = 1. The level of µ reflects the extent to which the repair services
performed by ISOs recover the “physical” quality of the good.
Let µw denote the unit cost of undertaking repair services when performed by ISOs. The unit costof repairs is increasing in µ because it should be more costly for the firm to return the quality to theoriginal quality. The ISOs may also incur a higher unit cost of repairs, but their less e↵ective repair
services may come with a lower cost. Therefore, we leave w to be either higher or lower than m.
First, suppose µ = 1. In other words, ISOs provide the same quality of repair services as the original
firm. In this case, even if the firm refuses to repair the PI good, consumers can repair the PI good bypaying w to an ISO. The overall price of the PI good becomes pF + t + (1set pD  pF + t + (1q)w to sell the authorized good. If (1q)w. Then, the firm needs toq)w is larger than peN
DpeN
F + t given by(9), the firm can set the same prices as those under market segmentation. Otherwise, the equilibrium
international price di↵erence becomes t + (1q)w, and becomes larger as q becomes smaller. Note that,unless w = 0, the entry of competitive ISOs realizes a higher profit for the firm than the profit that isrealized if the firm cannot discriminate repair services.
Second, suppose µ < 1. To make clear the analysis, we set w = 0 so that ISOs provides virtually free
repairs. However, the free repairs cannot realize full market integration because the authorized unit and
the PI unit repaired by ISOs are imperfect substitutes. If the firm refuses to provide the repair services
for the PI good, it can attract consumers to buy the authorized good by setting pD and pF , such thatpD =holds. Because µ < 1, we have pD
than peND

pF + tµ(pF + t) = (1µ) (pF + t) /µ > 0. If this price di↵erence is larger

peN
F + t , the full market segmentation is realized by the service discrimination.

If µ < 1 and w > 0: the equilibrium price di↵erence reflects the above two e↵ects. Accordingly, if theISOs’ quality of repair services is lower than the firm’s quality or the ISOs incur a positive cost of repair
services, the presence of competitive ISOs does not realize full market integration. The original firm’s
service discrimination becomes less e↵ective, but it is still e↵ective, and a decrease in q may expand theinternational price di↵erence and increase the firm’s profit.

32

5.4

Oligopoly

We have assumed that only a single firm can produce the good. Here, we discuss how the existence ofa rival firm a↵ects the firm’s incentives to discriminate services and to choose the level of the quality.
Suppose that there is a firm in country D (firm D) that compete with the firm in country F (firmF ), which produce a product that is imperfectly substitutable with the good produced by firm F . We
assume firm D does not export its product to country F , because of the high fixed cost of exporting.
With firm D, the market competition in country D reduces the equilibrium price of the authorized good
F in country D. Therefore, the price gap between the countries becomes smaller than the baselinemodel. Besides that, service discrimination becomes a less e↵ective tool to discriminate prices, because
firm F must take into account its price settings that an increase in the price of the authorized goodshifts the demand from good F to good D in country D. We call the e↵ect the demand-shift e↵ect ofservice discrimination. Because of the demand-shift e↵ect, firm F becomes less willing to reduce thequality of good F to increase the quality gap between the authorized unit and the PI unit of good F .
This is because a lower quality increases the price of the authorized good, shifting the demands fromgood F to good D in country D. Although the presence of the domestic firm changes the extent of
the price gap and that of profit gains from both service discrimination and reducing q, the qualitative
results of our model would remain unchanged.
Alternatively, suppose that there is another firm in country F (firm F 0 ), which produces a di↵erentiated product and sell it in both countries D and F . In this case, PIs exert downward pressure on theprices of both goods in country D. As in the case with firm D, the presence of the rival firm reduceseach firm’s gains from discriminating services and decreasing q. A di↵erence is that the levels of eachgood’s quality are determined by a Nash equilibrium of the two firms’ strategic choices of the quality.
Even though the choices of the quality becomes much more complicated under oligopoly, firms still
have incentives to lower the quality of their respective product if the market-segmentation e↵ect is large
enough to outweigh the cost-increasing e↵ect and the demand-shift e↵ect. Therefore, the qualitative
results of our model would remain unchanged.

5.5

A higher quality increases the marginal cost of production

We have assumed that the production of a good with higher quality incurs a higher fixed cost, K(q),but does not increase the marginal cost of production. Here, we discuss the case where marginal costdepends on the level of quality.
Suppose that the marginal cost of production depends on q and given by c(q), where c0 (q) > 0 and
33

c00 (q)0. The marginal (expected) cost of supplying the authorized good is now given by c(q)+(1 q)m.

In this case, an increase in q raises the marginal cost of production on the one hand and it decreases the
expected cost of repairs on the other hand, as is discussed in Section 4.2.1. An increase in q increases⇧N and ⇧I if c0 (q) < m holds, and it decreases them if c0 (q) > m holds.
Since c00 (q)0, if c0 (1) < m holds, an increase in q always reduces the cost of supplying theauthorized good. Therefore, it has the same qualitative e↵ects on ⇧N , ⇧I , and ⇧R as those in thebaseline model. If c0 (0) > m holds, however, an increase in q always raises the cost of supplying thegood. Since the market-segmentation e↵ect from a decrease in q benefits the firm in Regime R, it is
optimal for the firm to set q = 0 in all regimes. However, this case is unrealistic that the firm produces
the good which always fails.
Finally, if both c0 (0) < m and c0 (1) > m hold, there exists a cuto↵ level of q, q̂ = c0 (q̂) = m, underwhich an increase in q decreases the marginal cost of supplying the authorized good and above which
it increases the marginal cost. In this case, even if there is no fixed cost of producing the good with ahigher quality, F (q) = 0, the profit of the firm in each regime becomes an inverted-U shaped in q andthere is a case where q̃ R < q̃ N = q̃ I will hold.
In sum, as long as the firm chooses a positive level of q, the qualitative results remain unchanged
even if we consider the positive relationship between the quality and the marginal cost of production.

6

Conclusion

In this study, we have re-examined the e↵ect of parallel imports when the firm (trademark holder) ofa good might discriminate after-sales services against parallel imported goods. We have shown thatthe firm is willing to discriminate the repair and maintenance services against the parallel imported
good. A refusal to repair parallel imported goods realizes full market segmentation between countries
if the quality of the good is sufficiently low. In the middle range of quality, the firm successfully blocks
parallel importation even if the price of the authorized good is higher than the price of the parallel
imported good. If the quality is sufficiently high, the firm accommodates the parallel imported goodand consumers in the importing country buy either the authorized good or the parallel imported good,depending on their willingness to pay for the good. In the latter two cases, the two markets are only
partially integrated. Compared with the case where parallel imports are allowed and the firm does notdiscriminate services, service discrimination hurts consumers in the destination country, while it benefits
the firm and consumers in the source country. Despite the service discrimination, allowing parallel
imports benefits consumers in the destination country and hurts consumers in the source country, as
34

long as the quality of the good is unchanged.
The favorable e↵ect of parallel imports for consumers in the destination country may be overturned,
if the firm undertakes costly investments to improve the quality of the product. Without service discrimination, parallel imports have no e↵ect on the quality of the good, because both the price e↵ect
and the quantity e↵ect of improving quality are una↵ected, and the price gap between countries is independent of the quality. With service discrimination, parallel imports decrease the firm’s incentive toimprove the quality of the good. This is because the quality of the product is itself a strategic tool tomanipulate the degree of vertical di↵erentiation between the authorized good and the parallel imported
good. Therefore, with service discrimination, lower quality has an e↵ect to increase the equilibrium pricegap between the countries. Consequently, permitting parallel imports reduces the quality of the good in
the presence of service discrimination. When the changes in the quality is taken into account, parallel
imports may increase the equilibrium price in the destination country because the increased repair costwith lower quality is passed through to the prices of the good, and it may outweigh the conventional
price-convergence e↵ect of permitting parallel imports. In this situation, permitting parallel imports
may worsen consumers surplus and the social welfare in all countries.
Furthermore, we found that the possible negative e↵ect of parallel importation can be amplified as
trade liberalization proceeds. As the import tari↵ becomes lower, the firm gains more from exports
but at the same time it faces increased arbitrage pressure. Then, the firm becomes more willing to
reduce the quality for the sake of decreasing the substitutability between the authorized good and theparallel imported good. There is a case where allowing parallel imports benefits consumers and theimproves the welfare in the destination country when the import tari↵ is high, but hurts consumers andworsens the welfare in that country under free trade. If the firm cannot engage in service discrimination,
trade liberalization increases the quality, and permitting parallel imports improve consumer surplus, thewelfare of the importing country and world welfare.
These results imply that, in contrast to the conventional wisdom, permitting parallel imports may
hurt consumers and welfare in all countries if the firm can discriminate services and also manipulate thequality of the good. Countries should implement some restrictions on the firm’s service discrimination inallowing parallel imports. Our results also suggest that prohibiting service discrimination becomes more
important as trade liberalization proceeds. If it is technically difficult to rule out service discrimination
and welfare-worsening parallel imports emerge, the destination country should not allow parallel imports
in the first place.
We have conducted some robustness checks. Instead of refusing the repair services, the firm can

35

also mitigate the pressure of price arbitrage by charging a relatively high repair price for the parallel
imported good. Even if we consider price discrimination in repair services, rather than a simple refusalof repairs, we have confirmed that the qualitative results of this paper remain unchanged. Besides that,
if we consider the entry of many competitive independent service organizations, it helps to narrow theinternational price gap but it is not sufficient to eliminate the firm’s service discrimination. Therefore,
the main results still go through even in the presence of independent service organizations.

Appendix
Proof of Lemma 1
By (11) and (12), we have peIF

peN
pN
F = k{e
D

(e
pN
eID
F + t)}/(1 + k) > 0 and p

peN
D =

{e
pN
D

(e
pN
F +

t)}/(1 + k) < 0. Because peID = peIF + t holds, peID > peIF . Therefore, we have peN
eIF < peID < peN
F < p
D.

Proof of Lemma 2

A
PI
Suppose that the prices of two countries satisfy pD > (pF + t) /q so that vD> vD
holds. Then, theequilibrium prices become peRbF and peRbD (see (26) and (27)). These prices are consistent with
F = p
D = p
the supposition that pD > (pF + t) /q holds if
pbD

is satisfied, where (q) = (b + 2m)q 2(b
pF + t)= (1qq){kb + c + 2t + (1(q)
>0
2q (q + k)
k)m}q

(A1)

k (c + t).

(q) is either U-shaped or

decreasing in q 2 [0, 1]. We have (0) =k (c + t) < 0 and (1) = (1If b > {(1 + k) (ck) holds, then (1) > 0 and (q) is U-shaped in q. Therefore,m) + (2 + k) t}/(1k) b(1 + k) (cm)(2 + k) t.

there exists a unique value of q, qH (2 (0, 1)), that satisfies (qH ) = 0. This means that peReR
D > p
F + t /qholds for q 2 (qH , 1). If b  {(1 + k) (cm) + (2 + k) t}/(1k) holds, the equilibrium prices satisfy

peR
eR
D  p
F + t /q, which contradicts the supposition that pD > (pF + t) /q holds.

Even if a decrease in q reduces the price of the good sold in the domestic country (bpF ), it increases

the quality-adjusted price of the PI good ((bpF + t) /q) in the foreign country. The quality adjusted priceapproaches the infinity as q approaches zero. If a small decrease in q from q = 1 realizes pbD > (bpF + t) /q(i.e., if

I(1) > 0 holds), xP
pD , pbF ) is first increased and then decreased as q becomes smaller. ThisD (bimplies that if q is sufficiently small (i.e., q  qH ), consumers do not purchase the PI good. If a small

decrease in q from q = 1results in pbD  (bpF + t) /q (i.e., if (1)  0 holds), no consumers purchase the36

PI good irrespective of the level of q if the repair services are not available. For expositional convenience,
we set qH = 1 in this case.
PI
If q  qH is satisfied, vD

AvD
holds and all consumers in country D prefer the authorized good, if

they buy one. In this case, if peNeN
D  p
F + t /q holds, the firm is able to block PIs, even if it completely
discriminates the prices between the two countries. Therefore, the firm charges peR
eN
eR
eN
F = p
N and pD = p
D

in equilibrium because these are the prices under market segmentation and realize the highest profit forthe monopolist. We have peNDq{(1k) qb t} (1and ⌦(1) = {(1k)bThis means that peND

By comparing peN
D✓peN
F + t /q = ⌦(q)/(2q) where ⌦(q) = (12q) (kb + m). Since ⌦(q) is a quadratic function in q, ⌦(0) =2k) qbc2t} +(kb+c+2t+m) < 0,t} > 0, there exists a unique value of q, qL (2 (0, 1)), that satisfies ⌦(qL ) = 0.
peN
eN
eN
F + t /q holds for q 2 [qL , 1) and p
D < p
F + t /q holds for q 2 (0, qL ].
peN
bD
F + t /q and p

◆
peN
F +t
q
⇥
This equation tells us that peN
DpeN
Dq) {(1✓(b
pF + t) /q defined in (A1),◆q 2 + k {(b + m)q (kb + t + m)}(b
pF + t)=.
q
2q (q + k)⇤(e
pF + t) /q [bpD (bpF + t) /q] is positive if q > q1 ⌘ (kb + t + m) /(b+pbDm) is satisfied. At q = q1 , we have
✓

peN
D

peN
F +t
q

◆

✓

=
q=q1

=

This means that qL > q1 , peND

qL is lower than qH at which pbD

pbD

{(1

(b
pF + t)
q
k)b

◆

q=q1

2

[b (c

t}q1

2 (kb + t + m)peNbD
F + t /q = 0, and pkm) + m (cm) + bt] < 0.

(b
pF + t) /q < 0 are satisfied at q = qL , and(b
pF + t) /q = 0 holds. Therefore, there exists a unique value of q, qL(2 (0, qH )), such that peN
D 

peN
F +t

this range of q, we have peN
DpeR
D = k(q/q holds for q 2 (0, qL ].

We have proved that there exist the threshold values that satisfy 0 < qL < qH  1.
(i) If q 2 (qH , 1) holds, we have peR
bi and peReR
i =pF + t /q < p
D is satisfied by the definition of qH . In

q1 )/2[(b + m) (q + k)] where q1 is defined in the proof of Lemma

2. Since q > q1 holds whenever q > qL holds, we have peN
eR
eR
eR
eN
D > p
D . Therefore, p
F + t /q < p
D < pDholds.

(ii) If q 2 (qL , qH ) holds, we have peR
b0i . Section 2.3.2 suggests that peR
eR
i =p
D = p
F + t /q holds in thiscase. Besides that, we have peNDholds.

peR
pN
D = q{qe
D

2
(e
pN
eR
eR
eN
F +t)}/(q +k) > 0. Therefore, p
F + t /q = p
D <pD(iii) If q 2 (0, qL ] holds, we have peR
eN
eR
eN
eN
i =p
i . By the definition of qL , p
D =p
D  p
F + t /q holds.

37

Proof of Proposition 1
For convenience, let us prove (i), (ii), and (iii) in the reverse order.
(iii) If q 2 (0, qL ] holds, we have peR
eN
F = p
F by Section 2.3.2. By combining this with Lemmas 1 and

2, we have peID < peR
eN
pR
eN
eR
eIF .
D =p
D  (eF + t)/q and p
F =p
F <p

(ii) If q 2 (qL , qH ) holds, we have peR
eR
eID = (1i = p̀i . Then, p
D p

2
(e
pN
(k + 1)} > 0 holds for because qepN
F + t)}]/{q k + q
D

peR
F

peIF =

k (1

peR
F =

q(q

q) [ k + q 2 (pF + t)+k (1 + q) {qe
pN
D

(e
pN
F + t) > 0 holds for q 2 (qL , 1), andq) {t + (1 + k) m + 2kb}/{2 (k + 1) (q + k)} < 0 holds. By combining these with

Lemmas 1 and 2, we have peID < (e
pR
eR
eN
eN
eR
eIF .
F + t)/q = p
D <p
D and p
F <p
F <p
peN
F

(i) If q 2 (qH , 1) holds, we have peR
bi by Section 2.3.1. By comparing peNeR
i = pF and pF , we haveq1 )/2 (q + k) where q1 is defined in the proof of Lemma 2. Since q > q1 holds

whenever q > qL holds, peNeReNbD are always satisfied. By comparing pbi and p̀i , we have
F < pF and p
D < p
pbD p̀D = {qbpD (bpF +t)}q 2 /(k+q 2 ) > 0 and pbF

p̀F =

{qb
pD (b
pF +t)}kq/ k + q 2 < 0 hold because

qb
pD (b
pF +t) > 0 holds in this range of q. Because the proof of (ii) shows that p̀D > peID and p̀F < peIF holdfor any q 2 (qL , 1), we have peR
bD > peID and peR
bF < peIF . Besides that, we have (e
pR
D =p
F =p
F + t)/q(1q) [2bkq + (k + 1) {(k + q) (cpeID =mq) + mq} + k + 2q + kq + k 2 t]/{2 (k + 1) (k + q) q} > 0. By

combining these with Lemmas 1 and 2, we have peID < (e
pR
eR
eN
eN
eR
eIF .
F + t)/q < p
D <p
D and pF <p
F <p

Proof of Proposition 2

Irrespective of the level of q, we have ⇧I

⇧N =

n( pN

t)2 /{b(1 + k)} < 0. By (7), (8), (13)and (14), the functional forms of consumer surplus in each country are identical between Regime N
and Regime I. By Proposition 1, we have peID < peNeN
eIF given q. Therefore, CSFI
D and pF < pn peIFpeN
F {2kbI
peIF + peN
F }/(2kb) < 0 and CSD

always hold. Besides that, we have xD (epND ) = n(1NCSD
= n peND

peID {2bpeNpID ) = n(1D /b) < xD (eCSFN =

peID + peN
D }/(2b) > 0
peID /b). Therefore,

N
N
I
I
WD
= CSD
+ txD (epNpID ) and WFI = CSFI + ⇧I < WFN = CSFN + ⇧N hold.
D ) < WD = CSD + txD (e(i) Suppose q 2 (qL , 1) holds. When the firm provides the repair services for the PI good, the firm’s
profit function becomes the same as that without PIs and it is given by (4). For q 2 (qL , qH ], the firm’s
profit function is also given by (4). In this range of q, the firm sets pF = p̀F and pD = p̀D and blocks PIs.
without PIs, the firm sets the price that maximizes the profit it can earn in each market. This meansthat the profit earned in each country is higher as the price becomes closer to the optimal price without
PIs. By Proposition 1, peIF > p̀F > peNeNeID holds. This means that ⇧N > ⇧(p̀D , p̀F ) > ⇧I
F and p
D > p̀D > pholds for q 2 (qL , qH ]. If qH 6= 1, some consumers purchase the PI good that is not subject to repair
services in equilibrium, and the equilibrium profit, ⇧+ (bpD , pbF ), satisfies ⇧+ (bpD , pbF ) > ⇧(p̀D , p̀F ) holds
38

for q 2 (qH , 1) because the firm chooses pbF and pbD that satisfies qb
pD > pbF + t and accommodates theimports of the PI good even if it can choose p̀D and p̀F that satisfies q p̀D = p̀F + t to block the importsof the PI good.
Let ⇧N + be the profit of the producer, if it discriminates services and sells the authorized good thatis not subject to any repair services, even without PIs. We can prove that ⇧N > ⇧N + holds, that is,
the firm has no incentive to discriminate services between the authorized goods in the absence of PIs.
Suppose that PIs are banned in country D, and the firm has an option to sell two types of the authorized
good within the same country — the authorized good that is subject to free repair services, which wecall the S good, and the authorized good that is not subject to any repair services, which we call theS
N S good. Let pSi denote the price of the S good and pN
denote the price of the N S good. We againi

set t = 0 because the tari↵ does not a↵ect the analysis in this section.
As is Section 2.3, the consumers with v
(pSi

S
pN
i )/(1(pSi

S
pN
i )/(1

Sq) > v > pNi /q purchase the N S good.

q) purchases the S good, while those withThe demand for the N S good is positive if

S
and only if qpSi > pN
holds. The profit of the firm in country i is given by
i

 S
S
S
pSi
pN
qpi
pN
i
i
S
S
NS
⇡ i (pSi , pN
)
=
n[p
{c
+
(1
q)
m}]
1
+
n(p
c)
.
i
i
i
(1 q)b(1 q)qb(A2)

S
By di↵erentiating (A2) with respect to pN
i , we haveSn{2 qpSi@⇡ i (pSi , pN
i )
=
N
S
@pi

S
pN
+ (1 q) (ci(1 q)qb

qm)}.

S
Therefore, as long as the demand for the N S good is positive (i.e., qpSi > pNi ), an increase in the priceSof the N S good increases the firm’s profit. This means that the firm optimally chooses pSi and pNiSsuch that pSi = pN
i /q holds and eliminates the market for the authorized good for which repair services

are not provided. Therefore, ⇧N > ⇧N + holds. In regime R, the firm faces PIs and it must take into
account the price in country F in setting the optimal price in country D. Because of this constraint,
⇧N +

⇧+ (b
pF , pbD ) holds. Therefore, ⇧I < ⇧R < ⇧N holds for all q 2 (qL , 1).

For q 2 (qH , 1), some consumers in country D purchase the PI good and other consumers purchase
the authorized good. In this case, the functional form of consumer surplus of country D in Regime
R, which is given by (28), is di↵erent from those in Regime N and Regime I. By Proposition 1, themove from Regime N to R increases, while the move from Regime I to R decreases, both the price of
the authorized good and the quality adjusted price of the PI good (i.e., peID < (epReReN
F + t)/q < p
D < p
D ).
N
R
I
This implies that CSD
< CSD
< CSD
holds in q 2 (qH , 1). Since the functional form of consumer

surplus of country F in Regime R is still the same as the those in the other two regimes, peN
eR
eIF
F <p
F <p

means that CSFI < CSFR < CSFN holds given q 2 (qH , 1). For q 2 (qL , qH ], all consumers purchase the39authorized good in Regime R and the functional forms of consumer surplus in each country become
identical across the three regimes. Since peN
eR
eIF and peID < peR
eN
F < p
F < p
D < p
D hold by Proposition 1.
N
R
I
Hence, CSFI < CSFR < CSFN and CSD
< CSD
< CSD
hold.

Because CSFI < CSFR < CSFN and ⇧I < ⇧R < ⇧N holds, WFI = CSFI + ⇧I < WFR = CSFR + ⇧R <WFN = CSFN + ⇧N holds. By (2) and (23), the total imports of country D in the three regimes satisfyxD (epND ) = n(1

A R
PI R
peN
pD , peR
pD , peRD /b) < xD (eF ) + xD (eF ) = n{1(epRpID ) = n(1F + t)/(qb)} < xD (epeID /b),

I
I
I
because peID < (epReR
F + t)/q < p
D holds by Proposition 1. Therefore, we have WF = CSF + ⇧ <

N
N
R
R
A R
WFR = CSFR + ⇧R < WFN = CSFN + ⇧N and WD= CSD+ txD (epNpD , peRD ) < WD = CSD + t{xD (e
F) +
I R
I
I
xP
pD , peRpID ).
D (eF )} < WD = CSD + txD (e(ii) Suppose q 2 (0, qL ] holds. In this range of q, PIs with service discrimination have no e↵ect

IR
on the equilibrium prices, peReN= ⇧N , CSFI < CSFR = CSFN ,i = pi (i = D, F ). Therefore, ⇧ < ⇧
N
R
I
N
R
I
CSD
= CSD
< CSD
, WD
= WD
< WD
, and WFI < WFR = WFN hold given q.

Proof of Proposition 3(i) Suppose q 2 (qL , 1) holds. Let W W + (bpD , pbF ) denote the world welfare in Regime R when the firm

sets the prices such that it accommodates PIs (i.e., q 2 (qH , 1)) and W W (p̀D , p̀F ) denote the world
welfare in the same regime when the firm sets the prices such that it blocks PIs (i.e., q 2 (qL , qH ]).
We have W W 0 (bpD , pbF )W W (p̀D , p̀F ) =qt}]/{8bq (k + q) k + q 2 } < 0 because(1q)n (q)[ (q) + 4{(k + q) (cmq) + mq (1q) +(q) > 0 holds if the firm chooses to accommodate PIs (seethe proof of Proposition 1). This means that, if W W (p̀D , p̀F ) < W W I holds, W W R < W W I for
all q 2 (qL , 1). We have W W I
2q) (1 + k) {c + (1kq}bk + 3 (12{(4q) (1 + k) c + (1W W (p̀D , p̀F ) = (122q) m } + 2 (1q)n[{b(c + (1q)m)}{3(qk) + 1q) (1 + k) {3(1 q)c + (4 q)t}m + (1 + q) (4 + k) t2 +k + 2q) kb}t]/{8q (k + 1) k + q 2 } > 0. Hence, W W R < W W I holds. Besides

that, for q 2 (qH , 1), W W + (bpD , pbF )WWN = nq) (q + k) c2 + 2 (11 /{8q (k + q) b} whereb (qk) > {(k + q) c+q (1mq){m(1mq) {(k + 4q

q)(k + 8q

3q 2 )c + q 4

kq

q 2 m2q) (3 + k + q) mt {(1 q)k+(4 q)q}t2 . Since (q) > 0 holds in q 2 (qH , 1) and (q) > 0 requires(k + q) (c + t

q) 1

kq

2q (1

1 >

3q (1

2q(k

q)m + t}b + 3 (12q) m+(k + 2q) t}/q,3mq) cq) b}2q)((1kq) (k + q) (t1 ⌘ q{(k1 |b(q k)={(k+q)c+q(1 k 2q)m+(k+2q)t}/q =8q + 3q 2 m + k + 4q + q 2 t}/q > (k + q) (c + t

3q 2 ) + k + 4q + q 2 t}/q > 0. Hence, W W + (bpD , pbF ) > W W N holds forq 2 (qH , 1). For q 2 (qL , qH ], W W (p̀D , p̀F )W W N = n⌦(q)[⌦(q) + 4{(1q)c + (1q)2 m +t}]/{8 k + q 2 b} > 0 holds since ⌦(q) > 0 holds for q 2 (qL , 1) (see the proof of Proposition 1). Hence,
W W + (bpD , pbF ) > W W N holds for q 2 (qL , qH ]. Therefore, W W N < W W R < W W I always holds for40

q 2 (qL , 1).
(ii) For q 2 (0, qL ], the equilibrium outcomes in Regime R coincide with those in Regime N . For
any q 2 (0, 1), W W I

W W N = N {(1Therefore, we have W W

N

= WW

R

b)k + 3t}{(1b)kt}/8b (k + 1) > 0 holds by Assumption 1.

I< WW .

Proof of Proposition 5
Under the numerical example in Figure 4, qeN = qeI = 0.69737 > qeR = 0.51538 holds. Given qeN and qeR ,R
we have CSD
q=eqR

and W W

R

q=e
qR

N
CSD
=
q=e
qN

WW

N

q=e
qN

=

R
0.70619, {WDK(q)} q=eqR

N{WD

K(q)} q=eqN =5.6970,R
N
R
N
6.5369. Therefore, there is a case where CSD
< CSD
, WD
< WD
,

and W W R < W W N hold when q is endogenously determined.

Proof of Proposition 6
Let us set= 120 and keep the other parameters the same as those in Figure 4. Then, trade liberaliza-tion from t0 = 4.57 to t1 = 0 increases the optimal level of quality without PIs as well as that under PIs
without service discrimination from qeN t=t = qeI t=t = 0.55903 to qeN t=t = qeI t=t = 0.60870, where
0

0

1

1

qL |t=t0 = 0.55816, qL |t=t1 = 0.55816, qH |t=t0 = 0.76879 and qH |t=t1 = 0.76879. However, it decreases

the optimal level of quality under service discrimination from qeR t=t0 = 0.55819 to qeR t=t1 = 0.41919.

With the numerical calculations above, changes in consumer surplus, welfare of country D, and worldR
welfare with t = t0 become CSD
q=eqR

W W R q=eqR
R
WD
q=e
qR

N
R
CSD
= 0.70340, WD
q=e
qN
q=e
qR

N
WD
= 0.91764, and
q=e
qN

R
W W N q=eqN = 0.58536. These changes with t = t1 become CSD
q=e
qR
N
WD
=
q=e
qN

0.66338 and W W R q=eqR

W W N q=eqN =

N
CSD
=
q=e
qN

7.3833. Hence, when q isNRNR
endogenously determined, there is a case where CSD
< CSD
, WD
< WD
, and W W N < W W R holdR
NR
N
at t = t0 , but CSD
< CSD
, WD
< WD
, and W W R < W W N hold at t = t1 < t0 .

Proof of Proposition 7
If a consumer in country D buys a PI good and pays for repair services, his/her expected utility becomes
P I,r
UD
=v

(pF + t)

(1

q)r.

(A2)

By comparing (15) and (A2), consumers prefer to buy the authorized good, rather than purchasing the
PI good and paying for the repair services, if the overall price of the PI good is less than the price of
the authorized good, pD > pF + t + (1q)r. Because the expected quality of the authorized good andthe quality of the PI good become identical, the consumers purchase the good with the lower overall
41price. If pD = pF + t + (1q)r holds, consumers are indi↵erent between the authorized good and the

PI good. If pD < pF + t + (1q)r holds, all consumers prefer the authorized good because the repair

price is too high. This case can be regarded as the refusal of repairs.
For the time being, let us suppose pD > (pF + t) + (1q)r holds and all consumers in country D

purchase the PI good. We assume the firm continues to provide a full warranty for the authorized good.
If a consumer buys a PI good but does not utilize the repair services provided by the firm, then her
expected utility is given by (16). Therefore, consumers purchase the repair services if their willingness
to pay for quality satisfies v

PI
r. By comparing r and vD, we have

r

PI
vD
=

qr

(pF + t)q

If r > (pF + t) /q holds, which means that the repair price for the PI good is sufficiently high, consumers
PI
with parameter v 2 [vD, r] buy the PI good but do not purchase the repair services. Suppose thisinequality holds, then the demand for the PI good purchased by the consumers who will purchase therepair services in country D is given byhr] = n 1

I,rxP(r) = nfD [b
D

ri
,
b

and the demand for the PI good purchased by the consumers who do not purchase the repair services
in country D is given by
⇥
I,nr
xP
(pF , r) = nfD r
D


⇤
qr
PI
vD
=n

(pF + t).
qb

The demand of the good in country F is given by (1). The firm’ profit in this situation is given by⇧⇤ (pF , r)

=

[pF
+(pF

{c + (1q) m}]xF (pF ) + [pF + (1q)r{c + (1I,rq) m}]xP
(r)
D

I,nr
c)xP
(pF , r).
D

By maximizing ⇧⇤ (pF , r) with respect to pF and r, we have the optimal prices as
p⇤F

=

r⇤

=

(2qb

t) k + mq (1 q) + c (k + q),
2 (k + q)(b + m).
2

We confirm that p⇤F = pbF holds. By using (27), pbD = pbF +t+(1q) (b + m) /2 = p⇤F +t+(1q) r⇤ holds.

Therefore, the overall price for the PI good in country D coincides with the price of the authorized goodunder the refusal to repair. The condition of xIP,nr(p⇤F , r⇤ ) > 0, r⇤ > (p⇤F + t) /q, can be transformedD
into pbD > (bpF + t) /q, the condition under which the firm accommodates the PI good in the case of the42refusal of repairs. Therefore, some consumers who purchased the PI good leave the PI good unrepaired
if q 2 (qH , 1) holds.

I,nr ⇤
If r⇤  (p⇤F + t) /q holds, which means that q  qH holds, we have xP(pF , r⇤ )  0 with p⇤F and r⇤ .
DI,nr
In this case, xP(pF , r)D

0 becomes binding constraint and the firm cannot set pF and r separately.

In this case, the firm sets the prices such that all consumers who purchase the PI good also purchaseI,nr
the repair services (i.e., xP(pF , r) = 0). The firm maximizes ⇧⇤ (pF , r) such that r = (pF + t) /q
D⇤⇤⇤⇤holds, and we confirm the equilibrium prices, p⇤⇤
F and r , satisfy p̀D = pF + t + (1Under full market segmentation, by (9), peNeN
D = p
F + t + {(1the firm sets the repair price, r, such that (1q)r = {(1

k)b

k)b

q) r⇤⇤ .

t}/2 holds. This implies that ift}/2 and r < (epN
F + t)/q is satisfied,

the firm can practically set the same prices as those under the full price discrimination. The inequality
can be transformed into peD < (epF + t) /q, the same condition under which the refusal of repairs realizes
the full market segmentation. The full market segmentation occurs if q 2 (0, qL ) holds.

In sum, the overall price of the good in each country and the cut-o↵ values of q that are obtainedwith the price discrimination in repair services becomes the same as those obtained with the refusal of
repairs.

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46

Figure 1: No PIs (N) and PIs without service discrimination (I)pF

pD

Country F

Country D

d

f

f

xF (!
pIF )

xF (!
pN
F)

xF

d

pID )
xD (!
pN
D ) xD (!

xD

Figure 2: PIs with service discrimination (R) and high quality

pF

pD

Country F

Country D

d
a

f

a

f

xF

d

xD

Figure 3: PIs with service discrimination (R) and middle quality

pF

pD

Country F

Country D

d
a

a

f

f

xF

d

xD

Figure 4: Endogenous quality
Monopolist’s profit - fixed costFigure 5: Trade liberalization and the optimal quality
Monopolist’s profit - fixed cost