HIAS-E-73

Transfer Pricing and the Arm’s Length Principle
under Imperfect Competition
Jay Pil Choi(a),(b) , Taiji Furusawa(c) and Jota Ishikawa(d),(e)(a) Department of Economics, Michigan State University(b) Hitotsubashi Institute for Advanced Study, Hitotsubashi University(c) Faculty of Economics, University of Tokyo(d) Faculty of Economics, Hitotsubashi University(e) RIETIOctober, 2018

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Transfer Pricing and the Arm’s Length Principle
under Imperfect Competition∗
Jay Pil Choi†

Taiji Furusawa‡

Jota Ishikawa§

October 2, 2018

Abstract
This paper analyzes incentives of a multinational enterprise to manipulate an internal transfer price to take advantage of corporate-tax di§erences across countries
under both monopoly and oligopoly. We examine “cost plus” and “comparable uncontrollable price” as two alternative implementations of the so-called arm’s lengthprinciple (ALP) to mitigate this problem. Tax-induced foreign direct investment(FDI) may entail ine¢cient internal production. We show how the mechanisms behind such ine¢cient FDI di§er between alternative implementation schemes of the
ALP and explore implications of the ALP for welfare and dual sourcing incentives.
We also develop a novel theory of vertical foreclosure as an equilibrium outcome ofstrategic transfer pricing.
JEL Codes: F12, F23, H26, L12, L13, L51, L52
Key Words: Foreign Direct Investment; Multinational Enterprise; Corporate tax;
Transfer Pricing; Arm’s Length Principle; Vertical Foreclosure∗
We thank Hayato Kato, Yuka Ohno, Pascalis Raimondos, Martin Richardson, Jay Wilson and participants in various conferences and seminars for valuable discussions and comments. This research was
initiated during Choi’s visit to Hitotsubashi Institute for Advanced Study whose hospitality is greatly appreciated. Choi acknowledges financial support from the Ministry of Education of the Republic of Korea
and the National Research Foundation of Korea: Grant Number NRF-2016S1A5A2A01022389. Furusawa
and Ishikawa acknowledge financial support from the Japan Society of the Promotion of Science throughthe Grant-in-Aid for Scientific Research (S): Grand Number 26220503 and (A): Grant Number 17H00986.
†
Department of Economics, Michigan State University and Hitotsubashi Institute for Advanced Study,
Hitotsubashi University; E-mail: choijay@msu.edu‡
Faculty of Economics, University of Tokyo; E-mail: furusawa@e.u-tokyo.ac.jp§
Faculty of Economics, Hitotsubashi University & RIETI; E-mail: jota@econ.hit-u.ac.jp

1

Introduction

There exist di§erences in corporate tax rates and preferential tax measures among countries.1 Since multinational enterprises (MNEs) are actively engaged in intrafirm transactions across boarders,2 they have incentive to manipulate internal transfer prices to reduce
their tax obligations, which is called “transfer pricing”. It has been well documented that
MNEs shift their profits from high-tax countries to low-tax jurisdictions (see Hines andRice, 1994; Huizinga and Laeven, 2008; Bauer and Langenmayr, 2013). For instance,
inspections by the Vietnamese tax authorities found that “the most common trick playedby FDI enterprises to evade taxes was hiking up prices of input materials and loweringexport prices to make losses or reduce profits in books.”3 In addition, Egger et al. (2010)
find that an average subsidiary of an MNE pays about 32% less tax than similar local
firms in high-tax countries. According to Goldman Sachs, tax saving by US MNEs is
2 trillion dollars which are equivalent to 4 years’ worth of US corporate tax revenues(Nikkei, August 31, 2016).
If governments overlook internal exchanges within the firm, MNEs may shift all profits
to low-tax or no-tax jurisdictions via transfer pricing. Governments thus impose transfer
pricing rules to control tax manipulation. The Organisation for Economic Co-operation
and Development (OECD) published the guidelines for transfer pricing in 1995, whichwere reformed in 2010.4 The OECD proposed that internal transfer prices follow theso-called “Arm’s Length Principle (ALP)”.
The basic approach of the ALP is that the members of an MNE group should be treated“as operating as separate entities rather than as inseparable parts of a single unified
business” and the controlled internal transfer price should mimic the market price thatwould be obtained in comparable uncontrolled transactions at arm’s length. This kind of“comparability analysis” is at the heart of the application of the ALP. The 2010 OECD
Transfer Pricing Guidelines for Multinational Enterprises and Tax Administrations 2010
states that the “comparable uncontrolled price” (hereafter, CUP) method:1

Preferential tax measures are observed in many countries. For example, Vietnam grants special orpreferential tax rates to attract foreign direct investment (FDI). Thailand provides tax incentives for FDI.
The Taiwanese corporate tax rate is lower by 7 percentage points for foreign firms with a fixed place ofbusiness or a business agent in Taiwan.
2
Bernard et al. (2010) report that over 46% of U.S. imports composed of intrafirm transactions in
2000.
3
http://vietnamlawmagazine.vn/transfer-pricing-unbridled-at-fdi-enterprises-4608.html
4
The OECD also initiated a project called “Base Erosion and Profit Shifting” in 2012 and created theaction plan to address base erosion and profit shifting.

1

“compares the price charged for property or services transferred in a controlled transaction to the price charged for property or services transferred in
a comparable uncontrolled transaction in comparable circumstances. If there
is any di§erence between the two prices, this may indicate that the conditionsof the commercial and financial relations of the associated enterprises are notarm’s length, and that the price in the uncontrolled transaction may need tobe substituted for the price in the controlled transaction.” (p. 63)
Currently, the ALP is the international transfer pricing principle to which OECDmember countries have agreed should be used for tax purposes by MNE groups and tax
administrations. Thus, it is important to explore incentives of MNEs for transfer pricing
to take advantage of tax di§erences across countries and implications of the ALP as
countermeasures against profit shifting in various market structure scenarios.
This paper specifically investigates transfer pricing resulting from tax-induced FDI
and the e§ects of the ALP when imperfect competition prevails in the final-good market.
To this end, we consider a very stylized simple set-up of two countries with di§erent
corporate tax rates. We first analyze a setting in which a monopolist produces and sells
a final product in country H (Home) with a higher corporate tax rate, whereas it sources
its intermediate input from country F (Foreign) with a lower corporate tax rate. This
could be the case if the input is a labor-intensive good and the wage rate is much lower
in Foreign. Alternatively, the input is a natural resource that is available only in Foreign.
We specifically consider two channels for the monopolist to source the input. It can beoutsourced from independent firms in Foreign, or can be produced internally by the foreignsubsidiary established through FDI. In the presence of FDI, the monopolist becomes an
MNE.
Not surprisingly, FDI can be used even if it is less e¢cient to produce the input internally, because it can be used as a vehicle to lessen its tax burden with an inflated internal
price. Interestingly, however, such FDI benefits consumers, because tax manipulation by
the monopolist leads to more production which alleviates allocative ine¢ciency due tothe market power.
We examine the e§ects of the ALP introduced in the presence of transfer pricing.
As the CUP method is the most direct and reliable, it is the preferred method when
applying the ALP. In practice, however, it may be di¢cult to find a transaction between
independent enterprises that is similar enough. This would be particularly so in themonopoly context where the required input is demanded only by the monopolist and2there is no comparable input market available. In such a case, there are other methods
suggested as the ALP.5
In our theoretical set-up, we examine the “cost plus” (hereafter, CP) method, because
the CP method as well as the CUP method are traditional transaction methods. The
CP method mandates that the transfer price should reflect the production cost of theinternally-transacted input. However, the true production cost is typically non-observableby tax authorities and hard to ascertain. As a result, it can be manipulated at certain
costs. Following the existing literature, we introduce “concealment costs” to analyze
the incentive to engage in FDI and the determination of the internal price when the
CP method is used due to the absence of comparable transactions in the market. Morespecifically, when an MNE’s internal price deviates from its true marginal cost (MC) in
the presence of the CP method, there are some costs to avoid such institutional constraints
on the internal transfer price. These costs may be literally concealment costs to keep two
separate books or may reflect expected punishment for the deviation as in Allingham andSandmo (1972) and Kant (1988).
The MNE thus trades o§ potential tax benefits against concealment costs when determining the optimal transfer price. In particular, we show that the optimal transfer
price is equivalent to the minimization of what we call “perceived marginal cost (PMC)”.
This characterization provides a very simple condition for the optimality of FDI vis-a-vis
outsourcing if the concealment costs are linear in the quantity of internally-transferred
inputs. In addition, we show that if the ALP is introduced in the presence of transfer
pricing, profit shifting is obviously mitigated but consumers as well as the monopolist get
hurt. As a result, social welfare may deteriorate.
If the concealment costs are convex instead, there may be incentives for the MNE toengage in dual sourcing, that is, a part of the required input is produced from the foreignsubsidiary whereas the rest is outsourced. As a result, a dual sourcing strategy may provide
the tax authority with the ability to identify a comparable market price and adopt the
CUP method as an application of the ALP. In such a situation, we demonstrate that theimposition of the CUP method with dual sourcing leads to unintended consequences anddetrimental e§ects if it switches the MNE’s sourcing decision from the dual sourcing to
the internal sourcing alone in order to avoid the application of the CUP method.
We also analyze import tari§s as countermeasures against the potential tax shifting.
5

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

3

An import tari§ can completely o§set the incentive to engage in inflated transfer price forthe tax manipulation purpose. However, we show that some tax manipulation still arises
with the optimal tari§. The reason is that the tax manipulation by the MNE leads tomore production in the domestic market which can alleviate allocative ine¢ciency due tomonopoly power.
We next extend our analysis to an oligopolistic market structure in the home finalgood market. As the MNE has an incentive to produce more from profit-shifting motives,
it may have strategic e§ects vis-a-vis its rival firms in the final-good market. The rival
firms respond by reducing their outputs, which leads to lower profits for them in the caseof strategic substitutes. This implies that tax-induced FDI by the MNE has spillovere§ects that reduce tax revenues from the other domestic firms as well as the MNE.
We also consider implications of the ALP when there is a single foreign supplier which
has market power. If the input purchased by the downstream rivals is considered as acomparable input used by the MNE and the CUP method is applied by the regulator,
the price set by the foreign supplier a§ects the internal price of the MNE. Thus, theimposition of the ALP in this case may have implications of strategic price setting of thesingle input supplier in Foreign. We show that the CUP method also has implications for
the MNE’s incentives to supply to its downstream rival. As is standard in the verticalintegration literature, there are trade-o§s between raising rival’s costs and profit losses forthe upstream firm when the MNE engages in input foreclosure to the rival downstream
firm. In our set-up, there is an additional channel through which foreclosure can bebeneficial via transfer pricing, because the input foreclosure increases the rival firm’s
input acquisition costs, which the tax authorities regard as the benchmark transfer pricein the CUP regime. As a result, we find that the MNE may refrain from supplying to therival downstream firm even if it is more e¢cient than the foreign input supplier, providing
a novel theory of market foreclosure.
Our paper is at the intersection of international trade and public economics. Horst(1971) initiated the theory of multinational firms in the presence of di§erent tari§ andtax rates across countries and explored the profit-maximizing strategy for a monopolistic
firm selling to two national markets, that is, how much it should produce in each country
and what the optimal transfer price for goods exported from the parent to the subsidiarywould be. Horst (1971) and subsequent papers (such as Batra and Hadar, 1979; Itagaki,
1979, 1981) show that MNE’s optimum price would be either the highest or the lowest
possible allowed by the limits of government rules and regulations, depending on tax and4tari§ schedules among countries. Kant (1988) shows how an interior transfer price can bederived endogenously in the presence of so-called “concealment costs.”
In our model, the decision making process is centralized.6 Hirshleifer (1956) initiated another strand of literature on transfer pricing with “decentralized” decision making
process inside the firm. In this framework, transfer prices are instruments used by headquarters to control separate divisions from pursuing their own interests. For instance,
Hirshleifer (1956) assumes that decision-making across branches is decentralized and thetransfer prices in his model are chosen to align the production decisions of the various
divisions. Bond (1980) extends the analysis of optimal transfer pricing to a case wherebranches of a vertically integrated enterprise are located in multiple jurisdictions withdi§erent tax rates. He shows that the optimal transfer prices trade o§ the gains from tax
avoidance against the e¢ciency losses associated from resource misallocation.
In the presence of oligopoly, the transfer-pricing literature with decentralized decisions further considers strategic e§ects of transfer pricing as an instrument of strategicdelegation. For instance, Alles and Datar (1998) show how cost-based transfer prices
can be manipulated to dampen competition and sustain higher market prices in a closed
economy. Schjelderup and Sorgard (1997) is one of the first papers that analyze transfer
pricing for decentralized MNEs with an oligopolistic market structure. However, they do
not deal with the ALP.
Kato and Okoshi (2017) also adopt a decentralized decision structure and consider
the optimal location of production facilities in the presence of tax di§erences between
countries, and the e§ect of the ALP on the location choice. Their paper is closely related toours in the sense that their model also consider both strategic and tax-manipulation e§ectsof transfer pricing. However, both the set-up (including the decision making process) andfocus of their paper are very di§erent from ours. They consider a setting in which an MNE
faces competition in the downstream market but the MNE is a single input supplier forboth its downstream subsidiary and its rival. In their model, the imposition of the ALP is
equivalent to the prohibition of price discrimination for the MNE’s upstream monopoly.
Moreover, we consider other upstream suppliers and analyze the outsourcing vs. FDI
decision, whereas their focus is on the location choice of upstream monopoly production
facility.
Whether the MNE’s decision is centralized or decentralized, there are only a few
6

Nielsen et al. (2008) explicitly examine conditions under which a centralized decision is preferred toa decentralized decision.

5

studies that theoretically investigate the ALP under imperfect competition. Samuelson(1982) is the first study to point out that for an MNE subject to the ALP principle, thearm’s length reference price itself can be partially determined by the firm’s activities.
In a similar vein, Gresik and Osmundsen (2008) consider transfer pricing in a verticallyintegrated industries in the absence of transactions between independent entities. Morespecifically, they examine the implications of the ALP as a transfer price regulation when
all firms are vertically integrated and the only source of comparable data may be fromtransactions between a¢liated firms. In our framework with imperfect competition inboth upstream and downstream markets, the reference price for an MNE is determinedby an outsider firm which recognizes the strategic e§ects of its price decision on its input
demand via the transfer price of the MNE. It is shown that the outsider has an incentive
to set a lower price compared to the case without linkage via the transfer price.
The rest of the paper is organized in the following way. Section 2 introduces the basic
set-up of a monopoly model with transfer pricing. We first analyze the incentive to engage
in FDI due to a tax di§erential between the source and the host countries and the optimaltransfer price with the ALP. We then explore implications of such FDI for the e¢ciencyof global sourcing and identify the wedge between the e¢cient outcome and the market
equilibrium. We also explore implications of the ALP for social welfare and dual sourcing
incentives. Section 3 considers import tari§s as countermeasures against profit-shifting.
We derive the optimal tari§ in the presence of transfer pricing. Section 4 extends theanalysis to a duopoly setting to examine implications of strategic interactions in the finalgood market. We show that profit-shifting strategy of the MNE has further consequences
for tax revenues from its rival due to strategic e§ects. In section 5, we analyze how the
input market price can be endogenized with the imposition of the CUP method in thepresence of a single foreign input supplier. In particular, we uncover an additional motive
for foreclosure arising from tax concerns, therefore providing a novel theory of vertical
foreclosure. Section 6 concludes the paper.

6

2

The Monopoly Model with FDI: Transfer Pricing and the
ALP

2.1

The Basic Set-up

There are two countries, Home and Foreign, with di§erent corporate tax rates, t > e
t.7
There exists a monopolistic final-good producer. The headquarters that produces the final
good is immobile and tied to Home while its intermediate input is sourced from Foreign.
There are two possible channels to procure the input from Foreign. The headquarters
purchases the input from a foreign competitive open market at the price of $ (in section
4, we consider the external sourcing with market power and endogenize $). Alternatively,
the headquarters establishes its own input-production plant in Foreign through FDI. We
assume that one unit of the input is converted to one unit of the final good without
incurring any additional costs and that the input production is subject to constant returns
to scale. We also assume away the costs associated with FDI.8 The subsidiary’s unit costof the input production (i.e., marginal production cost) is given by c. The final good isconsumed only in Home.
The MNE can choose an internal transfer price, γ, when its foreign subsidiary supplies
its input to the headquarters. Without any tax rate di§erential between the two countries,
the MNE’s optimal internal transaction price for the input is simply its MC, c, in order toeliminate any double marginalization problem. However, with di§erent tax rates between
Home and Foreign, the MNE can choose γ as a mechanism to shift profits to minimize its
tax burden. Figure 1 describes the basic set-up.
2.2

The Benchmark Case: No Regulation (NR)As a benchmark case, we first consider the choice of internal price by the MNE when
there is no regulation and the MNE can set any internal price. In this case, the MNE sets
its internal price, γ, and output, q, to maximize the following global profits after tax:
M axΠN R = (1 − t) [P (q) − γ]q + (1 − et) (γ − c)q ,γ,q| {z }| {z }
Downstream Profits

7

Upstream Profits

Foreign parameters and variables are denoted by “tilde”.
If there exists a fixed cost to set up the subsidiary, FDI becomes less likely. However, the essence ofour results would not change.
87Figure 1: Monopolistic MNE with Transfer Price
where P (q) is the downward sloping inverse demand function the monopolist faces. We
should mention that the decision making is assumed to be centralized. That is, with
the MNE’s objective function above, the headquarters producing the final good makes
an output decision that would maximize the overall firm profit, not just the profit of thedownstream division.
Note that the objective function of the monopolist can be rewritten as
ΠN R = (1 − t)[P (q) − ξ N R ]q,
where(1 − et)c − (t − e
t)γ
.
(1)
1−t
That is, the MNE facing di§erent tax rates across countries behaves as if its marginal
production cost were ξ N R , which can be considered as the MNE’s “perceived marginal
cost (PMC)” of production adjusted for transfer price induced by the di§erential tax rates
across countries. Since the MNE’s profit decreases as ξ N R increases, the monopolist’s
optimal choice of γ is equivalent to the choice of γ that minimizes ξ N R , regardless of its
output level. Note that ξ N R is decreasing in its internal transfer price, γ, because it can beused as a vehicle to shift profit from the high-tax country (Home) to the low-tax country(Foreign).
As pointed out by Horst (1971), it immediately follows that the optimal choice is toξN R ≡

8set γ as high as possible with the constraint that the downstream profit is non-negative.
This implies that all profits from a high-tax country will be shifted towards to a lowtax country in the absence of any regulation. This simple model illustrates the need forregulations to counter such MNE’s profit-shifting motives to reduce the tax burden.
2.3

The Arm’s Length Principle (ALP)

In reality, there are regulations that would prevent the choice from being a corner solution
and limit the MNE’s profit-shifting motives. The most-widely adopted and agreed-uponstandard practice is the “Arm’s Length Principle (ALP)”, which requires intrafirm transfer prices to mimic the market price that would be obtained in comparable uncontrolled
transactions at arm’s length, as discussed in the Introduction. Even though this principle is conceptually sound and straightforward, its implementation as a regulatory policy
may be di¢cult and subject to di§erent interpretations. For instance, in the context ofmonopoly, such a “comparability analysis” is unlikely to be feasible, simply because there
is no comparable transactions as it is the only firm that produces the final good; no otherfirms acquire similar inputs. Even if similar inputs are transacted in the market by otherfirms for di§erent purposes, the monopolist may argue that the available inputs are notsuitable to meet its specifications and that is a reason why they are engaged in its own
production in the first place. In other words, what constitutes a similar input may not
be clear-cut and subject to disputes unless comparable inputs are identical.
In our analysis, we consider two alternative scenarios in which the ALP is implemented.
1. CUP Method with Comparable Input Available in the Market: We assume that
if a comparable input is available in the market, the firm is required to use thecomparable market price as the internal transfer price.
2. Cost-Plus Method without Comparable Input Available in the Market: If a comparable input is not transacted in the market, then the CUP method cannot beapplied and the lack of comparable inputs transacted by uncontrolled parties necessitates the use of other methods to regulate transfer pricing. In such a case, we
assume that the regulator uses the CP method which mandates that the transfer
price should reflect the production cost of the input internally transacted. However,
the true production cost is typically non-observable to tax authorities and hard toascertain. As a result, it can be manipulated at certain costs.

9

Our analysis proceeds in the following working assumptions. In the monopoly case,we consider the “cost plus” scenario as the main focus, which we believe is more realistic
because the monopolistic downstream firm is the only firm that demands such an input.9
In sections 3 and 4 where we analyze the duopoly case, we deal with both cases.
2.4

The “Cost Plus” Method and Concealment Costs

We analyze the choice of internal transfer price when the CP method is adopted as anapplication of the ALP for the monopoly case. As shown in the previous subsection,
without any external or regulatory restriction on the transfer price, all profits would beshifted towards to a low-tax country with FDI being used as a vehicle. However, this typeof behavior can be a violation of tax laws. We thus explore implications of institutional
constraints on the internal transfer price.
To this end, we assume that a deviation of MNE’s internal price from its true MCentails costs of Ψ(γ − c, q). This could be interpreted as concealment costs or could reflect
expected punishment for the deviation as in Allingham and Sandmo (1972) and Kant
(1988). For analytical tractability, we assume the concealment costs are separable in thedeviation of the internal price from its true MC and the amount of inputs transferred,that is, Ψ(γ − c, q) = φ(γ − c)q with φ0 > 0, φ00 > 0, and φ0 (0) = 0, as in Egger andSeidel (2013). This specification states that concealment costs increase with a deviationof the transfer price from its true MC and the amount of inputs transferred. In addition,
concealment costs are convex in the degree of deviations with the usual Inada condition.
The convexity assumption is standard in the literature on transfer pricing and tax evasion.
It may reflect additional costs to justify or conceal the di§erence between the reported
and the true marginal production cost of the input (Haufler and Schjelderup, 2000).
The dependence of concealment costs on the amount of inputs transferred can reflect
an increased probability of detection with a larger scale of operation and transfer. In
particular, the linearity assumption can be justified if we interpret concealment costs as an
expected penalty that is linear in the amount of transactions. Moreover, the assumptionof linear concealment costs in the MNE’s output allows a very clean characterization
concerning the MNE’s optimal transfer price and its sourcing decision.10 As in Gresik
and Odmundsen (2008), we assume that only the high-tax country (Home) has incentives
9

The CUP case for the monopolist can also be analyzed in a straightforward manner.
In subsection 2.6, we consider a more general form of concealment costs: Ψ(γ − c, q) = φ(γ − c)µ(q).
When µ is convex in q, dual sourcing may be optimal and section 2.6 explores implications of the ALP
in such a case.
1010to audit for evidence of profit shifting; auditing is self-defeating for the low-tax country(Foreign) because it only reduces tax revenues for Foreign.
2.4.1

The Optimal Transfer Price with Concealment Costs

More specifically, with concealment costs linear in the output, the MNE’s post-tax profit
function is given by11
Π = (1 − t) [P (q) − γ]q + (1 − et) (γ − c)q −| {z }| {z }
Downstream Profits

Upstream Profits= (1 − t)[P (q) − ξ]q,φ(γ − c)q
| {z }

Concealment Costs

where(1 − et)(γ − c) φ(γ − c)
(1 − et)c − (t − et)γ + φ(γ − c)
+
=
1−t
1−t
1−t
φ(γ
−
c)
= ξN R +.
1−tξ ≡ γ−

Thus, the optimal choice of the transfer price γ ∗ is equivalent to minimize the MNE’s
PMC, ξ, which is adjusted for transfer price induced by di§erential tax rates and concealment costs, and implicitly defined byt−et = φ0 (γ − c).

Thus, the optimal γ ∗ can be derived asγ ∗ = c + φ0−1 (t − et) > c.

For instance, if we specify the φ function as follows: φ(γ − c) = k2 (γ − c)2 , where ahigher k means better institutional monitoring and makes it more costly for the MNEs toeengage in profit shifting, then we have γ ∗ = c + t−k t .12 The optimal choice of the transfer
11
In the expression for the MNE’s total post-tax profit, we interpret concealment costs as an expectedpenalty for profit shifting, which creates a new liability (Gresik and Osmundsen, 2008). With thisinterpretation of concealment costs, they are not part of the taxable profits. However, this is not a
crucial assumption and our qualitative results are robust to including them in the taxable profits ateither Home or Foreign, depending on where concealment costs are incurred.
12
We implicitly assume that concealment costs (i.e., k) are su¢ciently high under regulation to warrant
an interior solution, that is, all downstream profits are not shifted to the host country with a lower tax

11price is consistent with empirical findings. Clausing (2003), for example, shows that the
US intrafirm import price becomes higher as the tax rate of the exporting country becomes
lower. Note that the di§erent prediction is obtained without concealment costs.
2.4.2

FDI vs. Outsourcing

Let ξ ∗ be the minimized PMC with the choice of optimal transfer price γ ∗ . Then, the
MNE’s profit from FDI can be written as
ΠF DI = (1 − t)[P (q) − ξ ∗ ]q,
whereas the monopolist’s profit from outsourcing can be written as
ΠOS = (1 − t)[P (q) − $]q.
Thus, the monopolist’s sourcing decision boils down to a simple comparison between ξ ∗and $. FDI takes place if and only if ξ ∗ < $.
We first show the following proposition, which implies that the MNE’s after-tax global
profit is greater due to tax manipulation compared to the case where the firm transfers
its input at its MC, c.
Proposition 1. ξ ∗ < c.
Proof. Note that ξ ∗ can be written asξ ∗ = c − λ,
e

∗

∗

−c)
where λ ≡ (t−t)(γ −c)−φ(γ. Using the FOC that defines γ ∗ , we find that the numerator
1−tof λ is positive because

23

6φ(γ ∗ − c) 767(t − et)(γ ∗ − c) − φ(γ ∗ − c) = (γ ∗ − c) 6φ0 (γ ∗ − c) −7 > 0.
(γ ∗ − c) 54|{z}
>0 by the convexity of φ

Therefore, ξ ∗ < c.
rate.

12

The MNE’s profit is as if its cost were the PMC of ξ ∗ which is lower than its true MCof c. As a result, the following corollary is immediate.
Corollary 1. Consumer surplus increases with profit shifting via transfer pricing.
As the MNE uses transfer pricing to shift profits from the high-tax country to the lowtax country, it produces more with a lower PMC than its true MC. As a result, consumer
surplus increases.
In addition, Proposition 1 implies that the MNE’s sourcing decision could be ine¢cientfrom the viewpoint of the global production e¢ciency (see Figure 2). The global e¢ciency
requires that FDI takes place if and only if c < $. However, the profit-shifting motives
due to tax di§erences across countries create a wedge of λ(> 0), which distorts the MNE’ssourcing decision. We can also easily show that the wedge is increasing in the tax-ratedi§erential across countries because of the following comparative statics results.
∗∗

Lemma 1. dξdt < 0 and dξdet > 0.

Proof. By the envelope theorem, we have
dξ ∗
@ξ ∗
(1 − et)(γ ∗ − c) − φ(γ − c)
,
=
=−
dt
@t
(1 − t)2
which is negative because (1 − et)(γ ∗ − c) − φ(γ − c) > (t − et)(γ ∗ − c) − φ(γ ∗ − c) > 0 as
shown in the proof of Proposition 1. Similarly, we obtain@ξ ∗γ∗ − c
dξ ∗
=
=
> 0.
1−t
de
t
@e
t

Thus, with respect to ine¢ciency of internal sourcing, we obtain the following proposition.
Proposition 2. With t > et, FDI is undertaken in equilibrium if and only if ξ ∗ < $.
∗ −c)
e ∗
Thus, if c 2 ($, $ + λ) (where λ ≡ (t−t)(γ −c)−φ(γ> 0), ine¢cient FDI arises. The
1−twedge λ increases in the tax di§erential between Home and Foreign (i.e., t − et).

13Figure 2: Globally E¢cient Sourcing vs. MNE’s Sourcing Decision
2.4.3

A Parametric Example

We now specify the φ function as follows: φ(γ − c) ≡ k2 (γ − c)2 . Then we haveγ∗ = c +

t−e
t
.
k

By plugging this back into ξ, we can easily verifyξ∗ = c −(t − et)2.
2k(1 − t)

This implies that FDI is undertaken if and only ifc<$+(t − et)2.
2k(1 − t)That is, unless the MNE’s internal production cost does not exceed the open market price
(t−e
t)2
(t−e
t)2
by 2k(1−t), FDI takes place. In particular, with c 2 ($, $ + 2k(1−t)), FDI is ine¢cient, but
is still optimal from the perspective of the MNE because of tax manipulation via transfer
pricing.

14

Figure 3: Optimal Transfer Price and "Perceived" MC
2.5

Impact of the ALP on Social Welfare

The home government can limit the MNE’s tax manipulation through the ALP, which
would increase tax revenue for Home. However, it would reduce consumer surplus because
the MNE contracts its output, as well as it would reduce the MNE’s profits. In thissubsection, we evaluate social welfare with and without the ALP to assess the welfare
impact of the ALP. More specifically, we show that social welfare in Home may decrease
as a result of the ALP regulation. To demonstrate this, we assume that the concealment
costs are the real resource costs devoted to the concealment activities.13 For illustration
with closed-form solutions, we further assume linear demand and quadratic concealment
costs: P (q) = 1 − q and φ(γ − c) = k2 (γ − c)2 .
Let us begin with the derivation of social welfare under no regulation. As we haveshown, in the absence of regulation the MNE has incentive to raise the transfer price γ
up to the level that completely eliminates the profits of the downstream division. That is,
the MNE will choose γ such that the profit-maximizing quantity induces the price to beequal to the transfer price γ. Viewing ξ N R in (1) as a function of γ and q(ξ) = (1 − ξ)/2
as the optimal quantity the MNE chooses when faced with the PMC of ξ, we can express
the condition that determines the optimal transfer price as P (q(ξ N R (γ))) = γ. This gives
13

We can make the same qualitative welfare comparison when the concealment costs are interpreted
as the expected penalty that the MNE has to pay to the home government and hence considered as atransfer in social welfare calculations. For details, see the Appendix.

15

us the optimal transfer price, γ ∗0 , asγ ∗0 =

1 − t + (1 − t̃)c.
2 − t − t̃

We substitute this back into (1) to obtainξ N R (γ ∗0 ) =2c(1 − t̃) − t + t̃
(1 − c)(1 − t̃), q(ξ N R (γ ∗0 )) =.
2 − t − t̃
2 − t − t̃Social welfare is defined to be the sum of consumer surplus, CS, producer surplus,
P S, and tax revenue, T R. In the absence of regulation, we haveCS0 =Z q(ξN R (γ ∗0 ))0

P (q)dq − P (q(ξ N R (γ ∗0 )))q(ξ N R (γ ∗0 )),P S0 = ΠN R = (1 − t)[P (q(ξ N R (γ ∗0 ))) − ξ N R (γ ∗0 )]q(ξ N R (γ ∗0 )),T R0 = t[P (q(ξ N R (γ ∗0 ))) − γ ∗0 ]q(ξ N R (γ ∗0 ))(= 0),

respectively. Consequently, we obtain social welfare under no regulation as
W0 =Z q(ξN R (γ ∗0 ))0

P (q)dq − ξ N RSP (γ ∗0 )q(ξ N R (γ ∗0 )),whereξ N RSP (γ ∗0 ) ≡ (1 − t)ξ N R (γ ∗0 ) + tγ ∗0 = c + t̃(γ ∗0 − c) = c +t̃(1 − t)(1 − c)
2 − t − t̃

representing the MC of FDI production from the perspective of the social planner of Home
under no regulation (NR). It consists of the physical production cost of c and tax transfer
to the host country (i.e., Foreign). Note that the MNE’s production level is determined
not by the social planner’s ξ N RSP (γ ∗0 ) but by its perceived MC of ξ N R (γ ∗0 ).
Next, we derive social welfare under the ALP. As we have shown earlier, the MNEchooses γ so as to minimize ξ = [(1 − t̃)c − (t − t̃)γ + φ(γ − c)]/(1 − t). The optimal γ isgiven byt − t̃
γ∗ = c +,k16and hence we haveξ(γ ∗ ) = c −(t − t̃)2
1(t − t̃)2, q(ξ(γ ∗ )) = (1 − c) +.
2k(1 − t)2
4k(1 − t)

To ensure that the above expressions are valid (i.e., the downstream profit is non-negative),
we impose the following condition: P (q(ξ(γ ∗ ))) ≥ γ ∗ + φ(γ ∗ − c), which is equivalent tok≥(t − t̃)[t − t̃ + 2(1 − t)(2 + t − t̃)]≡ k.
2(1 − t)(1 − c)With the maintained assumption of k ≥ k, the expressions for CS, P S, and T R are thesame as in the case of no regulation, except that ξ N R (γ ∗0 ) is replaced by ξ(γ ∗ ). Consequently, we obtain social welfare in this case as
W =Z q(ξ(γ ∗ ))0

P (q)dq − ξ SP (γ ∗ )q(ξ(γ ∗ )),where(t − t̃)(t + t̃)
2krepresenting the MC of FDI production from the perspective of the social planner of Home
under the ALP, which includes concealment costs.
To see the welfare impact of the ALP, we first notice that in the presence of concealment
cost, the MNE under the ALP does not raise γ as much as it does under no regulation.
As a consequence, ξ N R (γ ∗0 ) < ξ(γ ∗ ), and hence q(ξ N R (γ ∗0 )) > q(ξ(γ ∗ )). That is, the ALP
induces the MNE to produce less, meaning smaller CS.
As Figure 4 shows, therefore, the ALP unambiguously reduces social welfare if ξ N RSP (γ ∗0 ) <ξ SP (γ ∗ ). It is readily shown that this condition is equivalent toξ SP (γ ∗ ) ≡ (1 − t)ξ(γ ∗ ) + tγ ∗ = c +k<(t + t̃)(t − t̃)(2 − t − t̃)≡ k̂ SP .
2t̃(1 − t)(1 − c)We can readily show that k̂ SP > k. Thus, we find that there is a region for k, i.e.,(k, k̂ SP ], such that the ALP unambiguously reduces social welfare. The reason why the
ALP reduces social welfare when k is small is that the MNE would raise γ so much thatthe resulting large concealment cost significantly reduces social welfare.
This result suggests that the desirability of the ALP in terms of social welfare crucially17Figure 4: Impact of the ALP on Social Welfare
depends on the quality of institutional monitoring (represented by parameter k). Better
institutional monitoring and the ALP regulation are complementary. Imposing the ALP
without quality monitoring in place can be counterproductive. Indeed, we calculate both
W0 and W in the case where c = 0.3 and k = 3, and show that W0 > W holds if t is large
or t̃ is small, as Figure 5 illustrates.
Although the ALP discourages MNE’s profit shifting, it would induce the MNE toproduce less and hence could lead to the deterioration of social welfare. This basic message
regarding the welfare impact of the ALP will also be valid in a duopoly case that we
examine in section 4.
2.6

Non-Linear Concealment Costs and Dual Sourcing

With the concealment costs linear in the amount internally transferred, q (with an inflated
price, γ), the MNE will procure its input only from a single source (i.e., either all fromthe internal source or all from the open market). However, if the concealment costs areconvex in q, the MNE may source its inputs from both the internal and external sources.
To see this, let us assume that Ψ(γ − c, q) = φ(γ − c)µ(q) with µ0 and µ00 > 0. Then wehaveΠ = (1 − t)[P (q) − γ]q + (1 − et)(γ − c)q − φ(γ − c)µ(q)!
(1 − et)c − (t − et)γφ(γ − c)= (1 − t) [P (q) −]q −µ(q) .
1−t
1−t18

Figure 5: Welfare Impact of the ALP
Thus, given γ, the PMC from internal sourcing via FDI, ξ, is not constant and can be
expressed as[(1 − et)c − (t − et)γ] + φ(γ − c)µ0 (q)ξ(q; γ) =.
1−tThis also implies that depending on the production quantity, the optimal transfer pricechanges. For a given quantity, q, the transfer price that minimizes the total production
cost [(1 − et)c − (t − et)γ]q + φ(γ − c)µ(q) is given by the following FOC:(t − et)q = φ0 (γ − c)µ(q).

(2)

Totally di§erentiating (2), we can easily verify that the optimal internal price γ ∗ (q) is
decreasing in q:dγ[(t − et) − φ0 (γ − c)µ0 (q)]
=
< 0,
dq
φ00 (γ − c)µ(q)because φ0 (γ − c)µ0 (q) > φ0 (γ − c) µ(q)= (t − et) holds from the convexity of φ and (2).
q
Let qI and qO denote the amount of inputs from the internal source (i.e., FDI) and theoutside source (i.e., the open market), respectively. Then, the optimal sourcing decision
can be derived from the following optimization problem:[(1 − et)c − (t − et)γ]qI + φ(γ − c)µ(qI )+ $qO
qI ,qO ,γ
1−t
M in

19

subject toqI + qO = q and qI , qO ≥ 0.
The Lagrangian for this problem can be written as$=[(1 − et)c − (t − et)γ]qI + φ(γ − c)µ(qI )+ $qO + η[q − (qI + qO )],1−twhere η is the Lagrangian multiplier associated with the constraint qI + qO = q.
The FOCs can be written as@$@$= ξ(qI ; γ) − η ≥ 0,
qI = 0,
@qI
@qI
@$
@$
= $ − η ≥ 0,
qO = 0,@qO@qO@$−(t − et)q + φ0 (γ − c)µ(q)
=
= 0.
@γ
1−t
Let qb be the unique output level such that[(1 − et)c − (t − et)γ] + φ(γ − c)µ0 (q)(t − et)q = φ0 (γ − c)µ(q), ξ(q; γ) ≡
= $.
1−t

Then, the internal production is optimal up to qb and, beyond qb, outsourcing is optimal.
Therefore, the following two types of sourcing behavior are possible: (i) the dual sourcing
with qI > 0, qO > 0 and (ii) the internal sourcing with qO = 0. With the dual sourcing,
we have ξ(qI ; γ) = $. This would be the case when q > qb. Then, the amount of internalsourcing is given by qI = qb, and the rest is outsourced, i.e., qO = (q − qb). On the other
hand, with the internal sourcing, we have ξ(qI ; γ) = η < $. This would be the case whenq < qb.
Which sourcing will be adopted depends on the size of the market. Let M R(q) be
the marginal revenue curve corresponding to the inverse market demand P (q). Then, if
M R(bq ) > $, the dual sourcing arises. If not, then the internal sourcing alone arises. In
the latter case, the MNE solves[(1 − et)c − (t − et)γ]qI + φ(γ − c)µ(qI )
,
qI ,γ
1−t

M in

20

which defines γ(q). Thus, the cost function up to qb is given by[(1 − et)c − (t − et)γ(q)]q + φ(γ(q) − c)µ(q),1−t@C @C @γ[(1 − et)c − (t − et)γ(q)] + φ(γ(q) − c)µ0 (q)C 0 (q) =+== ξ(q; γ) < $,
@q
@γ @q
1−t
C(q) =

which is described by ξ curve in Figure 6.
As Figure 6 illustrates, with convex concealment costs, there will be internal sourcing
alone if the market demand is small, but dual sourcing if the market size is large. Notethat in our model, we abstract away from fixed costs of setting up a foreign subsidiary.
If there are any fixed costs associated with FDI, then our model would predict that fora very small market size, the sourcing will be done by outsourcing alone, but once themarket size grows enough to cover the fixed costs, the monopolist will switch to internalsourcing. If the market size becomes su¢ciently large, it will engage in the dual sourcing.
That is, the use of outsourcing is not monotonic with the market size if there exist the
fixed costs of FDI.
To illustrate this, let us work with a parametric example of Ψ(γ −c, q) = kφ(γ −c)µ(q),where φ(γ − c) = (γ − c)α with α > 1, and µ(q) = q β , that is, Ψ(γ − c, q) = k(γ − c)α q β .
Thus, φ0 (γ − c) = αk(γ − c)α−1 . As a result, the optimal γ and q satisfy(t − et)q = kα(γ − c)α−1 q β , [(1 − et)c − (t − et)γ] + kβ(γ − c)α q β−1 = (1 − t)$.

From the first equation, we have γ(q) = c +the second equation, we have
(1 − t)c − (t − e
t)

0

1
1 α−1

t−e
t
kα

β−1

q − α−1 . By substituting this for γ in

2
3α
1
1
! α−1
! α−1
e
e
β−1
β−1
t−t
t−t
q − α−1 + kβ 4
q − α−1 5 q β−1 = (1 − t)$.
kαkαThus, we obtainβ−1(1 − t)(c − $) = Ωq − α−1 .

21Figure 6: Internal vs. Dual Sourcing

22q ∗ is given byq
where Ω ≡2 α−β 3
α

4

(αk)

1
− α−1

2

β−1
α−1

=

Ω
,
(1 − t)(c − $)3 αt−et α−1 . Thus, we haveΩqb =(1 − t)(c − $)

5 α−1
β−1

4

α−β
=
α(1 − t)(c − $)

5 α−1
β−1

(αk)

−

1
β−1

2

3 α
t−e
t β−1 .

To illustrate the idea, let us assume that P (q) = θ − q, where θ represents the market
size. Then, M R = θ − 2q and the M R curve intersects with ! (the outsourcing M C) at
q = θ−!
. Thus, dual sourcing takes place if and only if θ−!
> qb, i.e.,
2
2
4

α−β
θ > 2bq+$ =2α(1 − t)(c − $)

2.7

5 α−1
β−1

(αk)

−

1
β−1

2

3 α
t−e
t β−1 + $.

Dual Sourcing and Invocation of the CUP Method

In the previous section, we analyzed the MNE’s sourcing behavior in the presence ofconcealment costs. The basic premise of the analysis was that for the monopoly case wehave considered the applicability of the CUP method is limited if there is only one firmthat produces a certain good and there are no similar transactions that can be observed
and used as a benchmark. This is especially so when all input acquisitions are doneinternally from its foreign subsidiary. Even if an alternative input is available at the priceof $, the MNE may argue that the input available in the open market is not suitable for
specific purposes of the MNE and the unavailability of suitable input is the reason for
FDI aiming at internal sourcing. This allowed the MNE to use an internal transfer pricethat is di§erent from $.
However, such an argument loses the convincing appeal once the MNE engages in dual
sourcing and acquires some of their input requirements through outsourcing, because itis an implicit admission that the open market input is also suitable for its final product.
This implies that dual sourcing may entail a risk that it may induce the government toadopt the CUP method instead of the CP method.
In such a scenario, the MNE may respond by engaging in only internal sourcing to
avoid the CUP method. Alternatively, it may choose dual sourcing even if the CUP
method will be imposed and the internal price is restricted to set at $. However, thenext proposition shows that if dual sourcing invokes the use of the CUP method as an23

application of the ALP, the MNE never engages in dual sourcing when c > $.
Proposition 3. If dual sourcing triggers the CUP method instead of the CP method, the
MNE never engages in dual sourcing when c > $.
Proof. Suppose that the MNE engages in dual sourcing when c > $, with qI > 0 and
qO > 0, where q = qI + qO . Then, its internal price should be γ = $. Thus, the profit
with dual sourcing that triggers the CUP method is given byΠD = (1 − t)[P (qI + qO ) − $](qI + qO ) + (1 − et)($ − c)qI
= (1 − t)[P (q) − $]q + (1 − et)($ − c)qI .

Alternatively, if the firm procures its input only from the outside source at the price of$, its profits isΠOS = (1 − t)[P (q) − $]q> (1 − t)[P (q) − $]q + (1 − et)($ − c)qI = ΠD .
| {z }(−)

Thus, the profit from dual sourcing is less than the profit under outsourcing alone simply
because the foreign subsidiary that produces internally makes a loss due to the CUP
method.
Proposition 3 shows that if dual sourcing triggers the CUP method, such an applicationof the ALP rule may fundamentally change the firm’s sourcing behavior. Note that
Proposition 3 does not imply that the monopolistic firm always do outsourcing when
its own production cost is higher than $. If internal sourcing makes the CUP method
inapplicable, it may instead engage in internal sourcing just to avoid the imposition of the
CUP method. Such a possibility is illustrated in Figure 7. The profit from outsourcing at
the price of $ can be represented by the area (B + C) whereas the profit from insourcing
with concealment costs can be represented by the area (A + B). Thus, if area A is bigger
than area C, the insourcing will be chosen. In this case, the output decreases from q to
q CU P .
We now show that when the imposition of the CUP method with dual sourcing changes
sourcing behavior, the e§ects can be very di§erent depending on which single sourcing
method the monopolist employs. More specifically, if the imposition of the CUP methodwith dual sourcing induces only outsourcing, it limits tax manipulation and increases
24Figure 7: Sourcing Decision Change with CUP Method
tax revenues without a§ecting consumer surplus. However, if the imposition of the CUP
method with dual sourcing induces insourcing alone, it actually reduces tax revenue andconsumer surplus as well as MNE’s profit. As a result, such a policy may backfire.
Proposition 4. Suppose that dual sourcing triggers the CUP method instead of the CP
method with c > w.
e If the MNE switches its sourcing from dual sourcing to outsourcing
alone, tax revenue increases with consumer surplus unchanged. However, if insourcing
alone is induced instead, both tax revenue and consumer surplus decrease.
Proof. Suppose that the home government switches the ALP method from CP to CUP
when the MNE engages in dual sourcing. If the MNE switches from dual sourcing tooutsourcing alone, then its M C remains to be $, implying that the output level does notchange. However, the tax revenue increases, because the downstream profit increases:
P (q)q − $q > P (q)q − γqI − $qO .
If the MNE switches from dual sourcing to insourcing alone, on the other hand, its

25

output given by q CU P becomes smaller. In addition, we have
P (q)q − γqI − $qO = [P (q) − w] q − (γ − $)qI
6
7
≥ P (q CU P ) − w q CU P − (γ − $)qI
6
7
2
3
≥ P (q CU P ) − γ q CU P + (γ − $) q CU P − qI
6
7
≥ P (q CU P ) − γ q CU P .

Thus, the downstream profit also decreases.

3

Import Tari§s as Countermeasures against Profit-Shifting

We consider a specific industry in which the MNE is operating. Implicitly we assume thatthe overall corporate tax rate is determined by factors beyond the specific industry weconsider. The overall corporate tax rate thus cannot be tailored for this particular industry
and is considered exogenously given. However, in face of MNE’s profit-shifting incentives,
the government may impose industry-specific ad-valorem import tari§s to eliminate suchincentives. We explore import tari§s adopted as countermeasures against profit shifting.
Let τ m denote ad-valorem import tari§ imposed by country H where the headquarter
is located. Now the MNE’s problem with FDI can be written as

where

b = (1 − t)[P (q) − (1 + τ m )γ]q + (1 − eΠt)(γ − c)q − φ(γ − c)q= (1 − t)[P (q) − b
ξ]q,

(3)
(4)

(1 − et)c − (t − et)γ + φ(γ − c)b
ξ = τ mγ +1−t
= τ mγ + ξeeet)γ+φ(γ−c)
with ξ = (1−t)c−(t−= c − (t−t)(γ−c)−φ(γ−c)
.14
1−t
1−t
In the presence of import tari§s, the optimal choice of the transfer price γb∗ is equivalent
14

We denote all variables in the presence of import tari§s with a hat (^)

26

to minimize the MNE’s "PMC cum tari§s", bξ, and implicitly defined by23t−et − τ m (1 − t) = φ0 (bγ − c).

Totally di§erentiating the first order condition above, we obtain00−(1 − t)dτ m = φ (bγ ∗ − c)db
γ∗.
Thus, we have@bγ∗
(1 − t)= − 00 ∗
<0
@τ m
φ (b
γ − c)

indicating that the incentives to inflate the internal price by the MNE can be mitigatedby an import tari§. Note that the optimal γb∗ chosen by the MNE can be written as23γb∗ = c + φ0−1 ( t − e
t − τ m (1 − t)).
et−tThis implies that τ m = τ m (= 1−t) completely o§sets any incentives for profit shifting.
b
In addition, with τ m = τ m , ξ = c holds and the MNE will engage in FDI only when its
internal production is more e¢cient than the open market. However, consumer welfare
goes down compared to the case without import tari§s. Thus, the optimal import tari§
can be lower than τ m (i.e., the import tari§ that eliminates any incentives for profit
shifting) as shown below.

3.1

The Optimal Import Tari§Let us analyze the government’s optimal choice of import tari§ given (t, et) when it maximizes domestic social welfare, W , which is defined as the sum of producer surplus (i.e.,
profit), consumer surplus and tax revenue. We consider import tari§s as a second-best∗
policy when the transfer price and output choices are left to the firm. Let bξ be theminimized PMC with the choice of optimal transfer price γb∗ , that is,∗(1 − et)c − (t − et)bγ ∗ + φ(bγ ∗ − c)b
ξ = τ mγ
b∗ +
.
1−t

27

∗
Let the corresponding output level be q(bξ ). Then, social welfare with FDI can be written
as
"Z b∗
#
q(ξ )
∗
∗
∗
∗
∗
W = (1 − t)[P (q(bξ )) − bξ ]q(bξ )+P (x)dx − P (q(bξ ))q(b
ξ )
|
{z
}
0
Producer Surplus|{z}Consumer Surplus
h
i
∗
∗
∗
+ t [P (q(bξ )) − (1 + τ m )bγ ∗ ]q(bξ ) + τ mγb∗ q(bξ )|{z}
Tax and Tari§ Revenues

∗

∗

∗

∗

= (1 − t)[P (q(bξ )) − (1 + τ m )bγ ∗ ]q(bξ ) + (1 − et)(bγ ∗ − c)q(bξ ) − φ(bγ ∗ − c)q(b
ξ )
#
"Z b∗
h
i
q(ξ )
∗
∗
∗
∗
∗
+
P (x)dx − P (q(bξ ))q(bξ ) + t [P (q(bξ )) − (1 + τ m )bγ ∗ ]q(bξ ) + τ mγb∗ q(bξ )0Collecting terms, we can write social welfare in a more compact form as follows:W =Z q(bξ∗ ) h
0

SP

i
SP
P (x) − bξdxwhere b
ξ = c+et(bγ ∗ − c) + φ(bγ ∗ − c) and represents the MC of FDI production fromthe perspective of the social planner of country H. It consists of the physical production
cost of c, tax transfer to the host country, and any concealment costs incurred by the
MNE. Note that the MNE’s production level is determined not by the social planner’s
SP
∗
SP
MC, b
ξ , but by its PMC, b
ξ . This implies that the choice of τ m that minimizes b
ξ isnot necessarily the optimal import tari§.
It is instructive to investigate the relationship between PMC and social cost associatedwith transfer pricing as the import tari§ changes. To this end, let us define the wedge
SP
between the MNE’s PMC and the social planner’s MC as δ = b
ξ(γ(τ m )) − bξ (γ(τ m )).
Then, we haveSPb
ξ(γ(τ m )) − bξ (γ(τ m )) = τ m γ +23
where γb∗ = c + φ0−1 ( t − e
t − τ m (1 − t)).
t−etSince γ = c when τ m = 1−t, we have7
t 6
φ(γ − c) − (1 − et)(γ − c) ,
1−t

SP
t−e
t
δ|τ m = t−te = b
ξ(γ) − bξ (γ)|τ m = t−te =c > 0.
1−t
1−t
1−t

28

We can also easily verify thatSP
δ|τ m =0 = b
ξ(γ) − bξ (γ)|τ m =0 =7
t 6
φ(γ − c) − (1 − et)(γ − c) |τ m =0 < 0.
1−t

2
3
To see this, note that γ satisfies the first order condition t − e
t = φ0 (γ − c). Since φ isconvex, we have3
2
φ(γ − c)< φ0 (γ − c) = t − e
t < 1−et.
γ−cThus, (1 − et)(γ − c) > φ(γ − c). We also know that
h
i
SP
d b
ξ(γ(τ m )) − bξ (γ(τ m ))
dτ m

6
7 @b
γ
=γ− e
t + φ0 (γ − c)>0@τ mbecause φ0 (γ − c) > 0 and @τ@bγm < 0. Thus, we obtain the following lemma.
et−t
Lemma 2. There is a unique τ om 2 (0, 1−t) such that

8
o
b
bSP
>
>
< ξ(γ) < ξ (γ) if τ m < τ mSPbξ(γ) = bξ (γ) if τ m = τ om
>
>
SP
:b
ξ(γ) > bξ (γ) if τ > τ omm

Lemma 2 implies that if τ m ≥ τ om , the output level by the MNE is unambiguously too
low from the social planner’s viewpoint. When τ m = τ om ,the PMC and social planner’s
cost coincide, but due to the exercise of monopoly power, the output is still too low.
If τ m > τ om , the output is further restricted because PMC exceeds the social MC. This
concern may induce the social planner to set an import tari§ lower than τ om and we derive
such conditions below.
Now let us analyze the marginal e§ect of an import tari§ on social welfare:
2

3

SP
h
i dq(τ ) 6
SP
dW
db
ξ 7
6
7
m
b
= P (q(τ m )) − ξ (τ m )+ 6−q(τ m )
7
dτ m
dτ
dτ 5
4
| {zm }
| {zm}
(−)

29

(−)

(5)

where2∗dq(τ m )
dq 6
ξ
6 @b
=
+
6
dτ m
db
ξ 4 @τ m

SP
db
ξ
and
dτ m

∗

=

@b
ξ @b
γ∗
@b
γ @τ
| {z m}=0 by the envelope theorem

SP

@b
ξ

3

2

7
dq ∗
7
γ
b <0
7=
5
db
ξ
|{z}
(−)

3

(b
γ ) @b
γ∗
γ∗
6
7 @b
= 4e
t + φ0 (bγ ∗ − c)5
< 0.
|{z
} @τ m@bγ @τ m(+)

Equation (5) illustrates the trade-o§s involved in setting an import tari§. The firstterm on the RHS represents the negative e§ect on consumer welfare as the impositionof import tari§s increases the MNE’s PMC which induces the firm to reduce outputs inthe domestic market. The second term on the RHS is the positive e§ect of reducing tax
shifting to country F and concealment costs.
t−et
It is clearly not optimal to set an import tari§ higher than τ m = 1−tbecause it issimply an overkill as countermeasures against profit shifting: an import tari§ beyond τ monly reduces consumer welfare without any corresponding positive benefits in terms ofsocial welfare. We thus consider only import tari§s with τ m ≤ τ m .
A su¢cient condition for the optimal import tari§ to be less than τ m isdWd|τ m =τ m =
dτ m
dτ m

"Z

0

q(b
ξ(γ))

SP

P (x) − bξ#(γ)dx |τ m = t−te < 0.
1−t

The following proposition provides a su¢cient condition for this.
0

Proposition 5. Let ρ = P dq
denote the cost-price pass-through rate for the monopolist.
dξdW|< 0 if ρ >dτ m τ m =τ m##
# dbξSP #### dτ m #dξdτ m|τ m = t−te .
1−tProof. We haveSPhi dq(τ )
b
SP
dW
d
ξ
m
= P (q(τ m )) − bξ (τ m )− q(τ m )
dτ m
dτ m
dτ
| {z }| {zm}
(−)

=

h

(+)

SP
i dq(τ )
∗
∗
SP
db
ξ
m
b
b
b
P (q(τ m )) − ξ + (ξ − ξ (τ m ))− q(τ m )
dτ m
dτ m

30

∗
SP
By Lemma 2, we know b
ξ −b
ξ > 0 at τ m = τ m . In addition, we know that∗

P (q(τ m )) − b
ξ = −P q
0m)by the first order condition for the MNE’s profit maximization and dq(τ< 0. As a result,dτ mwe haveSPdWdb
ξ0 dq(τ m )|τ =τ
< −P q− q(τ m )|t−tedτ m m mdτ mdτ m τ m = 1−t
"
SP #
db
ξ
0 dq dξ= −q P+|t−te .
dξ dτ mdτ m τ m = 1−t

Therefore,@ SP @@ dbξ @SP #@ dτ m @bdWdξ
0 dq dξ|τ m =τ m < −q P+|τ m = t−te < 0 if ρ > dξ |τ m = t−te .
1−t
1−t
dτ m
dξ dτ m
dτ m
dτ
"

m

e

t−t
Thus, we can conclude that the optimal import tari§ τ ∗m < τ m = 1−t, that is, theoptimal import tari§ mitigates incentives to engage##in tax manipulation via transfer price,

but does not completely eliminate it, if ρ ># dbξSP #### dτ m #dξdτ m|τ m =τ m . This is because the transfer

price induces the MNE to produce more, which enhances consumer
welfare. For instance,@ SP @b@@dξthis condition is satisfied if e
t is su¢ciently small because @ dτ m @=et φ00(1−t)' 0 and(bγ ∗ −c)τ m =τ mdξ
|= c.
dτ m τ m =τ m

Without imposing further structures on the model, it is di¢cult to further characterize
the optimal tari§. However, if we assume a constant cost pass-through rate and aquadratic function in the concealment cost specification, we can derive conditions underwhich the optimal import rate is lower than τ om .15
Proposition 6. Let ρ be the constant cost pass-through rate. If ρ >quadratic, we have τ ∗m < τ om .

### dbξSP #### dτ m #dξdτ m|τ m =τ om and φ is

Proof. See the Appendix.
15
For instance, constant elasticity demand curves and linear demand curves have a constant cost passthrough rate. See Bulow and Pfleiderer (1983) and Weyl and Fabinger (2013).

31

Figure 8: Duopoly Model with Strategic Interactions
The logic of the proof
is similar
to the one for Proposition 5. The condition that φ is
@ SP@
@ dbξ @ dξ
quadratic ensures that @ dτ m @ / dτ m is decreasing in τ m . Thus, when the pass-through ratedW
is constant, the condition guarantees that dτ
< 0 for all τ m ≥ τ om .
m

4

The Duopoly Model with Strategic Interactions

In this section we consider a duopoly model in which an MNE competes with anotherdownstream firm in Home in order to explore implications of strategic e§ects. The set-up isotherwise the same as in the monopoly model. More specifically, two final-good producers,
firm 1 and firm 2, compete in Home. Firm 2 is a home firm and simply procures its input
from Foreign with an exogenously given market price γ
e = $ (in section 4, we extend
the model to endogenize γe). Firm 1 has two sourcing choices as before. It can procure
its input from Foreign like firm 2. Alternatively, it can set up its own input-production
plant in Foreign. In this case, the MC of input production is given by c. The MNEchooses an internal transfer price , γ, when its foreign subsidiary supplies its input to theheadquarters that produces the final good. Figure 8 illustrates the duopoly model.
In the monopoly case, we assumed that the CUP method is not applicable, because
there is no comparable downstream firm and the input market simply does not exist in
the case of FDI (unless the MNE is engaged in dual sourcing that also relies on outside
suppliers). As a result, the ALP was based on the CP method and the MNE was assumed to incur concealment costs when its transfer price deviates from its MC. In the32duopoly case, the applicability of the CUP method depends on whether the transactions
between the rival downstream firm and its input suppliers can be regarded as “externallycomparable” to internal transactions of the MNE (OECD 2010, p. 71).
We present two sets of results depending on the comparability of the external transactions. In section 3.1, we first consider a scenario in which the external transactions are notconsidered as comparable. This would be the case if the two downstream firms produce
di§erentiated products and use di§erent types of inputs. Then, the ALP should be basedon the CP method and the MNE operates with concealment costs. In contrast, if theexternal transactions are considered as comparable, then the MNE is constrained to use
the comparable market price ($) as the internal transfer price. This second scenario isanalyzed in section 3.2.
4.1

The CP Method: Non-Comparable External Transactions

We first analyze the case in which the transactions between the rival downstream firm
and its input suppliers are not comparable to the internal transactions of the MNE. In
this case, the MNE’s behavior can be described with the presence of concealment costs fortransfer price that deviates from its true MC, as in the monopoly case. We maintain theassumption that concealment costs are linear in output, that is, Φ(γ − c, q) = φ(γ − c)q
with φ0 > 0, φ00 > 0 with φ0 (0) = 0.
To obtain the implications of strategic interactions for the MNE’s behavior, we assume
that in the downstream market, the two firms compete in quantities with the standard
assumption of strategic substitutes. More specifically, let Pi (q1 , q2 ) denote firm i’s pricewhen firm 1 and firm 2 produce q1 and q2 , respectively.
Firm 1 solves the following problem:
M ax Π1 = (1 − t) [P1 (q1 , q2 ) − γ]q1 + (1 − et) (γ − c)q1 − φ(γ − c)q1 .
q1
|
{z
}
| {z }| {z }
Downstream Profits

Upstream Profits

Once again, by collecting terms with q1 , we can rewrite it asΠ1 = (1 − t)[P1 (q1 , q2 ) − ξ]q1 ,
where
ξ≡

(1 − et)c − (t − et)γ + φ(γ − c)
.
1−t
33

Concealment Costs

The FOC for firm 1 is given by
1 @Π1@π 1 (q1 , q2 ; ξ)=
= 0.
1 − t @q1
@q1

(6)

Firm 2 similarly makes its decision on q2 to solve the following problem:
M axπ 2 (q1 , q2 ; $) = (1 − t) [P2 (q1 , q2 ) − $]q2 .
q2

The FOC is@π 2 (q1 , q2 ; $)
= 0.
@q2

(7)

Given a transfer price γ, the FOCs (6) and (7) implicitly define reaction functions
for firm 1 and firm 2, respectively. The equilibrium quantities for each firm, q1∗ (ξ, $) andq2∗ (ξ, $) are @at the@ intersection@@ of these two reaction functions, given the transfer price γ.
@ @ 2 πi @@ @ 2 πi @Assume @ @q2 @ > @ @qi @qj @ , where i = 1, 2 and j 6= i. Then, we have the followingistandard result.
Lemma 3.

@q1∗ (ξ,$)@q ∗ (ξ,$)< 0 and 2@ξ > 0.
@ξ

Proof. See the Appendix.
Let π ∗i (ξ, $) denote the equilibrium profit of firm i when the MCs for firm 1 and firm
2 are given by ξ and $, respectively. Lemma 2 then immediately implies thatdπ ∗1 (ξ, $)@π 1 @π 1 @q2∗ (ξ, $)@P1 ∗@q ∗ (ξ, $)=+= −q1∗ (ξ, $) +q1 (ξ, $) 2
< 0,
dξ
@ξ
@q2
@ξ
@q2
@ξ
dπ ∗2 (ξ, $)@π 2 @q1∗ (ξ, $)@P2 ∗@q ∗ (ξ, $)==q2 (ξ, $) 1
> 0.
dξ
@q1
@ξ
@q1
@ξ
That is, the equilibrium profit of each firm is decreasing in its own MC and increasing in
its rival’s MC.
Since we can write firm 1’s equilibrium profit after tax as Π1 = (1 − t)π ∗1 (ξ, $) andπ ∗1 (ξ, $) is decreasing in ξ, the optimal choice of transfer price is equivalent to the choice ofγ that minimizes ξ, as in the monopoly case. When the rival firm’s input is not considered
comparable and the CP method is used as a regulatory policy, we replicate the same result
as in the monopoly case.
We compare the case with transfer pricing regulated by the CP method against thecase without transfer pricing. The use of artificially inflated internal price is used to shift34its profit at the downstream stage to the upstream subsidiary in Foreign (the low-tax
country). As a result, the tax revenue from the MNE is reduced in Home. However,
it is not the end of the story; there is a collateral damage due to spillover e§ects. The
aggressive behavior of the MNE with transfer pricing also reduces the rival’s profit. Thus,
the tax revenue from the other firm that is not engaged in tax manipulation also decreases(even though consumer surplus increases by transfer pricing). In other words, we uncoveran additional tax-revenue loss from other firms in the presence of imperfect competition
due to strategic e§ects.
Two remarks are in order. First, it is also possible to compare transfer pricing with andwithout the CP method as in the monopoly case. The introduction of the CP method in
the presence of transfer pricing harms the MNE and consumers but increases tax revenue
from both firms 1 and 2.
Second, there exists a crucial di§erence between the strategic e§ects driven by tax
di§erences in our model and strategic transfer pricing in the IO and management literature (see, for example, Alles and Datar, 1998). The basic premise of strategic transfer
pricing in oligopoly models is to assume decentralized decision making and each division
maximizes its own profits, rather than the overall profits of the firm. Otherwise, the optimal decisions would be based on true MCs and the transfer prices would not matter andwould not generate any strategic e§ects, because internal transfer prices are just transfers among divisions within the firm and cancel out each other from the perspective offirm’s overall profits. Only when the decision of each division is driven by its own profit,
transfer price can have any meaningful e§ects. In contrast, our model assumes centralized
decision making; besides the headquarters (the downstream division) and its subsidiary(the upstream division) are located in the di§erent countries with deferent tax rates. If
the transfer price is inflated to reduce the tax burden without centralized decision, thestrategic e§ects will work the other way around.
4.2

The CUP Method: Comparable External Transactions

We now consider a scenario in which the transactions between the rival downstream firm
and its input suppliers can be considered comparable. In this case, the ALP can beapplied with the CUP method, which requires that the transfer price be equal to similar
input price in the market, i.e., the input price paid by firm 2.16
16
Gresik and Osmundsen (2008) analyze the ALP when all firms are vertically integrated and comparable but independent transactions, on which the application of the ALP can be based, is not available.

35

If the input market for firm 2 is perfectly competitive at the price of $, the analysis
with the CUP method is straightforward. As its transfer price is constrained to be at $with the CUP method, firm 1 will engage in FDI if and only if FDI is e¢cient from thepoint of global e¢ciency, that is, c < $. In this case, profit-shifting will take place tosome extent, but it is limited by the competitive market price $. If c > $, there is noine¢cient FDI for the profit-shifting purpose.
If we assume that the input available in the open market is supplied by a firm withmarket power, strategic interactions between the MNE and the foreign input supplier withmarket power restore various ine¢cient outcomes, as shown in the next section.

5

The Duopoly Model: “Imperfect” Input Market with the
CUP Method

We now consider a case where the transactions between the rival downstream firm and its
input supplier can be considered “comparable”, but the foreign input market is imperfectand thus the external reference price under the CUP method cannot be treated as an
exogenous parameter. More specifically, we assume that there is a single foreign input
supplier with market power. The foreign input supplier behaves as a monopolist either if
FDI is absent or if the MNE does not supply the input to the rival downstream firm (i.e.,
firm 2). It should be noted that we allow the MNE’s subsidiary to supply its input to thedownstream competitor if it chooses so.
With the CUP method, the transfer price with in the MNE, γe, must be equal to CUP,
that is, the price charged by the foreign input supplier. The dependence of the MNE’s
internal price on CUP creates novel strategic e§ects when CUP is endogenously determined. More specifically, ine¢cient FDI is restored in the presence of internal sourcing
for tax manipulation; besides, there could be an ine¢cient refusal to sell to the competing
downstream firm when the MNE’s upstream subsidiary is more e¢cient than the foreign supplier. This outcome results from the incentive for tax manipulation and departs
from the standard rationale for market foreclosure based on raising rival’s costs in the IO
literature (Salop and Sche§man, 1983; Ordover et al., 1992).
We assume the following timing for the analysis. Let c and ec be the respective constant
MCs of input production for the MNE and the foreign supplier. Given (c, ec), which is
Such a issue does not arise in our model because the rival downstream firm acquires its input from an
independent source.

36

assumed to be common knowledge for industry participants, but unknown to the regulator,
firm 1 decides whether to engage in FDI. If it sets up an upstream subsidiary, it procures
its input internally and at the same time sets a price at which it commits to supply toits downstream rival, i.e., firm 2. The internal transfer price is determined by the input
acquisition price of the downstream rival under the CUP method. Given the input pricecommitment by the MNE, the foreign input supplier sets its own price. The downstream
rival acquires its input from the input supplier with the lower price. If firm 1 does not set
up an upstream subsidiary, the foreign supplier sets the monopoly price to sell to bothdownstream firms.
We should mention that this timing assumption is equivalent to a dynamic negotiatingprocess in which the price stage game is modeled as a descending price auction in which
the MNE’s subsidiary and the foreign supplier are bidders (see Rei§en, 1992; Ordover etal., 1992).17
The equilibrium outcomes in this setting have di§erent characterizations dependingon the relative e¢ciency of the MNE’s subsidiary, c, and the foreign input supplier, ec. In
the following, we consider two cases: c > ec and c < ec.
5.1

The Case with c > e
c: Ine¢cient FDI

We first analyze the case in which the MNE is less e¢cient than the foreign supplier, i.e.,c >ec. We show that FDI arises even if c > ec. Again, such FDI is ine¢cient from theviewpoint of the global production.
With c > e
c, any input price (≥ ec) set by the MNE will be undercut by the foreign
supplier. This means that it is a weakly dominant strategy for the MNE’s subsidiary to
set a price very high (which is equivalent to the MNE’s refusal to sell to firm 2). Under
the CUP method, firm 1 behaves as if its input cost wereξ CU P (eγ) ≡(1 − et)c − (t − e
t)e
γ
1−t

if the foreign supplier sets a price of γe. Let q(x, y) denote the equilibrium output level fora downstream firm when its input cost is x while the rival firm’s cost is given by y.
17

We adopt this particular assumption to facilitate comparison of our results to the standard IO
foreclosure literature. We can derive a similar set of results with di§erent timing assumptions. For
instance, we can obtain similar results if the foreign supplier sets its input price first and firm 1 candecide whether or not to engage in FDI after observing the input price.

37

If firm 1 sets up a subsidiary and does internal sourcing, firm 2’s input demand at
price γe can be written as
q2CU P (eγ ) = q(eγ , ξ CU P (eγ )).

The input demand expression above indicates that there are two channels through which
the foreign supplier’s price a§ects firm 2’s demand. First, firm 2’s input demand is directlya§ected by the price it pays to the foreign supplier. Second, there is an indirect e§ect
through the PMC of firm 1 because firm 1’s transfer price is determined by the price firm
2 pays to the foreign supplier under the CUP method. The foreign input supplier thus
faces the following problem:
M axπ mγ −ec)q(eγ , ξ CU P (eγ )).
2 = (eγ
e

In contrast, if firm 1 does outsourcing from the foreign input supplier, the foreign input
supplier sets its input price to maximizeπmγ −ec) 2q(eγ, γe).
b = (em
For analytical simplicity, let us assume that both π me.
2 and π b are concave in γ
Let us consider the case of FDI by firm 1. Then, the FOC for the foreign supplier isgiven by

2

6
@π m
6
2
= q(e
γ , ξ CU P ) + (e
γ −e
c) 6
@e
γ
4

@q
@x
|{z}

+

Direct E§ect (−)

Indirect E§ect via Transfer Pricing (−)

Thus, the optimal price, γe∗ , is implicitly defined byγe∗ = ec− h@q @ξ CU P
@y @eγ
| {z }q(eγ ∗ , ξ CU P )@q@q @ξ CU P
+ @y
@x
@e
γ

3

7
7
7 = 0.
5

(8)

i >e
c.

With the CUP method applied as the ALP, the input price of the foreign supplier,γe, influences the MNE’s transfer price and indirectly a§ects MNE’s competitive behavior
CU P
e
t)
in the downstream market via its e§ect on ξ CU P . Since @ξ@eγ = −(t−< 0, a higher
1−t
2 CU P 3
input price to firm 2 decreases firm 1’s PMC ξ
and indirectly reduces firm 2’s
output because of strategic e§ects via transfer pricing. Thus, if firm 1 produces its input
38internally with FDI, the foreign supplier charges a lower input price under the CUP
method compared to the case in which such an indirect channel is absent.
To reduce the number of cases to consider, we assume that the gap between ec and cis not too large. More specifically, we assume

that is,

@
@
@π m
2 @
= q(c, c) + (c − ec)@e
γ @γe=c@q(c, c) @q(c, c) (t − e
t)
−
@x
@y
1−t

!

> 0,

q(c, c)@.
(c − ec) < @@@q(c,c)@q(c,c) (t−et) @@ @x − @y 1−t @(9)This condition guarantees that the input price for the downstream rival (i.e., firm 2) inthe presence of FDI, denoted as γe∗ , is higher than c.
To analyze the incentive for firm 1 to set up a foreign subsidiary, let us analyze theinput price in the absence of FDI. The FOC for the optimal input price without FDI,
denoted by γe∗∗ , is given by
4
A
B5
@π m
@q(e
γ, γ
e) @q(eγ, γe)b= 2 q(eγ, γe) + (e
γ −e
c)
+
= 0.
@e
γ
@x
@y

Then, we obtain the following lemma.

Lemma 4. Under condition (9), γe∗∗ > γe∗ .

Proof. Note that under condition (9), γe∗ > c and we haveξ

CU P

(1 − et)c − (t − e
t)e
γ∗
(e
γ )=
< c.
1−t
∗

Thus, ξ CU P (eγ∗) < γe∗ . This implies that q(eγ∗, γe∗ ) > q(eγ ∗ , ξ CU P (eγ ∗ )). We can evaluate the
FOC for γe∗∗ at γ
e=γ
e∗ :
@
A
B
@
1 @π m
@q
@q
∗
∗
∗
b @
= q(e
γ ,γ
e ) + (e
γ −e
c)
+
2 @e
γ @γe=eγ ∗
@x @y
∗

> q(e
γ ,ξ

Thus, γe∗∗ > γ
e∗ .

CU P

∗

∗

(e
γ )) + (e
γ −e
c)
39

@q
@q (t − et)−@x @y 1 − t

!

@
@
@π m
2 @
=
= 0.
@e
γ @γe=eγ ∗The intuition for the lemma above can be explained by the dependence of the MNE’s
internal price on the price set by the foreign input supplier. As the MNE’s internal priceis inversely related to the price, the foreign supplier has less incentive to increase its pricewhen FDI is present and the internal price is regulated to be equal to CUP.
The following proposition is established regarding firm 1’s incentive for FDI.
Proposition 7. Under condition (9), firm 1 engages in FDI even if c > ec.

Proof. We consider firm 1’s FDI incentive. The equilibrium profit for firm 1 in the absenceof FDI is given by π ∗ (eγ ∗∗ , γe∗∗ ) whereas its profit under FDI is given by π ∗ (ξ CU P (eγ ∗ ), γe∗ ).
By lemma 3, we have γe∗∗ > γe∗ > c > ξ CU P (eγ ∗ ). As a result, we haveπ ∗ (ξ CU P (eγ ∗ ), γe∗ ) > π ∗ (eγ∗, γe∗ ) > π ∗ (eγ ∗∗ , γe∗∗ ) .
|
{z
}
|
{z
}
Profit with FDI

Profit without FDI

With imperfect input market, there are three factors that a§ect firm 1’s incentive
for FDI. First, there exists the profit-shifting motive which facilitates FDI. Second, FDI
enables firm 1 to avoid the exercise of market power by the foreign input supplier. Lastly,
FDI results in a lower input price for the rival downstream firm under the CUP method,which discourages FDI. Taken together, Proposition 5 shows that the first two e§ects
dominate the third one unless the MNE is su¢ciently ine¢cient compared to the foreign
supplier.
5.2

The Case with c > e
c: Market Foreclosure

In this section, we analyze the case in which the MNE’s subsidiary is more e¢cient than
the foreign input supplier (c < ec) and firm 1 always sets up its subsidiary. In particular, weaddress the MNE’s incentives to supply its input to the domestic final-good competitor,
firm 2.
With the timing assumption we have, the MNE has the following options. If it decides
to supply to firm 2, its optimal pricing strategy is to set a price equal to the foreign
supplier’s MC to prevent undercutting, that is, γ = ec because a lower price makes the18
rival firm more competitive and its own PMC higher. With this choice, the equilibrium
18
We make the tie-breaking assumption that if firm 2 is indi§erent across suppliers, it purchases fromthe most e¢cient supplier. This assumption is made without any loss of generality to avoid the open set
problem.

40

outputs of firms 1 and 2 can be written as q(ξ CU P (ec), ec) and q(ec, ξ CU P (ec)), respectively,(1−et)c−(t−et)ec
CU P
where ξ(ec) ≡. The corresponding MNE’s profit can be written as1−tΠ = (1 − t)π(ξ CU P (ec), ec) + (1 − et)(ec − c)q(ec, ξ CU P (ec)).
If the subsidiary refuses to sell to firm 2 and the foreign input supplier supplies to firm
2, the foreign input supplier will set a price of γe∗ (characterized by condition (8) above),
and the MNE’s profit can be written as
ΠF oreclosure = (1 − t)π(ξ CU P (eγ ∗ ), γe∗ ).

As is standard in the vertical-integration literature, there are trade-o§s between raising
rival’s costs against loss of the upstream profit when the MNE engages in input foreclosure to the rival downstream firm. In our set-up, it turns out that the e§ect of raising
rival’s costs becomes weaker compared to the standard IO model, as will be shown below.
However, there is an additional benefit of foreclosure in terms of tax payments because
the input foreclosure increases the input price faced by firm 2 from ec to γe∗ which is usedas the benchmark transfer price in the CUP method.
To be more specific, firm 1’s subsidiary refuses to sell to firm 2 if ΠF oreclosure > Π.
This condition can be decomposed as follows:ΠF oreclosure − Π67= (1 − t) π(ξ CU P (eγ ∗ ), γe∗ ) − π(ξ CU P (e
c), e
c)
|
{z
}

Beneficial E§ects of Input Foreclosure
for Downstream Division− (1 − et)(ec − c)q(ec, ξ CU P (ec)) >(10)0|{z}Loss of Upstream Profit

Note that the expression for the beneficial e§ects of input foreclosure for the downstream
division can be further decomposed as
6 CU P ∗ ∗
7
6
7
π(ξ
(e
γ ), γe ) − π(ξ CU P (ec), ec) = π(ξ CU P (eγ ∗ ), γe∗ ) − π(ξ CU P (e
c), γ
e∗ )
|
{z
}
Tax Manipulation Motives

6
7+ π(ξ CU P (ec), γe∗ ) − π(ξ CU P (ec), ec) . (11)|{z}
Weakened Raising-Rival’s-Costs E§ects (WRR)

41

The first beneficial e§ect comes from the fact that a higher input price paid by firm 2
due to market foreclosure leads to a higher transfer price under the CUP method whichenables more profit shifting resulting from a lower PMC for the MNE. The second benefit
is the standard raising-rival’s-cost e§ect.
However, the raising rival’s cost in our set-up is weaker owing to the dependence offirm 1’s transfer price on the foreign supplier’s price as shown in section 4.1: a lower PMC
for the MNE as a result of a higher input price leads to a more aggressive response byfirm 1, reducing firm 2’s demand for its input. This limits the foreign supplier’s incentive
to raise the input price. To see this, let γ ∗s denote the MNE’s optimal input price if there
were no dependence of PMC on its price. Then, γ ∗s > γe∗ and we can write
W RR ≡

6 CU P
7
6
7
π(ξ
(e
c), γ
e∗ ) − π(ξ CU P (ec), ec) = { π(ξ CU P (ec), γ ∗s ) − π(ξ CU P (e
c), e
c)
|
{z
}
|
{z
}
Weakened Raising Rival’s Costs E§ects

6
7− π(ξ CU P (ec), γ ∗s ) − π(ξ CU P (ec), γe∗ ) }.
|{z}Standard Raising Rival’s Costs E§ects

Weakening Factor due to Price Dependence

Taken together, if the two beneficial e§ects in (11) are larger than the loss of upstream
profit, the MNE engages in input foreclosure and commits not to supply to firm 2 even if
it is more e¢cient producer of the input. More precisely, let γ be the rival firm’s inputacquisition cost which will make the MNE indi§erent between supplying the rival firm
and not supplying, that is,Π = ΠF oreclosure (γ) = (1 − t)π(ξ CU P (γ), γ).
Then, if γe∗ > γ, the MNE decides not to supply the rival firm even though its production
cost is lower than the foreign input supplier.
We thus provide a novel mechanism through which input foreclosure can takes placeeven in the absence of raising rival’s costs. To isolate our mechanism, consider an extreme
case in which firm 1 and firm 2 are not direct competitors, which eliminates any incentives
to raise rival’s costs. We assume symmetric market for both firms and let q m (c) denotethe monopoly quantity of each firm when its cost is c and let π m (c) be the corresponding
monopoly profit in each market. When the two firms are not direct competitors, π m (c) is42

independent of the other firm’s costs and we have W RR = 0. Then, (10) becomes6
7
ΠF oreclosure − Π = (1 − t) π(ξ CU P (eγ ∗ )) − π(ξ CU P (ec) − (1 − e
t)
|
{z
}
Tax Manipulation Motives(ec − c)q m (e
c)
|
{z
}

.

Loss of Upstream Profit

As the loss of upstream profit goes to zero as ec approaches c, we have ΠF oreclosure −Π|ec=c >0. By the continuity argument, we can conclude that the MNE essentially refuses to sell its
input to the downstream rival and foreclosure takes place unless the MNE is su¢ciently
more e¢cient than the foreign supplier.
For instance, suppose demands for both final goods are given by P (q) = θ − q andc=0<ec < θ. When the MNE commits not to supply to firm 2, it can be easily verified
2 c3∗cthat γe = θ+e
and the loss of MNE’s upstream profit from foreclosure is given by e
c θ−e
2
2
whereas the tax-manipulation-motives term becomesπ(ξ CU P (eγ ∗ )) − π(ξ CU P (e
c)) =

e

t) (θ+ec)θ + (t−
1−t
2
2

e

e

∗

!2

−

e

t)e
c
θ + (t−
1−t
2

!2

,

e

t)e
c
t)e
γ
t) (θ+ec)
because ξ CU P (ec) = − (t−and ξ CU P (eγ ∗ ) = − (t−1−t= − (t−. We can easily confirm
1−t
1−t
2
F oreclosure
F oreclosurethat Π
− Π|ec=c=0 > 0 and hence Π− Π > 0 for any ec su¢ciently close toc = 0, which results in an ine¢cient outcome. The MNE’s incentive for tax manipulation
via transfer price induces the less e¢cient input supplier to supply the input to firm 2.
In addition, the exercise of market power leads to a higher consumer price in market 2,
meaning an additional welfare loss.

6

Concluding Remarks

We have analyzed MNE’s incentives to manipulate an internal transfer price to takeadvantage of tax di§erences across countries and OECD’s ALP to mitigate such incentives
under imperfect competition. We specifically focused on the case in which the downstream
production and the upstream production are, respectively, done in Home and Foreign andthe corporate tax rate is higher in Home than in Foreign. We considered the CP and the
CUP methods as two alternative implementations of the ALP.
We first analyzed the case where the home final-good market is monopolized by a single
home firm. We derived the conditions under which it establishes a foreign subsidiary forthe purpose of transfer pricing. Such tax-induced FDI could entail ine¢cient internal
43

production but benefits home consumers. The application of the CP method makes the
MNE and consumers worse o§ and social welfare may deteriorate. With the concealment
costs convex in output, dual sourcing may arise under the CP method. If dual sourcing
triggers the CUP method instead, then it is possible that the MNE and consumers get
hurt and tax revenue decreases.
With oligopolistic competition in the home final-good market, the internal transfer
price has additional strategic e§ects that further strengthen incentives to inflate the transfer price at the expense of rivals’ profits. The tax-induced FDI by the MNE has spillovere§ects that reduce tax revenue from the other home firms as well as the MNE. Furthermore, we uncovered a novel mechanism for input foreclosure when the input market is also
imperfectly competitive and the CUP method is applied. The MNE may have incentive
for input foreclosure even if is a more e¢cient input producer. The new mechanism stems
from dependence of the transfer price on the market price of a “comparable” input, whichis endogenously determined.
We have considered a specific industry in which the MNE is operating. We implicitly assumed that the overall corporate tax rate is determined by factors outside of themodel. The overall corporate tax rate thus cannot be tailored for this particular industry
and is considered exogenously given. However, in the face of MNE’s profit-shifting incentives, the home government may impose industry-specific import tari§s to eliminate suchincentives. We have explored import tari§s adopted as countermeasures against profit
shifting. In particular, the optimal tari§ in general allows some profit shifting due toconsumer-surplus considerations (see Corollary 1) even though there exists a tari§ levelthat completely o§sets any incentives for profit shifting. Our welfare analysis of the ALP
also has important policy implications. We showed that better institutional monitoring
and the ALP regulation are complementary. They need to be implemented simultaneously.
Imposing the ALP without high-quality monitoring in place can be counter-productive.
Finally, we have analyzed FDI decision of only one firm in isolation in the oligopoly
case assuming that the other firms engage in outsourcing. However, each firm’s FDI
decision may also depend on the other firms’ FDI decisions. This is an area of future
research.

44

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46

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47

Appendix
Social Welfare Analysis of the ALP when the Concealment Cost is the
Expected Fine:
Welfare under the ALP is higher if the concealment cost is not a wasteful activity (asanalyzed in section 2.5), but is the expected penalty that is a pure transfer which goesfrom the MNE to the government. The expected penalty, φ(γ − c)q, can be interpreted
as the probability that the MNE is caught, φ(γ − c)/α times the fine, F = αq, for some
α > 0. Or it can be interpreted as the exogenous probability of being caught, p, times thefine φ(γ − c)q/p. In any event, the MNE, faced with the concealment cost of φ(γ − c)q
behaves exactly the same as under the ALP with the real concealment costs. In particular,
it chooses γ ∗ = c + t−k t̃ , and hence the perceived marginal cost equals ξ(γ ∗ ). But the social
planner’s perceived marginal cost is di§erent from the previous case, because the penalty
is a mere transfer from the MNE to the government. Noting that the penalty does notenter the social planner’s perceived marginal cost, we can write the social welfare in thiscase asZ∗
q(ξ(γ ))

P (q)dq − ξ N RSP (γ ∗ )q(ξ(γ ∗ )),

WP =

0

where
t̃(t − t̃).
kUnlike the welfare comparison in section 2.5, we have a clear trade-o§ in this case.
The ALP increases the MNE’s perceived marginal cost, i.e., ξ N R (γ ∗0 ) < ξ(γ ∗ ), and hence
reducing the production, while it lower’s the social planner’s perceived marginal cost, i.e.,ξ N RSP (γ ∗0 ) > ξ N RSP (γ ∗ ). Despite the fact that social welfare under the ALP in this caseis higher than that in the case of the real concealment cost, we obtain qualitatively thesame numerical result that the ALP does reduces social welfare if t is large or t̃ is small.
Although the ALP limits the MNE’s incentive to choose ine¢cient production location
for the sake of saving the corporate tax, it would induce the MNE to produce less andhence could lead to the deterioration of social welfare. This basic message regarding thewelfare impact of the ALP will also be valid in a duopoly case that we examine in thenext section.
ξ N RSP (γ ∗ ) = (1 − t)ξ N R (γ ∗ ) + tγ ∗ = c + t̃(γ ∗ − c) = c +Proof of Proposition 6:∗SP

By Lemma 3, we know b
ξ −bξ

≥ 0 for all τ m ≥ τ om . As in the proof of Proposition48

2, for all τ m ≥ τ om , we thus have
SP
dW
db
ξ
0 dq(τ m )< −P q− q(τ m )
dτ m
dτ m
dτ m
"
SP #
db
ξ
0 dq dξ= −q P+.
dξ dτ mdτ mdWA su¢cient condition for dτ< 0 to be true for all τ m ≥ τ om is ρ >m000

When φ is quadratic with φ = 0, it can be easily verified thatd### dbξSP #### dτ m #
dξ
dτ m

dτ m

=

(1 − t)
(b
γ∗)

2

"

#
#
# dbξSP #### dτ m #
dξ
dτ m

=

#
#
# dbξSP #### dτ m #
γ
b∗

< 0.

#
0
e
t
+
φ
db
γ∗
γ
b∗ +
< 0.
dτ m
φ00
|{z}
(−)

Thus, if ρ >### dbξSP #### dτ m #dξdτ m|τ m =τ om ,the su¢cient condition is satisfied for all τ m ≥ τ om .

Proof of Lemma 3:
Totally di§erentiating the two FOCs (6) and (7), we have
@ 2 π 1 (q1 , q2 ; ξ)
@ 2 π 1 (q1 , q2 ; ξ)
@ 2 π 1 (q1 , q2 ; ξ)
dq
+
dq
+
dξ = 0,1
2@q12@q1 @q2@q1 @ξ
@ 2 π 2 (q1 , q2 )@ 2 π 2 (q1 , q)dq1 +dq2 + 0 · dξ = 0.
@q1 @q2@q22
To conduct a comparative static analysis on ξ, we can rewrite the equations above as" @ 2 π (q ,q ;ξ)
1

1 2
@q12
2
@ π 2 (q1 ,q2 )@q1 @q2@ 2 π 1 (q1 ,q2 ;ξ)@q1 @q2@ 2 π 2 (q1 ,q)@q22# 4 dq 5
1

dξ
dq2
dξ

=−

"

@ 2 π 1 (q1 ,q2 ;ξ)@q1 @ξ

0
2#.

1 (q1 ,q2 ;ξ)Note that @π1 (q@ξ1 ,q2 ;ξ) = −q1 by the envelope theorem and hence @ π@q= −1. Applying
1 @ξ

49

the Cramer’s rule, we obtain

dq1
=
dξ
dq2
=
dξ
h 2

@
@ 1
@
@
@ 0

@ 2 π 1 (q1 ,q2 ;γ)@q1 @q2@ 2 π 2 (q1 ,q)
@q22

D

@
@
@
@
@

@ @ 2 π (q ,q ;γ)
@
1 1 2
@
@
1
2
@
@
@ @ 2 π2@q(q11 ,q2 )@@0 @@q1 @q2D=@ 2 π 2 (q1 ,q2 )
@q22

=−

D

< 0,

@ 2 π 2 (q1 ,q2 )@q1 @q2

D
i

> 0,

2
2
@ π 1 (q1 ,q2 ;γ) @ 2 π 2 (q1 ,q)
1 (q1 ,q2 ;γ) @ π 2 (q1 ,q2 )− @ π@q> 0. We obtain the desired result,@q1 @q2
@q12
@q22
1 @q2
2 π (q ,q )@ 2 π 2 (q1 ,q2 )2 1 2
because we have
< 0 by the second-order condition and @ @q
< 0 by the
@q22
1 @q2

where D ≡assumption of strategic substitutes.

50