Kato, Hayato und Okoshi, Hiofumi:
Economic Integration and Agglomeration ofMultinational Production with Transfer Pricing

Munich Discussion Paper No. 2019-2
Department of Economics
University of Munich
Volkswirtschaftliche Fakultät
Ludwig-Maximilians-Universität München

Online at https://doi.org/10.5282/ubm/epub.62013

Hayato Kato und Hiofumi Okoshi:
Economic Integration and Agglomeration ofMultinational Production with Transfer Pricing

Munich Discussion Paper No. 2019
Department of Economics
University of Munich
Volkswirtschaftliche Fakultät
Ludwig-Maximilians-Universität München

Online at http://epub.ub.uni-muenchen.de/62013/

Economic integration and agglomeration of multinational
production with transfer pricing
Hayato Kato a ∗ , Hirofumi Okoshi baGraduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka, 560-0043,
Japanb

Munich Graduate School of Economics, University of Munich, Seminar for Economic Policy,
Akademiestr. 1/II, D-80799 Munich, Germany
This version: May 9, 2019

Abstract
Do low corporate taxes always favor multinational production in the course of economic
integration? We build a two-country spatial model with different corporate tax rates inwhich multinational enterprises (MNEs) can manipulate transfer prices in intra-firm trade.
Using transfer pricing, MNEs can shift profits between domestic production plants andforeign distribution affiliates. In the initial stage of integration, more MNEs locate theirproduction plants in the low-tax country, and then in the later stage, this location patternreverses. Contrary to conventional wisdom, high taxes may favor multinational production,
which does not yet necessarily bring greater tax revenues. The results have implications for
empirical studies and tax competition between unequal-sized countries.
Keywords: Transfer price; Production location; Economic integration; Intra-firm trade;
Economic geography.
JEL classification: F12; F23; H25; H26.

We would like to thank David Agrawal, Nobuo Akai, Cristina Angelico, Robin Boadway, Andreas Haufler, Kazunobu Hayakawa, Fukunari Kimura, Kozo Kiyota, Toshiyuki Matsuura, Yuhei Miyauchi, Tadashi
Morita, Kohei Nagamachi, Yukihiro Nishimura, Toshihiro Okubo, Sönje Reiche, Hisamitsu Saito, YasuhiroSato, Dirk Schindler, Hajime Takatsuka, and Emmanuelle Taugourdeau for their helpful suggestions. Thanks
also to seminar and conference participants at Kagawa U, Kochi U, U of Munich, IIPF 2018 (U of Tampere), and 2019 Symposium of Public Economics (Osaka U). Financial supports from the Japan Society
for the Promotion of Science (Grant Numbers: JP16J01228; JP18H00866; JP17K03789), the German Research Foundation through GRK1928, the Nomura Foundation, and the Obayashi Foundation are gratefully
acknowledged. All remaining errors are our sole responsibility. E-mail addresses: hayato.kato@econ.osakau.ac.jp (Kato: corresponding author); hirofumi.okoshi1@gmail.com (Okoshi).
∗11. Introduction
Continuing economic integration in the last few decades brought more international
mobility to multinational enterprises (MNEs) and allowed them to diversify activities acrosssubsidiaries in different countries. Considering the complexity of multinational activities,
governments today need to carefully design policies to attract MNEs. Among many factors,
corporate taxation is one of the essential determinants of foreign direct investment (FDI)(Navaretti and Venables, 2004, Ch.6). One naturally expects that countries with a low
corporate tax rate will succeed in hosting more FDI inflow than those with a high tax rate.
However, the type of MNE activities that operate in such low-tax countries is not obvious.
Governments lower taxes with an aim of hosting production plants, which contribute to local
employment and tax revenues. Contrary to host governments’ expectations, MNEs reportedly establish affiliates in low-tax countries to save taxes and do not engage in production(Horner and Aoyama, 2009). 1
We can illustrate this point by looking at the profits and manufacturing activities of U.S.
affiliates in Europe. In Fig. 1, we take U.S. affiliates in twelve European countries and draw
the share of their profits from two low-tax countries, Ireland and Switzerland, over the last
15 years (thick line). The profit share of low-tax countries is disproportionately large for
their size and doubled from 17% in 1997 to 34% in 2012. The manufacturing employment
share of low-tax countries (dotted line), on the other hand, has been less than their profit
share, indicating that U.S. affiliates there rely more on non-production activities, such as
distribution, than those in the other countries. Although both the profit and manufacturing
employment shares increased over time, there is no clear sign of convergence between thetwo.

1

Horner and Aoyama (2009) provide a list of Irish company relocations, with several examples indicatingthat MNEs move production from Ireland—with the world’s lowest corporate tax rate at the time—abroadwhile maintaining non-production activities such as service centers and marketing. This implies that low-tax
countries do not necessarily retain multinational production.

2

Fig. 1. Profit share and manufacturing employment share of low-tax countries in U.S.
affiliates in Europe.
Sources: The U.S. Bureau of Economic Analysis (the BEA) and Zucman (2014).
Notes: Data on profit are from Zucman (2014) (“U.S. Direct Investment Abroad, Direct Investment Income Without Current-Cost Adjustment”), who compiled data originally from the BEA. Either Ireland or
Switzerland had the lowest or the second lowest corporate tax rates among the sample countries for mostof the period from 1997 to 2012: the average rates are 17.5% (Ireland), 23.3% (Switzerland), and 30.3%(overall) (source: OECD tax database). Data on employment are also from the BEA (“Employment ofAffiliates, Country of UBO by Industry of Affiliate”). Because the BEA reports employment data for only
selected countries, we take twelve countries in Europe with consistent reporting for 1997-2012: Belgium,
Denmark, Finland, France, Germany, Ireland, Italy, the Netherlands, Spain, Sweden, Switzerland, and theU.K.

The diverging shares of profits versus manufacturing employment in low-tax countries
may be explained by profit shifting of MNEs. MNEs allocate their activities between low-tax
and high-tax countries and transfer profits by controlling prices for intra-firm trade, known astransfer prices. 2 For example, headquarters in high-tax countries makes profits by producing
final goods and sells them to affiliates in low-tax countries by setting low transfer prices toinflate the affiliates’ profits. As expanding intra-firm trade due to economic integration made2

Empirical evidence on transfer pricing can be found in Swenson (2001); Bartelsman and Beetsma (2003);
Clausing (2003); Bernard et al. (2006); Cristea and Nguyen (2016); Gumpert et al. (2016); Guvenen et al.
(2017); and Davies et al. (2018).

3

profit shifting easy, the geographical separation of production and profits may continue torise.
When firms can shift profits and relocate, it is no longer clear how MNEs optimally
set up their firm structure in the presence of international tax differences. We examine this
aspect in the present study. We extend a two-country geography model developed by Martin
and Rogers (1995) and Pflüger (2004) to incorporate MNEs with profit-shifting motives. In
the main analysis, the model contains two countries of equal size, but with (exogenously
given) different corporate tax rates. Each MNE sets up a production plant in one country
and a distribution affiliate in the other. MNEs engage in intra-firm trade; their production
plants sell goods to the domestic market and export them to their foreign affiliates for
distribution. Firms use the internal transaction price, or transfer pricing, for profit shifting.
The effectiveness of profit shifting crucially depends on the volume of intra-firm trade, which
is subject to trade costs. We investigate in which country, the low-tax or the high-tax one,
multinational production is agglomerated and how the location pattern changes in response
to a decline in trade costs.
Our findings are as follows. In the initial stage of economic integration marked by hightrade costs, the low-tax country attracts a higher share of multinational production thanthe high-tax country does. When high trade costs hamper intra-firm trade and thus profit
shifting, MNEs rely on their domestic production plant for profits. They simply prefer tolocate production in the low-tax country to save taxes on their plant.
A further reduction in trade costs, however, reverses this location pattern. Especiallywhen trade costs are sufficiently low, all multinational production is agglomerated in thehigh-tax country. This result seems surprising, but it is indeed consistent with MNEs’ profitshifting motive. As low trade costs expand intra-firm trade, MNEs with production plants
in the high-tax country lower the transfer price to shift their domestic plants profits to theirforeign affiliate in the low-tax country. Furthermore, the lowered transfer price reduces themarginal cost of the foreign affiliates, and thus makes them competitive in their market. On
the other hand, MNEs with production plants in the low-tax country raise the transfer priceto move profits from the foreign affiliate in the high-tax country back to the domestic plant.
4

The high transfer price decreases the affiliate’s competitiveness. The direction of profit
shifting from the high-tax to the low-tax country works such that MNEs with production in
the high-tax country become competitive, resulting in production agglomeration there.
These results may explain the fact that U.S. affiliates in low-tax European countries engage disproportionately more in non-production activities than those in high-tax European
countries do, as Fig. 1 shows. In addition, Overesch (2009) provides supporting empiricalevidence. He finds that multinationals in high-tax Germany increase real investments because the cross-country corporate tax difference between their home country and Germany
is larger.
The agglomeration of multinational production in the high-tax country, however, does
not necessarily lead to greater tax revenues there, since a large portion of profits shift tothe foreign affiliates in the low-tax country. Amid growing concerns about tax base erosion,
the OECD recently reported that the estimated revenue losses from MNEs’ tax avoidanceis at most 10% of global corporate income tax revenues. 3 Our finding may justify theconcern about low-tax countries attracting multinationals that contribute little to the hosteconomies.
Based on our theoretical findings, we can draw implications for empirical studies on FDI
and corporate taxes. The empirical literature largely supports the positive effect of low
corporate tax rates on FDI inflow but does not agree on the significance and magnitudeof the effect (Navaretti and Venables, 2004, Ch.10). It is unsurprising, according to ourfindings, that host countries with lower corporate tax rates may not enjoy inward FDI if thehost and source countries are integrated enough to make profit shifting easy.
Our results also have implications for tax competition over multinational production
between unequal-sized countries. Existing studies on tax competition in agglomeration
economies tell us that large countries set a higher tax rate, while keeping the agglomeration of production (Kind et al., 2000; Ludema and Wooton, 2000; Andersson and Forslid,3

See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-project-for-discussion-at-g20-f
htm, accessed on 20 February 2019. To tackle this issue, the OECD set up a project called “Base Erosion
and Profit Shifting” (BEPS), involving over eighty countries. See http://www.oecd.org/tax/beps,
accessed on 20 February 2019.

5

2003; Baldwin and Krugman, 2004; Ottaviano and van Ypersele, 2005; Borck and Pflüger,2006). 4 If transfer pricing can be used, however, the large country still keeps the agglomeration, but sets a lower tax rate than it would if transfer pricing is impossible. A bigger tax
difference would bring more opportunities to manipulate transfer pricing, thus triggering anerosion of taxable profits. Therefore, introducing profit shifting exerts downward pressure
on the large country’s tax rate and thus narrows the equilibrium tax difference.

Relation to the literature.

This paper fits into the literature on transfer pricing pioneeredby Copithorne (1971) and Horst (1971). The literature points out that MNEs use transfer
prices to make affiliates competitive as well as for shifting profits. The former is calleda strategic effect and the latter a tax manipulation effect. Earlier studies examining thestrategic use of transfer pricing include those by Elitzur and Mintz (1996); Schjelderup and
Sørgard (1997); Zhao (2000); and Nielsen et al. (2003). 5 The literature looks only at profit
shifting with a fixed location of each affiliate. Our contribution is to uncover how these two
effects of transfer pricing affect the MNEs’ location choices.
Recent studies focus on the FDI decision of MNEs with profit-shifting motives; thatis, whether MNEs should undertake FDI and manufacture inputs within their firms, orsource inputs from independent suppliers, known as the make or buy decision (Bauer andLangenmayr, 2013; Egger and Seidel, 2013; Keuschnigg and Devereux, 2013; Choi et al.,2018). 6 Egger and Seidel (2013), for example, theoretically predict and empirically confirm
that larger tax differences are more likely to lead MNEs to engage in FDI, rather thanoutsourcing. Choi et al. (2018) find a possibility that MNEs do both FDI and outsourcing
to avoid regulations by tax authorities. While these studies fix the supplier’s location andlook at MNEs’ organizational choices, we fix the MNEs’ organization form and allow for the4

Recent studies in the literature allow for heterogeneity among firms (Davies and Eckel, 2010; Haufler
and Stähler, 2013; Baldwin and Okubo, 2014), forward looking behavior by governments (Han et al., 2014;
Kato, 2015), and lobbying by firms (Ma, 2017; Kato, 2018).
5
While these studies (and ours) deal exclusively with tangible assets, recent studies examine intangible
assets (Juranek et al., 2018).
6
For studies on MNEs without profit shifting motives, see Antràs and Yeaple (2014); Section 3.6 ofCostinot and Rodrı́guez-Clare (2014).

6

endogenous location of production. Our companion study, Kato and Okoshi (2018), focuseson the location decision within MNEs, though accounts for neither MNEs’ various activities(production and distribution), nor trade costs, unlike the present one.
Due to analytical inconvenience, only a handful of studies examine tax competition for
MNEs using transfer prices (Haufler and Schjelderup, 2000; Kind et al., 2005; Stöwhase,
2005, 2013; Ma and Raimondos, 2015). 7

In models with two unequal-sized countries,

Stöwhase (2005, 2013) find that introducing profit shifting will not generally put downward
pressure on tax rates, which is in contrast to our findings. These different results are mainly
due to the strategic effect of transfer prices in our model, which strengthens profit-shifting
incentives and thereby leads to tougher tax competition. In terms of setting, the closest
study to ours is Ma and Raimondos (2015), who allow for both trade costs and unequalsized countries. In a tax-competition game over a single MNE, they show the possibility
that the large country will win the MNE while setting a higher tax rate, which is similar
to our findings. 8 However, due to the analytical inconvenience arising from the location
discontinuities of a single MNE, their analysis relies heavily on numerical simulations. It isthus unclear whether or not introducing profit shifting increases the tax difference between
the large and small countries. By contrast, we can obtain sharp predictions in analyticalform by employing an economic geography model with a continuum of MNEs and focusing
on a full agglomerated situation.
The rest of the paper is organized as follows. The next section develops the model.
Section 3 examines the case where the tax rates of two equal-sized countries are exogenously
given and derives the equilibrium distribution of production plants. Section 4 discusses theimplications for empirical studies and tax competition between unequal-sized countries. The
final section concludes.

7

More recent studies introduce a low-tax country with no production or consumption, calling it a tax
haven country, and consider tax competition between a home country and the tax haven (Krautheim andSchmidt-Eisenlohr, 2011; Langenmayr et al., 2015; Hauck, 2019). This setting greatly enhances analyticaltractability but is not suitable to investigate the MNEs’ production location.
8
In other numerical examples, they allow for asymmetry in the leniency of tax regulations and asymmetriccountry sizes, in which case, the small country may win the MNE while setting a higher tax rate.

7

2. Basic setting
Consumers.

We consider an economy with two countries, indexed by 1 and 2, and two

goods, homogeneous and differentiated ones. Letting L be the world population, country 1
has a population of L1 = s1 L, while country 2 has a population of L2 = s2 L = (1 − s1 )L,
where s1 ∈ (0, 1) is country 1’s share of the world population. Each individual owns one
unit of labor.
Following Pflüger (2004), each consumer has an identical quasi-linear utility function
with a constant-elasticity-of-substitution (CES) sub utility. Consumers in country 1 solve
the following maximization problem:max

q̃11 (ω),q̃21 (ω),q1O

where Q1 ≡u1 = µ ln Q1 + q1O ,
" 2 Z
X
i=1

q̃i1 (ω)
ω∈Ωi

σ−1
σ

dω

σ
# σ−1

,

subject to the budget constraint:
2 Z
X
i=1

ω∈Ωi

pi1 (ω)q̃i1 (ω)dω + q1O = y1 + q O
1.

µ > 0 captures the intensity of the preference for the differentiated goods. q1O and q O
1 are
the individual demand for the homogeneous good and its initial endowment, respectively.
We assume that q O
1 is large enough for the homogeneous good to be consumed. q̃i1 (ω) is
the individual demand from consumers in country 1 for the variety ω ∈ Ωi , where Ωi is theset of varieties produced in country i ∈ {1, 2}. Q1 is the CES aggregator of differentiatedvarieties with σ > 1 being the elasticity of substitution over them.
Solving the above problem gives the aggregate demand for the variety ω produced in8country i ∈ {1, 2} and consumed in country 1:
qi1 (ω) ≡ L1 q̃i1 (ω) =where P1 ≡

" 2 Z
X
i=1



pi1 (ω)
P1

−σ

µL1
.
P1
1
# 1−σ

pi1 (ω)1−σ dω
ω∈Ωi

(1)
.

P1 is the CES price index of the varieties. Although we will mainly present the results forcountry 1 in the following, analogous expressions hold for country 2. As firms are symmetric,
we will suppress the variety index ω for notational brevity.

Homogeneous good sector.

The homogeneous good sector uses a constant-returns-to-scaletechnology. That is, one unit of labor produces one unit of the good. The technology leads
to perfect competition, making the good’s price equal to its production cost, or the wage
rate. Letting wi be the wage rate of country i ∈ {1, 2}, the costless trade of the homogeneous
good equalizes the wage rates between countries; that is w1 = w2 . We choose the good as
the numéraire such that w1 = w2 = 1.

Differentiated goods sector.

The differentiated goods sector uses an increasing-returns-to-scale technology. Each MNE needs f units of capital for a production plant in one country
and another f units for a foreign affiliate in the other. 9 Supposing the world amount of
capital is 2K, we choose f such that the world has 2K/(2f ) = L MNEs, or f = K/L. The
post-tax profits are repatriated to capital owners living in a third country (outside of theeconomy). We denote the number of production plants located in country 1 (or country 2)
by N1 = n1 L (or N2 = n2 L = (1 − n1 )L), where n1 ∈ [0, 1] is country 1’s share of production
plants. Once established, each MNE needs a units of labor to produce one unit of variety.
Consider an MNE with its production plant in country 1. The plant produces quantities
q11 and sells them at a price p11 to domestic consumers. In addition, it produces quantities q12
9

Similar specifications in the context of transfer pricing can be found in Kind et al. (2005); and Matsui(2012), although they fix the location of plants and affiliates.

9and exports them at a transfer price g1 to its foreign affiliate in country 2. When exporting,due to iceberg trade costs τ > 1, 1/τ < 1 units of quantities melt away, so the plant has toproduce τ units to deliver one unit to the affiliate. The affiliate sells the imported goods toconsumers in country 2 at a price p12 .
MNEs have decentralized decision making. In other words, the headquarters (or the
production plant) of the MNE sets the transfer price to maximize global post-tax profits,
while the foreign affiliate sets the retail price to maximize its own profits. The idea that theheadquarters lets affiliates make decisions for strategic purpose is known as the delegation
principle, and is adopted by many studies in the literature. 10 In practice, it is sensible todelegate decisions to local managers who are familiar with their local business environments.
In many cases, a company’s acquisition of a rival often involves the latter receiving divisional
autonomy (e.g., Volkswagen’s acquisition of Audi, Ford’s acquisition of Volvo, and GM’s
acquisition of Saab). 11 We examine the case of centralized decision making in Appendix 6
and confirm the robustness of our results.
The timing of actions proceeds as follows. First, each MNE chooses the country inwhich to locate a production plant and a foreign affiliate, endogenously determining theshare of plants n1 . The decision is based on a comparison of the post-tax profits in the twocountries. Second, the MNE chooses the transfer price. Third, production plants and foreign
affiliates engage in price competition in each country. Finally, production and consumption
take place. We solve the game in a backward fashion. For convenience, we refer to theresults with fixed capital allocation as a short-run equilibrium and refer to the results in theendogenous case as a long-run equilibrium. We will examine the two situations in turn.

2.1. Optimal prices in the short-run equilibrium
Let us derive the optimal prices given the distribution of plants and affiliates. The pretax profits of the production plant in country 1 (π11 ) and those of the foreign affiliate in
10
11

See, for example, Zhao (2000); Nielsen et al. (2003, 2008); and Kind et al. (2005).
See Ziss (2007) for more on this issue.

10

country 2 (π12 ) are, respectively,
π11 = (p11 − a)q11 + (g1 − τ a)q12 ,{z}|
Shifted profit

π12 = (p12 − g1 )q12 ,where q11 is given by Eq. (1) and q12 is defined analogously. The second term in π11 represents
the profits from intra-firm trade subject to trade costs τ . As we will see shortly, this term
captures profit shifting within MNEs. At the third stage of the game, the production plant
and the foreign affiliate choose their prices to maximize their own profits. The optimal prices
are
p11 =

σa
,
σ−1

p12 =

σg1
.
σ−1

At the second stage, the MNE with its production plant in country 1 sets the transfer
price to maximize the following global post-tax profits:
Π1 = (1 − t1 )π11 + (1 − t2 )π12 ,where ti ∈ [0, 1] is the tax rate of country i ∈ {1, 2}. The optimal transfer price is 12
g1 =

στ a
,
σ − ∆t1

where ∆t1 ≡t2 − t1,
1 − t1(2)which is positive because σ − ∆t1 > 0. We can check that g1 decreases with t1 and increases
with t2 . As a higher tax rate in country 1 reduces the post-tax profit of the production
plant, the MNE tries to move profits from country 1 to 2 by lowering the transfer price.
When the tax rate in country 2 increases, the direction of profit shifting reverses, and the
MNE raises the transfer price.
12

We can confirm that the second order condition (SOC) is satisfied at the optimal point. The SOC
is ∂ 2 Π1 /∂g12 < 0, which reduces to (1 − t2 )g1 − (1 − t1 )[(σ + 1)τ a − σg1 ] < 0. This inequality holds at
g1 = στ a/(σ − ∆t1 ).

11

Similarly, the MNE with its production plant in country 2 sets the optimal transfer priceas follows:
g2 =

στ a
,
σ − ∆t2

where ∆t2 ≡t1 − t2,
1 − t2(3)

which is also positive because σ − ∆t2 > 0.
To see the direction of profit shifting, we assume t1 > t2 and have ∆t1 < 0 < ∆t2 . Using
the optimal transfer prices, we can rewrite the profit from intra-firm trade asτ a∆t1
q12 < 0σ − ∆t1
τ a∆t2(g2 − τ a)q21 =q21 > 0σ − ∆t2(g1 − τ a)q12 =for the MNE with production in country 1,(4-1)

for the MNE with production in country 2.

(4-2)

The MNE with production in country 1 cuts the transfer price to below the true marginal
cost, making negative profits from intra-firm trade. In doing so, the plant shifts profits
made in the high-tax country 1 to the foreign affiliate in the low-tax country 2. As for the
MNE with production in country 2, the direction reverses: from the affiliate in the high-tax
country 1 to the plant in the low-tax country 2.

12

We can rewrite the post-tax profit asΠ1 = (1 − t1 )π11 + (1 − t2 )π12

φγ1 µL2(σ − 1)∆t1
φγ1 µL2µL1+,+ (1 − t2 ) ··= (1 − t1 )σ(N1 + φγ2 N2 )σσ(φγ1 N1 + N2 )σ(φγ1 N1 + N2 ){z}|
Shifted profits(5-1)

Π2 = (1 − t1 )π21 + (1 − t2 )π22

φγ2 µL1(σ − 1)∆t2
φγ2 µL1µL2,= (1 − t1 ) ·+ (1 − t2 )+·σ(N1 + φγ2 N2 )σ(φγ1 N1 + N2 )σσ(N1 + φγ2 N2 ){z}|
Shifted profits(5-2)

where φ ≡ τ 1−σ , γi ≡σσ − ∆ti

1−σ

,

∆ti ≡

tj − ti,
1 − tii 6= j ∈ {1, 2}.

The second term in the square brackets in Π1 and Π2 expresses the profits shifted throughtransfer pricing. φ = τ 1−σ ∈ [0, 1] is an inverse measure of trade costs, or the freeness of
trade. φ = 0 (i.e., τ = ∞) corresponds to a prohibitively high level of trade costs, while
φ = 1 (i.e., τ = 1) indicates zero trade costs.
If the tax difference is large, profit shifting is so excessive that taxable profits can be
negative. To ensure positive profits, we assume the condition that 1 + (σ − 1)∆t1 /σ > 0.
This simply requires that the tax difference should not be too large. See Appendix 3 fordetails.
When the difference in the above post-tax profits is positive; that is, ∆Π ≡ Π1 − Π2 > 0,
the MNE prefers to locate its production plant in country 1, and vice versa. In the long-run
equilibrium, the profit differential is zero and no MNEs are willing to change their allocationof plants.

13

3. Equilibrium allocation of production plants
To highlight the role of tax difference, we suppose that the tax rate is higher in country
1 (t1 > t2 ), but the two countries are of the same size (s1 = 1/2). 13 By solving the long-run
equilibrium condition (∆Π = 0) for the share of production plants in country 1, we obtain
interior equilibria n1 ∈ (0, 1). If ∆Π = 0 does not have interior solutions, then we obtaincorner equilibria in which all multinational production takes place in one country; that is,n1 ∈ {0, 1}.
To see how a reduction in trade costs affects the long-run equilibrium allocation, we
consider the two extreme cases: prohibitive trade costs (φ = 0) and zero trade costs (φ = 1).
An extremely high level of trade costs does not allow for intra-firm trade, leaving noroom for profit shifting. 14 As the MNEs earn profits only from the domestic sales of theirproduction plants, they prefer to locate them in the low-tax country 2. We note that theequilibrium distribution involves a small but positive share of plants in the high-tax country
1; that is, n1 |φ=0 ∈ (0, 1/2). Since competition in the domestic market works as a dispersion
force, the corner distribution where all production plants are in country 2 (n1 |φ=0 = 0)
cannot be an equilibrium.
Zero trade costs, on the other hand, allow MNEs to engage in intra-firm trade fully,
making profit shifting through transfer pricing effective. 15 In our model, transfer pricing
does not just shift profits between domestic plants and foreign affiliates, but also affects
the competitiveness of the affiliates. As we showed, MNEs with production in the high-tax
country 1 set a low transfer price to shift profits to their foreign affiliates in the low-tax
country 2 (see Eqs. (2) and (4-1)). Due to the low sourcing cost, the foreign affiliates cansell varieties at a low price and become competitive against local production plants. By
contrast, MNEs with production in the low-tax country 2 set a high transfer price (see Eqs.
(3) and (4-2)), which makes their foreign affiliates in the high-tax country 1 less competitive.
13

The assumption of symmetric market size is for simplicity and is not crucial for our main result, which
we will discuss after Proposition 1.
14
In Eqs. (5-1) and (5-2), the profits from intra-firm trade and those from the foreign affiliate disappear
if φ = 0.
15
We can confirm that the shifted profit increases with φ; that is, ∂[(gi −τ a)qij ]/∂φ > 0 for i 6= j ∈ {1, 2}.

14

They are at a disadvantage in both the domestic and foreign markets. Therefore, MNEs
prefer to locate production in the high-tax country so the direction of profit shifting makes
foreign affiliates competitive.
From the results of the two polar cases, it is expected that more production plants arein the low-tax country 2 if trade costs are high, whereas they are in the high-tax country
1 if trade costs are low. We can prove that this is the case and summarize the findings asfollows (see Appendix 1 for a proof).

Proposition 1 (Plant distribution).

Suppose that country 1 has a higher corporate tax

rate than country 2 does. The equilibrium allocation of production plants is summarized asfollows:(i). With high trade costs such that φ ∈ [0, φ∗ ), the high-tax country 1 hosts a smaller shareof plants than the low-tax country 2 does; that is, n1 < 1/2.
(ii). With low trade costs such that φ ∈ (φ∗ , 1], the high-tax country 1 hosts a greater shareof plants; that is, n1 > 1/2.
At φ = φ∗ , the two countries have an equal share of plants; that is, n1 = 1/2.

Fig. 2 shows a representative pattern of equilibrium plant distribution for different levelsof the freeness of trade φ (thick curve), along with the equilibrium plant distribution underno profit shifting (dotted line). 16 As φ increases from zero, the high-tax country 1 has adecrease in plants in both cases, with and without profit shifting. When high trade costs
prevent exporting, MNEs make profits mostly from their domestic production plant andthus prefer to locate it in the low-tax country. Along with a further decrease in φ from φ# ,however, the high-tax country 1 increases plants in the case with profit shifting, whereas it
continues to decrease plants in the case without profit shifting. Sufficiently low trade costs
expand intra-firm trade and thus the opportunities for profit shifting, leading to a sharp
contrast in location patterns.
16

The parameter values are σ = 5, t1 = 0.8, t2 = 0.7, L = 10, s1 = 0.5, µ = 1, and a = 1.

15

The result that the high-tax country attracts more multinational plants for low trade
costs does not depend on the assumption of a symmetric market size. If the high-tax country
is larger, then its market-size advantage strengthens the agglomeration of plants (see Section
4.2). If it has a smaller size, then its market-size disadvantage may weaken the agglomeration
force. Even in this case, we can numerically confirm that multinational production would
be agglomerated in the high-tax country for sufficiently low trade costs.
This finding seems consistent with the fact that in the last two decades, which are marked
by globalization, U.S. affiliates in Europe make a disproportionate share of profits from lowtax countries compared to manufacturing activities there, as Fig. 1 shows. Moreover,Overesch (2009) finds empirically that the cross-country tax difference between high-tax
Germany and a low-tax home country increases German inbound investments.

Fig. 2. Share of production plants in the high-tax country 1.

Full agglomeration.

If φ is sufficiently high such that φ > φS , which is called a sustain

point, then all production plants are located in country 1. 17 It can be checked that φS
17

Formally, a sustain point is the level of the freeness of trade above which full agglomeration is sustain-

able.

16

decreases with t1 − t2 . A larger tax difference offers more room for profit shifting and thus
leads to more aggressive transfer pricing (very low g1 or very high g2 ). This strengthens
the competitiveness of MNEs with production in country 1, since they set a much lower
price than their rivals in both the domestic and foreign markets (i.e., p11 < p21 ; p12 < p22 ).
Consequently, full agglomeration in country 1 is more likely to occur since the tax differenceis larger. We summarize these findings as follows (see Appendix 2 for a proof).

Proposition 2 (Full agglomeration).

With sufficiently low trade costs such that φ ∈[φS , 1], where φS > φ∗ , all production plants locate in the high-tax country 1, that is, n1 = 1.
As the tax difference increases, the sustain point φS decreases, and thus full agglomeration
is more likely to occur.

Tax revenues.

Although the high-tax country 1 may host more multinational production,

this does not necessarily guarantee greater tax revenues. The tax revenues of each countryare
T R1 ≡ t1 (N1 π11 + N2 π21 ),T R2 ≡ t2 (N2 π22 + N1 π12 ).
Fig. 3 illustrates the profits and tax revenues. 18 In both countries, the profit of the production plant, πii , decreases with φ since a fall in trade costs leads to tougher import competition(see Eqs. (5-1) and (5-2)). As a mirror image of this result, the profit of the affiliate, πji ,generally increases with φ.
Although the profits of plant and affiliate in both countries behave similarly, π11 declines
at a faster rate than does π22 , and π21 increases at a slower rate than does π12 . Lower trade
costs increase profit shifting from country 1 to 2, and thus reduce π11 further. This in turnmakes the foreign affiliates in country 2 competitive through low transfer prices, raising
π12 more. Especially when trade costs are low, such that φ ∈ (φ† , 1], these effects are so
18

The parameter values are the same as those in Fig. 2.

17strong that tax revenues in country 1 become smaller than those in country 2. The hightax country 1 can attract more multinational production, which nevertheless does not mean
it earns greater tax revenues. Unlike the case without profit shifting, the high tax country
cannot fully enforce taxes because MNEs shift some of the operating profits to the low tax
country.
We summarize these findings as follows (see Appendix 5 for a proof).

Proposition 3 (Tax revenues).

With high trade costs such that φ ∈ [0, φ† ), the high-tax

country 1 earns greater tax revenues than the low-tax country 2 does. With low trade costs,
such that φ ∈ (φ† , 1], this pattern reverses.

Fig. 3. Profits and tax revenues: Country 1 on the left and country 2 on the right.

Centralized decision making.

We assumed that MNEs have decentralized decision making,where foreign affiliates choose prices to maximize their own profits. Our main result holds
true if MNEs have centralized decision making, in which the MNE chooses all prices to18

maximize global profits. Note that the direction of profit shifting does not change dependingon the decision making style. That is, foreign affiliates source goods from production plants
by paying high (or low) transfer prices if they are in the low-tax country (or the high-tax
country). By locating in the low-tax country, foreign affiliates enjoy a higher price-cost
margin than those located in the high-tax country (p12 − g1 > p21 − g2 ) and earn larger
profits. As in the decentralized decision making case, profit shifting affects the profitabilityof foreign affiliates asymmetrically, leading to agglomeration of production plants in thehigh-tax country. See Appendix 6 for details.

4. Discussion and extensions
The main result in the previous analysis is that the high-tax country gains agglomerationof multinational production if trade costs are low. We discuss here (i) its implications for
empirical studies investigating the determinants of FDI and (ii) those for tax competition
between unequal-sized countries.

4.1. Implications for empirics
Our results have implications for empirical research on the relationship between FDI andthe host country’s taxes. By interpreting production plants in our model as FDI, we canthink of the following regression:
F DIh,s = β0 + β1 (T AXs − T AXh ) + β2 · φh,s · (T AXs − T AXh ) + Xβ + εh,s ,where F DIh,s is the inflow of FDI from source country s to host country h, T AXi is thecorporate tax rate in country i ∈ {h, s}, φh,s is a measure of economic integration between
country h and s, X is a vector of other explanatory variables, and εh,s is the error term.
One proxy for φh,s is an inverse of the distance between two countries.
Holding other factors fixed, it is expected that a larger tax difference encourages FDI
inflow, meaning β1 > 0. Our results indicate that the impact of the tax difference varies
19

according to the freeness of trade. As two countries are more integrated, a larger tax
difference discourages FDI inflow, implying β2 < 0. Empirical studies using country-level
data have yet to reach a consensus on the impact of corporate tax on FDI (Navaretti and
Venables, 2004, Ch.10 for a survey). Some obtain significant and large coefficients, whileothers find weak and small coefficients (De Mooij and Ederveen, 2003; Bellak and Leibrecht,
2009; Jensen, 2012). These mixed findings may be because these studies do not consider the
degree of economic integration between the host and source countries.

4.2. Implications for tax competition
We showed that MNEs’ profit-shifting motives may lead to the agglomeration of production in the high-tax country, which challenges the conventional view that countries with
low-taxes attract production plants. The profit-shifting channel is also expected to affectcompetition between governments for multinational production. This section allows countries to choose their tax rate non-cooperatively and compare the results of tax competition
with profit shifting to those without profit shifting.
We introduce country-size asymmetry and assume that country 1 is larger than country
2 is; that is, L1 = s1 L > (1 − s1 )L = L2 , or s1 > 1/2. To highlight the asymmetric size,
suppose for a moment that country 1’s tax rate is exogenous and is higher than country 2’s.
If country 1’s size advantage is sufficiently stronger than its tax disadvantage, MNEs prefer
to locate their production plants in country 1. 19
Fig. 4 illustrates a representative pattern of equilibrium plant share in country 1 in thecase with and without profit shifting. 20 Declining trade costs accelerates the concentrationof production in the large country, and eventually leads to full agglomeration, known as thecore-periphery situation. Fig. 4 also shows that the sustain point in the case without profit
shifting, φ̂S , is larger than that in the case with profit shifting, φS . 21 As the competitive
19

See Appendix 5 for the condition of this case.
The parameter values are σ = 5, t1 = 0.8, t2 = 0.75, L = 10, s1 = 0.6, µ = 1, and a = 1.
21
To avoid the abuse of notation, we use the same symbol φS as in the previous section, in which the twocountries are of equal size. We formally prove φ̂S > φS in Appendix 5.
2020

effect of transfer pricing favors the high-tax country (Proposition 2), introducing profit
shifting further motivates MNEs to locate production in country 1.

Fig. 4. Share of production plants in the large, high-tax country 1.

Following Baldwin and Krugman (2004); Borck and Pflüger (2006); and Kato (2015),
the objective function of the government in each country takes the form of
Gi = T Ri −β,
1 − tiwhere T Ri ≡ ti (Ni πii + Nj πji ),i 6= j ∈ {1, 2},

where β is a positive constant. 22 The first term represents tax revenues and the second termis the administration cost associated with collecting taxes. 23 The timing of actions proceeds
22

The objective function captures the basic conflicts governments face: they attempt to raise tax revenues
while maintaining a low tax rate, which is thought of as a reduced-form objective that either selfish or
benevolent governments adopt (Baldwin and Krugman, 2004).
23
Tax administration cost is well recognized as an important determinant of raising revenues (OECD,
2017; Profeta and Scabrosetti, 2017). OECD (2017) states that “Even small increases in compliance rates
or compliance costs can have significant impacts on government revenues and the wider economy.” (p.5)

21

as follows. First, the two governments simultaneously and non-cooperatively decide theirtax rates, and then MNEs choose their plant allocations. Finally, MNEs set their prices andboth domestic and foreign affiliates make sales. We solve the tax-competition game in a
backward fashion.
To make our results as comparable as possible to those of prior studies (Baldwin andKrugman, 2004, in particular), we analyze tax competition in the core-periphery situation.
That is, we focus on the range of the freeness of trade such that φ ∈ [φS , 1].
No-profit-shifting case.

As a benchmark, we first derive the difference in equilibrium tax

rates when profit shifting is not allowed. The inability to manipulate transfer prices meansgi = τ a, resulting in zero profits from intra-firm trade: (gi − τ a)qij = 0 for i 6= j ∈ {1, 2}.
In the core-periphery situation (i.e., n1 = 1), the objective functions becomeGi =µLi tiβ−,σ1 − tii ∈ {1, 2}.

The equilibrium tax rates are given bytO
i = 1−

s

βσ
,
µLi

i ∈ {1, 2}.

O
It is easy to see that tO
1 > t2 , suggesting that the large country 1 sets a higher tax rate than

the small country 2, while keeping all production plants. 24 This is in line with the resultsin the literature (Baldwin and Krugman, 2004).

Profit-shifting case.

We will see how the results above change if MNEs can utilize transfer

24

For Gi to be positive in equilibrium, we assume that the intensity of administration costs is not toolarge: β < µL2 /(2σ). Under this assumption, tO
i lies between [0, 1].

22

pricing. The objective functions are modified as


β
µt1
(σ − 1)∆t1
G1 =
L1 +
L2 −
,
σ
σ
1 − t1βµL2 t2−.
G2 =σ
1 − t2
Country 1’s payoff now involves the tax difference since plants in the high-tax country 1
move their profits to the low-tax country 2. If country 1 keeps its tax rate as high as it
does in the no-profit-shifting case, then it earns less tax revenues. Thus, country 1 has anincentive to lower its tax rate to prevent the erosion of taxable profits.
The equilibrium tax rates aret∗1 = 1 −st∗2 = 1 −s√βσ 2 + (σ − 1) βσµL2,µL(σ + s1 − 1)
βσ
µL2

(= tO
2 ).

It can be checked that t∗1 > t∗2 and t∗1 < tO
1 . Although country 1 still chooses a higher tax rate
and maintains all production plants, its tax rate is lower than that in the no-profit shiftingcase. In terms of equilibrium tax rates, profit shifting leads to more intense tax competition.
We summarize these findings as follows.

Proposition 4 (Tax competition). Consider tax competition between unequal-sized countries in the core-periphery outcome.
(i) The large country 1 sets a higher tax rate than the small country 2 does, while keeping
full agglomeration of production: t∗1 > t∗2 ; n1 = 1.
(ii) Compared to the no-profit-shifting case, country 1’s tax rate is low, whereas countryO∗
2’s tax rate is unchanged: t∗1 < tO
1 ; t2 = t2 .

That is, introducing transfer pricing makes tax competition tougher in the sense that theequilibrium tax differential is smaller.
23

A similar result can be found in Haufler and Schjelderup (2000), who employ a frameworkof perfect competition with equal-sized countries. 25 Our result partly extends theirs to asetting with imperfect competition and unequal-sized countries. Stöwhase (2005, 2013), by
contrast, obtain the opposite result: the presence of profit shifting softens tax competition
by increasing the equilibrium tax rates of both large and small countries. 26 Introducing
profit shifting reduces MNEs’ tax payments and makes them less sensitive to internationaltax differences; thus, tax competition becomes less severe. On the other hand, taxable
profits decrease due to profit shifting, which makes tax competition for the shifted profits
more severe. In Stöwhase (2005, 2013), the former effect dominates the latter, whereas the
opposite is true in our model. These differing results are mainly because our imperfectlycompetitive framework gives rise to the strategic purpose of transfer pricing. The strategic effect strengthens profit-shifting incentives and thus increases the tax-base sensitivity,
leading to tougher tax competition.

5. Conclusion
We introduced a profit shifting mechanism through transfer pricing into a simple economic geography model for MNEs. We show that in the early stage of economic integration,
the low-tax country attracts more production plants than the high-tax country does. Further integration, however, completely reverses this pattern and leads to the agglomeration of
production in the high-tax country. By lowering transfer prices for intra-firm transactions,
MNEs compress the pre-tax profits of plants in the high-tax country and inflate those offoreign affiliates in the low-tax country. In addition, the lowered transfer prices make theaffiliates competitive in their markets. Transferring profits from a high-tax to a low-tax
25

Agrawal and Wildasin (2019) also show that globalization (a decline in relocation costs) leads to tougher
tax competition in a linear spatial model where agglomeration is exogenously given.
26
Becker and Riedel (2013) also obtain a similar result, although MNEs in their model cannot shift profits
for tax-saving purposes.

24country is more effective than transferring profits in the other way around if trade costs are
low enough for intra-firm trade to expand. MNEs thus prefer to locate production in thehigh-tax country in the late stage of economic integration. The result sheds new light on
tax competition in the core-periphery case and on the empirical relationship between thehost country’s corporate tax rate and its FDI inflow.
Although our model is admittedly stylized, we believe that it is versatile enough to accommodate several extensions. One interesting extension is to introduce tax haven countries.
While we assume that MNEs shift profits between affiliates in two countries, MNEs may do
so using non-production affiliates in a third country with almost zero taxes. The question iswhich non-tax haven country, the high-tax or the low-tax one, benefits from the presence oftax haven countries. Another extension is to examine the impact of different internationaltax systems, such as separate accounting and formula apportionment. The system that prevents profit shifting effectively may differ depending on the degree of economic integration.
We leave these avenues for future research.

Appendices
Appendix 1. Equilibrium allocation of production plants
We first prove Proposition 1 by showing whether the equilibrium share of plants n1
exceeds one-half depending on trade costs. Then, we further investigate how a marginalchange in trade costs affects n1 .

Proof of Proposition 1.

Using Eqs. (5-1) and (5-2), we can write the profit differential asµ (1 − t1 )(1 − φγ2 ) − φγ2 (t1 − t2 )(σ − 1)/σ·2σ
n1 + φγ2 n2µ (1 − t2 )(1 − φγ1 ) − φγ1 (t2 − t1 )(σ − 1)/σ·.
−2σ
φγ1 n1 + n2σ−1
σ − ∆titj − tiwhere γi ≡, for i 6= j ∈ {1, 2}.
, ∆ti ≡σ1 − ti∆Π ≡ Π1 − Π2 =

25

(A1)

We evaluate this at n1 = 1/2:
∆Π|n1 =1/2 =µ(t1 − t2 ) · F (φ),
2
σ (1 + φγ1 )(1 + φγ2 )where F (φ) ≡ γ1 γ2 (2 − σ)(t1 − t2 )φ2+ [2σ{γ1 (1 − t1 ) − γ2 (1 − t2 )} + (γ1 + γ2 )(t1 − t2 )]φ − σ(t1 − t2 ),The sign of the profit differential is determined by F (φ). At the level of φ that satisfies
F (φ) = 0, the equilibrium distribution of plants becomes one-half.
We denote this value of φ by φ∗ , and it is given by the larger (smaller) root of F (φ) = 0
under σ < 2 (σ > 2). We can confirm that φ∗ falls within (0, 1) from the facts that (i) F (φ)
is a quadratic function of φ, (ii) f (0) < 0, and (iii) f (1) > 0.
If φ < φ∗ or F (φ) < 0, then the profit differential is negative, implying that MNEs withproduction in country 1 have an incentive to relocate their plants to country 2. Thus, thelong-run equilibrium must be n1 < 1/2. Similarly, if φ > φ∗ or F (φ) > 0, then the positive
profit differential at n1 = 1/2 requires that the long-run equilibrium be n1 > 1/2. Thesefindings establish Proposition 1.

Equilibrium plant allocation and trade costs.

Here, we show that as trade costs decline,

the equilibrium share of production plants in country 1 first decreases, then increases. By
solving the profit differential for n1 , we obtain(1 − t1 )(1 + φ2 Γ1 γ2 ) − φ(1 − t2 )(Γ2 + γ2 ),(1 − t1 )[1 − φ(Γ1 + γ1 ) + φ2 Γ1 γ2 ] + (1 − t2 )[1 − φ(Γ2 + γ2 ) + φ2 Γ2 γ1 ]σσ − ∆tiwhere Γi ≡
.
σ

n1 =

We differentiate this with respect to φ:
G(φ)
dn1
=
,
dφ
H(φ)

26

(A1)

whereG(φ) ≡ [{t1 (2 − t1 ) − 1}Γ1 γ2 (Γ1 + γ1 ) − {t2 (2 − t2 ) − 1}Γ2 γ1 (Γ2 + γ2 )]φ2
+ 2(1 − t1 )(1 − t2 )(Γ1 γ2 − Γ2 γ1 )φ+ {t2 (2 − t2 ) − 1}(Γ2 + γ2 ) − {t1 (2 − t1 ) − 1}(Γ1 + γ1 ),H(φ) ≡ {Γ1 γ2 (1 − t1 ) + Γ2 γ1 (1 − t2 )}φ2 − {(Γ1 + γ1 )(1 − t1 ) + (Γ2 + γ2 )(1 − t2 )}φ . . .
2· · · + 2 − t1 − t2 > 0.
We note that (i) the numerator is a quadratic function of φ and that (ii) H(φ) > 0 for any
φ ∈ [0, 1]. Furthermore, we can verify that (iii) the slope is negative at φ = 0:
t2 − t1dn1< 0,≃dφ φ=0 σ(2 − t1 − t2 )where we use a Taylor approximation such that Γi ≃ 1 − ∆ti + [(σ − 1)/σ](∆ti )2 andγi ≃ 1 − [(σ − 1)/σ]∆ti + [(σ − 1)(σ − 2)/σ 2 ](∆ti )2 .

We then find φ ∈ [0, 1], where dn1 /dφ = 0. From (ii), it suffices to solve G(φ) = 0, whose

solution, denoted by φ# , is
φ# ≃

σ
,
σ − (σ − 1)∆t1 ∆t2(A2)

where the approximation was used as before. We can confirm that φ# is within (0, 1). From(i) and (iii), we observe that dn1 /dφ changes its sign at φ# from negative to positive. Insummary,
< 0 if φ ∈ [0, φ# )






#
dn1 = 0 if φ = φ

dφ 


> 0 if φ ∈ (φ# , φS )





= 0 if φ ∈ [φS , 1]

.

(A3)

27

Appendix 2. Proof of Proposition 2
We first confirm that the high-tax country 1 hosts all production plants when the trade
costs are zero. Then, we derive the level of the freeness of trade above which the full
agglomeration is realized; that is, the sustain point φS . Finally, we show that φS decreases
with t1 , but increases with t2

Full agglomeration at zero trade costs.

Evaluating the profit differential (A1) at φ = 1

yieldsµ(t2 − t1 )(σ − 1)
∆Π|φ=1 =
2
2σ
|
{z
}
<0

where ωi ≡ γi +σ(1 − γi ),(σ − 1)∆tj

ω2
ω1+
γ 1 n1 + n2 n1 + γ 2 n2,

for i 6= j ∈ {1, 2},noting that ∆t1 < 0 < ∆t2 and γ1 > 1 > γ2 . The profit differential is positive (negative)
if the big bracket term is negative (positive). We will check that the big bracket term isindeed negative, the condition for which is
ω2
ω1
+
< 0,
γ 1 n1 + n2 n1 + γ 2 n2
→ ω1 (n1 + γ2 n2 ) + ω2 (γ1 n1 + n2 ) < 0,
→ n1 [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] +ω1 γ2 + ω2 < 0,
{z
}
|
>0

noting that n2 = 1 − n1 . The inequality holds for any n1 ∈ [0, 1] if the following holds
n1 [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2 < 1 · [ω1 (1 − γ2 ) + ω2 (γ1 − 1)] + ω1 γ2 + ω2 < 0,
→ ω1 + ω2 γ1 < 0.
Using a Taylor approximation such that γi ≡ (1 − ∆ti /σ)σ−1 ≃ 1 − [(σ − 1)/σ]∆ti , we can28

confirm that the inequality holds:(t1 − t2 )2
ω1 + ω2 γ1 ≃ − 2< 0.
σ (1 − t1 )(1 − t2 )Hence, the profit differential at φ = 1 is positive for any n1 ∈ [0, 1]. All MNEs are willingto establish production plants in the high-tax country 1, that is, n1 |φ=1 = 1.
Sustain point.
∆Π|n1 =1 =Evaluating the profit differential (A1) at n1 = 1 givesµ · I(φ),
2σ 2 φγ1

where I(φ) ≡ −γ1 γ2 (1 − t2 )(σ − ∆t2 )φ2 + γ1 (1 − t1 )(2σ − ∆t1 )φ − σ(1 − t2 ).
Since the denominator is positive, the sign of the profit differential is determined by I(φ).
Solving I(φ) = 0 for φ ∈ [0, 1] gives the sustain point φS (if any).

We observe that I(φ) is a quadratic function of φ with a negative coefficient of φ2 . A

further inspection reveals that
I(0) = −σ(1 − t2 ) < 0,
I(1) = σ[2γ1 (1 − t1 ) − (1 + γ1 γ2 )(1 − t2 )] + γ1 (1 + γ2 )(t1 − t2 ) > 0,
noting that 2γ1 (1−t1 )−(1+γ1 γ2 )(1−t2 ) > 2γ1 (1−t1 )−(1+γ1 )(1−t2 ) = (γ1 −1)(1−t1 ) > 0
holds because γ1 > 1 > γ2 .
These observations imply that (i) the sustain point φS ∈ (0, 1) always exists and isgiven by the smaller root of I(φ) and that (ii) I(φ) or the profit differential is negative forφ ∈ [0, φS ) but positive for φ ∈ (φS , 1].
Sustain point and taxes.

As Fig. 2 and (A3) in Appendix 1 clearly show, a higher (lower)

φ# (see Eq. (A2)) makes the sustain point φS higher (lower). A close inspection of φ#29

reveals thatdφ#σ(σ − 1)(1 − t2 )(2 − t1 − t2 )(t2 − t1 )
=
< 0,
dt1
[(σ − 1)(t1 − t2 )2 + σ(1 − t1 )(1 − t2 )]2dφ#
σ(σ − 1)(1 − t2 )(2 − t1 − t2 )(t1 − t2 )
> 0,
=
dt2
[(σ − 1)(t1 − t2 )2 + σ(1 − t1 )(1 − t2 )]2
implying that φS also decreases (increases) with t1 (t2 ). That is, multinational production
is more likely to be agglomerated in the high-tax country 1 because the tax difference islarger.

Appendix 3. Conditions for positive profits
The taxable profits are π11 , π12 , π21 , and π22 , but only π11 can be negative:
1(σ − 1)∆t1
φγ1
µ
,
+
π11 =
2σ n1 + φγ2 n2 |σ{z
} φγ1 n1 + n2<0because ∆t1 < 0. Note also that π11 > 0 at φ = 0. We check whether π11 remains positive
if the following assumption holds:
1+(σ − 1)∆t1
> 0.
σ

(A4)

Differentiating this with respect to φ yields(1 − φ)(2 − t1 − t2 )[φ(−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2 ]
dπ11
≃
,
dφ
2(1 − t1 )[φ2 (σ − ∆t1 )(σ − ∆t2 ) − σ 2 ]where we use Eq. (A1) and a Taylor approximation such that γi ≃ 1 − [(σ − 1)/σ]∆ti . The
numerator is always negative:φ(−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2 ≤ 1 · (−∆t1 )(σ − 1)(σ − ∆t2 ) − σ 2= −(1 + ∆t1 )σ 2 + ∆t1 (1 + ∆t2 )σ − ∆t1 ∆t2 < 0,30

because −(1 + ∆t1 ) < 0 (from Ineq. (A4)) and σ > 1.
The sign of the derivative is determined by the square bracket term in the denominator.
We can see that

> 0 if φ ∈ [0, φ† )dπ11 
,= 0 if φ = φ†
dφ 




< 0 if φ ∈ (φ† , 1]σwhere φ† ≡ p∈ (0, 1).
(σ − ∆t1 )(σ − ∆t2 )(A5)This result and π11 |φ=0 > 0 imply that π11 takes the minimum value at φ = 1:(σ − 1)∆t1µ
1+,
π11 |φ=1 =2σσnoting that n1 = 1 at φ = 1. The condition for π11 |φ=1 > 0 is equivalent to Ineq. (A3).

Appendix 4. Proof of Proposition 3
The tax revenues in the two countries are(σ − 1)∆t1 φγ1 n1
µLt1
,
1+
T R1 =2σσ
φγ1 n1 + n2
(σ − 1)∆t2 φγ2 n2
µLt2
.
1+
T R2 =2σσ
n1 + φγ2 n2Taking the difference yields




µL
t2 γ2 n2 ∆t2
σ−1
t1 γ1 n1 ∆t1∆T R ≡ T R1 − T R2 =.
t1 − t2 + φ−
2σσφγ1 n1 + n2 n1 + φγ2 n2Using Eq. (A1) and a Taylor approximation such that γi ≃ 1 − [(σ − 1)/σ]∆ti , we can

31express this as∆T R ≃µL(t1 − t2 ) · J(φ),
22σ (1 − t1 )(1 − t2 )[σ 2 − φ2 (σ − ∆t1 )(σ − ∆t2 )]where J(φ) ≡ −(σ − ∆t1 )(σ − ∆t2 )[σ{3t1 t2 − 2(t1 + t2 ) + 1} − 2t1 t2 + t1 + t2 ]φ2+ σ(σ − 1)[σ(2t1 t2 − t1 − t2 ) + (t1 − t2 )2 ]φ+ σ 3 (1 − t1 )2 (1 − t2 )2 .
We note thatthe sign of the coefficient of φ2 : −[σ{3t1 t2 − 2(t1 + t2 ) + 1} − 2t1 t2 + t1 + t2 ] < 0,J(0) = σ 3 (1 − t1 )2 (1 − t2 )2 > 0,J ′ (0) = σ(σ − 1)[σ(2t1 t2 − t1 − t2 ) + (t1 − t2 )2 ] < 0,J(1) = (σ − 1)2 (t1 − t2 )2 (t1 + t2 − 2t1 t2 ) > 0,
where the inequality in the first line holds due to (A4). This implies that J(φ) > 0 forφ ∈ [0, 1].
The sign of ∆T R is determined by the square bracket term in the denominator. Thus,
we have
> 0 if φ ∈ [0, φ† )∆T R = 0 if φ = φ†
,





< 0 if φ ∈ (φ† , 1]

where φ† is defined in Eq. (A5). This establishes Proposition 3.

32

Appendix 5. Sustain points in the case of asymmetric country size
In the case without profit shifting, the profit differential at n1 = 1 is∆Π̂|n1 =1 =µ · Θ̂(φ),σφ

where Θ̂(φ) ≡ −s1 (1 − t1 )φ2 + [s1 (1 − t1 ) + (1 − s1 )(1 − t2 )]φ − (1 − s1 )(1 − t2 )],Clearly, the sign of the profit differential is determined by Θ̂(φ), which is a quadratic functionof φ. We note thatthe sign of the coefficient of φ2 : −s1 (1 − t1 ) < 0,
Θ̂(0) = −(1 − s1 )(1 − t2 ) < 0,
Θ̂′ (0) = s1 (1 − t1 ) + (1 − s1 )(1 − t2 ) > 0,
Θ̂(1) = 0.
Θ̂(φ) = 0 has two solutions, φ = 0 and φ = φ̂S :φ̂S ≡1 − s1 1 − t 2·.
s1
1 − t1

Assume that φ̂S is in [0, 1], or, equivalently,
1 − t2s1 >2 − t1 − t2



1
>
2



.

(A6)

Under this condition, Θ̂(φ), and thus the profit differential is greater than zero if the freenessof trade is larger than the sustain point φ̂S . That is, if φ ∈ [φ̂S , 1], then all multinational
production takes place in the large, high-tax country 1.

33

In the case with profit shifting, the profit differential at n1 = 1 is∆Π|n1 =1 =µ · Θ(φ),σφ

where Θ(φ) ≡ −γ2 s1 (1 − t2 )[(σ − ∆t2 )/σ]φ2+ (1 − t1 )[{σ − (1 − s1 )∆t1 }/σ]φ − (1 − s1 )(1 − t2 )/γ1 .
The sign of the differential is determined by Θ(φ), which is a quadratic function of φ. As in
the previous case, we note thatthe sign of the coefficient of φ2 : −γ2 s1 (1 − t2 )[(σ − ∆t2 )/σ] < 0,
Θ(0) = −(1 − s1 )(1 − t2 )/γ1 < 0,
Θ′ (0) = (1 − t1 )[{σ − (1 − s1 )∆t1 }/σ] > 0,

(2s1 − 1)(1 − t1 )(1 − t2 )σ 2 − (t1 − t2 )[s1 (3t2 − 2t1 − 1) + 1 − t2 ]σ − 2s1 (t1 − t2 )2< 0,
σ 2 (1 − t2 )(σ − 1)(t1 − t2 )[σ 2 (1 − t1 ){s1 (2 − t1 − t2 ) − (1 − t2 )} + (σ − 1)(1 − s1 )(t1 − t2 )2 ]> 0,
Θ(φ̂S ) ≃s1 σ 2 (1 − t1 )(σ − ∆t2 )Θ′ (1) ≃ −where the inequalities in the fourth and fifth lines hold due to the Taylor approximationsuch that γi ≃ 1 − [(σ − 1)/σ]∆ti and Ineq. (A6).
From these observations, we can illustrate Θ̂(φ) and Θ(φ) as in Fig. A1. We can thus
conclude that the sustain point in the case with profit shifting, φS , is lower than that in thecase without profit shifting, φ̂S .

34

Fig. A1. Sustain points in the case of unequal-sized countries.

Appendix 6. Centralized decision making
In the main text, we considered the case of decentralized decision making, in which theforeign affiliate chooses a price to maximize its own profit. Here, we will examine the caseof centralized decision making, in which the MNE chooses all prices to maximize its total
profit, using the same framework as in the main text. As we will show, the two different
organizational forms give qualitatively similar results.
An MNE with production in country 1 solves the following problem:max Π1 = max (1 − t1 )π11 + (1 − t2 )π12 ,p11 ,g1 ,p12

p11 ,g1 ,p12

where π11 = (p11 − a)q11 + (g1 − τ a)q12 − C(g1 , q12 ),π12 = (p12 − g1 )q12 .
In contrast to decentralized decision making, p12 is chosen to maximize Π1 rather than π12 .
C(·) is the concealment cost specified as C(gi , qij ) = δ(gi − τ a)2 qij with δ ≥ 0 (see Nielsen
et al., 2003; Kind et al., 2005; Haufler et al., 2018 for similar specifications).

35

The first order conditions give the following optimal prices:
σa
p11 =
,
σ−1

∆t1
σa
g1 = τ a +, p12 =2δσ−1
tj − tiwhere ∆ti ≡, i 6= j ∈ {1, 2}.
1 − ti∆t1 ∆t2
τ+
4aδ



,

Mirror expressions hold for MNEs with production in country 2:
σa
,
p22 =
σ−1

∆t2
g2 = τ a +
,
2δ

σa
p21 =
σ−1



∆t1 ∆t2
τ+
4aδ



.

As in the decentralized case, gi decreases with ti , while it increases with tj . Since p12 = p21
and g1 < g2 hold, the affiliate of the MNE with production in the high-tax country 1 hasa higher price-cost margin than the affiliate of the MNE with production in the low-tax
country 2 does; that is, p12 − g1 > p21 − g2 . Transfer pricing does not just shift profits,
but also affects the profitability of affiliates. The direction of the profit shifting from thehigh-tax to the low-tax country allows affiliates to source goods at a lower cost, and thus
earn more profits. The mechanism here is very close to the one in the decentralized-decisioncase we show in the text.
Using the optimal prices, we can rewrite the post-tax profit asσ
γ σ−1 µL/2
(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )(1 − t1 )µL/2+ (1 − t2 ) τ +,Π1 =σ(N1 + γN2 )4aδ
σ(γN1 + N2 )σ(2σ − 1)∆t1 ∆t2 − 2(σ − 1)(∆t1 + ∆t2 )γ σ−1 µL/2
(1 − t2 )µL/2+ (1 − t1 ) τ +,Π2 =σ(γN1 + N2 )4aδσ(N1 + γN2 )1−σ
∆t1 ∆t2
where γ ≡ τ +.
4aδ
The equilibrium distribution of plants is interior if Π1 − Π2 = 0 has a solution for
n1 ∈ (0, 1). If Π1 − Π2 > 0 (Π1 − Π2 < 0), then the economy reaches the corner equilibrium36

of n1 = 1 (n1 = 0). We obtain1(γ + 1)(t1 − t2 )+if τ ∈ (τ S1 , ∞) (i)


2
2(γ
−
1)(2
−
t
−
t
)
1
2




0
if τ ∈ (τ S2 , τ S1 ] (ii)
n1 =
,


S2

[0, 1]
if τ = τ
(iii)






1
if τ ∈ [1, τ S2 )
(iv)

1−σ
∆t1 ∆t2
tj − tiwhere γ ≡ τ +, i 6= j ∈ {1, 2},, ∆ti ≡
4aδ
1 − ti 1
∆t1 ∆t2
1 − t1 1−σ ∆t1 ∆t2
S1, τ S2 ≡ 1 −,−τ ≡1 − t24aδ
4aδ
which is illustrated in Fig. A1. The horizontal dotted line represents the share at which theequilibrium share converges as trade costs go to infinity:n̂1 ≡ lim n1 =τ →∞1t2 − t1.
+
2 2(2 − t1 − t2 )If trade costs are high, such that τ ∈ (τ S1 , ∞), then the low-tax country hosts moreproduction plants than the high-tax country does. If trade costs are low, such that τ ∈[1, τ S1 ), on the other hand, then the high-tax country attracts all production plants. The
result is qualitatively the same as that under decentralized decision making.

37

Fig. A2. Equilibrium distribution of production plants under centralized decision making.

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