Institute for Economic Studies, Keio University
Keio-IES Discussion Paper Series

Production Location of Multinational Firms under Transfer Pricing:
The Impact of the Arm's Length Principle
Hayato Kato , Hirofumi Okoshi
28 April, 2017
DP2017-016
https://ies.keio.ac.jp/en/publications/7680/

Institute for Economic Studies, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
ies-office@adst.keio.ac.jp
28 April, 2017

Production Location of Multinational Firms under Transfer Pricing: The Impact of the Arm's Length
Principle
Hayato Kato, Hirofumi Okoshi
Keio-IES DP2017-016
28 April, 2017
JEL classification: F12; F23; H25
Keywords: Transfer pricing; Intra-firm trade; Production location choice; Arm's length principle

Abstract
In what situation does a vertically-integrated multinational enterprise (MNE) establish an upstream
affiliate in a different country from its downstream affiliate? When MNEs separate the location of
two affiliates, they can shift prots between affiliates by manipulating intra-firm prices. The location
choice of the MNE depends on the difference in corporate taxes between the parent and the hostcountries. This paper shows that if the international tax difference is small, the upstream affiliate is
located in the same country as the downstream affiliate. It also investigates the impact of the arm's
length principle (ALP) on the location choice, which requires that the intra-firm price of inputs should
be set equal to that of similar inputs for the independent downstream firms. The imposition of the
ALP may change the location choice of MNEs. This location change brings smaller tax revenues tothe host country, but generally greater revenues globally.

Hayato Kato
Faculty of Economics, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
hayato.kato2@gmail.com

Hirofumi Okoshi
Graduate School of Economics, Hitotsubashi University
2-1 Naka, Kunitachi, Tokyo 186-0004, Japanhirofumi.okoshi1@gmail.com

Acknowledgement: The authors are grateful to financial support from Japan Society for the Promotion of
Science (Grant Number: JP16J01228) and MEXT-Supported Program for the Strategic Research Foundation
at Private Universities (Grant Number: JPS1391003). They also thank Prof. Toshihiro Okubo for making thispaper included in Keio-IES Discussion Paper Series.

Production location of multinational firms under transfer
pricing: The impact of the arm’s length principle∗
Hayato Kato†

Hirofumi Okoshi‡

April 27, 2017

Abstract
In what situation does a vertically-integrated multinational enterprise (MNE) establish an upstream affiliate in a different country from its downstream affiliate? When
MNEs separate the location of two affiliates, they can shift profits between affiliates bymanipulating intra-firm prices. The location choice of the MNE depends on the difference in corporate taxes between the parent and the host countries. This paper showsthat if the international tax difference is small, the upstream affiliate is located in thesame country as the downstream affiliate. It also investigates the impact of the arm’s
length principle (ALP) on the location choice, which requires that the intra-firm priceof inputs should be set equal to that of similar inputs for the independent downstream
firms. The imposition of the ALP may change the location choice of MNEs. Thislocation change brings smaller tax revenues to the host country, but generally greater
revenues globally.

Key words: Transfer pricing; Production location choice; Intra-firm trade; Arm’s lengthprinciple.
JEL classification: F12; F23; H25; H26.
∗

We would like to thank Jay Pil Choi, Dave Donaldson, Taiji Furusawa, Jota Ishikawa, Kozo Kiyota,
Yoshimasa Komoriya, Yasusada Murata, Hikaru Ogawa, Toshihiro Okubo, Yasuhiro Sato, Nicolas Schmitt,
Yoichi Sugita and Eiichi Tomiura for helpful suggestions. Thanks also go to seminar participants at HITSMJT (Kanazawa Seiryo U), Hitotshubashi-Sogang Trade Workshop (Hitotsubashi U), Public Economics
Workshop (U of Tokyo) and Study Group on Spatial Economics (Kyushu Sangyo U) for useful comments.
Kato acknowledges financial support from Japan Society for the Promotion of Science (Grant Number:
JP16J01228) and MEXT-Supported Program for the Strategic Research Foundation at Private Universities(Grant Number: JPS1391003). All remaining errors are our own.
†
Corresponding author. Faculty of Economics, Keio Univerisity. E-mail: hayato.kato2@gmail.com‡
Graduate School of Economics, Hitotsubashi University. E-mail: hirofumi.okoshi1@gmail.com

1

1

Introduction

The manner in which multinational enterprises (MNEs) organize their production structureis essential for their international strategy. As MNEs can substantially benefit from theopportunity to locate their affiliates in several countries, their location decisions depend on
country-specific characteristics, such as the extent of competition and policies proposed by
the governments. Considerable research has been undertaken to investigate the determinantsof MNEs’ locations from both theoretical and empirical standpoints.1 Among other factors
affecting the location choice, the corporate taxation prevalent in both the host and parent
countries is known to have a significant impact.2
When considering a firm with a single plant, the consequences of corporate taxation are
straightforward; the firm locates its production in a country with a lower tax rate to savetaxes. However, the impact of taxation on MNEs’ location choice is not this simple. The
striking difference between MNEs with multiple plants or affiliates and single-plant firms
is that MNEs’ transactions may take place within their organization across borders, which
is not the case for single plant firms. This means that MNEs can partly control prices ofintermediate goods for foreign affiliates, which are known as transfer prices, through intrafirm trade in order to reduce global tax payments. Thus, it is possible that using such atransfer pricing strategy, MNEs locate their production in a high-tax country, while exporting
inputs to their affiliates located in a low-tax country.
The relationship between corporate tax rates and the location choice of MNEs undertransfer pricing is not just a theoretical curiosity, but is of great importance to the modern
economy. Along with the progress of economic integration, intra-firm trade has grown dramatically in recent years, which provides MNEs room for tax manipulations through transfer
pricing.34 Recently, the OECD launched a project involving over 80 countries to address thetax avoidance behavior of MNEs, which includes transfer pricing.5 According to the OECD,1

For comprehensive surveys, see Markusen (2004); Navaretti and Venables (2004); and Blonigen (2005).
Hebous et al. (2011) show that lower corporate tax induces inflows of foreign capital irrespective of thetype of investment, such as greenfield foreign direct investment and cross-border mergers and acquisitions.
Voget (2011) finds that one percent decline in foreign effective tax rate augments the likelihood of headquarters’ relocation by 0.22 percent. Karkinsky and Riedel (2012) and Griffith et al. (2014) investigate the link
between corporate taxation and patent location.
3
Bernard et al. (2010) show that over 46 percent of U.S. imports composed of intra-firm transactions in
2000. Lanz and Miroudot (2011) report that U.S. imports of intermediate products score around 50 percent
in 2009. See also Slaughter (2000) and Hanson et al. (2005) for the importance of intra-firm trade.
4
For empirical evidence on transfer pricing, see Swenson (2001); Clausing (2003); Bernard et al. (2006);
and Davies et al. (2015).
5
The project is called “Base Erosion and Profit Shifting:” https:// www.oecd.org/g20/topics/taxation/2

2

revenue losses from tax avoidance by MNEs are estimated to be between 4% and 10% of
global corporate income tax revenues.6 Despite the growing concern globally, limited work
seems to be undertaken in terms of the interaction between MNEs’ location choice and theirtransfer pricing strategy. The first objective of this paper is to examine how corporate tax
rates affect the production location decision of MNEs with profit-shifting motives.
From the government’s perspective, there is no doubt that steps preventing MNEs fromtax manipulations are indispensable for collecting tax revenues. Many countries adopt atransfer pricing tax system to infer whether MNEs avoid tax payments. The key idea toappropriate the transaction price for related affiliates is the arm’s length principle (ALP)
which is set out in Article Nine of the OECD Model Tax Convention. The principle points
out that transfer price should be the same used for an unrelated firm under similar conditions,the so-called “arm’s length price.” The second objective of this paper is to investigate theimpact of the ALP on MNEs’ tax avoidance and production location choice.
This paper presents a simple two-country model with a vertically-integrated MNE, whose
headquarters is located in the parent country, and a downstream local rival in the hostcountry. The link between the location choice of upstream production and tax-avoidance
strategy under the cases with and without the ALP are investigated. We show that if the
ALP is not imposed (i.e., different input prices for related and unrelated downstream firms
are permitted), the MNE may locate an upstream affiliate in a high-tax country. However,if the ALP is imposed (i.e., equal prices for the two downstream firms are mandatory), the
MNE simply chooses a low-tax country for upstream production. There exist tax rates forwhich the imposition of the ALP changes the location pattern. We also show that the location
change induced by the ALP leads to smaller tax revenues in the host country, but generally
greater revenues globally.
At first glance, it seems surprising that the upstream affiliate may be located in the hightax country. To grasp the intuition behind the result, consider how the MNE chooses input
prices. If the MNE separates the location of its affiliates, the optimal transfer price for its
affiliates is based on tax-manipulation and strategic purposes. The tax-manipulation motive
drives the MNE to set the transfer price so as to shift profits from a high-tax country to a
low-tax country. If the host country, where the downstream affiliate is located, has a lower
tax rate than the parent country, the MNE attempts to decrease the transfer price to reduce
tax payments in the high-tax parent country.
beps.htm, accessed on 17 March 2017.
6See
http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-project-for-discussion-at-g20finance-ministers-meeting.htm, accessed on 17 March 2017.

3

The strategic motive suggests that as the upstream affiliate of the MNE has a monopoly
power on inputs, the MNE can partly control the downstream market by discriminating input
prices for the two downstream firms. Specifically, the MNE has an incentive to choose a lowtransfer price for the downstream affiliate, and a high arm’s length price for the local rivalin order to obtain a large share of the downstream market. In short, if the host country has
a lower tax rate than the parent country, both tax-manipulation and strategic effects workin the same direction to lower the transfer price. Particularly, if the host’s tax rate is much
lower than the parent’s tax rate, the MNE may locate upstream production in the high-tax
parent country to best achieve the transfer pricing strategy. Imposing the ALP requires
the MNE to set equal input prices and thus limits the effectiveness of transfer pricing. As
such, under the ALP, the MNE simply prefers to locate its upstream affiliate in the low-tax
country.
Most of the previous studies on profit shifting and transfer pricing have provided limited
attention to the production location choice of MNEs. The main interest of the previous
studies is to understand how transfer prices are affected by international differences in, e.g.,
corporate tax rates, tax systems and trade barriers.7 Schjelderup and Sørgard (1997) andZhao (2000) made early attempts to introduce the strategic purposes of transfer price andtax manipulation.8 They find that under Cournot competition, MNEs tend to set a transfer
price lower than the marginal cost, even when there are no corporate tax differences. Withina similar framework, Nielsen et al. (2003) examine how different corporate tax systems,
separate accounting and formula apportionment, affect the incentive to engage in transfer
pricing differently. Kind et al. (2005) ask the same question in a tax competition framework
and also look at the impact of reduction in trade barriers. However, the production location
choice of MNEs is outside the scope of these papers.
There are a few papers that address the choice of organization structure of MNEs withprofit shifting motives. Nielsen et al. (2008) analyze the impact of different decision structures on transfer prices. The decision on production is made by the headquarters of MNEs
(centralization) or the local affiliate (decentralization). Unlike our model, their model fixes
the location of affiliates. Using the property-rights approach, Bauer and Langenmayr (2013)and Egger and Seidel (2013) investigate the organization decision on whether to integrate local suppliers or import inputs from independent foreign suppliers. Keuschnigg and Devereux(2013) examine the same in a model with financial frictions. While they focus on sourcing
7

Earlier contributions include Copithorne (1971); Horst (1971); Samuelson (1982); and Kant (1988).
Based on our knowledge, the first paper that introduced both tax-manipulation and strategic purposes
is Elitzur and Mintz (1996), but there are no interactions with competitors in their model.
84decisions across the boundaries of MNEs (“make or buy” inputs), we emphasize production
location decisions within the boundaries of MNEs. Closer to the interests of our study, Yao(2013) analyzes the impact of the ALP on MNEs’ location choice in a spatial competition
model à la Hotelling. In his model, MNEs choose where to locate within a host country, thatis, they choose a point on the “linear-city,” whereas in our model MNEs choose whether tolocate in a host or parent country.9
The location choice of internationally-mobile firms is at the core of the literature on tax
competition.10 Haufler and Wooton (1999) consider tax competition between potential hostcountries for a single MNE (or its affiliate) without profit shifting motives.11 Based on theirframework, Ma and Raimondos (2015) allow the MNE to use transfer pricing and examine
the effect of the market size of potential host countries. They simplify the vertical structure
within the MNE, and are thus unable to analyze the impact of the ALP. In contrast, we takecorporate taxes as given, and describe the vertical structure more precisely to address the
ALP issue.
The rest of the paper is organized as follows. Section 2 describes the setup of the model.
The main analysis is presented in Sections 3 and 4 where the equilibrium outcomes in thebenchmark (no-ALP) and the ALP cases are derived. Section 5 analyzes the impact of the
ALP on tax revenues and Section 6 concludes the paper.

2

Basic setting

The economy consists of two countries, a host and a parent country, with two verticallylinked industries, an upstream industry (intermediate input) and an downstream industry(final good). Our focus is on the host country, as the consumption and production of final
goods take place only in the host country. An MNE, whose headquarters is located in
the parent country, has a downstream affiliate in the host country to compete with a local
rival firm in the final goods’ market. The downstream affiliate and the local rival produce
differentiated products using the intermediate input and engage in Cournot competition.
The (headquarters of the) MNE can choose the location, between the parent and the hostcountries, where production of intermediate inputs for both the downstream affiliate and
9

The role of the ALP on transfer prices is also studied by Gresik and Osmundsen (2008); Bauer andLangenmayr (2013); Choe and Matsushima (2013); and Keuschnigg and Devereux (2013). However, they do
not consider the location choice of MNEs.
10
See Keen and Konrad (2013) for a comprehensive survey.
11
For subsequent development in the literature on bidding for a firm, see, e.g., Bjorvatn and Eckel (2006);
Haufler and Wooton (2006); Ferrett and Wooton (2010); and Furusawa et al. (2015).

5

the independent local firm would take place. By contrast, the location of the downstream
affiliate is fixed. The upstream affiliate is the only supplier, which can sell inputs throughintra-firm transaction to the downstream affiliate at different prices from those charged to
the local firm. If the upstream affiliate is established in the host country together with thedownstream affiliate, termed as a co-location scheme, it produces inputs in the host country,
and sells to both the related and unrelated downstream firms. The price for the related
affiliate is called an internal price and the price for the independent local firm is called an
arm’s length price. On the other hand, if the upstream affiliate is established in the parent
country separate from the downstream affiliate, termed as a separate-location scheme, it
produces in the parent country and exports to the two downstream firms. The internal priceunder this scheme can also be called a transfer price due to the transactions across borders.
The two schemes are illustrated in Fig. 1.

Fig. 1. Model structure: (a) co-location scheme; (b) separate-location scheme.

The timing of the game is as follows. First, the MNE locates an upstream affiliate ineither the host or the parent country. Second, it sets input prices to maximize the total
post-tax profit, which is the sum of the post-tax profits of the upstream and the downstream
affiliates. Third, the downstream affiliate and the local firm choose outputs to maximize

6their own profits.12 We proceed by analyzing in turn the case where the MNE is free fromthe arm’s length principle (ALP), and the case where it obeys the ALP.

3

Benchmark caseWe first consider the case where the ALP is not imposed: the upstream affiliate can sell tothe related downstream affiliate and the independent firm at different prices. The equilibriumoutcomes are derived in both the co-location and the separate-location schemes. Comparing
the equilibrium profits under the two schemes, we analyze in which country the MNE locates
an upstream affiliate, given the tax rates of the host and the parent countries.

3.1

Co-location scheme

Given the location of upstream production, the MNE first chooses input prices and then
the two downstream firms source the inputs to produce final goods. We solve the problem
backward.
The two downstream firms choose quantities to maximize their own pre-tax profits. Let
π and π∗ be the pre-tax profits of the downstream affiliate and the local firm, respectively;
the maximization problems are formulated as
max π = (p − g)q,q

max π∗ = (p∗ − g∗ )q∗ ,q∗where p = 1 − q − bq∗ ,p∗ = 1 − q∗ − bq.
p (p∗ ) is the final good’s price of the downstream affiliate (the local firm) and q (q∗ ) is thequantity produced by the downstream affiliate (the local firm). The downstream firms use
linear production technology, resulting in a one-to-one transformation from intermediate to
final goods. g is the price of the intermediate inputs for the downstream affiliate, called theinternal price, and g∗ is the price for the local firm, called the arm’s length price. b ∈ (0, 1)
12

We consider a decentralized decision structure and the MNE leaves quantity choice to the downstream
affiliate. The principle may benefit from delegating its decision to the agent as the delegation works as acommitment device, which is known as the delegation principle (see e.g., Fershtman and Judd, 1987; Sklivas,
1987). Decentralized decision making is the source of the strategic effect and is widely adopted in theliterature on transfer pricing mentioned in the Introduction.

7

represents the degree of substitutability of the two final goods. Solving the maximization
problems givesb(g∗ − 1) + 2(1 − g),
4 − b2b(g − 1) + 2(1 − g∗ )q∗ =.
4 − b2q=(1)(2)

Taking into account these demand schedules, the MNE sets input prices for the two
downstream firms. Let πu be the pre-tax profits of the upstream affiliate and Π be the total
post-tax profits of the MNE, the MNE faces the following problem:max Π = (1 − T )π̄ + (1 − t)(πu + π)g,g∗

= (1 − T )π̄ + (1 − t)[(g − c)q + (g∗ − c)q∗ + (p − g)q],
where T and t are the corporate tax rate of the parent and host countries, respectively. It is
assumed that t ≤ T throughout the analysis.13 π̄ is constant profits earned (from different
businesses) in the parent market.14 c ∈ [0, 1) is the constant marginal cost of the upstream
production.
Deriving the two first-order conditions (FOCs) from the MNE’s problem (dΠ/dg = 0;dΠ/dg∗ = 0) and solving the system of equations for (g, g∗ ), the result is
1 + c (2 − b)(1 − c)−,22(2 − b2 )
1+c
g∗ =
,
2

(3)

g=

(4)

where the second-order conditions (SOCs) trivially hold. As both the upstream and downstream firms co-locate in the host country and face the same tax rate, the equilibrium input
prices are independent of tax rates. To earn positive profits from selling inputs, the MNEcharges input prices higher than the marginal cost, i.e., g > c and g∗ > c. The second termin Eq. (3) is negative (noting that c < 1 and b < 1), implying that the internal price islower than the arm’s length price, i.e., g < g∗ . This gap can be explained from the factthat the MNE attempts to expand the profits of its downstream affiliate, π. As the inter13

If t > T , the upstream affiliate is always located in the low-tax parent country (separate location) in
both the benchmark and ALP cases. Thus, the focus is on the range of t ≤ T , where the imposition of the
ALP may change the location pattern. See also footnotes 21 and 25.
14This term ensures positive taxable profits in the parent country.

8nal price falls, the downstream affiliate becomes more competitive against the local firm,and earns more profits. The second negative term in Eq. (3) is called the strategic effectof input prices.15 Due to this strategic motive, the transfer price is likely to be set lower
than the arm’s length price without tax-manipulation motives, which will be observed in theseparate-location scheme.
Calculating the total post-tax profits Π using the equilibrium choices yields
Π = (1 − T )π̄ +3.2(1 − t)(3 − 2b)(1 − c)2.
4(2 − b2 )(5)

Separate-location scheme

In the separate-location scheme, where the upstream affiliate is located in the parent country,
the two downstream firms behave similarly to the co-location scheme. Suppose S is used todenote variables in the separate-location scheme, using Eqs. (1) and (2), the outputs of final
goods can be written asb(g∗S − 1) + 2(1 − g S ),4 − b2b(g S − 1) + 2(1 − g∗S )q∗S =,4 − b2qS =where g and g∗ have been replaced with g S and g∗S in Eqs. (1) and (2), respectively.
Given these demand schedules, the MNE chooses input prices to maximize the following
total post-tax profit:max ΠS = (1 − T )(π̄ + πuS ) + (1 − t)π S
g S ,g∗S= (1 − T )[π̄ + (g S − c)q S + (g∗S − c)q∗S ] + (1 − t)(pS − g S )q S .
15This point can be formally stated as follows. We modify the maximization problem of the MNE asmax Π = (1 − T )π̄ + (1 − t)(πu + βπ),g,g∗where β is a weight attached to the profits of the downstream affiliate. Solving the modified problem givesg=

1 + c β(2 − b)(1 − c)−,22(4 − b2 − 2β)

g∗ =

1+c
.
2

The second term of g, i.e., the strategic effect, vanishes if the MNE puts β = 0 on π.

9Our focus is on a certain range of tax rates where the maximization problem has a uniqueinterior solution:t > t ≡ max{ta , tb },(A1)

where ta ≡ (2 − b)T − (1 − b),(2 − b)(3 + bc + b + c)T − (2 − b2 )(1 + c).
t ≡4 − b(1 − c)b

If t and T satisfy (A1), the equilibrium quantities and final goods’ prices are positive, and the
SOCs hold in all cases of the following analysis.16 The regularity condition (A1) is assumed
throughout the analysis.17
The equilibrium input prices are given bygS =1 + c (2 − b)(1 − c)(2 − b)2 (2 + b)(1 − c)(T − t)−,−22(2 − b2 )2(2 − b2 )[2t − (4 − b2 )T + 2 − b2 ]
|
{z
}

(6)

1+c
(= g∗ ).
2

(7)

=g

g∗S =

The sum of the first and second terms in Eq. (6) equals the internal price under the co-location
scheme (g defined in Eq. (4)). The third term involves the tax difference, which is termed as
the tax-manipulation effect of input prices. Under the regularity condition, the denominatorof the third term is positive and thus its sign depends on the tax difference. If both thecountries have the same tax rate (t = T ), then there is no room for tax manipulation andthe equilibrium prices are reduced to the ones in the co-location scheme. If the host country
has a lower tax rate than the parent country (t < T ), then the MNE attempts to shift profits
from the high-tax parent country to the low-tax host country in order to reduce the transfer
16

More precisely, the SOCs are
d 2 ΠS
4[2t − (4 − b2 )T + 2 − b2 ]d2 ΠS2[b2 t − (4 − b2 )T + 8 − 3b2 ]
=−
< 0,
=−
< 0,
S
2
2
2
S
2
d(g )
(2 − b) (2 + b)d(g∗ )(2 − b)2 (2 + b)2
 2 S 2d 2 ΠSd2 ΠS
8[2t − (4 − b2 )T + 2 − b2 ][b2 t − 2(4 − b2 )T + 8 − 3b2 ]
d Π
·
=
> 0.
−
d(g S )2 d(g∗S )2
dg S dg∗S(2 − b)4 (2 + b)4These inequalities hold under (A1).
17
In all cases of the following analysis, the upstream affiliate (or the headquarters of the MNE) is not allowed
to supply inputs only to the downstream affiliate due to, e.g., antitrust laws. If we further assume that thedegree of differentiation and the host’s tax rate are high enough: b < 1/2 and t > tf ≡ [2(2−b)T −(1−2b)]/3,
the upstream affiliate always finds it profitable to sell to both the two downstream firms so that the analysis
in the text is unchanged.

10price to allow the downstream affiliate to earn more profits in the host country. Both taxmanipulation and strategic effects work in the same manner to lower the transfer price incomparison to the arm’s length price, i.e., g S < g∗S . 18
To summarize, for tax-manipulation and strategic motives, the transfer price is likely to
be set lower than the arm’s length price. As a consequence, the downstream affiliate produces
more goods at cheaper prices than their local rival, i.e., q S > q∗S and pS∗ > pS .19 It is notedthat the arm’s length price g∗S defined in Eq. (7) is the same as in the co-location scheme,
and does not depend on taxes, as the tax manipulation effect is best achieved only throughthe use of the transfer price g S .
The total post-tax profits evaluated at the equilibrium choices are given by(1 − c)2 {t − 2(2 − b)T + 3 − 2b},Π = (1 − T ) π̄ +4{2t − (4 − b2 )T + 2 − b2 }


S

(8)

where the second term in the square bracket is positive under (A1).

3.3

Location choice

Comparing the total post-tax profits under the two schemes, the MNE chooses a location for
upstream production. From Eqs. (5) and (8), the profit difference can be calculated asΠ − ΠS =Θ(1 − c)2 (T − t),2(2 − b2 )[2t − (4 − b2 )T + 2 − b2 ]where Θ ≡ (3 − 2b)t − (4 − 2b − 2b2 + b3 )T + 1 − 2b2 + b3 ,where the denominator is positive. Noting that Θ can take negative values and is increasing
in t, the profit difference can be positive or negative.
18

If t > T , the MNE seeks more profits in the low-tax parent country rather than in the high-tax hostcountry in order to set the transfer price high to favor the upstream affiliate. In this case, tax-manipulationand strategic effects work in the opposite direction. However, it can be verified that the strategic effectoutweighs and makes the transfer price lower, i.e., g S < g∗S .
19
To check these formally, evaluating the downstream quantities and prices at equilibrium input prices
gives
q S − q∗S =(1 − c)(1 − t)
> 0,
2[2t − (4 − b2 )T + 2 − b2 ]pS∗ − pS = (q S − q∗S )(1 − b) > 0.
In fact, the regularity condition (A1) ensures positive quantities and prices; q∗S > 0 holds if t > ta and pS > 0
holds if t > tb .

11

It is can be easily observed that Π − ΠS = 0 holds at t = t∗ and t = T , where t∗ is definedbyt∗ ≡(4 − 2b − 2b2 + b3 )T − 1 + 2b2 − b3(< T ).
3 − 2b(9)t∗ is not necessarily positive; it is likely to be positive if the tax rate of the parent country is
sufficiently high:t∗ > 0,→ T >T ≡1 − 2b2 + b3.
4 − 2b − 2b2 + b3

(A2)

If t∗ is negative, the profit difference is always positive for t ≤ T .
The profits under the two schemes are drawn in Fig.2.20 If (A2) does not hold (Fig.2.(b)),
then Π − ΠS ≥ 0 holds for t ≤ T . The MNE always chooses co-location, where it simply
establishes an upstream affiliate in the low-tax host country, together with the downstream
affiliate.
If (A2) holds (Fig.2.(a)), the location choice is more complex. Π − ΠS > 0 holds if t isclose to T (t ∈ (t∗ , T )). If the tax rates of the two countries are fairly different (t ∈ (t, t∗ )),then Π − ΠS < 0 holds. The equality Π = ΠS holds at t = t∗ and t = T . The MNE chooses
to produce intermediate inputs in the host country (co-location), if the two countries have
similar tax rates. Otherwise, it prefers the parent country for upstream production (separate
location).21
20

These figures are derived using the following parameter values: b = 0.2; c = 0.3; π̄ = 3; (a)T = 0.35;(b)T = 0.2. In this numerical example, t = 0 holds.
21
If t > T , it can be checked that Θ > 0, and thus Π − ΠS < 0 hold. The upstream affiliate is located in
the parent country simply for its low tax rate (separate location).

12Fig. 2. Production location choice in the benchmark case: (a) high T and (b) low T .

If the two countries have equal tax rates, the tax manipulation effect disappears so thatthe location choice does not matter, i.e., Π = ΠS at t = T . Consider then a marginal
decrease in the tax rate of the host country. This reduction in the host tax rate naturally
raises the MNE’s profits; the marginal impacts on the profits in the co-location and the13separate-location schemes are respectively given by
−

dΠ
∂Π
=−
dt t=T∂t t=T= πu + π t=T= (g − c)q + (g∗ − c)q∗ + (p − g)q t=T=−(1 − c)2 (3 − 2b)> 0,
4(2 − b2 )dΠS∂ΠS dg S∂ΠS−=−
dt t=T∂t∂g S dt t=T= π S t=T
= (pS − g S )q S t=T=(1 − c)2 (2 − b)2> 0,
4(2 − b2 )2where we have used ∂ΠS /∂g S = 0 from the MNE’s FOCs. Noting that the prices andquantities are equal under both the schemes at equal tax rates, where it holds that p =pS ; g = g S ; q = q S at t = T , the marginal impact on the profits is higher under theco-location scheme than under the separate-location scheme:


dΠS
dΠ
− −
= (g − c)q + (g∗ − c)q∗ t=T−
dt t=Tdt t=T(1 − c)2 (1 − b)(1 + b − b2 )> 0.
=
2(2 − b2 )2This indicates that if the host country has a slightly lower tax rate than the parent country,
upstream production in the host is more profitable than in the parent. Having an affiliate
in the parent country is beneficial to the MNE to manipulate tax payments, but it is at
the same time disadvantageous due to the higher tax rate of the parent. Under small tax
differences between the two countries, there is little room for manipulating tax payments;
thus, upstream production in the high-tax parent country becomes less profitable than thatin the low-tax host country.
If the two countries have different tax rates, the MNE may prefer upstream productionin the parent country in order to exploit the tax difference through transfer pricing. As wehave seen, under small tax differences, it is preferable to locate upstream production in the14low-tax host country. However, under fairly large tax differences, host production does notnecessarily lead to higher total profits. To focus on this point, let us assume (A2) and lookat the marginal impacts of taxes on the total profits at t = t∗ > 0, where Π = ΠS holds. As
in the equal-taxes situation, it can be confirmed that


dΠ
dΠS
−
− −
dt t=t∗dt t=t∗= (πu + π) − π S t=t∗
= [(g − c)q + (g∗ − c)q∗ + (p − g)q] − (pS − g S )q S t=t∗=−

(1 − b)(3 − 2b)(1 + b − b2 )(1 − c)2< 0.
2(2 − b)2 (2 − b2 )In contrast to the equal-taxes situation, a reduction in t increases total profits in the separatelocation scheme more than in the co-location scheme. For t < T , the transfer price g S is
set lower to avoid tax payments in the parent country. This lowered price strengthens thestrategic effect, and thus makes the downstream affiliate more competitive and earn higher
profits π S .22 If T is so high that (A2) holds, fairly large tax differences makes the separatelocation scheme more profitable.
The results are summarized below
Proposition 1 (Benchmark case).

Suppose the MNE can set different input prices for

its downstream affiliate and the local firm and assume t ≤ T and the regularity condition(A1): t > t. Two cases may arise:(i) Suppose the parent country’s tax rate is sufficiently high (T > T ). If the host country’s
tax rate is not sufficiently low (t ∈ (t∗ , T ]), the MNE locates an upstream affiliate in
the low-tax host country (“co-location”). On the other hand, if it is sufficiently low(t ∈ (t, t∗ ]), the upstream affiliate is located in the high-tax parent country (“separate
location”).
(ii) Suppose the parent country’s tax rate is not sufficiently high (T ≤ T ). For any host’s
tax rate (t ∈ (t, T ]), the MNE always locates an upstream affiliate in the low-tax hostcountry (“co-location”).

22

It holds that dg S /dT < 0 and dπ S /dg S < 0, which gives dπ S /dT > 0.

15

4Arm’s length principle (ALP) caseWe move on to the case where the MNE follows the ALP. It now sets equal prices for both
the downstream affiliate and independent local firm.

4.1

Co-location scheme

As in the previous section, we first solve the third stage game, where the downstream firms
choose quantities, and then solve the second stage game, where the MNE chooses input
prices. Maximization problems facing the downstream firms are exactly the same as in thebenchmark (no-ALP) case, except that both the affiliate and the local firm source inputs atthe same price, g̃, where the tilde (˜) represents the variables in the ALP case. Replacing g
and g∗ with g̃ in Eqs. (1) and (2) givesq̃ = q̃∗ =1 − g̃
.
2+b

As the MNE is unable to discriminate prices, its maximization problem is formulated as
e = (1 − T )π̄ + (1 − t)(π̃u + π̃)
max Π
g̃

= (1 − T )π̄ + (1 − t)[2(g̃ − c)q̃ + (p̃ − g̃)q̃].
The profits from selling inputs, 2(g̃ − c)q̃, are doubled because prices and quantities for thetwo downstream firms are the same.
From the FOC with respect to g̃, the following optimal input price is obtained:
g̃ =

1+c
1−c
−
,
2
2(3 + 2b)(10)

where the SOC trivially holds. Comparing this with the input prices under the host production scheme in the benchmark case, g and g∗ defined in Eqs. (3) and (4), reveals thatthe input price in the ALP case falls between the two, i.e., g < g̃ < g∗ . In the benchmark
case, the MNE exercises its market power against the local firm and sets the arm’s length
price higher than the marginal cost (g∗ > c). For the downstream affiliate, the MNE sets thetransfer price lower than the arm’s length price to enhance competitiveness of the affiliate in
the downstream market (g < g∗ ). In the ALP case, however, input prices cannot be discrim-

16inated so that the unique price reflects the two opposing motives. Therefore, the (absolute)magnitude of the strategic effect captured by the second term in Eq. (10) is smaller than thesecond term in Eq. (3).
The total post-tax profits in equilibrium are given by2

e = (1 − T )π̄ + (1 − t)(1 − c) .
Π
3 + 2b

4.2(11)

Separate-location scheme

The quantities that the downstream firms choose are the same as in the co-location scheme:q̃ S = q̃∗S =1 − g̃
(= q̃),
2+b

where the superscript S represents the separate-location scheme as before. Given thesedemand schedules, the MNE chooses an input price to maximize the total post-tax profits:e S = (1 − T )[π̄ + 2(g̃ S − c)q̃ S ] + (1 − t)(p̃S − g̃ S )q̃ S .
max Π
g̃ S

Solving the FOC yields the equilibrium input price:g̃ S =

1+c
1−c(1 − c)(2 + b)(T − t)−.
−22(3 + 2b) (3 + 2b)[t − 2(2 + b)T + 3 + 2b]
|
{z
}

(12)

g̃

The SOC holds under the regularity condition (A1).23 The third term in Eq. (12) captures
the tax manipulation effect as seen in g S defined in Eq. (6), and its sign depends only on T −t
because the denominator is positive under (A1). For t < T , the third term becomes negative,
implying that the MNE reduces the input price to bring more profits to the downstream
affiliate in the low-tax host country. Comparing g̃ S with g S reveals that the tax-manipulation
effect is smaller in g̃ S than in g S .24 Since the first two terms in g̃ S equal g̃, it is observed
23

The SOC is given byd2 Π̃S
2[t − 2(2 + b)T + 3 + 2b]
=−
< 0,
dt2
(2 + b)2

which holds under (A1).
24
To see this formally, we calculate the difference between the absolute coefficients of T − t in g̃ S and those17that the ALP mitigates both the strategic and tax-manipulation effects. The input price is
no longer an effective device for making the downstream affiliate competitive, or for shifting
profits. Consequently, the input price in the ALP case falls between the transfer price andthe arm’s length price in the benchmark case, i.e., g S < g̃ S < g∗S , similar to the co-location
scheme.
The equilibrium total post-tax profits are calculated as(1 − c)2 (1 − T ).
Π = (1 − T ) π̄ +t − 2(2 + b)T + 3 + 2b
eS

4.3



(13)

Location choice

Using the equilibrium total profits under the two different locations, we can determine inwhich country the MNE locates an upstream affiliate in the ALP case. From Eqs. (11) and(13), the profit difference is given by2e −Π
e S = (1 − c) [t − (3 + 2b)T + 2(1 + b)](T − t) .
Π
(3 + 2b)[t − 2(2 + b)T + 3 + 2b]
The profits under the two schemes are illustrated in Fig. 3. It can be verified that the second
term in the numerator and the denominator are positive under (A1), and thus the sign of thee −Πe S > 0 hold, the MNE chooses
difference depends only on T − t. If T − t > 0 and hence Π
to locate the upstream affiliate in the host country.25 If the opposite is true, it chooses tolocate in the parent country. In other words, the upstream affiliate is always establishedin the low-tax country. In contrast to the benchmark case, the separate-location scheme isin g S :
∂g̃ S
∂g S
−
∂(T − t)∂(T − t)(2 − b2 )(2 + b)(1 − c)
(1 − c)(2 + b)−=
(3 + 2b)[t − 2(2 + b)T + 3 + 2b] 2(2 − b2 )[2t − (4 − b2 )T + 2 − b2 ]Ω(2 + b)(1 − c)=−
< 0,2(3 + 2b)(2 − b2 )[t − 2(2 + b)T + 3 + 2b][2t − (4 − b2 )T + 2 − b2 ]where Ω ≡ (4 − 4b − b2 + 2b3 )t − 2(4 − b2 )(4 + b − b2 )T + 28 + 12b − 15b2 − 4b3 + 2b4 > 0.
25e −Πe S < 0 holds, implying that the MNE chooses the separate-location scheme.
Notice that if t > T , Π
The upstream affiliate is located in the parent country simply for its low tax rate as in the benchmark caseunder t > T (see footnote 21).

18

never optimal even if T is much higher than t. The input prices can neither be effectively
used to enhance the competitiveness of the downstream affiliate, nor to shift profits, thereby
reducing the benefit of choosing the separate-location scheme.

Fig. 3. Production location choice in the ALP case.

Proposition 2 (ALP case). Suppose the MNE sets equal input prices for its downstream
affiliate and the local firm, and assume t ≤ T and the regularity condition (A1): t > t. For
any host’s tax rate (t ∈ (t, T ]), the MNE always locates an upstream affiliate in the low-tax
host country (“co-location”).

4.4

Extensions and robustness

We have seen that the upstream affiliate may be located in the parent country (separate
location) even if the parent’s tax rate is higher than the host’s tax rate (Proposition 1),
and the imposition of the ALP may change the separate-location scheme to the co-location
scheme (Proposition 2). One may wonder these results crucially depend on our simplified
structure, where the intermediate inputs are supplied only by the upstream affiliate, andthere is only one local rival in the downstream market. We briefly discuss the robustnessof the results against two extensions by introducing (i) a local upstream rival and (ii) many
downstream rivals. The detailed derivations are relegated to the Appendices.
19

Local rival firm in the upstream industry.

In addition to the upstream affiliate, a local

upstream rival in the host country is added. The upstream rival has the same marginal costof c, supplies the same type of intermediate inputs as the upstream affiliate, and competes
with the upstream affiliate in prices. Bertrand competition with homogeneous products leads
both the two upstream firms to set their prices equal to or lower than their marginal cost.
The upstream rival is unable to set its price lower than the marginal cost in order to earn
non-negative profits. On the other hand, the upstream affiliate, if it is located in the parent
country, is able to do so because its negative profits are compensated by the profits fromdifferent businesses π̄. Thus, the MNE locates the upstream affiliate in the high-tax parent
country as in Proposition 1, and takes the market share in the upstream industry.
In the ALP case, however, it is not profitable for the MNE to have an input price lower
than the marginal cost. As both the related and unrelated downstream firms face the same
input price, a lowered input price would make the local downstream rival as competitive
as the downstream affiliate, thereby reducing the affiliate’s profits. The ALP makes theseparate-location scheme less effective than before and may change the location pattern as
in Proposition 2.
Many local rival firms in the downstream industry. We allow for many local downstream
rivals, each of which produces its own variety of products. The greater number of downstream
rivals yields more input sales. This implies that the downstream affiliate’s profits relative to
profits from local downstream rivals become less important in the MNE’s total profits. The
MNE now lays less emphasis on the role of transfer prices and relies more on input sales frommany local downstream rivals. Thus, it tends to prefer the co-location scheme simply for the
low tax rate in the host country. However, if the number of downstream rivals is not toolarge, Propositions 1 and 2 still hold.

5

The impact of the ALP on tax revenues

It has been shown that the imposition of the ALP may change the location of upstream
production from the parent to the host country. At first glance, this location change seems
to enhance economic activities in the host and bring larger tax revenues. However, this is20

not true. It can be verified that for t ∈ (t, t∗ ), tax revenues under the co-location scheme ing
the benchmark case (without the ALP), denoted by T
RH , are lower than those under the
separate-location scheme in the ALP case, denoted by T RH :26
g
T
RH < T RH ,gwhere T
RH = t(π̃u + π̃ + π̃∗ )= t · 2(p̃ − c)q̃,
T RH = t(π S + π∗S )= t[(pS − g S )q S + (pS∗ − g∗S )q∗S ],where it is noted that p̃ = p̃∗ and q̃ = q̃∗ . The tax base in the benchmark case consists of the
profits of the two downstream firms (π S + π∗S ), while in the ALP case the tax base includes
the profits of the upstream affiliate (π̃u ) as well as the two profits (π̃ + π̃∗ ). If the MNE
can discriminate between the transfer price and the arm’s length price, the two input prices
are chosen in a manner that the tax-manipulation effect strengthens the strategic effect. As
a result, the downstream affiliate expands significantly, so that more goods are produced
compared to the ALP case, i.e., q S + q∗S > 2q̃.27 In fact, the imposition of the ALP helps the
local rival firm expand (q̃∗ > q∗S ), but discourages the production of the downstream affiliate(q̃ < q S ).28 The contraction of host production combined with a narrower price-cost marginresults in smaller tax revenues.
In contrast, it can be verified that in most cases, the location change induced by the ALP
26
27

For t∗ (defined in Eq. (9)) to be positive, we assume (A2), i.e., a sufficiently high T .
To see this formally, we have2g̃ − (g S + g∗S )> 0,
2+b→ (5 − 2b)t − 2(2 − b)T − 1 < 0,

q S + q∗S − 2q̃ =→t<2(2 − b)T + 1≡ tq .
5 − 2bThere exists t satisfying the above inequality because it holds that ta < tq < t∗ and t > t ≡ max{ta , tb } from
(A1).
28
Noting that g S < g∗S and g̃ > g∗S , we haveq̃ − q∗S =(2 − b)(g∗S − g)
2g∗S − bg S − (2 − b)g̃>
> 0.
(2 − b)(2 + b)
(2 − b)(2 + b)

Combining this result with q S + q∗S > 2q̃ gives q̃ < q S . This also implies that the gap between price andmarginal cost is smaller in the ALP case than in the benchmark case: q̃ = p̃ − g̃ < pS − g S = q S .

21

increases tax revenues globally:g
T
RW > T RW ,gwhere T
RW = T π̄ + t(π̃u + π̃ + π̃∗ )= T π̄ + t · 2[(p̃ − g̃) + (g̃ − c)]q̃,
T RW = T (π̄ + πuS ) + t(π S + π∗S )= T [π̄ + (g S − c)q S + (g∗S − c)q∗S ] + t[(pS − g S )q S + (pS∗ − g∗S )q∗S ].
where tax revenues in the parent country are now taken into account. In the benchmark case,the upstream affiliate sets the transfer price lower than the marginal cost (g S < c), and earns
negative profits. The host country benefits from larger tax revenues at the expense of theparent country, but in general the benefit does not exceed the loss from a global viewpoint.29
By imposing the ALP, the internal price is set higher than the marginal cost (g̃ > c), whichbrings positive profits to the upstream affiliate in the host country and generally leads togreater tax revenues globally.
These results are summarized as follows (see the Appendices for the proof):
Proposition 3 (Tax revenues).

The imposition of the ALP changes the location of

upstream production from the parent to the host country (from “separate location” to “colocation”) if the international tax difference is large (t ∈ (t, t∗ )). This location change decreases tax revenues in the host country, but generally increases those globally.
Considering the fact that countries adopt transfer pricing taxation to raise their tax
revenues, the implementation of the ALP may give rise to an unintended consequence forcountries with low corporate tax rates. Proposition 2 also suggests a conflict of interest in the
ALP between low-tax and high-tax countries.30 Although it is not part of the formal analysis,
we conjecture that the results also apply to social welfare. The ALP limits the use of transfer
price and thereby leads to higher prices of final goods, which reduces consumer surplus in
the host country. Thus the location change caused by the ALP would lower not only tax
revenues, but also social welfare (consumer surplus and profits as well as tax revenues) in thehost country. For a full analysis on welfare in a related model but without location choice,29

Only if the parent country has a extremely high tax rate which exceptionally expands the downstream
affiliate, it is possible that the location change decreases global tax revenues. See the Appendices for thedetailed conditions.
30
Similar results can be found in Yao (2013) in a different setting mentioned in the Introduction.

22

we refer an independent work by Ishikawa et al. (2017).

6

Conclusion

This paper analyzed how corporate tax rates affect the production location choice of MNEs.
One may think that internationally-mobile firms locate their production in low-tax countries,
but this simple reasoning may not hold true for MNEs with multiple affiliates. MNEs attempt
to reduce tax payments globally by manipulating transfer prices for intra-firm trade. Thus,
they have an incentive to locate their upstream and downstream affiliates separately to exploit
international tax differences. Contrary to the conventional wisdom, this paper shows thatthe upstream affiliate is likely to be located in the parent country, if its tax rate is muchhigher than the tax rate of the host country where the downstream affiliate is located.
With a view to preventing tax manipulations, the transfer pricing tax system requires
MNEs to follow the ALP, where MNEs should not set different prices for related affiliates
and unrelated firms. We have also analyzed the impact of the ALP on the location choiceof MNEs. Under the ALP, MNEs are unable to fully utilize intra-firm transactions acrossborders for tax manipulation. The ALP makes the transfer pricing strategy less effective, andthus may change the location pattern from a separate-location to a co-location of upstream
and downstream affiliates. This location change seems to bring greater tax revenues to thecountry hosting the two affiliates, but we have demonstrated that this is not true. In contrast
to a separate location, a co-location in the host country does not provide the scope of profit
shifting from the parent country, which leads to the loss of tax base in the host country.
Owing to this, the host government may hesitate to implement the ALP strictly. However,the decrease in the host country’s tax revenues due to the ALP is in general smaller than theincrease in the parent tax revenues. As such, the ALP may be desirable globally.
We conclude by proposing possible extensions worth investigating. One extension is toallow taxes to be endogenously chosen by governments. In addition, one can think of manyother policies to attract MNEs such as production and entry subsidies. Considering thepolicy importance of international tax planning, further analysis on different national tax
systems is also needed such as the impact of a change from the separate accounting to theformula apportionment system, or the role of the advance pricing agreement. These issues
are left to future research.

23

Appendices
Appendix 1. List of key variables
BenchmarkCo-location

Separate location

Internal price of the inputgg S (transfer price)

Arm’s length price of the input

g∗

g∗S

Price of the affiliate’s final goodp

pS

Price of the local firm’s final good

p∗

pS∗

Quantity of the affiliate’s final goodq

qS

Quantity of the local firm’s final good

q∗

q∗S

Pre-tax profits of the upstream affiliate

πu

πuS

Pre-tax profits of the downstream affiliateππSPre-tax profits of the local firm

π∗

π∗S

Total post-tax profits of the MNEΠΠS

Arm’s Length Principle (ALP)

Co-location Separate location

Arm’s length price of the input

g̃

g̃ S

Price of the affiliate’s final good

p̃

p̃S

Price of the local firm’s final good

p̃∗

p̃S∗

Quantity of the affiliate’s final good

q̃

q̃ S

Quantity of the local firm’s final good

q̃∗

q̃∗S

Pre-tax profits of the upstream affiliate

π̃u

π̃uS

Pre-tax profits of the downstream affiliate

π̃

π̃ S

Pre-tax profits of the local firm

π̃∗
e
Π

π̃∗S
eS
Π

Total post-tax profits of the MNE

We note that (i) in the ALP case, the internal price is equal to the arm’s length price, (ii)the downstream firms produce one unit of final goods using one unit of intermediate inputs,and (iii) the pre-tax profits from the parent country π̄ are always constant.

Appendix 2. Proof of Proposition 3
Tax revenues in the host country.

Assuming the condition (A2), we will show that when∗t ∈ (t, t ), tax revenues in the benchmark case, T RH , are greater than those in the ALP case,24

gT
RH . It suffices to check the difference of taxable profits:gT
RH − T RH = t[π̃u + π̃ + π̃∗ − (π S + π∗S )] < 0,→ π̃u + π̃ + π̃∗ − (π S + π∗S ) ≡ Γ < 0.
If it is shown that (i) Γ < 0 holds at t = t∗ and (ii)Γ is increasing in t, we can conclude
that Γ is positive for t ∈ (t, t∗ ). First we check (i):Γ|t=t∗ = −B(1 − c)2< 0,4(2 − b)2 (3 + 2b)2where B ≡ 4b6 − 4b5 + b4 + 12b3 − 46b2 + 8b + 26 > 0.
(ii) requires the following condition:∂(π S + π∗S ) dg S
dΓ
=−
> 0,
dt
∂g S
dt
dg S
(2 − b)2 (2 + b)(1 − c)(1 − T )
where
=
> 0,
dt
2[2t − (4 − b2 )T + 2 − b2 ]noting that profits earned in the host under the ALP, π̃u + π̃ + π̃∗ , are independent of transfer
price and thus of tax rates. We only need to check that profits in the host in the benchmark
case, π S + π∗S , are decreasing in transfer price, g S :∂(π S + π∗S )2[b2 g S − 4bg∗S + 4g S − (b2 − 4b + 4)]=∂g S(2 − b)2 (2 + b)2
2[b2 g∗S − 4bg∗S + 4g∗S − (b2 − 4b + 4)]<(2 − b)2 (2 + b)22(g∗S − 1)
< 0,=
(2 + b)2
where from the first to the second line we made use of g S < g∗S and in the third line it holds
that g∗S < 1 from c < 1. Both (i) and (ii) are proved to be true and thus we complete theproof.
Tax revenues in the world.

We first show g S < c for t ∈ (t, t∗ ) while assuming (A2).

25

g S < c requires the following condition:(1 − c)[(4 − b)t − (4 − b2 )T − b(1 − b)]< 0,
2[2t − (4 − b2 )T + 2 − b2 ](4 − b2 )T + b(1 − b)→t<
≡ tg .
4−bgS − c =It can be verified that the above inequality holds for t ∈ (t, t∗ ) because(1 − b)[(b3 − 3b2 + 4)T − b3 + 7b2 − 6b − 4]t −t =−> 0,(4 − b)(3 − 2b)∗gnoting that b < 1 and T > T from (A2).
We then show the following:gT
RW − T RW = −T πuS + t[π̃u + π̃ + π̃∗ − (π S + π∗S )]= −T πuS + tΓ ≡ ∆ > 0,gwhere T RW and T
RW are world tax revenues in the benchmark and the ALP cases, respectively.
Analogous to the previous case, if it is shown that (i)∆ is positive at t = t∗ and (ii)∆ isdecreasing in t, we can conclude that ∆ > 0 holds for t ∈ (t, t∗ ). First we see (i):
∆|

t=t∗

Ω(1 − c)2=,4(3 − 2b)(2 − b)2 (3 + 2b)2where Ω ≡ B1 T + B0 ,B1 ≡ −(2 − b)(4b8 − 4b7 − 23b6 + 28b5 + 36b4 − 50b3 − 14b2 + 20b + 2) ∈ (−1, 10),B0 ≡ (1 − b)(1 + b − b2 )(4b6 − 4b5 + b4 + 12b3 − 46b2 + 8b + 26) ∈ (0, 26).
B1 becomes negative if the degree of differentiation b is close to unity (larger than 0.89).
Therefore Ω can be negative if b is close to unity and T is sufficiently high. Except for suchan extreme case, Ω is positive and thus ∆|t=t∗ is also positive.

26

To prove (ii), it suffices to show
d∆
dπ S
dΓ
= −T u + Γ + t
dt
 dt
 dt
dΓ dπuS
<t
−
+Γ
dt
dt
∂(π S + π∗S − πuS ) dg S
+ Γ < 0,=t
∂g S
dt
where from the first to the second line we have made use of t < t∗ < T . As we have seen
dg S /dt > 0 and Γ < 0, we only need to check2b(8 − b2 )g∗S − 2(12 − b2 )g S + (2 − b)2 (bc + b + 2c + 4)∂(π S + π∗S − πuS )=−∂g S(2 − b)2 (2 + b)22b(8 − b2 )g∗S − 2(12 − b2 )c + (2 − b)2 (bc + b + 2c + 4)<−
(2 − b)2 (2 + b)24(1 − c)(4 − b)=−
< 0,
(2 − b)2 (2 + b)2
noting that g S < c from the first to the second line. We complete the proof.

Appendix 3. Local rival firm in the upstream industry
In the main text, the upstream affiliate is the only supplier of inputs. One may wonder thissetting is crucial for the results, but it is not the case. We will see that the upstream affiliate
may be located in the high-tax parent country (“separate location”) in the benchmark case
(Proposition 1) and the imposition of the ALP may change this location pattern (Proposition2). We introduce a rival upstream firm in the host country. The rival upstream firm has thesame marginal cost c as the MNE’s upstream affiliate and competes with the affiliate in a
Bertrand fashion. The timing proceeds in the same manner as in the text. First, the MNEchooses a location for upstream production. Then the MNE and the rival upstream firm
set input prices. Finally the downstream affiliate and the rival downstream firm source theinputs and produce final goods.
As inputs produced by the two upstream firms are homogeneous, the downstream firms
buy inputs from the lowest price supplier. Hence, the dominant strategy for the rival upstream
is to set its input price equal to the marginal cost c. Considering this strategy of the rival
upstream, the MNE sets input prices equal or lower than c. We need to modify the MNE’s
27

maximization problem so as to include inequality constraints on input prices.
Benchmark case.

Let us first look at the separate-location scheme. The maximization

problem for the MNE is modified as31
max ΠS = (1 − T )[π̄ + (g S − c)q S + (g∗S − c)q∗S ] + (1 − t)(pS − g S )q S ,g S ,g∗Ss.t. g S ≤ c, g∗S ≤ c,where the final good’s price pS and quantities (q S , q∗S ) are defined in Section 3 and we assume
that the MNE upstream affiliate takes all the input demand if its prices are equal to the onesof the rival upstream.
Letting λ and µ be the Lagrange multipliers for the constraints of g S ≤ c and g∗S ≤ crespectively, we solve the above problem to get
gS = c −b2 (2 − b)(1 − c)(2 + b)(2 − b)2 (1 − c)(T − t)−
< c,4(2 − b2 )2(2 − b2 )[2t − (4 − b2 )T + 2 − b2 ]λ = 0,g∗S = c,µ = (1 − c)(1 − T )/2 > 0,
where we maintain the assumptions (A1) and t ≤ T . As the multipliers are all non-negative,the equilibrium prices satisfy the Kuhn-Tucker conditions for optimization. g S allows asimilar interpretation to the one for the unconstrained optimal transfer price defined in Eq.
(6). The first term is the base price equal to the arm’s length price. The second and thirdterms respectively represent the strategic and the tax-manipulation effects.
The associated post-tax profits are then given by(1 − T )(2 − b)2 (1 − c)2
Π = (1 − T ) π̄ +.
8{2t − (4 − b2 )T + 2 − b2 }SUnder the co-location scheme in the benchmark case as discussed in Section 3.1, the MNE
sets input prices higher than c in the unconstrained maximization problem, i.e., g > c andg∗ > c. Hence, in the constrained problem here, it can be confirmed that the MNE sets input
31

We do not distinguish the notation of variables between the unconstrained problem in the text and theconstrained problem here.

28

prices equal to c, i.e., g = c and g∗ = c, and obtains the following post-tax profits:Π = (1 − T )π̄ +(1 − t)(1 − c)2.
(2 + b)2

As easily seen, Π is smaller than ΠS at t ∈ (t, T ]. In other words, the MNE’s optimal choice isthat the upstream affiliate is always located in the parent country (separate location). Even
when considering the rival upstream, our conclusion still holds; the upstream production may
be located in the high-tax country for the strategic and tax-manipulation purposes.
ALP case.

In the ALP case, the optimal input prices in the unconstrained problem

discussed in Sections 4.2-4.3 are never below the marginal cost c under the two schemes,i.e., g̃ > c and g̃ S > c. By the same reasoning as before, it can be confirmed that theconstrained problem gives the input prices equal to the marginal cost, i.e., g̃ = c and g̃ S = c.
Hence, the associated profits are identical with the one under the co-location scheme in thee =Π
e S = Π at t ∈ (t, T ]. Unlike the benchmark case, the strategic andbenchmark case, i.e., Π
tax-manipulation effects disappear and the two countries are indifferent as to the location
choice. In this generalized setting, we still see that the imposition of the ALP may change
the location pattern as argued in the text.

Appendix 4. Many local rival firms in the downstream industry
As in Appendix 3, we will see that our main conclusions are maintained in a more generalized
setting than in the text. Consider N local rival firms in the downstream industry. The local
rival firms are assumed to be symmetric and have the same marginal cost of c. If N is set to
be unity, all the following results reduce to the corresponding results in the text.
The demand functions for the downstream affiliate and the local rival firm j are respectively given by
p=1−q−b

N
X

q∗i ,

i=1

p∗j = 1 − q∗j − b q +

N
X

!
q∗k

.

k6=j

The following procedure is the same as in the text and we solve the problem backward.
29

Taking into account the above demand schedules, the downstream firms choose quantities tomaximize their own profits:b[N g∗ + (1 − N )g − 1] + 2(1 − g∗ ),(2 − b)(2 + N b)b(g − 1) + 2(1 − g∗ )q∗ =,(2 − b)(2 + N b)q=where we have used the symmetry to obtain q∗j = q∗ for all j ∈ {1, . . . , N }.
Benchmark case.

Given the equilibrium quantities the downstream firms choose, the

MNE sets inputs prices to maximize its post-tax profits. In the co-location scheme, theequilibrium input prices are given by
1+c(2 − b)(1 − c)−,22[2 − b + N b(1 − b)]
1+c
,
g∗ =
2
g=

where the SOCs trivially hold. The second term in g is negative and captures the strategic
effect as in Eq. (3) in the text. We can see that the internal price g is increasing in thenumber of downstream local rivals N . The more local rivals there are, the more inputs theysource from the upstream affiliate. The upstream affiliate can earn more profits so that the
profits of downstream affiliate are of less importance for the MNE. This is why as the numberof local rivals increases, the MNE weakens the strategic effect and sets a higher internal price.
The total post-tax profits in equilibrium are calculated as
Π = (1 − T )π̄ +(1 − t)(1 − c)2 [2 + N − b(1 + N )].
4[2 − b + N b(1 − b)]

The equilibrium input prices in the separate-location scheme are given by
gS =

1+c
(2 − b)(1 − c)−...
22[2 − b + N b(1 − b)]
|
{z
}
=g

··· +
g̃∗S =(2 − b)2 (2 + N b)(1 − c)(t − T ),2[2 − b + N b(1 − b)][{2 + b(N − 1)}t − (2 − b)(2 + N b)T + 2 − b + N b(1 − b)]

1+c
,
2

30

where the SOCs require{2 + b(N − 1)}t − (2 − b)(2 + N b)T + 2 − b + N b(1 − b) > 0.
The total post-tax profits in equilibrium are calculated as(1 − c)2 {N t − (2 − b)(1 + N )T + 2 + N − b(1 + N )}
Π = (1 − T ) π̄ +.
4{(2 + b(N − 1))t − (2 − b)(2 + N b)T + 2 − b + N b(1 − b)}SUnder t ≤ T , the third term in g is negative so that the tax-manipulation effect works in thesame way as in Eq. (6).
Taking difference between the post-tax profits in both schemes givesΠ − ΠS =Θ0 (1 − c)2 (T − t),
4[2 − b + N b(1 − b)][(2 + b(N − 1))t − (2 − b)(2 + N b)T + 2 − b + N b(1 − b)]where Θ0 ≡ (2 − b + N b)[2 − b + N (1 − b)]t + (2 − b)(1 + N )[2 − b + N b(1 − b)]T · · ·· · · + N (1 − b)[2 + b(1 − b)(1 + N )].
The profit difference becomes zero at t = T and t = t0 where t0 is the solution of Θ0 = 0. It
can be confirmed that t0 is in between (t, 1] if N is not sufficiently large.32 In this case, wehave Π − ΠS < 0 for t ∈ (t, t0 ) and Π − ΠS ≥ 0 for t ∈ [t0 , T ]. We can conclude that the MNEchooses the separate location if the tax difference is large as in Proposition 1.
ALP case.

Analogous to the benchmark case, the equilibrium input price under theco-location scheme becomes
g̃ =

1+c
1−c
−
,
2
2[1 + 2N + N b(1 + b)]

where the SOC trivially holds. It can be confirmed that the second term of the above
expression, i.e., the strategic effect, is smaller than the counterpart of g and that g < g̃ < g∗holds as in the text. The total post-tax profits are given by22

e = (1 − T )π̄ + (1 − t)(1 − c) (1 + N ) .
Π
4[1 + 2N + N b(1 + b)]
It always holds that t0 < T . t0 is decreasing in N if N is not sufficiently large so that it t0 > t holds fornot sufficiently large N .
3231

Turning to the separate-location scheme, the equilibrium input price becomesg̃ S =

1−c
1+c
−
···
2
2[1 + 2N + N b(1 + b)]
|
{z
}
=g̃

··· −

(1 − c)(1 + N )(2 + bN )(T − t).
2[1 + 2N + N b(1 + b)][t − (1 + N )(2 + N b)T + N (1 + N )b + 1 + 2N ]We can check that as long as N is not sufficiently large, the third term of the above expression,i.e., the tax-manipulation effect, is smaller than the counterpart of g S and g S < g̃ < g∗ holds
as in the text.
The total post-tax profits under the separate-location scheme are given bySeΠ = (1 − T ) π̄ +

(1 − T )(1 − c)2 (1 + N )2,4{t − (1 + N )(2 + N b)T + N (1 + N )b + 1 + 2N }where the SOCs requiret − (1 + N )(2 + N b)T + N (1 + N )b + 1 + 2N > 0.
The profit difference then becomes
2

2

2

e −Π
e S = (T − t)(1 − c) (1 + N ) [t − (1 + 2N + N b + N b)T + N (1 + N )b + 2N )] ,Π4(1 + 2N + N b + N 2 b)[t − (1 + N )(2 + N b)T + N (1 + N )b + 1 + 2N ]which is positive because of the SOC. This implies that in the ALP case the MNE always
chooses the co-location scheme as in Proposition 2.

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