DPRIETI Discussion Paper Series 20-E-035

Transfer Pricing Regulation and Tax Competition

CHOI, Jay PilMichigan State University

FURUSAWA, TaijiUniversity of Tokyo

ISHIKAWA, JotaRIETI

The Research Institute of Economy, Trade and Industryhttps://www.rieti.go.jp/en/

RIETI Discussion Paper Series 20-E-035

April 2020

Transfer Pricing Regulation and Tax Competition*

Jay Pil Choi

Michigan State University

Taiji Furusawa

University of Tokyo

Jota Ishikawa

Hitotsubashi University & RIETI

Abstract

The paper analyzes multinational enterprises' incentives to manipulate internal transfer prices to take

advantage of tax differences across countries, and implications of transfer-pricing regulations as a

countermeasure against such profit shifting. We find that tax-motivated foreign direct investment

(FDI) may entail inefficient internal production but may benefit consumers. Thus, encouraging

transfer-pricing behavior to some extent can enhance social welfare. Furthermore, we consider tax

competition between two countries in order to explore the interplay with transfer-pricing regulations.

We show that the FDI source country will be willing to set a higher tax rate and tolerate some profit

shifting to a tax haven country if the regulation is tight enough. We also indicate a novel mechanism

through which it is the larger country that undertakes tax-motivated FDI, the pattern we often observe

in reality.

Keywords: Multinational enterprise; Corporate tax; Transfer pricing; Foreign direct investment; Arm's

length principle; Tax competition

JEL classification: F12, F23, H21, H26, L12, L51

The RIETI Discussion Paper Series aims at widely disseminating research results in the form of professional

papers, with the goal of stimulating lively discussion. The views expressed in the papers are solely those of

the author(s), and neither represent those of the organization(s) to which the author(s) belong(s) nor the

Research Institute of Economy, Trade and Industry.

* This paper is an extensively revised version of a part of Choi et al. (2018) and is presented as a part of the Project

“Analyses of Offshoring” undertaken at the Research Institute of Economy, Trade and Industry (RIETI). The authors

wish to thank Arnaud Costinot (coeditor) and two anonymous referees for helpful comments and suggestions. We

also thank Hayato Kato, Yuka Ohno, Pascalis Raimondos, Martin Richardson, Jay Wilson and participants in various

conferences and seminars for their valuable discussions and comments. This research was initiated during Choi's

visit to Hitotsubashi Institute for Advanced Study whose hospitality is greatly appreciated. Choi acknowledges

financial support from the Ministry of Education of the Republic of Korea and the National Research Foundation of

Korea: Grant Number NRF-2016S1A5A2A01022389. Furusawa and Ishikawa acknowledge financial support from

the Japan Society of the Promotion of Science through the Grant-in-Aid for Scientific Research (A): Grand Numbers

19H00594 and 17H00986.

1 Introduction

Corporate tax rates substantially differ across countries, and some countries adopt prefer-

ential tax measures.1 Since multinational enterprises (MNEs) actively engage in intrafirm

transactions across borders,2 they have an incentive to manipulate internal transfer prices

to save tax payments, an activity often called “transfer pricing”. MNEs tend to shift

their profits from high-tax countries to low-tax jurisdictions (see Hines and Rice, 1994;

Huizinga and Laeven, 2008; Bauer and Langenmayr, 2013; Davies et al., 2018). For in-

stance, inspections by the Vietnamese tax authorities have found that “the most common

trick played by FDI enterprises to evade taxes was hiking up prices of input materials

and lowering export prices to make losses or reduce profits in books”.3 In addition, Egger

et al. (2010) find that the average subsidiary of an MNE pays about 32% less tax than

similar local firms in high-tax countries. According to Goldman Sachs, the tax saving by

U.S. MNEs amounts to $2 trillion, equivalent to four years’ worth of U.S. corporate tax

revenues (Nikkei, August 31, 2016).

If governments do not regulate transfer pricing, MNEs may shift a large proportion

of their profits away from their countries to low-tax or no-tax jurisdictions, narrowing

their tax bases significantly. Governments thus impose transfer-pricing rules to control

transfer-price manipulation. In particular, the Organisation for Economic Co-operation

and Development (OECD) proposed that internal transfer prices follow the so-called arm’s

length principle (ALP) in its guidelines for transfer pricing published in 1995 and revised

in 2010.4

The basic approach of the ALP is that the headquarters and affiliates of an MNE

should be treated as “operating as separate entities rather than as inseparable parts of

a single unified business” and the controlled internal transfer price should mimic the

market price that would be obtained in comparable uncontrolled transactions at arm’s

length. This kind of comparative analysis is at the heart of the application of the ALP.

Currently, the ALP is the international transfer-pricing principle to which OECD member

1Preferential tax measures are observed in many countries. For example, Vietnam grants special orpreferential tax rates to attract foreign direct investment (FDI). Thailand provides tax incentives forFDI. The Taiwanese corporate tax rate is lower by 7 percentage points for foreign firms with some fixedplaces of business or some business agents in Taiwan.

2Bernard et al. (2010) report that over 46% of U.S. imports comprised intrafirm transactions in 2000.3http://vietnamlawmagazine.vn/transfer-pricing-unbridled-at-fdi-enterprises-4608.html4The OECD also initiated a project in 2012 to create an action plan to address base erosion and profit

shifting.

1

countries have agreed.

Against this background, the purpose of this study is twofold. The first purpose is

to closely examine MNEs’ incentive to manipulate transfer prices to avoid tax payments,

and governments’ regulatory responses to such practices. We specifically investigate the

transfer pricing resulting from tax-motivated FDI and the implication of the ALP, when

imperfect competition prevails in the final-good market. To this end, we consider a

stylized set-up of two countries with different corporate tax rates, where a monopolist

that produces and sells its final products in the high-tax country can set up its subsidiary,

which produces intermediate goods, in the low-tax country to engage in tax-saving transfer

pricing. We show that this monopolistic MNE shifts all its profits to the low-tax country

by choosing the standard monopoly price as the transfer price, replicating the monopoly

outcome in the market.

To counter such extreme transfer-pricing activities, the MNE’s home country may

tighten transfer-pricing regulation by lowering the transfer-price cap. In this study, we

consider transfer-price caps to be a regulatory measure.5 Tax authorities audit tax-

avoidance behaviors by comparing the prices used in intrafirm transactions with those of

similarly uncontrolled transactions between independent parties (i.e., arm’s length prices);

this method of the ALP is called the comparable uncontrolled price (CUP) method. In

practice, however, it is often difficult to find a comparable transaction of similar products

between independent enterprises. In such cases, other ALP methods such as the cost

plus (CP) method, are applied.6 The price cap which we consider in this study can be

thought of as a CP method, as regulatory authorities often regard the cost plus a reason-

able mark-up as a transfer price that meets the ALP.7 The CP method is also a natural

ALP in the case of monopoly, because in many monopolistic environments it is hard to

find other transactions of comparable inputs.

We show that transfer pricing entails lowering what the MNE perceives as its marginal

cost of production. The “perceived marginal cost” declines as a result of transfer pricing,

because the marginal tax saving that arises from an additional shipment of intermediate

goods serves as the marginal benefit of production for the MNE. Not surprisingly, there-

5This assumption has often been made to investigate transfer-pricing regulations. See Raimondos-Moler and Scharf (2002), Peralta et al. (2006), Becker and Fuest (2012), and Matsui (2012), amongothers.

6Other suggested methods include the resale price method, transactional net margin method, andtransactional profit split method. See OECD (2010) for more details.

7Other ALP methods (except for the CUP method) indirectly regulate the ceiling of the transfer price.

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fore, FDI occurs even if it is less efficient to produce the intermediate goods internally

at its foreign subsidiary, because it can be used as a vehicle to lessen its tax burden

with an inflated internal price. Interestingly, however, profit shifting with the regulation

may also benefit consumers, because transfer pricing lowers the monopolist’s perceived

marginal cost, thereby leading to more production which alleviates allocative inefficiency

due to market power. Thus, the MNE’s home country may want to encourage its firm’s

tax-saving, transfer-pricing activities.

The second purpose of the paper is to identify the economic environment in which a

country is indeed willing to select a higher tax rate than another country to encourage

its monopolistic firm to engage in FDI and transfer pricing, hoping that the resulting

alleviation of allocative inefficiency enhances its social welfare. To this end, we first

investigate a sequential-move, tax-competition game (i.e., a Stackelberg tax-competition

game) played by two welfare-maximizing governments within our baseline model with

transfer-pricing regulation.8 We show that the nature of tax competition can depend

on the tightness of transfer-pricing regulation. In particular, the MNE’s home country

is willing to set a higher tax rate and tolerate some profit shifting to an endogenously-

determined, tax-haven country, if the regulation is sufficiently tight. However, if regulation

is too lax, tax competition leads to a “race to the bottom” that eliminates any incentives

for tax-motivated FDI. Interestingly, this implies that a tax haven country does not always

prefer lax transfer-pricing regulation. Thus, the incentives of the host and FDI source

countries can be aligned to set up global regulatory standards for transfer pricing.

Finally, we extend the sequential-move game to a simultaneous-move, tax-competition

model with multiple industries, played by two countries with different population sizes.9

This set-up allows us to endogenously determine the FDI source country that selects

a higher tax rate and investigate the characteristics of such countries. We show that

a pure-strategy, subgame-perfect equilibrium exists if countries are sufficiently different

in size. The large country sources FDI, choosing a higher tax rate than the smaller

country. It is willing to create an environment in which its firm engages in FDI to save

tax payments because, for the large country, the benefit of the resulting increase in the

8For example, Baldwin and Krugman (2004) and Stowhase (2013) also analyze tax competition in asequential-move game.

9We treat transfer-pricing regulation as given in our analysis, because the ALP is agreed as the transfer-pricing regulation among OECD member countries. By contrast, Mansori and Weichenrieder (2001) andRaimondos-Moler and Scharfy (2002) focus on the strategic use of transfer-pricing rules rather than taxeswhen analyzing transfer pricing in a single industry. In their analyses, governments non-cooperativelychoose their optimal transfer-pricing rule, taking the tax rates as given.

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consumer surplus is large relative to the tax revenue that it would have earned if it hosted

FDI. The smaller country, on the contrary, undercuts the large country’s tax rate, because

the tax revenue collected from the subsidiary of the firm operating in the large market

is large. This novel result is consistent with the fact that most low-tax countries or tax

havens are small countries.10 The result also gives some justification to use a model

with the Stackelberg tax-setting nature, because it is reasonable to think that in reality

small tax-haven countries set their tax rates after observing large countries’ tax rates.

The welfare impacts of transfer pricing, which are readily obtained in the sequential-move

game, can also extend to the setting of the simultaneous-move game.

Our study is thus at the intersection of international trade and public economics.

Horst (1971) initiated the theory of MNEs in the presence of different tariff and tax rates

across countries and explored the profit-maximizing strategy of a monopolistic firm selling

to two national markets (i.e., how much it should produce in each country and what the

optimal transfer price for goods exported from the parent to the subsidiary would be).

Horst (1971) and subsequent studies (e.g., Itagaki, 1979) show that an MNE’s optimum

price would be either the highest or the lowest possible allowed by the limits of government

rules and regulations, depending on tax and tariff schedules among countries. Samuelson

(1982) is the first study to point out that for an MNE subject to the ALP, the arm’s

length reference price itself can be partially determined by the firm’s activities.

Lee (1998) analyzes the effects of profit taxes on firm behaviors and shows that a

monopolist engaged in tax avoidance may produce either more or less than it would in

the absence of a tax.11 The focus of his analysis is on deriving the conditions under which

profit taxes are non-neutral in terms of the monopolist’s output decision. It is shown

that the effects of tax avoidance on the consumer surplus depend crucially on the shape

of the audit probability and penalty rate. Our model identifies a different channel (i.e.,

transfer pricing to shift profits across jurisdictions with different tax rates) through which

the consumer surplus is affected when the monopolist aims to minimize the overall tax

burden.

In our model, the welfare of the high-tax country can improve because the consumers

there benefit from regulated transfer-pricing activities. In particular, welfare can improve

even if intermediate-good production is less efficient with FDI than without FDI. Matsui

(2012) is closely related to our study in that he considers internal transfer prices in MNEs

10These countries include Ireland, Luxembourg, Singapore, Switzerland and the Netherlands.11We thank an anonymous referee for directing our attention to this study.

4

as the channel for tax avoidance and shows that an MNE’s transfer pricing can benefit

consumers through an increase in its output. In a Dixit–Stiglitz model of monopolistic

competition, he shows that tax authorities face a trade-off between consumer welfare and

tax revenue.12 However, he deals with neither tax-motivated FDI nor tax competition.

We also show that the relationship between the transfer-price cap and consumer price is

not monotonic.

Tax competition between countries of different size has been explored extensively

(Bucovetsky, 1991; Wilson, 1991; Haufler and Wooton, 1999; Stowhase, 2005, 2010). The

literature also shows that the smaller country is likely to set a lower tax rate in various

settings. Stowhase (2005, 2010) is related to our analysis in the sense that profit shifting

is explicitly taken into account in a tax-setting game between two tax-revenue-maximizing

governments. In our analysis, however, the governments maximize social welfare, caring

about not only tax revenue but also profits and consumer welfare. Moreover, Stowhase

(2005, 2010) does not deal with transfer-pricing regulation. We identify an aforementioned

novel logic of an equilibrium outcome that the larger country is willing to set a higher

corporate tax rate than the smaller country in the presence of transfer-pricing regulation.

Although tax competition has been examined in the presence of profit shifting (Stowhase,

2005, 2010; Bucovetsky and Haufler, 2008; Slemrod and Wilson, 2009; Johannesen, 2010;

Marceau et al., 2010), only a few theoretical studies take transfer-pricing regulation into

consideration. Elitzur and Mintz (1996) study tax competition between the MNE’s home

country and its host country, both of which try to maximize individual tax revenues. The

MNE operates under rigid transfer-pricing regulation along the lines of the CP method.

In their model, however, there is no consideration of whether the firm sets up a subsidiary

in the host country. Hence, they are unable to discuss the possible inefficiency caused

by tax-motivated FDI to a high-cost country. Moreover, in their model, transfer pricing

is used not only for profit shifting but also for an incentive scheme to improve the sub-

sidiary’s efficiency. Peralta et al. (2006) identify an interesting role of transfer-pricing

regulation in the context of bidding for a firm: loosening the control of profit shifting

can mitigate tax competition so that winning becomes more beneficial in the presence of

indigenous firms that also pay corporate taxes.13 In some cases, therefore, the winning

country does not strictly enforce the regulation even though it entails tax revenue leak-

12Matsui (2012) focuses on the long-run equilibrium in which the MNE’s post-tax profits are zero.13Becker and Fuest (2012) introduce a model that does not require the presence of indigenous firms

and obtain qualitatively the same result as Peralta et al. (2006).

5

age. Hosting a firm (or the headquarters of a firm in our context) is different from getting

hold of its profits. Because of its reduced-form structure of the model, however, they

are unable to examine the effect of transfer pricing on the firm’s output and its welfare

consequences through the effect on the consumer surplus. In our study, this channel is

crucial to identifying the importance of market size in the endogenous determination of

the FDI source country and a tax haven that hosts FDI.

The rest of the paper is organized as follows. Section 2 introduces the basic set-up

of a monopoly model with transfer pricing. In the model in which the monopolist has

already set up a subsidiary in the foreign country, we examine this monopolistic MNE’s

transfer-pricing behavior when its home tax rate is exogenously given at a higher rate

than the foreign rate. In particular, we show that the MNE increases its output from

the monopolistic production level when its home country imposes a binding cap on the

transfer price. In Section 3, we model a sequential-move, tax-competition game, played by

two countries, still assuming that only one firm, in the first-mover country, sources inputs

from the foreign country. We show that the home country selects a higher tax rate than

the foreign country if and only if transfer-pricing regulation is sufficiently tight. Section 4

extends the tax-competition game to a simultaneous-move game with a monopoly in each

country operating in each of the two industries. Moreover, we allow the two countries

to differ in size. Then, we show that there is a pure-strategy equilibrium in which the

larger country sets a higher tax rate than the smaller one to become the source country

of tax-motivated FDI. Section 5 concludes.

2 Monopoly Model with FDI: Transfer Pricing and Regulations

2.1 Baseline Model

There are two countries, Country 1 and Country 2, with possibly different corporate tax

rates, t1 and t2. In Country 1, there is a monopolistic final-good producer, which we often

call the MNE. The MNE’s headquarters that produces the final good is immobile and tied

to Country 1, while its intermediate input can be procured either from the open market

at a price of ω or from its subsidiary in Country 2.14 We assume that one unit of the input

is converted into one unit of the final good without incurring any additional costs and

that input production is subject to constant-returns-to-scale technology. We also assume

14Alternatively, we can assume that ω is the headquarters’ constant marginal production cost of theintermediate input.

6

away the costs associated with FDI.15 The subsidiary’s unit cost of input production (i.e.,

the marginal production cost) is given by c. The final good is consumed only in Country

1.

The MNE can choose an internal transfer price of γ, when its foreign subsidiary sup-

plies its input to the headquarters. Without any tax rate differential between the two

countries, the MNE’s optimal internal transaction price for the input is simply its marginal

cost, c, to eliminate the double marginalization problem. However, as the two countries

have different tax rates, the MNE can engage in transfer pricing such that it chooses γ to

optimally allocate its profits between its headquarters and subsidiary and thus minimize

its tax burden.

In this section, we assume that the two countries’ corporate tax rates are exogenously

given such as t1 > t2, meaning that the MNE in Country 1 has an incentive to manipulate

its internal transfer price to avoid tax payments. We also assume throughout this section

that the MNE has already set up its subsidiary in Country 2 to procure intermediate

goods, thereby focusing the analysis on the MNE’s transfer-pricing strategy and its home

country’s regulatory response.

2.2 The Benchmark Case: No Regulation

As a benchmark case, we first consider the choice of transfer price by the MNE without

any transfer-pricing regulation. In this case, the MNE selects its transfer price, γ, and

output, q, to maximize the following global profits after tax:

Π = (1− t1) [P (q)− γ]q︸ ︷︷ ︸Downstream Profits

+ (1− t2) (γ − c)q︸ ︷︷ ︸Upstream Profits

, (1)

where P (q) is the downward-sloping inverse demand function faced by the monopolist

(with the corresponding demand function q = D(p)). Decision making is assumed to be

centralized. That is, with the firm’s objective function above, the headquarters producing

the final good makes an output decision that maximizes the overall profit of the firm, not

only the profit of the downstream division.

We can rewrite the objective function of the monopolist, expressed by (1), as

Π = (1− t1)[P (q)− ξ]q, (2)

15If a fixed cost of setting up the subsidiary exists, FDI becomes less likely. However, the essence ofour results would not change.

7

where

ξ ≡ (1− t2)c− (t1 − t2)γ

1− t1. (3)

That is, the MNE facing different tax rates across countries behaves as if its marginal pro-

duction cost were ξ, which can be considered as its perceived marginal cost of production.

Since the MNE’s profit decreases as ξ increases, the monopolist’s optimal choice of γ is

to minimize ξ regardless of its output level. Note that ξ is decreasing in its transfer price

γ because it can be used as a vehicle to shift profit from the high-tax country (Country

1) to the low-tax country (Country 2).

As pointed out by Horst (1971), it immediately follows that the optimal choice is to

set γ as high as possible with the constraint that the downstream profit is non-negative.

This would imply that all profits from a high-tax country are shifted toward to a low-

tax country in the absence of any regulation. This simple model illustrates the need for

regulations to counter such MNE’s profit-shifting motives to reduce the tax burden.

To show this rigorously, we first derive q∗(γ), which we define as the MNE’s optimal

output when its transfer price is set at γ. Let qm(ξ) denote the optimal monopoly quantity

that maximizes the monopolist’s profits when its perceived marginal cost is ξ. Since

qm(ξ(γ)) is increasing in γ and hence P (q∗(γ)) is decreasing in γ, there is a unique γ = γ0

such that P (q∗(γ0)) = γ0. In other words, if γ < γ0, the optimal output by the MNE

is given by q∗(γ) = qm(ξ(γ)) with the downstream division in the high-tax Country 1

making a positive profit. However, if γ > γ0, the non-negative profit constraint for the

headquarters is binding because P (q(γ)) < γ. Therefore, the MNE’s optimal output q∗(γ)

cannot be qm(ξ(γ)). The maximum output that can be used to transfer profit is capped

by P−1(γ). That is, if γ > γ0, we have q∗(γ) = P−1(γ) = D(γ), which is decreasing in γ.

We can conclude that

q∗(γ) =

{qm(ξ(γ)) if γ < γ0

P−1(γ) = D(γ) if γ ≥ γ0.

The following lemma helps us determine the MNE’s optimal choice of γ.

Lemma 1. Without any transfer-pricing regulation, the MNE’s optimal choice of γ can-

not be less than γ0. This implies that all the downstream profits are transferred to the

subsidiary located in the country with a lower tax rate, that is, P (q∗(γ)) = γ.

Proof. Suppose, on the contrary, that γ < γ0. Then, the optimal output by the MNE is

given by q∗(γ) = qm(ξ(γ)) With an infinitesimal increase in γ, the new transfer price is

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still less than γ0 while reducing ξ. As a result, the MNE’s profit increases, resulting in a

contradiction.

Given Lemma 1, we can rewrite the optimal choice of γ by the MNE as

maxγ

(1− t2)(γ − c)D(γ). (4)

This is mathematically equivalent to the standard monopoly pricing problem where γ can

be considered as the monopolist’s price. This implies that the MNE chooses a monopoly

price equal to P (qm(c)). Proposition 1 summarizes our discussion in the case of no reg-

ulation and calls for regulations to counter the MNE’s profit-shifting motives to reduce

the tax burden.

Proposition 1. (Full Profit Shifting with the Monopoly Outcome under No Regulation)

In the absence of any transfer-pricing regulation, the MNE shifts all its profits to the

country with the lower tax rate by choosing the transfer price at the standard monopoly

price, replicating the monopoly outcome in the market.

2.3 Transfer-pricing Regulation and the MNE’s Decisions

In reality, regulations would prevent the choice from being a corner solution and limit the

MNE’s profit-shifting motives. The most-widely adopted and agreed-upon standard prac-

tice is the ALP, which requires intrafirm transfer prices to mimic the market prices that

would be obtained in comparable uncontrolled transactions at arm’s length, as discussed

in the Introduction. Although this principle is conceptually sound and straightforward,

its implementation as a regulatory policy may be difficult and subject to different inter-

pretations. For instance, in the monopoly context, such a comparative analysis is unlikely

to be feasible, simply because there is no comparable transactions as it is the only firm

that produces the final good; no other firms acquire similar inputs. Even if similar inputs

are transacted in the market by other firms for different purposes, a firm may argue that

the available inputs are not suitable to meet its specifications, which explains why they

are engaged in its production in the first place. In other words, what constitutes a similar

input may not be clear-cut and could be subject to disputes unless comparable inputs are

identical.

In our analysis, we simply model Country 1’s transfer-pricing regulation as a price cap

for the transfer price to limit the extent to which the MNE can shift its profits to the

9

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qm(c) =1 � c

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P (qm(c))<latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit>

�̄<latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">AAACbnichVHLSsNAFD2Nr1pfVUEEEYtFcVVuRFBcFdy4bKtVoRWZxLEG8yJJC7X4A+7FhaAoiIif4cYfcOEniBtBwY0Lb9OAqKg3TObMmXvunLmjuabhB0QPMaWtvaOzK96d6Ont6x9IDg6t+U7V02VRd0zH29CEL03DlsXACEy54XpSWJop17W9peb+ek16vuHYq0HdlZuWqNjGjqGLgKlSWRNeqlwRliW2kmnKUBipn0CNQBpR5JzkFcrYhgMdVViQsBEwNiHg81eCCoLL3CYazHmMjHBf4gAJ1lY5S3KGYHaP/xVelSLW5nWzph+qdT7F5OGxMoUpuqdreqE7uqFHev+1ViOs0fRS51lraaW7NXA4uvL2r8riOcDup+pPzwF2sBB6Ndi7GzLNW+gtfW3/+GVlsTDVmKYLemL/5/RAt3wDu/aqX+Zl4QQJfgD1e7t/grXZjEoZNT+Xzmaip4hjDJOY4X7PI4tl5FAMO3aEU5zFnpURZVyZaKUqsUgzjC+hzHwAqquN4A==</latexit>

q = P�1(�̄)<latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">AAACeXichVHLLgRBFD3T3uM1HguJDSZkSExuIyESicTGcjwGiWFS3cro6JfunkmY+AE/YGGDRASfYeMHLHyCWJJYsHCnpxNBcCtVderUPbdOVWmuafgB0UNMqamtq29obIo3t7S2tSc6Old8p+jpMqs7puOtacKXpmHLbGAEplxzPSkszZSr2u5cZX+1JD3fcOzlYN+VG5Yo2Ma2oYuAqXyie28ms1keVQ9TOU14uYKwLDGcTyQpTWH0/QRqBJKIIuMkLpHDFhzoKMKChI2AsQkBn9s6VBBc5jZQZs5jZIT7EoeIs7bIWZIzBLO7PBZ4tR6xNq8rNf1QrfMpJnePlX0YpHu6ome6oxt6pPdfa5XDGhUv+zxrVa108+1HPUuv/6osngPsfKr+9BxgG1OhV4O9uyFTuYVe1ZcOjp+XphcHy0N0Tk/s/4we6JZvYJde9IsFuXiCOH+A+v25f4KVsbRKaXVhIjmbjr6iEb0YQIrfexKzmEcGWT73AKe4wnXsTelXUspINVWJRZoufAll/AN3C5FO</latexit>

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P�1(c) =1 � c

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Figure 1: MNE’s optimal output level

low-tax country. Country 1 caps the transfer price at γ̄. Under this regulation, the MNE

can only select γ that is less than or equal to γ̄.

We derive the MNE’s optimal choice of γ under the restriction and its optimal output

level as a function of γ̄. As shown in the previous subsection, the MNE raises γ as much as

it can, all the way up to the monopoly price P (qm(c)) if possible. If γ < γ0, for example,

the MNE can raise its profit by increasing γ, thereby decreasing the perceived marginal

cost ξ. If γ ≥ γ0, it can also raise its profit by increasing γ because γ here serves as

the price of the products and increasing γ is equivalent to bringing the price closer to

the monopoly price P (qm(c)), as shown in (4). Therefore, the MNE chooses the largest

possible γ under the price cap of γ̄, as long as this regulation is binding, that is, as long

as γ̄ ≤ P (qm(c)). If γ̄ > P (qm(c)), the MNE simply chooses γ at the monopoly price and

produces qm(c) units of the good in such a case. Figure 1 illustrates the MNE’s optimal

output level as a function of the price cap γ̄ (in the case of linear demand, as given by

(5)-(7) below). An increase in γ̄ increases the optimal output if c ≤ γ̄ ≤ γ0 but decreases

it if γ0 < γ̄ ≤ P (qm(c)).

Lemma 2. With the given transfer-price cap γ̄, the MNE chooses γ = γ̄ if γ̄ ≤ P (qm(c)),

and γ = P (qm(c)) if γ̄ > P (qm(c)). The optimal output level is given by

q∗(γ̄) =

qm(ξ(γ̄)) if c ≤ γ̄ ≤ γ0,

P−1(γ̄) if γ0 < γ̄ ≤ P (qm(c)),

qm(c) if γ̄ > P (qm(c)).

10

As an illustration and for later purposes, we explicitly derive some of the above key

functions and variables in the case of linear demand, such that P (q) = 1− bq:

qm(ξ(γ̄)) =1− c

2b+

(t1 − t2)(γ̄ − c)2b(1− t1)

, (5)

P−1(γ̄) =1− γ̄b

, (6)

γ0 =(1− t1) + (1− t2)c

(1− t1) + (1− t2). (7)

2.4 Optimal Taxation and Transfer-pricing Regulation

Figure 1 shows the possibility that Country 1, the home country of the MNE, can mitigate

the monopoly distortion by relaxing transfer-pricing regulation and hence inducing the

MNE to produce more. Here, we investigate whether Country 1 can indeed enhance

its social welfare by optimally adjusting the transfer-price cap. In addition, we derive

its optimal policy when both the transfer price cap and the corporate tax rate can be

freely chosen, for the given tax rate in Country 2 (i.e., the country that hosts the MNE’s

subsidiary).

Country 1’s social welfare is defined as the sum of the consumer surplus (CS), producer

surplus (PS), and tax revenue (TR). It follows from

CS =

∫ q∗(γ̄)

0

P (q)dq − P (q∗(γ̄))q∗(γ̄),

PS = Π1 = (1− t1)[P (q∗(γ̄))− ξ(γ̄)]q∗(γ̄),

TR = t1[P (q∗(γ̄))− γ̄]q∗(γ̄)

that Country 1’s social welfare can be written as

W1 =

∫ q∗(γ̄)

0

[P (q)− ξs(γ̄)]dq, (8)

where the social marginal cost ξs is defined and can be written with the use of (3) as

ξs(γ̄) = (1− t1)ξ(γ̄) + t1γ̄

= (1− t2)c+ t2γ̄. (9)

Obviously, W1 increases with the MNE’s output level, q∗(γ̄), and decreases with the social

11

marginal cost, ξs(γ̄).

Lemma 3. The optimal transfer price cap for Country 1 is greater than γ0. It equals γ0

if t2 is small, while it is less than γ0 if t2 is sufficiently large to be close to t1.

Proof. As Figure 1 shows, q∗(γ̄) increases by lowering γ̄ when γ̄ > γ0. Because a decrease

in γ̄ also decreases ξs(γ̄) as (9) shows, W1 increases by lowering γ̄ in this range of γ̄. Thus,

the optimal γ̄ is greater than γ0.

In the range that c ≤ γ̄ ≤ γ0, a reduction in γ̄ involves a trade-off between the

beneficial effect of lowering ξs(γ̄) and adverse effect of decreasing q∗(γ̄). If t2 is small,

the latter adverse effect outweighs the former effect. Indeed, if t2 = 0 at the extreme, (9)

shows that ξs(γ̄) = c, and hence decreasing γ̄ from γ0 only reduces q∗(γ̄) leaving ξs(γ̄)

as it is. Hence, it is optimal for Country 1 to set γ̄ = γ0. However, if t2 is not so small,

the beneficial effect of lowering ξs(γ̄) outweighs the adverse effect at γ̄ = γ0, making it

optimal for Country 1 to set γ̄ below γ0. At the extreme where t2 is so large to be equal

to t1, we know from (3) that ξ(γ̄) = c and thus q∗(γ̄) = qm(c). Hence, the optimal γ̄ is as

small as c to minimize ξs(γ̄).

What if Country 1 can adjust t1, for the given t2, as well as choose an arbitrary

γ̄? Redefining ξ as a function of t1 as well as γ̄ (i.e., ξ(γ̄, t1)), we obtain from (3) that

∂ξ/∂t1 = −(γ̄ − c)(1 − t2)/(1 − t1)2 < 0. Since qm is decreasing in ξ, this means that

qm increases as t1 rises, except at γ̄ = c. This relationship is easily verified from (5) in

the linear demand case, as illustrated by the counterclockwise rotation of the qm line in

Figure 2. As this figure shows, an increase in t1 coupled with a decrease in γ̄ (from γ0 to

γ0′) enables Country 1 to increase q∗(γ̄) and decrease ξs(γ̄) at the same time.

Proposition 2. The MNE’s home country can enhance its social welfare by increasing its

corporate tax rate and tightening transfer-pricing regulation simultaneously. The monopoly

distortion is completely eliminated, meaning social welfare is maximized at the limit where

the tax rate approaches 1, whereas the transfer-price cap approaches the marginal cost of

the intermediate good.

Proof. As t1 increases, so does qm(ξ(γ̄, t1)) for any γ̄. It also follows from γ0 = P (qm(γ0, t1)),

the definition of γ0, that γ0 decreases accordingly, as Figure 2 illustrates. Thus, Country 1

can induce the MNE to produce more and lower the social marginal cost, as seen in (9), by

raising t1 and simultaneously lowering γ̄ to keep γ̄ = γ0. That is, Country 1 can increase

its social welfare by raising t1 and lowering γ̄, while keeping P−1(γ̄) = qm(ξ(γ̄, t1)). As

12

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qm(c) =1 � c

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P (qm(c))<latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">AAACbHichVG7SgNBFD1Z3/EVH4UgQjAosVnuiqBYCTaWMTGJEh/srmNc3Je7m4AGf8DWwkItFETEz7DxByz8BBFsFGwsvNksiIp6h5k5c+aeO2dmNNc0/IDoISY1Nbe0trV3xDu7unt6E339Bd+peLrI647peMua6gvTsEU+MAJTLLueUC3NFEVtZ76+X6wKzzcceynYc8WapZZtY8vQ1YCplUx6d91K6xMTG4kUyRRG8idQIpBCFBkncYVVbMKBjgosCNgIGJtQ4XMrQQHBZW4NNeY8Rka4L3CAOGsrnCU4Q2V2h8cyr0oRa/O6XtMP1TqfYnL3WJnEGN3TNb3QHd3QI73/WqsW1qh72eNZa2iFu9F7OJR7+1dl8Rxg+1P1p+cAW5gJvRrs3Q2Z+i30hr66f/ySm82O1cbpgp7Y/zk90C3fwK6+6peLInuCOH+A8v25f4LCpKyQrCxOpebk6CvaMYxRpPm9pzGHBWSQ53MtHOEUZ7FnaVAalkYaqVIs0gzgS0jjH1kJjE0=</latexit><latexit sha1_base64="Q5pfn6PClAnStJTq1O80qPcW5+s=">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</latexit>

�̄<latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">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</latexit><latexit sha1_base64="myiteofBN2Ixrg5ybcZRjhlzkeg=">AAACbnichVHLSsNAFD2Nr1pfVUEEEYtFcVVuRFBcFdy4bKtVoRWZxLEG8yJJC7X4A+7FhaAoiIif4cYfcOEniBtBwY0Lb9OAqKg3TObMmXvunLmjuabhB0QPMaWtvaOzK96d6Ont6x9IDg6t+U7V02VRd0zH29CEL03DlsXACEy54XpSWJop17W9peb+ek16vuHYq0HdlZuWqNjGjqGLgKlSWRNeqlwRliW2kmnKUBipn0CNQBpR5JzkFcrYhgMdVViQsBEwNiHg81eCCoLL3CYazHmMjHBf4gAJ1lY5S3KGYHaP/xVelSLW5nWzph+qdT7F5OGxMoUpuqdreqE7uqFHev+1ViOs0fRS51lraaW7NXA4uvL2r8riOcDup+pPzwF2sBB6Ndi7GzLNW+gtfW3/+GVlsTDVmKYLemL/5/RAt3wDu/aqX+Zl4QQJfgD1e7t/grXZjEoZNT+Xzmaip4hjDJOY4X7PI4tl5FAMO3aEU5zFnpURZVyZaKUqsUgzjC+hzHwAqquN4A==</latexit>

q = P�1(�̄)<latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit><latexit sha1_base64="nA5Oi59UXZV1p0CqtxXmTHWk1Yg=">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</latexit>

q = qm(⇠(�̄))<latexit sha1_base64="jG3sAYOYYLWRVytn21rHqrgkl+c=">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</latexit><latexit sha1_base64="jG3sAYOYYLWRVytn21rHqrgkl+c=">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</latexit><latexit sha1_base64="jG3sAYOYYLWRVytn21rHqrgkl+c=">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</latexit><latexit sha1_base64="jG3sAYOYYLWRVytn21rHqrgkl+c=">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</latexit>

P�1(c) =1 � c

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Figure 2: The effect of an increase in the source country’s tax rate

shown in (3), at the limit where t1 approaches 1, γ̄ approaches c, meaning that ξ remains

finite to satisfy the above equality. Noting that ξs(γ̄) also approaches c, we conclude that

Country 1 can maximize its social welfare by raising t1 and lowering γ̄, thereby attaining

a market outcome equivalent to that under perfect competition at the limit where t1 = 1

and γ̄ = c.

In the current scenario in which the MNE’s home country has two policy tools, namely

the transfer-price cap and corporate tax rate, it can manage to increase the MNE’s output

and minimize tax leakage at the same time. Even though the country lowers γ̄, which

dampens the MNE’s incentive to produce more, it can increase t1 sufficiently large to

more than offset the incentive; hence the MNE is induced to increase its output because

of the increased incentive to save tax payments. This benefits the country because it can

increase the MNE’s output while reducing tax leakage. Indeed, this proposition indicates

that the country can lower the price of the good all the way to the MNE’s actual marginal

cost of production by tailoring its tax rate and price-cap.

3 Tax Competition between the MNE’s Home Country and the

Host Country

We have thus far analyzed how the MNE reacts to transfer-pricing regulation and corpo-

rate taxation in its home country, and discussed the optimal policy for the home county.

13

Proposition 2 reveals that the home country can completely eliminate the monopoly dis-

tortion through extreme transfer-pricing regulation and taxation. In reality, however, the

transfer price is regulated by the ALP, which suggests that it should be set at the level

that provides reasonable markups to the marginal production cost of intermediate goods.

On the contrary, sovereign countries have more freedom to set their individual corporate

tax rates. In this section, therefore, we fix γ̄, and discuss how the tax rates are determined

between the MNE’s home government and host government.

We consider a sequential-move game in which Country 1 (the MNE’s home country)

first sets its tax rate, and then Country 2 tries to undercut Country 1’s tax rate to

attract FDI, given the transfer-pricing regulation represented by the price cap of γ̄. We

show that the nature of tax competition can depend on the tightness of transfer-pricing

regulation. In particular, if γ̄ is not too large, Country 1 selects a relatively high tax rate

to allow Country 2 to undercut its tax rate in a unique subgame perfect equilibrium. The

monopolist in Country 1 sets up a subsidiary in Country 2 and engages in transfer pricing

to save tax payments. Country 1 is willing to let its own firm do so, because it leads to

an expansion of production and helps increase its social welfare. If regulation is too lax,

(i.e., γ̄ is sufficiently large), however, tax competition leads to the “race to the bottom”

and eliminates any incentive for tax-motivated FDI.

The next section considers a simultaneous-move game between the two countries,

where the direction of FDI is endogenously determined. Although the model setting in

the next section may be considered as more general than the one here, it entails multiple

equilibria in some cases and no pure-strategy equilibrium in other cases. Thus, it is

meaningful to consider a sequential-move game that pins down a unique equilibrium, to

gain insights into the tax competition when a monopolistic firm may engage in transfer

pricing. Moreover, the timing assumption seems rather realistic, especially when Country

2 merely acts as a tax haven.

Here, we relax the assumption that the MNE has already set up its subsidiary in

Country 2. That is, we now explicitly incorporate the firm’s choice of FDI for intermediate-

goods procurement, while maintaining the assumption that the firm’s headquarters and

its production facility for the final goods is located in Country 1.

Social welfare for either country depends on whether the firm engages in FDI. In the

case where the firm engages in FDI, Country 1’s social welfare can be written as

W1 =

∫ q∗(t1,t2)

0

[P (q)− ξs(t2)]dq, (10)

14

where ξs(t2) = c+ t2(γ̄− c), and the MNE’s output is now written as a function of t1 and

t2. When the firm does not engage in FDI, then it loses the opportunity of tax avoidance

while its marginal cost is ω. Country 1’s social welfare in this case is given by

W1 =

∫ qm(ω)

0

[P (q)− ω]dq =3(1− ω)2

8.

Country 2’s social welfare, by contrast, only consists of the tax revenue from the

MNE’s subsidiary, and can be written as

W2 = t2(γ̄ − c)q∗(t1, t2), (11)

if the firm engages in FDI, whereas it equals 0 otherwise.

With sequential moves, Country 1 maximizes W1 subject to

t2 ∈ BR2(t1) ≡ arg maxt2

t2(γ̄ − c)q∗(t1, t2),

taking into account that Country 2 will undercut its tax rate to obtain tax revenue. We

solve this problem by backward induction as usual.

For the sake of concreteness, we henceforth assume that the demand for the final good

is linear such that P (q) = 1− bq.

3.1 Country 2’s Best Response

Let us first consider the best response for Country 2, whose social welfare is given by

(11). Now, we see from (5) that qm decreases with t2. Therefore, if t2 is smaller than

the threshold given by (7), the firm’s output is constant at P−1(γ̄). Hence, Country 2 is

better off by increasing t2 up to the threshold. If t2 is sufficiently large that qm(ξ(t1, t2)) ≤P−1(γ̄), we have q∗(t1, t2) = qm(ξ(t1, t2)). Therefore, we can use (5) to write (11) as

W2 = t2(γ̄ − c)[

1− c2b

+(t1 − t2)(γ̄ − c)

2b(1− t1)

].

It is readily verified that the t2 that maximizes W2 in this case is given by

t2 =1− c− (1− γ̄)t1

2(γ̄ − c) . (12)

15

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Figure 3: Country 2’s reaction curve

This t2 is a valid best response only if the resulting γ0 is greater than or equal to γ̄. To

see the condition for this requirement, we substitute (12) into (7) and find that γ0 ≥ γ̄ if

and only if

t1 < t̄ ≡ 3(1− γ̄)− (γ̄ − c)3(1− γ̄)

.

If this condition is violated, t2 is chosen to satisfy γ0 = γ̄, i.e.,

t2 = 1− 1− γ̄γ̄ − c (1− t1).

Another condition that is required for the t2 in (12) to be the best response is t2 ≤ t1,

which reduces to

t1 ≥ t ≡ 1− c2(γ̄ − c) + (1− γ̄)

.

Consequently, Country 2’s best response function is given by

B2(t1) =

t1 if t1 ≤ t,

1−c−(1−γ̄)t12(γ̄−c) if t < t1 ≤ t̄,

1− 1−γ̄γ̄−c (1− t1) if t̄ < t1 < 1,

(13)

where it is readily verified that t < t̄. Figure 3 depicts Country 2’s best response function.

The intuition for this result is as follows. When t1 is low (more precisely, when t1 ≤ t),

it is optimal for Country 2 to just undercut Country 1’s tax rate, as reducing the tax rate

16

further and inducing more output does not raise tax revenue. Thus, in this range, Country

2’s tax rate is a strategic complement to Country 1’s tax rate. However, if t1 becomes

moderately large (i.e., t < t1 ≤ t̄), then it can be optimal for Country 2 to lower the tax

rate to induce more output and hence tax revenue in response to an increase in Country

1’s tax rate. In this case, Country 2’s tax rate is a strategic substitute to Country 1’s

tax rate. Finally, if the tax rate in Country 1 becomes sufficiently large (i.e., t̄ < t1 < 1),

the incentive to shift profit by raising production becomes too large, while the zero profit

condition for the MNE’s headquarters is binding. As the output is capped and cannot

increase any more, Country 2 follows suit as Country 1 increases its tax rate. Once again,

Country 2’s tax rate becomes a strategic complement to Country 1’s tax rate.

3.2 Country 1’s Optimal Tax Rate

Now, we analyze Country 1’s optimal tax rate when it considers the undercutting threat

by Country 2. To avoid unnecessary complication in the exposition, we assume henceforth

(1 − c)2/2b > 3(1 − ω)2/8b, which means that the highest social welfare Country 1 can

achieve through regulation and tax policies in the presence of FDI, which is the same as

welfare under perfect competition as Proposition 2 shows, is greater than its social welfare

without FDI. If this condition is violated, Country 1 will never set a higher tax rate than

Country 2. In the subgame perfect equilibrium, both countries thus set their tax rates

to 0, whereas the monopolist engages in FDI if and only if c < ω. Here, we make the

following assumption

(1− c)2 >3

4(1− ω)2, (14)

which is equivalent to (1− c)2/2 > 3(1−ω)2/8 to focus on the interesting and meaningful

case.

As Country 2 will always choose a point on its reaction curve, Country 1’s optimal

choice can be considered as the choice of a point on Country 2’s reaction curve, as shown

in Figure 3. Then, we have the following proposition.

Proposition 3. The subgame perfect equilibrium of tax competition can be summarized

as follows. There is a critical level of γ̄, denoted by γ̄∗(< (1 + c)/2), such that (i) the

equilibrium tax profile is (t1, t2) = (t̄, 2/3) if γ̄ < γ̄∗ and (ii) (t1, t2) = (0, 0) otherwise.

Proof. We consider three segments on Country 2’s reaction curve: the segments between

A = (0, 0) and B = (t, t), B and C = (t̄, 2/3), and C and D = (1, 1) (Figure 3). First,

17

we argue that Country 1 prefers point A to any other points in the segment AB because

along this segment, ξ = [(1− t2)c− (t1− t2)γ]/(1− t1) = c. Thus, the monopolist’s output

is fixed at q∗(t1, t2) = qm(c) = (1+ c)/2. By contrast, ξs = c+ t2(γ̄− c) is increasing as we

move from A to B as t2 increases with t1. Thus, point A is preferred to any other points in

the segment AB. Moreover, point C is preferred to any other points in the segment BC.

Along the BC segment, output is increasing from qm(c) to P−1(γ̄). In addition, Country

2 responds by decreasing its tax rate as t1 increases. Thus, on both accounts, Country 1

is better off, and hence it prefers point C to any other points in the segment BC. Finally,

in the segment CD, output is once again fixed at the level of P−1(γ̄). Thus, as in the

segment AB, ξs = c+ t2(γ̄ − c) increases as we move from C to D as t2 increases with t1.

This leaves us two candidate equilibrium points, A and C. When point A is chosen,

Country 1’s welfare is given by

W1(A) = W1(0, 0) = max

{3(1− ω)2

8b,3(1− c)2

8b

}.

In this case, the monopolist’s FDI decision is always efficient from the viewpoint of global

production efficiency. When point C is chosen by the monopolist, it can be easily verified

that

W1(C) = W1(t̄, 2/3) =(3− 2c− γ̄)(1− γ̄)

6b. (15)

Observe that W1(C) is decreasing in γ̄, while W1(C)|γ̄=c = (1 − c)2/2b > W1(A) under

the assumption expressed by (14), and W1(C)|γ̄= 1+c2

= 5(1− c)2/24b < W1(A). Therefore,

there is a unique γ̄∗ such that W1(C)|γ̄=γ̄∗ = W1(A). This implies that in the subgame

perfect equilibrium, (i) (t1, t2) = (t̄, 2/3) if γ̄ < γ̄∗ and (ii) (t1, t2) = (0, 0) otherwise.

Proposition 3 reveals that Country 2 will undercut Country 1’s tax rate so that the firm

in Country 1 establishes a foreign subsidiary to engage in transfer pricing, if and only if

transfer-pricing regulation is tight. Otherwise, the two countries race to the bottom in tax

competition, and the firm undertakes FDI if and only if c < ω (i.e., no tax-motivated FDI

occurs). It is rather counter-intuitive that loosening regulation deters transfer pricing. If

the price cap is high, however, so is the resulting price for the final good. Then, Country

1 would obtain an insufficient benefit from allowing its firm to engage in transfer pricing.

Consequently, it selects zero tax rate to prevent Country 2 from undercutting the tax

rate; then the firm has no incentive to engage in FDI to avoid tax.

18

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W1 #, W2 "W1 + W2 #

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W1 #, W2 "W1 + W2 "

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W1 ", W2 "W1 + W2 "

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Figure 4: Welfare impacts

3.3 Welfare Impacts

Next, we assess the welfare impacts of opening the possibility of the firm’s FDI. We

examine the impact on world welfare, W1 + W2, as well as on each country. It follows

from (10) and (11) as well as t2(γ̄ − c)− ξs = −c that world welfare can be written as

W1 +W2 =

∫ q∗(t1,t2)

0

[P (q)− c]dq, (16)

when the firm engages in FDI. As the expression in (16) indicates, there is a trade-

off between enhancing allocative efficiency, namely, the efficiency attained by increasing

quantity from the monopolistic production level, and sacrificing production efficiency,

namely, the cost-minimizing production location. As we have seen, Country 1 can induce

the firm to produce more, only by encouraging it to engage in FDI in Country 2, which

may have a higher cost of production. It is readily shown, on the contrary, that W2 = 0

and hence world welfare equals W1 = 3(1− ω)2/8, if the firm does not undertake FDI.

Let us first consider the case in which γ̄ < γ̄∗. In this case, the firm engages in FDI

if and only if ω > ξ, as illustrated in Figure 4. Since Country 2 enjoys a positive welfare

level if and only if the firm sets up its subsidiary there, Country 2’s welfare improves if

and only if ω > ξ. As Figure 4 illustrates, Country 1’s welfare increases if and only if

ω > ω∗1, and world welfare enhances if and only if ω > ω∗.

Country 1’s welfare increases, if and only if W1(C) > 3(1 − ω)2/8, which is readily

shown to be equivalent to ω > ω∗1, where

ω∗1 ≡ 1− 2

3

√(1− γ̄)(3− γ̄ − 2c).

The threshold ω∗1 lies between ξ and c. We know from the definition of γ̄∗ that if ω = c,

then W1(C) > 3(1 − ω)2/8. That is, under tight transfer-pricing regulation, Country 1

prefers an equilibrium with FDI because of the increase in allocative efficiency, and this

is particularly so in the absence of production inefficiency when ω ≥ c. As ω falls and

19

hence c− ω rises, the gain in allocative efficiency decreases, while the loss in production

efficiency increases. The open-market marginal cost ω reaches the threshold before it

reaches ξ, where the gain in allocative efficiency disappears.

Similarly, world welfare increases, if and only if W1(C) +W2(C) > 3(1−ω)2/8, where

W1(C) +W2(C) is calculated from (16) with C = (t̄, 2/3). Deriving the threshold

ω∗ ≡ 1− 2√3

√(1− γ̄)(1 + γ̄ − 2c)

from

W1(C) +W2(C) ≡ (1− γ̄)(1 + γ̄ − 2c)

2b=

3(1− ω∗)2

8b,

it is readily shown that ω∗ < ω∗1, and W1(C)+W2(C) > 3(1−ω)2/8 if and only if ω > ω∗.

Now, both Country 1 and Country 2 enjoy gains from allocative efficiency. Consequently,

the threshold for world welfare is less than that for Country 1’s welfare.

Under tight transfer-pricing regulation, both countries benefit from the firm’s FDI and

transfer pricing, even though it involves a loss of production efficiency. However, these

gains diminish as foreign production costs c rise above home production costs ω.

In the case where γ̄ > γ̄∗, (t1, t2) = (0, 0) in the equilibrium, and the firm engages in

FDI, if and only if c < ω. Production efficiency is guaranteed with FDI. The countries,

however, do not enjoy gains from allocative efficiency with FDI because the firm sets γ = c

and the standard monopoly equilibrium is realized.

The above analysis is summarized in the following proposition.

Proposition 4. (i) Suppose γ̄ < γ̄∗. Then, there are three welfare level thresholds:

ξ < ω∗ < ω∗1. FDI arises and Country 2’s welfare improves if and only if ω > ξ, Country

1’s welfare increases if and only if ω > ω∗1, and the world welfare increases if and only

if ω > ω∗. (ii) Suppose γ̄ > γ̄∗. Then, FDI arises if and only if ω > c. FDI improves

Country 1’s welfare but does not affect Country 2’s welfare.

Before closing this section, we should mention an interesting, counter-intuitive effect

of transfer-pricing regulation on Country 2. Since Country 2, as a tax haven, can generate

tax revenue from the MNE only when γ̄ < γ̄∗, it does not always prefer laxer transfer-

pricing regulation, once we take into consideration that Country 1’s willingness to allow

transfer pricing depends on the tightness of such regulation. Thus, there is some room

for harmonizing and setting up global regulatory standards in transfer pricing. As Figure

4 indicates, tighter transfer-pricing regulation benefits both countries as long as the loss

20

in production efficiency is small.

4 Endogenous Selection of the FDI Source Country

We have thus far assumed that the MNE’s headquarters is located in Country 1 and

thus Country 1 always sources FDI. What characteristics does the FDI source country

have? Does it always have an incentive to select a higher tax rate to become an FDI

source country? To answer these questions, we consider here a simultaneous-move, tax-

competition game, played by two countries, either of which can be an FDI source country.

Each country has its own industry: Industry 1 in Country 1 and Industry 2 in Country

2.16 In Country 1, a monopolist, Firm 1, sells its products only in Country 1. Similarly, in

Country 2, Firm 2 in Industry 2 produces goods and sells them only in Country 2. Each

firm, however, can set up its subsidiary in the other country to produce intermediate

goods, which are shipped to its headquarters for final-goods production. Demand for

Firm 1’s final goods is characterized by the inverse demand function P1(q1) = 1− q1/L1,

whereas that for Firm 2’s goods is given by P2(q2) = 1−q2/L2, where L1 and L2 represent

the two countries’ populations, respectively.17

We suppose L1 ≥ L2, and show that otherwise symmetric countries have different tax

strategies in the equilibrium when L1 is sufficiently larger than L2: the larger country,

Country 1, will select a tax rate higher than Country 2’s, to deliberately allow its own

firm to engage in transfer pricing to save tax payments. Thus, this section provides a

theoretical foundation for the commonly observed phenomenon that tax-haven countries

tend to be small and that firms in large countries set up subsidiaries there to engage in

transfer pricing.

Let us first derive Country 1’s best response function. If Country 1 chooses a higher

tax rate than Country 2, it becomes an FDI source country that maximizes its social

welfare, given by (10), for the given t2. We find immediately that t1 can affect W1 only

through q∗(t1, t2). As shown in Figure 1, if t1 is sufficiently large that γ0 ≤ γ̄, Firm 1

selects q∗ = P−1(γ̄), which is independent of t1. On the contrary, if t1 is so small that

γ0 > γ̄, Firm 1 chooses qm(ξ(γ̄)), which is smaller than P−1(γ̄) and hence less favorable

for Country 1. Thus, Country 1 chooses any t1 that yields γ0 ≤ γ̄. It follows from (7)

16We thank Arnaud Costinot (the co-editor of this journal) for suggesting this extended model.17The specified linear demand functions can be derived if we assume that consumers’ valuations are

uniformly distributed on [0,1] in each country.

21

that the threshold t1 that yields γ0 = γ̄ should satisfy

1− t1 =γ̄ − c1− γ̄ (1− t2), (17)

so that Country 1’s best response function as an FDI source country is a correspondence

given by

Bs1(t2) =

{t1

∣∣∣∣1− γ̄ − c1− γ̄ (1− t2) ≤ t1 < 1

}. (18)

Any effective price cap must satisfy γ̄ < (1 + c)/2 = P (qm(c)), which directly means that

(γ̄ − c)/(1− γ̄) < 1. Thus, we have Bs1(t2) > t2 for any t2 < 1.

If Country 1 chooses a lower tax rate than Country 2, on the contrary, it becomes an

FDI host country and its best response is given by

Bh1 (t2) =

t2 if t2 ≤ t,

γ̄−c+(1−γ̄)(1−t2)2(γ̄−c) if t < t2 ≤ t̄,

1− 1−γ̄γ̄−c (1− t2) if t̄ < t2 < 1,

(19)

as it was derived as a best response function for Country 2, shown in (13), in the last

section.

The following lemma shows the two countries’ individual best response functions.

Lemma 4. For the given L1/L2, there is a threshold t̃2 such that Country 1’s best response

function is

B1(t2) =

{Bs

1(t2) if t2 < t̃2,

Bh1 (t2) otherwise,

(20)

and t̃2 is increasing in L1/L2. Country 2’s best response function is symmetric to Country

1’s. The only substantial difference is that the threshold t̃1 decreases with L1/L2.

Proof. See the Appendix.

Figure 5 illustrates Country 1’s reaction curve, which is characterized by (20).

Given the above lemma, we are ready to derive the Nash equilibrium of the simultaneous-

move, tax-competition game played by the two countries. We consider two cases. In the

first case, γ̄ is sufficiently small that t̃1 = t̃2 ≥ 2/3 holds when L1 = L2. In the second

case, γ̄ is large, meaning that t̃1 = t̃2 < 2/3 when L1 = L2. The threshold of 2/3 here

is derived from Bhi (t̄) = 2/3 for i = 1, 2. As a preliminary investigation, consider the

22

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Bh1

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Bs1

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Figure 5: Country 1’s reaction curve

knife-edge case where t̃1 = t̃2 = 2/3 holds when L1 = L2. The two countries are perfectly

symmetric when L1 = L2. If t2 = t̃2 = 2/3, one of Country 1’s best responses to t2 = 2/3

is to select t1 = t̄ to become the FDI source country, as Figure 6 shows, while Country

2’s best response to t1 = t̄ is to select t2 = 2/3. Similarly, if t1 = t̃1 = 2/3, one of

Country 2’s best response is to select t2 = t̄, while Country 1’s best response to t2 = t̄

is to select t1 = 2/3. Consequently, as Figure 6 illustrates, there are two Nash equilibria

(t1, t2) = (t̄, 2/3), (2/3, t̄).

When t̃1 = t̃2 ≥ 2/3 holds with L1 = L2, there is a continuum of equilibria; however,

when t̃1 = t̃2 = 2/3, as shown above, Country 1 becomes the source country and the host

in each of the cases. As illustrated in Figure 7, the Nash equilibrium set is then given by{(t1, t2)|1− t2 =

1− γ̄γ̄ − c (1− t1), t1 ≥ t̃1, t2 ≤ t̃2

}∪{

(t1, t2)|1− t1 =1− γ̄γ̄ − c (1− t2), t2 ≥ t̃2, t1 ≤ t̃1

}. (21)

In the first equilibrium set, Country 1 plays the role of the source country, whereas

Country 2 plays the role of the host. The roles are switched in the second equilibrium set.

In this case, each country is willing to be the source because γ̄ is so small that the tax

leakage to the host country is small. Each country also has an incentive to be the host

country because the source country’s tax rate is so high that it can maintain a relatively

high tax rate while undercutting the other country’s.

23

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Figure 6: Nash equilibrium when L1 = L2 and t̃1 = t̃2 = 23

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Figure 7: Nash equilibrium when L1 = L2 and t̃1 = t̃2 >23

24

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Figure 8: Nash equilibrium when L1 > L2

As L1/L2 increases, however, the equilibrium set under which Country 1 is the host

shrinks and eventually disappears. As Figure 8 depicts, t̃1 decreases and t̃2 increases as

L1/L2 rises. Consequently, the first equilibrium set in (21) expands, whereas the second

set shrinks. The second equilibrium set eventually disappears when t̃1 becomes smaller

than 2/3. In this asymmetric case, the equilibrium set is{(t1, t2)|1− t2 =

1− γ̄γ̄ − c (1− t1), t1 ≥ t̄1, t2 ≤ t̃2

}. (22)

In the second case where t̃1 = t̃2 < 2/3 holds with L1 = L2, there is no pure-strategy

Nash equilibrium as long as the two countries are completely symmetric. As L1/L2 rises,

however, the Nash equilibrium set, as described by (22) and graphically represented in

Figure 8, will appear.

We summarize the above results as a proposition.

Proposition 5. If Country 1 is sufficiently large relative to Country 2, there is a Nash

equilibrium set of the tax-competition game, in which Country 1 sets a higher tax rate than

Country 2 so that the firm in Country 1 sets up a subsidiary in Country 2 and engages

in transfer pricing. If the two countries are of a similar size and regulation is so tight

that the transfer-price cap is low, then in addition to this Nash equilibrium set, there is a

Nash equilibrium set in which Country 2, the smaller country, selects a higher tax rate to

become the FDI source country.

25

Since the transfer pricing caused by tax-motivated FDI shifts profits from the FDI

source country to the FDI host country, tax revenue decreases in the former country

but increases in the latter country. This tax-revenue increase becomes larger as the FDI

source country becomes larger. Furthermore, transfer pricing with regulation increases

output in the FDI source country, implying that the consumers in this country gain. This

gain also becomes larger as the country becomes larger. Thus, the larger country has an

incentive to be the FDI source country, whereas the smaller country has an incentive to

be the FDI host country. Hence, as was discussed in the sequential-move game, it may

not be optimal for the smaller country (i.e., the FDI host country) to “just” undercut the

tax rate of the large country (i.e., the FDI source country), because the tax revenue may

not be maximized for the smaller country.

5 Concluding Remarks

We have analyzed MNE’s incentives to manipulate an internal transfer price to take ad-

vantage of tax differences across countries and discussed implications of transfer-pricing

regulation as a countermeasure against such profit shifting. We found that tax-motivated

FDI may entail inefficient internal production but could benefit consumers. Thus, en-

couraging transfer-pricing behavior to some extent can enhance social welfare.

We have also considered tax competition between (exogenously determined) source

and host countries to explore the interplay between tax competition and transfer-pricing

regulation. In tax competition, each government non-cooperatively sets the tax rate to

maximize its social welfare. We showed that the nature of tax competition can depend on

the tightness of transfer-pricing regulation. In particular, the source country is willing to

set a higher tax rate and tolerate profit shifting to a tax-haven country under sufficiently

tight regulation. However, if regulation is too lax, tax competition leads to a “race to

the bottom” and eliminates any incentives for tax-motivated FDI. This finding implies

that a tax-haven country does not always prefer lax transfer-pricing regulation. Thus, the

incentives of the host and FDI source country can be aligned to set up global regulatory

standards for transfer pricing.

Finally, we have extended our tax competition model to endogenously determine the

identity of the source country in a set-up with multiple industries. This extended set-up

allows us to rationalize our basic model by deriving an equilibrium outcome that the

larger country is willing to set a higher corporate tax rate than the smaller country in

26

the presence of transfer-pricing regulation. We often observe in reality that firms in large

countries establish subsidiaries in small tax-haven countries and engage in transfer pricing.

The result that the large country sources FDI also provides some justification for using

a model with the Stackelberg tax-setting nature because it is reasonable to think that in

reality small tax-haven countries set their tax rates after observing large countries’ tax

rates. The welfare impacts of transfer pricing obtained in the sequential-move game can

also be extended to the setting of the simultaneous-move game.

Our study has mainly focused on a simple the monopoly setting. With oligopolistic

market competition, additional issues could arise, however. For instance, with oligopolistic

competition in the final-good market of the FDI source country, the internal transfer price

has additional strategic effects that further strengthen the incentive to inflate the transfer

price at the expense of rivals’ profits. Tax-motivated FDI by the MNE has spillover effects

that reduce tax revenue from other final-good producers as well as the MNE. Moreover,

with the presence of competitors that use similar inputs, the CUP method may be adopted

as an application of the ALP. In such a case, we can also uncover a novel mechanism for

input foreclosure when the input market is also imperfectly competitive. The MNE may

have an incentive for input foreclosure even if it is a more efficient input producer. The

new mechanism stems from the dependence of the transfer price on the market price

of a “comparable” input, which is endogenously determined. Some of these issues are

analyzed by Choi et al. (2018). In addition, with oligopolistic competition, each firm’s

FDI decision may depend on other firms’ FDI decisions. These issues represent potential

areas for future research.

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29

Appendix: Proof of Lemma 4

To show that Country 1’s best response is given by (20), we derive Country 1’s social

welfare when it sources and hosts FDI, respectively.

When County 1 sources FDI, it chooses t1 so that the price equals γ̄ regardless of t2

as we have seen. Country 1’s social welfare in this case consists only of the total surplus

in Industry 1. Thus, it follows from q∗ = L1(1− γ̄) and ξs = c+ (γ̄ − c)t2 that its social

welfare as a source country is given by

W s1 =

L1

2(1− γ̄)2 + (γ̄ − ξs)L1(1− γ̄)

=L1

2(1− γ̄)2 + L1(γ̄ − c)(1− γ̄)(1− t2),

for any t2. It is readily verified that W s1 is decreasing in γ̄, meaning that W s

1 takes the

largest value of L1(1− c)2/2 when γ̄ = c.

Country 1 compares this welfare W s1 with that when it selects a lower tax rate than

Country 2 and hence hosts a subsidiary of Firm 2. Social welfare as an FDI host country

consists of the total surplus in Industry 1 and that in Industry 2, and it thus takes a

different form depending on the level of t2 as (19) suggests.

When t2 ≤ t, the best response of Country 1 is to slightly undercut t2, or t1 is set equal

to t2 while Country 1 hosts FDI. In this case, Firm 2’s perceived marginal cost becomes

ξ2 = c and hence q∗2 = L2(1− c)/2, meaning that we have

W h1 =

3L1(1− ω)2

8+ t2(γ̄ − c)L2(1− c)

2.

Consequently, we have W s1 ≥ W h

1 if and only if

L1

L2

[(1− γ̄)2

2+ (γ̄ − c)(1− γ̄)(1− t2)− 3(1− ω)2

8

]≥ t2(γ̄ − c)(1− c)

2. (23)

It follows from the assumption expressed by (14) that as γ̄ decreases to c, the left-hand

side of this inequality approaches to a positive number, while the right-hand side converges

to 0. Thus, this inequality is satisfied for any t2 if γ̄ is sufficiently small. If γ̄ is not that

small, there exists a t̃2 such that W s1 ≥ W h

1 if and only if t2 ≤ t̃2. It is easy to see that

the threshold t̃2 increases with L1/L2.

We obtain a similar result when t < t2 < t̄. In this case, we have t1 = [1 − c + (1 −

30

γ̄)(1− t2)]/[2(γ̄ − c)] as indicated in (19). Then, we have

ξ2 =(1− t1)c− (t2 − t1)γ̄

1− t2= γ̄ − γ̄ − c− (1− γ̄)(1− t2)

2(1− t2),

and hence

q∗2 =L2(1− ξ2)

2=L2[γ̄ − c+ (1− γ̄)(1− t2)]

4(1− t2).

Country 1 obtains a tax revenue of

t1(γ̄ − c)q∗2 =L2[γ̄ − c+ (1− γ̄)(1− t2)]2

8(1− t2),

meaning that social welfare as an FDI host country is given by

W h1 =

3L1(1− ω)2

8+L2[γ̄ − c+ (1− γ̄)(1− t2)]2

8(1− t2).

Thus, we have W s1 ≥ W h

1 if and only if

L1

L2

[(1− γ̄)2

2+ (γ̄ − c)(1− γ̄)(1− t2)− 3(1− ω)2

8

]≥ L2[γ̄ − c+ (1− γ̄)(1− t2)]2

8(1− t2).

(24)

As γ̄ falls to c, the right-hand side of this inequality converges to L2(1 − c)2(1 − t2)/8.

However, we haveL2(1− c)2(1− t2)

8<

L2(1− c)2(γ̄ − c)8[2(γ̄ − c) + (1− γ̄)]

under t2 > t, while the right-hand side of this inequality converges to 0 as γ̄ falls to c.

This implies that W s1 > W h

1 for any t2 if γ̄ is small enough. In addition, the right-hand

side of (24) is increasing in t2 if and only if 1− t2 < (γ̄ − c)/(1− γ̄), which is true when

t2 > t since 1− t2 < (γ̄− c)/[2(γ̄− c) + (1− γ̄)] < (γ̄− c)/(1− γ̄). This implies that when

the threshold t̃2 falls in this range, t̃2 rises with L1/L2.

We also obtain a similar result in the final case where t2 ≥ t̄. In this case, we have

t1 = [γ̄ − c− (1− γ̄)(1− t2)]/(γ̄ − c) and q∗2 = L2(1− γ̄). Thus, we have

W h1 =

3L1(1− ω)2

8+ t1(γ̄ − c)L2(1− γ̄)

=3L1(1− ω)2

8+ L2(1− γ̄)[γ̄ − c− (1− γ̄)(1− t2)].

31

We have W s1 ≥ W h

1 if and only if

L1

L2

[(1− γ̄)2

2+ (γ̄ − c)(1− γ̄)(1− t2)− 3(1− ω)2

8

]≥ (1− γ̄)[γ̄ − c− (1− γ̄)(1− t2)].

It is readily verified that this inequality is satisfied if γ̄ is sufficiently small, and that if t̃2

falls in this region it increases with L1/L2.

Before turning to Country 2’s best response, we show the relationship between γ̄ and

t̃2 more rigorously. We restrict γ̄ to the range (c, (1 + c)/2), that is, the transfer price

lies between the marginal cost and monopoly price. As we have shown, if γ̄ is sufficiently

close to c, we have W s1 > W h

1 under the assumption (14), meaning that t̃2 = 1. As γ̄

increases, W s1 decreases while W h

1 increases. At a certain level of γ̄, these two payoffs

become equal, and t̃2 starts to decrease as γ̄ further increases. Tentatively assuming that

t̃2 becomes smaller than t when γ̄ reaches its upper bound, the equation W s1 = W h

1 , which

is characterized by (23) with equality when t2 = t̃2 and γ̄ = (1 + c)/2, can be written as

L1

L2

[3(1− c)2

8− 3(1− ω)2

8− t̃2(1− c)2

4

]=t̃2(1− c)2

8.

If c < ω, the t̃2 that satisfies this equation is positive and thus the threshold t̃2 is positive

even at the limit. This is because FDI itself is beneficial for the source country, because

of the gains in production efficiency. We may rather focus on the more interesting case

where c ≥ ω, while satisfying the assumption (14). In that case, t̃2 reaches 0 before γ̄

reaches its upper bound: the assumption that t̃2 < t is thus satisfied in this case.

Country 2’s best response is similarly derived. Recall that Bs1 and Bh

1 do not de-

pend on L1/L2, as (18) and (19) show, and that L1/L2 only affects Country 1’s best

response function B1 through t̃2, as (20) shows. Country 2’s best response function is

therefore symmetric to Country 1’s. The only substantial difference is that the threshold

t̃1 decreases with L1/L2, whereas t̃2 increases.

32