DPRIETI Discussion Paper Series 21-E-036

Wake Not a Sleeping Lion:
Free Trade Agreements and Decision Rights in Multinationals

MUKUNOKI, Hiroshi
Gakushuin University

OKOSHI, Hirofumi
Okayama University

The Research Institute of Economy, Trade and Industry

https://www.rieti.go.jp/en/

RIETI Discussion Paper Series 21-E-036
April 2021

Wake Not a Sleeping Lion: Free Trade Agreements and Decision Rights in Multinationals*
Hiroshi Mukunoki
Gakushuin University
Hirofumi Okoshi
Okayama University
Abstract
Free trade agreements (FTAs) with rules of origin (ROO) affect the location of input production forvertically integrated, multinational enterprises (MNEs). FTA-induced relocation changes the
allocation of decision rights within MNEs and the purpose of transfer pricing from avoiding high taxes
to strengthening their product-market competitiveness. This study shows that an FTA with ROO may
hurt both MNEs and local firms despite tariff elimination, when the relocation occurs and the decisionrights change from centralized to decentralized. Moreover, such an FTA can hurt consumers.
Nevertheless, ROO increase the feasibility of FTAs thanks to larger tax revenues.
Keywords: Rules of origin; Free trade agreements; Transfer pricing; Input relocation
JEL classification: F15; F23; H26; L13; L23
The RIETI Discussion Paper Series aims at widely disseminating research results in the form of professional
papers, with the goal of stimulating lively discussion. The views expressed in the papers are solely those of
the author(s), and neither represent those of the organization(s) to which the author(s) belong(s) nor the
Research Institute of Economy, Trade and Industry.

This study is conducted as a part of the Project “Economic Policy Issues in the Global Economy” undertaken at the
Research Institute of Economy, Trade and Industry (RIETI). The authors are grateful for helpful comments andsuggestions by Jay Pil Choi (Michigan State University), Taiji Furusawa (University of Tokyo), Andreas Haufler(University of Munich), Keisaku Higashida (Kwansei Gakuin University), Jung Hur (Sogang University), Jota
Ishikawa (Hitotsubashi University), Yoshimasa Komoriya (Chuo University), Ngo Van Long (McGill University),
Kiyoshi Matsubara (Nihon University), Martin Richardson (Australian National University), Eiichi Tomiura(Hitotsubashi University), Akihiko Yanase (Nagoya University) and Discussion Paper seminar participants at RIETI.
*

1 Introduction
For the last few decades, a proliferation of regional trade agreements (RTAs) has played a key role inliberalizing trade among countries.1 As RTAs eliminate or reduce trade barriers, they are supposed
to lower consumer prices and raise export prices, benefiting consumers and exporters. However,the preferential nature of RTAs may make their effects more complicated than they seem because of
specific rules in implementing RTAs. Among others, setting rules of origin (ROO) is indispensable
to form a free trade agreement (FTA) to avoid exports from third countries to FTA regions througha member country with the lowest external tariff, which is known as “trade deflection.” To prevent
trade deflection, ROO require firms to prove that the exported products originated within the FTA.2
Although ROO are aimed at preventing trade deflection, Felbermayr et al. (2019) show that mosttrade deflection is not profitable even without ROO because of small differences in external tariffs
and non-negligible transportation costs. Nevertheless, ROO affect exporting firms’ strategies suchas their input procurement or location choices. For example, Conconi et al. (2018) concluded that the
ROO of the North American Free Trade Agreement (NAFTA) reduced imports from non-member
countries, which indicates that ROO cause inefficiency in input procurement.
Such a change in global procurement patterns can create another negative impact on multinational enterprises (MNEs) from the viewpoint of tax avoidance. If an MNE procures inputs from its
related company outside an FTA region, the MNE freely determines the price of intra-firm trade,which makes it possible that the related entity saves overall corporate tax payments by shifting
profits via price manipulation on the traded products. This price manipulation is called transfer
pricing and the manipulated price is called the transfer price.3 As some MNEs relocate their input
production in the same country inside the FTA region to satisfy ROO, they lose the opportunity ofsaving overall tax payments. Thus, FTA formation with ROO can prevent MNEs from tax avoidance.
The change in MNEs’ input procurement can also negatively influence local firms inside theFTA. After vertically-integrated MNEs locate their upstream affiliate inside the FTA, they can del1 As of March 2021, 343 RTAs are in force.

See http://rtais.wto.org/UI/PublicAllRTAList.aspx. Many articles
have investigated them both theoretically and empirically. See Freund and Ornelas (2010) for a review of the literature
on RTAs.
2 Unlike a custom union, member countries of an FTA independently set their external tariffs against non-member
countries. If the external tariffs are different for the same product, firms producing outside the FTA can save tariff
payments by exporting a product to the member country whose external tariff is lowest and then re-exporting it toother FTA member countries whose external tariffs are higher. For instance, Stoyanov (2012) empirically examined firms’
incentive to transship goods through FTA members. To forestall firms from tariff avoidance, member countries of FTAs
stipulate ROO.
3 Some empirical research has provided evidence of transfer pricing to save tax payments. For instance, Cristea andNguyen (2016), Davies et al. (2018), and Liu et al. (2020) provide empirical evidence of transfer price manipulation.
Blouin et al. (2018) found conflicting motives of transfer price when MNEs use it for corporate tax saving and also fortariff saving.

1

egate decision rights to their downstream affiliates and strategically use their internal prices on
inputs to make their downstream affiliates more aggressive in the product market. Existing studies
have suggested the role of internal input pricing to make the behavior of managers of downstream
affiliates aggressive and shift profits from rival firms.4 For example, Fershtman and Judd (1987)
and Sklivas (1987) showed that firm owners have incentives to give their managers decision-making
rights in the product market. It has also been reported that some MNEs conduct transfer pricing for
managerial use. For instance, Czechowicz et al. (1982) reported that 89% of U.S. MNEs manipulated
a transfer price for both tax avoidance and strategic motives. Ernst & Young (2003) also reported
that over 80% of their sample firms use a single transfer price for these two purposes. As MNEs
can use their internal prices solely for managerial purposes after they locate both an upstream anda downstream entity in the same country, the output decision becomes more aggressive. Thesechanges may hurt other local firms in the country.
Although the above argument seems realistic, no studies have considered all the above factors
simultaneously. Exploring MNEs’ location decisions, their delegation decisions, and FTA formations is an essential step for both researchers and policymakers to understand the impacts of tradeliberalization through FTAs.

1.1 Preview of the model and the results
Based on the hypothesis argued above, this study builds an international duopoly model to investigate how an MNE responds to FTA formation with ROO when it manipulates transfer pricing andhow the welfare effect of the FTA formation depends on the MNE’s response. The MNE produces
a final good within an FTA member country and exports the good to another FTA member country. The MNE’s location for input production is either in the final-good-production country or in a
low-tax country outside the FTA. The MNE can shift profits across countries by manipulating thetransfer price if it locates its input production outside the FTA countries. The MNE competes withthe local firm, which also produces the final good within the FTA and exports its product to thesame member country.
In the absence of ROO, the MNE prefers to locate its upstream and downstream affiliates indifferent countries when the tax gap is large. This is because a larger tax differential increases the
MNE’s gains from tax savings. The decision-making of the two affiliates is centralized in this casebecause a high transfer price to save tax payments discourages the downstream affiliate if the MNEchooses decentralization. In this case, the MNE (regarded as a “Lion”) is sleeping in the sense that
4 See Göx and Schiller (2006) for a survey of transfer pricing manipulation for strategic motives.

2

it is less aggressive in the product market. When the tax gap is small, however, the MNE prefers
to locate both affiliates in the same country, and the decision-making of the downstream affiliate isdecentralized for managerial purposes. Then, the upstream affiliate sets a low input price to makethe downstream affiliate more competitive in the product market.5 In this case, the MNE as theLion is waking in the sense that it is aggressive in the product market and uses its transfer price to“attack” the rival firm.
We show that the formation of an FTA can induce the relocation of the MNE’s input production
from a country outside the FTA to a country inside the FTA. A notable result is that FTA formation
with the MNE’s input relocation may hurt the local firm even though the local firm benefits fromtariff elimination as part of the FTA. This is because the loss from the strategic effect of transfer
pricing outweighs the gain from tariff elimination for the local firm. Thus, an FTA hurts the local
firm despite tariff elimination because it awakens the Lion.
In the presence of ROO, the MNE is not always qualified for tariff-free exports and chooses
between the following two options: (i) producing inputs inside an FTA to comply with the ROO andenjoying tariff elimination, or (ii) producing inputs outside an FTA and manipulating the transfer
price to save tax payments. If the MNE produces inputs in the same country where its downstream
affiliate is located, the MNE is able to comply with the ROO and exports its product without tariff,though it cannot save tax payments by transfer pricing. Instead, it delegates the output decision to its
downstream affiliate and adjusts the transfer price to shift rents in the product market. Alternatively,
if the MNE locates its upstream affiliate in a country outside the FTA, the MNE saves corporate tax
payments by setting a high transfer price with tariff. Therefore, this model exhibits the MNE’s
choice of “tariff elimination versus tax avoidance” via its input procurement strategies.
Unlike the case without ROO, FTA formation can reduce the profits of both the MNE and the
local firm, even though both of them comply with ROO and make tariff-free exports within the FTA.
This happens when the MNE relocates its upstream production to a country within the FTA. The
MNE’s (post-tax) profit decreases because it no longer saves tax payments, whereas the local firm’s
profit decreases because the strategic effect of low intra-firm input price of the MNE intensifies
market competition. This exporter-hurting FTA occurs when the tariff is low because the direct
gains from elimination of the tariff are small. An FTA with ROO hurts the awakened Lion itself in
addition to the local firm, but the MNE’s profit is still larger than the profit when it is sleeping.
We also show that an FTA with ROO can decrease total exports and hurt consumers in the
5 This is in line with Schjelderup and Sorgard (1997), who showed that, when the decisions of the headquarters andforeign affiliates are decentralized and those affiliates compete with rival firms in the product market, MNEs may use
their transfer price as a strategic tool to shift rents from rival firms.

3

importing country, even if all firms comply with ROO and make tariff-free exports. When the tax
gap is large, the MNE has an incentive to make a large amount of exports to increase the value of
intra-firm transaction and save its tax payments. After the FTA formation, if the MNE changes thelocation of input production from offshoring to inshoring to comply with ROO, it no longer makes
large exports to avoid a high tax. Although the inshoring provokes a strategic delegation of thedecision rights and has an effect of increasing exports, it decreases exports and hurts consumers if
the former effect dominates the latter. The negative trade effect of RTAs are found in some empiricalstudies. For instance, Cipollina and Salvatici (2010) conducted a meta-analysis on the coefficients of
RTA dummy variables in gravity analyses, which reported that the estimated coefficients are evennegative in 312 out of 1827 studies.
Furthermore, we also identify the condition under which ROO improve the total welfare ofcountries inside the FTA. In the absence of ROO, FTA formation can worsen the welfare of FTA
countries. This is because the MNE shifts more of its tax base to an outside FTA country, and thehost country collects a small or no tax revenue from the MNE. In this situation, ROO can transforma welfare-worsening FTA into a welfare-improving one because the host country can collect tax
revenue from the MNE if it induces input relocation. Besides that, even if ROO do not induce input
relocation, they can still improve the total welfare of the FTA countries when the MNE does notcomply with the ROO. Because tariff is not eliminated for the MNE in this case, the profit of thelocal firm increases and the countries inside the FTA can collect tariff revenues from the MNE.

1.2 Relationship to the literature
The welfare effects of FTAs with ROO have been previously analyzed by some articles, but theirfocuses are mainly on intermediate goods markets. Krishna and Krueger (1995) showed that ROO
may work as a hidden protection against the input suppliers outside the FTA. Ju and Krishna(2005) showed that ROO increase the price of FTA-made inputs and reduce the total output if
the ROO are not overly stringent such that all firms comply with them. However, ROO have theopposite effects if they are sufficiently stringent such that some firms choose not to comply withthem. In Ju and Krishna (2005), the price of the output is fixed, and they did not consider how
ROO affect consumers. Demidova and Krishna (2008) extended Ju and Krishna (2005) to include
heterogeneity in productivity among final-good producers and showed that productivity sorting
ensures a negative relationship between the stringency of ROO and the demand for FTA-madeinputs. Ishikawa et al. (2007) focused on final good markets and showed that ROO have a role4

in segmenting markets within the FTA; both inside and outside firms producing final goods may
benefit from ROO at the cost of consumers. Mukunoki (2017) showed that FTAs with ROO may
be consumer-hurting if they change the outside firms’ location decisions. Mukunoki and Okoshi(2021) investigated a firm’s manipulation of the output price for complying with ROO. None ofthese articles, however, have considered the effects of FTA formation when an MNE manipulates
its transfer price. The most closely related article is Mukunoki and Okoshi (2020), which explores
the impact of a value-added criterion of ROO on a monopolistic MNE’s transfer pricing. However,the focus of this article is different in the sense that it considers strategic interactions between firms
and explores how FTA formation affects the MNE’s delegation of decision rights to its downstream
affiliate.
Another strand of literature related to this article is the analyses on the use of transfer pricing
for managerial purposes. For instance, Elitzur and Mintz (1996) derived the optimal transfer pricewhen it is used for both saving tax payments and increasing the effort level of the local manager of aforeign affiliate. Schjelderup and Sorgard (1997) considered a decentralized MNE and calculated the
optimal transfer pricing when there is a trade-off between saving tax payments and shifting rents
from rival firms. Hyde and Choe (2005) also considered two international tax schemes and focusedon the use of two books for transfer pricing, namely an MNE setting two internal prices: one forsaving tax payments and the other for providing appropriate incentives to local managers. Some
articles considered an MNE’s decision between centralization and decentralization. For instance,
Nielsen et al. (2008) showed that an MNE chooses centralization when the tax gap between countries
is large but chooses decentralization when it is small. Dürr and Göx (2011) showed that using
one transfer price for both tax and managerial purposes, rather than two transfer prices for eachpurpose, may increase an MNE’s profit. Our article also considers the endogenous choice of an
MNE between centralization and decentralization, and the decision is linked to the formation of an
FTA with ROO and the MNE’s location choice.
This article also contributes to the literature on the link between tax avoidance and location
choice. Peralta et al. (2006) and Stöwhase (2013) considered tax competition between two (potential)
host countries. Kato and Okoshi (2019) also investigated the impact of transfer price regulation on
the location of an upstream affiliate. Our article is different from these articles in that we consider
the impact of FTA formation with ROO on the location choice of an MNE.
The rest of the article is organized as follows. Section 2 sets up a model. Section 3 derives theequilibrium without ROO and the equilibrium with ROO separately, and compares them. Section5

4 investigates the welfare effects of FTA formation. Section 5 discusses the determination of thedecision rights and the robustness of the main results by relaxing some key assumptions. Section 6summarizes and concludes the article.

2 ModelWe consider a three-country model with two firms, an MNE (firm M) and a local firm (firm L). The
model is illustrated in Figure 1. Two of the three countries are potential FTA member countries,
whereas the rest is the outside, non-member country (country O). The headquarters of the MNE islocated in country O and is owned by residents in country O. The MNE has a downstream affiliate(firm MD ) in one of the member countries to supply final goods to consumers in the FTA region.6
We assume the two downstream firms, firm MD and firm L, are located in one of the member
countries, which is referred to as the host country (country H). Country H is chosen because it
has location advantages to attract firms, such as low factor prices, a large pool of skilled workers,
and so on. The two downstream firms produce homogeneous goods and serve them to consumers
in another member country (country F). Countries H and F are potential members of an FTA. To
simplify the analysis, the baseline model does not consider the output market in country H. As isdiscussed in section 5.3, this assumption does not qualitatively change our main results.
The representative consumer’s utility in country F is given by U = a( x L + x M ) −( x L + x M )2
, where2

xi is the consumption of the final good produced by firm i (i ∈ { L, M }). By utility maximization,
the inverse demand function is given by p = a − ( x L + x M ), where p is the price of the final good.
As policy instruments, we consider both a corporate tax and an import tariff. The governments
in countries O and H respectively impose t and T as a corporate tax on reported profits.7,8 Hereafter,
we focus on the case of T ≥ t, with which our main findings are obtained.9
In addition, country F imposes a specific tariff, τ, on imports of the final good. An FTA between
countries H and F eliminates this tariff. In order to focus on the impact of FTA formation on competition in the final-goods market, tariffs on inputs are assumed away. We focus on the case where
6 This type of foreign direct investment (FDI) is known as export-platform FDI, by which FDI firms export theirproducts from the host country to other countries. For example, see Tekin-Koru and Waldkirch (2010) for evidence from
Mexico of an increasing role of export-platform FDI. Tintelnot (2017) also shows that the share of U.S. MNEs’ outputs
exported to countries outside the host country increases. For instance, the share in Belgium was 63% in 2004, which was
the third highest share.
7 Note that we use the terms “tax rate” and “tax revenue” to represent the corporate tax rate and corporate tax
revenue, respectively. The tax rate and tax revenue are distinguished from tariff rate and tariff revenue.
8 In this model, we postulate that both governments in countries O and H adopt a territorial tax system rather thana worldwide one. After the U.S. moved from a worldwide tax system to a territorial tax system, most OECD countries
have adopted a territorial tax system.
9 This situation is consistent with real-world observations. For instance, Mexico and Belgium have higher corporate
taxes than other countries, and these countries are major host countries of export-platform FDIs. See also footnote 6.

6

Figure 1: Model
both firms always supply their products in country F.10 In the presence of ROO, the downstream
firms need to meet the ROO to be eligible for the non-application of τ. We assume that the inputs
imported from country O cannot satisfy any criteria of ROO.11 Therefore, the only way to meet the
ROO is to produce inputs in the FTA countries or procure inputs from the local markets in thesecountries.12
The downstream firms use the same production technology, where one unit of inputs is transformed into one unit of final products. Other production costs are constant and normalized tozero.13 Firm L is always eligible for the FTA tariff because it always procures inputs with the input
price w from the perfectly competitive input market in country H.
Meanwhile, firm M produces inputs by itself that are to be used for the production of firm
MD . It establishes an upstream affiliate (firm MU ), either in country H or O. Firm MU produces
inputs more efficiently in country O than in H because country O has location advantage of input
production. Specifically, if firm MU produces inputs in country H, its marginal cost is given by w.
If inputs are produced in country O, firm MU ’s marginal cost is given by w − ∆. This implies thatlocating firm MU in country O gives firm M not only a cost advantage over local input suppliers but
10 The detailed conditions will be shown in Section 3.
11 For instance, the ROO of the US-Mexico-Canada Agreement (USMCA) requires exporters of automobiles to produce

some core inputs, such as engines and shafts, inside USMCA.
12 If a value-added criterion of ROO is employed, the multinational firm has an option to adjust the transfer price tomeet the ROO without changing the location of its input procurement. This possibility is analyzed in another article ofours, Mukunoki and Okoshi (2020).
13 We assume that only the MNE has an option to procure inputs from country O, even though both firms share thesame production technology. Empirical evidence, such as Tomiura (2007), suggests that some firms engage in global
production such as outsourcing and FDI whereas the others do not, even if they have similar productivity.

7

No FTAFTA w/o ROO
FTA w/ ROO

SchemeInshoring
Offshoring
Inshoring
Offshoring
Inshoring
Offshoring

λsM
1
1
0
0
0
1

λL
1
1
0
0
0
0

Variable v“∗” (vs∗ )“ b ” (bvs )“ e ” (evs )Table 1: Schemes considered in the model
also a tax saving opportunity. In this case, firm MU exports the produced inputs to its downstream
affiliate by charging an intra-firm transfer price denoted by rO . However, firm M cannot meet therequirement of ROO, and it does not enjoy tariff-free access to the market even after the formationof an FTA.14 We call this case scheme O (Offshoring).
To utilize the FTA tariff, firm M must comply with ROO by procuring inputs in the host country.
We call this case scheme I (Inshoring). Let λsM denote a state variable that takes zero if firm M
is qualified for zero tariff and takes unity otherwise. The same rule is applied to λ L for firm
L. To distinguish the equilibrium variables in the three regimes, we use asterisk “∗” for pre-FTA
equilibrium, hat “ b ” for the post-FTA equilibrium without ROO, and tilde “ e ” as a circumflex forthe post-FTA equilibrium with ROO. These are summarized in table 1.
The MNE chooses its organization structure, and it depends on the location of the upstream
affiliate. When the decision making is decentralized, firm MD becomes more aggressive in the
product market if the input cost, that is, the level of the transfer price, is lower. This implies that the
MNE can shift rents from the local firm by lowering the transfer price, r I . This strategic motive oftransfer pricing is the reason why the MNE always chooses decentralization when the two affiliates
are located in the same country. In this case, firm MD sets the quantity to maximize its own profits,
although the objective of the upstream affiliate is to maximize the total profits.
Alternatively, when the locations of the two affiliates are separate, the MNE may prefer centralized decisions to the decentralized decisions under T ≥ t because of the tax-avoidance motive oftransfer pricing. To avoid the high tax of the host country, the MNE sets a transfer price that ishigher than the marginal cost of input production. The MNE chooses centralization in most cases,
so as not to discourage the downstream firm’s decision in quantity setting.15 Since our main results are obtained when an FTA formation changes the MNE’s allocation of decision rights from
14 Some empirical evidence shows that not all firms can use FTA tariffs because of the existence of ROO, whichmeans the impacts of FTA formation are heterogeneous across firms. See, for example, Takahashi and Urata (2010) andHayakawa et al. (2013).
15 Nielsen et al. (2008) demonstrates that centralization is more profitable than decentralization when T ≥ t and thetax gap is large. When the tax gap is small, decentralization realizes higher profits for the MNE.

8

centralization to decentralization, hereafter we focus on the case where the MNE chooses centralization when it locates the upstream affiliate in country O. In Section 5.1, we discuss how the MNE
decides the allocation of the decision rights. Thus, the MNE faces a trade-off in the location of
its input production: the MNE is able to use the transfer price to save tax payments in producing
inputs in country O, whereas it can use the transfer price to take advantage of a strategic effect ofdecentralization in producing them in country H.
We solve the following three-stage game. In the first stage, the headquarters of the MNE decides
the location of firm MU . In the second stage, the headquarters determines the optimal input price.
In the third stage, the MNE and firm L compete à la Cournot in country F.

3 The equilibrium
This section derives the equilibrium outcomes in each scheme and investigates how the MNEchooses the location of its input production.

3.1 Market equilibrium
Let us first derive the market equilibrium determined in the last stage. The unit cost of the local
firm, firm L, in producing a final good and exporting it to country F is given by c L = w + λ L τ.
Then, firm L maximizes the following (pre-tax) profit,
πL = ( p − cL )xL .

(1)

As described in the previous section, there are two schemes for the MNE’s input sourcing: (i) an
offshoring scheme in which the MNE produces inputs in country O and (ii) an inshoring scheme inwhich the MNE produces inputs in country H. Below, we subsequently derive the equilibrium ineach scheme.

Offshoring scheme

When the MNE locates its input production in country O, the MNE centralizes

its decision-making and determines the amount of supply to maximize the following global post-tax
profit:OOOOΠO
M = (1 − t )(r − ( w − ∆ )) x M + (1 − T )( p − r − λ M τ ) x M= (1 − T )( p − cOM ) xO
M,

(2)

9

wherecO
M =(1 − t)(w − ∆) + (1 − T )λOM τ − ( T − t)rO
1−T

(3)

is the perceived marginal cost. The centralized MNE’s decision in the product market is based on theperceived marginal cost, which is different from the sum of the input production cost and trade
16 In this cross-border production, the MNE’s unit cost is adjusted by the tax
cost, w − ∆ + λO
M τ.

differential. As a marginal increase in the transfer price, rO , saves per-unit tax payments as muchas ( T − t) > 0, it reduces the effective marginal cost of firm MD in the production of the final good.
This is because the per-unit, post-tax profit is larger with tax avoidance, and it gives the MNE an
incentive to increase the quantity of sales. Therefore, the “perceived marginal cost” becomes lower,
and the MNE supplies more as rO becomes higher. Note that the perceived marginal cost underO
an offshoring scheme cO
M is equivalent to w − ∆ + λ M τ only if T = t holds and is decreasing in

T and increasing in t. This means that the perceived marginal cost is less than the true marginalO
cost, cO
M ≤ w − ∆ + λ M τ, when T > t holds. In other words, transfer pricing makes the MNE moreaggressive in the product market under an offshoring scheme.

Inshoring scheme

When the MNE locates its input production in country H, the MNE’s decision-

making is decentralized. Thus, how much to produce of the final good is delegated to the managerof the downstream affiliate (i.e., firm MD ), who only takes into account the profit of firm D, which
is given byI
π D = { p − (r I + λ Mτ )} x M .
{z
}
|

(4)

I
cM

I as the perceived marginal cost under the inshoring
For expositional convenience, we denote c M
I , whereas the true marginal cost of the MNE is w + λ τ.
scheme. Firm MD ’s decision is based on c M
M

By maximizing (1), (2), and (4) with respect to each firm’s quantity, we have the equilibrium
outputs of the firms as:
x sM =

a − 2csM + c L
,
3

and

x sL =

a − 2c L + csM,3s ∈ {O, I }.

(5)

3.2 Manipulation of the transfer price
Next, we consider how the MNE sets the transfer price in the second stage. As described above,
depending on the MNE’s location choices in input production, there are two motives for which the
16 The terminology “perceived marginal cost” is often used in the analysis of a vertically-related industry in the context
of industrial organization. See Choi et al. (2020) for an application of this terminology in tax avoidance literature.

10

MNE manipulates the transfer price. We derive the optimal transfer prices separately in these cases.

Offshoring scheme

O
Given (2) and (5), the first derivative of ΠO
M with respect to r is always

positive. Therefore, the optimal transfer price is set as high as possible. This means that p − rO −17 We haveλO
M τ = 0 holds.

rO = w − ∆ +(1 − T ){ a − w + 2∆ − (2λOM − λ L )τ }.
1 − t + 2(1 − T )
|
{z
}

(6)

Tax avoidance motive

By substituting (6) into (3), the perceived marginal cost that reflects the equilibrium transfer pricebecomescO
M = w − ∆ + λM τ −( T − t) { a − w + 2∆ − (2λOM − λ L )τ },1 − t + 2(1 − T )(7)which is decreasing in T. The corresponding equilibrium output and profits, respectively, becomexO
M =(1 − t)( a − w + 2∆ − (2λOM − λ L )τ )O 2
and ΠOM = (1 − T )( x M ) .
1 − t + 2(1 − T )(8)

a−w+2∆I. The
xO
M is the smallest when λ M = 1 and λ L = 0, and it is positive if and only if τ <2equilibrium output and profits of the local firm, respectively, becomexO
L =(1 − T )( a − w − λ L τ ) − (1 − t){∆ + (λ L − λOM )}τ
O 2and ΠO
L = (1 − T )( x L ) .
1 − t + 2(1 − T )(9)I
In the offshoring scheme, xO
L is smaller in the pre-FTA equilibrium (λ M = λ L = 1). It is positive if()
and only if τ < a − w − 11−−Tt ∆.

The optimal transfer price is higher than the marginal cost of producing inputs. The transfer
price is set to shift profits from a high-tax country H to a low-tax country O. The second term of(6) represents a tax-avoidance motive, whose sign is always positive. Moreover, (8) indicates that the
MNE’s output expands as the corporate tax in country H, T, is higher. This is because the perceived
marginal cost is decreasing in T. As the induced increase in the output lowers the equilibrium priceof the final good, p, the transfer price that realizes zero profits of firm MD also becomes lower.
Inshoring scheme

Given (5), the overall profit of the MNE is[IΠM= (1 − T )({r − w + p − (r
I

I

I
+ λM
τ )}

I − λ )τa + w − 2r I − (2λ M
L
3

)]
.

(10)

17 We assume away an additional cost for manipulating the transfer price. We relax this assumption by introducing a
concealment cost in section 5.4.

11

By differentiating (10) with respect to r I , the optimal transfer price becomesrI = w −|I − λ )τa − w − (2λ M
L
.
4
{z
}

(11)

Strategic motive

The corresponding equilibrium output and profits of the MNE are given byIxM=

I − λ )τa − w − (2λ M(1 − T ) I 2
LI, and Π M=
(x M ) .
2
2(12)

The equilibrium output and profits of the local firm are given by
x LI =I )τ
a − w − (3λ L − 2λ M
, and Π LI = (1 − T )( x LI )2 .
4

(13)

I = λ = 1 or λ I = λ = 0 in the inshoring scheme, and the equilibrium outputs
We have either λ M
LLM
I and x I are positive if and only if τ < a − w holds.
are smaller in the former case. Therefore, x M
LIn the inshoring scheme, the production and export decisions in the final-goods market aredelegated to firm MD . Then, the MNE uses the transfer price to make firm MD behave moreaggressively in the product market by setting a low transfer price. In other words, lowering thetransfer price works as a “strategic intra-firm subsidy” and shifts rents from firm L to firm M. Thisis captured by the second term in (11), which is always negative. Unlike the offshoring scheme, theoptimal transfer price under inshoring is independent of T.

3.3 Location choice of the input production
In the first stage, the MNE chooses between country O or H for the location of firm MU . We focus() ][on the situation where τ < min a−w2+2∆ , a − w − 11−−Tt ∆ holds, such that exports of both firms(1− t ) ∆are positive. Rearranging this inequality, we have the maximum level of T, T max ≡ 1 − a−w−τ (< 1),
below which the equilibrium exports of both firms are positive given τ < a−w2+2∆ .
By comparing the profits between the two schemes, we have
3−tIΠO
− (1 − t )M ≥ Π M ⇐⇒ T ≥2(

a − w + 2∆ − (2λO
M − λ L )τI
a − w − (2λ M − λ L )τ

)

√

2,

(14)

The MNE chooses the offshoring scheme and shifts profits for the tax-avoidance motive when thecorporate tax in country H is sufficiently high. Otherwise, it chooses the inshoring scheme andenjoys the strategic effect of transfer pricing. Specifically, the MNE prefers the offshoring scheme

12Figure 2: The MNE’s input production√(1−t)( a−w+2∆−τ ) 2
3− t∗
to the inshoring scheme if and only if T > T ≡ 2 −holds before formationa−w−τ√b ≡ 3−t − (1−t)(a−w+2∆) 2 holds after formation of an FTA without ROO, andof an FTA, T > T
2
a−w
√
(
1
−
t
){
a
−
w
+
2
(
∆
−
τ
)}
2
3
−
t
e ≡
holds after formation of an FTA with ROO. We can easily confirm
T
2 −
a−w

b<T
e hold.
that T ∗ < T
The elimination of the tariff increases the equilibrium sales of the MNE, magnifying the strategicb holds, however, the tax-avoidance motive still dominates the
motive of transfer pricing. If T > T
strategic motive even after FTA formation. Thus, by formation of an FTA without ROO, the MNE
that initially chooses the offshoring scheme (T ∗ < T) changes its scheme to the inshoring scheme ifb holds.
T∗ < T < T
The result also indicates that FTA formation causes efficiency loss, similar to the conventional,
trade-diversion effect. The trade-diversion effect is caused by the substitution of imports from lessefficient member countries for those from more efficient non-member countries. In our model, input
production is relocated from a more efficient country whose production cost of the input is w − ∆to a less inefficient country whose production cost is w.
In the absence of ROO, the location of input production is unrelated to tariff elimination. In thepresence of ROO, however, the MNE complies with the ROO, and the tariff on the final good is
eliminated only if the MNE locates input production within FTA countries. Thus, firm M faces a
trade-off between tax avoidance and tariff elimination. Because the MNE needs to incur tariff under13

b < T.
e This implies
scheme O, the threshold of T is larger than that of the case without ROO, T
that ROO expand the range of T such that input relocation occurs. Moreover, as a higher tariffediscourages the MNE to choose scheme O, ∂∂τT > 0 holds.
The equilibrium choice of the MNE is depicted in Figure 2. We summarize the equilibriumoutcomes in the following proposition.
Proposition 1. FTA formation induces the MNE to relocate its input production from an outside country tob holds in the absence of ROO and if T ∗ < T < Te holds in the presence
an inside FTA country if T ∗ < T < T
b<Te holds. In the presence of ROO, the MNE produces inputs in an outside country andof ROO, where T
e ≤ T holds.
does not comply with ROO if T
The following two points are notable. First, input relocation induced by FTA formation is consistent with empirical results. For instance, Hanson et al. (2005) empirically showed a substantial
increase in inward investments to Mexico and Canada after the formation of NAFTA. The increasein FDI to these countries might be caused by input relocation of MNEs, which leads to the magnified strategic effect of transfer pricing. Furthermore, as Conconi et al. (2018) showed, ROO lower
the likelihood of input procurement from outside FTA countries. This corresponds to the case withb ≤ T ≤ T.
e As the MNE’s input production remains in country O in this range of T if ROO areTabsent, they may have a role to prevent the MNE’s tax avoidance.
Second, as Takahashi and Urata (2010) and Hayakawa et al. (2013) empirically pointed out, somefirms may not utilize FTA tariffs because of the burden of ROO, which corresponds to the case withe ≤ T. Although traditional interpretation attributes non-compliance to the costs of meeting ROO
Tsuch as documentation costs and adjustment costs in input procurement, our model indicates thatthe loss of tax avoidance opportunities can be another reason why firms choose non-compliancewith ROO.

4 The welfare effects of FTA formation
In this section, we subsequently explore the effects of FTA formation on the MNE, the local firm,
consumers, and the total welfare of the FTA countries.

4.1 The effect on the MNE
In the absence of ROO, FTA formation always benefits the MNE. It is obvious that an FTA favors
the MNE when it does not change the MNE’s procurement strategy because only the gains from14

tariff elimination exist. When the MNE relocates its input production, it loses an opportunity tosave tax payments. Nevertheless, the gains from the magnified strategic effect exceed the loss of thetax saving opportunity in the absence of ROO.
In the presence of ROO, FTA formation can hurt the MNE. There are three cases, dependingon the level of T. First, when the MNE chooses the inshoring scheme both before and after theformation of an FTA (i.e., T < T ∗ ), the FTA always benefits the MNE because the MNE does notengage in tax avoidance and only the gains from tariff elimination exist. Second, when the MNE
e < T holds),
chooses the offshoring scheme both before and after the formation of an FTA (i.e., T
the FTA formation necessarily reduces the profits of the MNE because the MNE incurs the tariff
whereas firm L takes advantage of tariff elimination.
Third, when FTA formation induces the MNE to shift from the offshoring scheme to the ine it can either benefit or hurt the MNE. FTA formation with ROO
shoring scheme (i.e., T ∗ < T < T),decreases the MNE’s profits if the tax difference is large enough. Specifically, there exists a uniquee I = ΠO∗ holds, which is given by
threshold of T, TM , such that ΠMM√
3 − t (1 − t)( a − w + 2∆ − τ ) 2
−
.
TM ≡
2
( a − w)

(15)b < TM < Te always holds, implying that only FTA formation with ROO can hurt theNote that T
MNE.18 As the corporate tax rate in country H gets higher, the loss from the missed opportunity of
tax avoidance gets larger. Therefore, FTA formation with ROO hurts the MNE if T > TM holds andbenefits the MNE otherwise. The following lemma summarizes the effects of FTA formation on the
MNE’s profits (see Appendix A.1 for the proof).
Lemma 1. FTA formation without ROO always benefits the MNE. FTA formation with ROO hurts the
MNE if the post-FTA MNE’s choice is (i) not complying with ROO by choosing the offshoring scheme or (ii)complying with ROO by choosing the inshoring scheme and T > TM holds. Otherwise, it benefits the MNE.
It is noteworthy that the MNE becomes worse off by FTA formation even if it complies with
ROO and the tariff imposed on the MNE’s product is eliminated. Nevertheless, the MNE prefers
to comply with ROO because the tariff is also eliminated for the local firm, which is its rival in
the product market. If the MNE chooses the offshoring scheme and does not comply with ROO
in this situation, the MNE’s profits further reduce. Therefore, the elimination of tariff on the rival
firm forces the MNE to give up using transfer pricing for tax purposes, and the negative effect frompaying more corporate taxes outweighs the positive effect from tariff elimination.
18 Because T
b < TM holds, FTA formation without ROO never hurts the MNE even if the FTA induces input relocation.

15

4.2 The effect on the local firmbWhen an FTA without ROO does not affect the MNE’s procurement strategy (i.e., T ≤ T ∗ or T ≥ T),b
it benefits the local firm. When it changes the MNE’s location of input production (i.e., T ∗ < T < T),however, firm L can be negatively influenced by the FTA. This is because input relocation makes the
MNE more aggressive in the product market.
The equilibrium profit of firm L is increasing in its equilibrium output. By comparing the post∗
FTA output (bx LI ) with the pre-FTA output (xOL ) of firm L, we have∗xbLI ≤ xO⇐⇒ T ≤ TL ≡ 1 −
L(1 − t)( a − w + 4∆).
2( a − w − 2τ )(16)

L
We can easily confirm that ∂T∂τ < 0 holds. As the tariff becomes lower, the positive effect from thetariff elimination becomes lower, and FTA formation that induces input relocation is more likely tob < TL holds without ROO and T
e < TL holds
hurt firm L. If the tariff is sufficiently small such that Twith ROO, an FTA that induces input relocation always hurts firm L because the negative effectfrom the intensified competition dominates the positive effect from the tariff elimination. On theother extreme, if the tariff is high enough such that TL ≤ T ∗ holds, an FTA always benefits firm L
irrespective of the MNE’s input relocation.
In the intermediate tariff level, it depends on the level of T whether an FTA inducing input
b holds in the absence of ROO andrelocation benefits or hurts the local firm. If T ∗ < TL ≤ T
e holds in the presence of ROO, an FTA hurts the local firm if T ∗ < T < TL holds.19
T ∗ < TL ≤ T
Otherwise, it benefits the local firm. The following lemma summarizes the effects of FTA formationon the local firm (see Appendix A.2 for the proof).
b TL ] holds without ROO and if T ∗ <Lemma 2. FTA formation hurts the local firm if T ∗ < T < min[ T,e TL ] holds with ROO. Otherwise, it benefits the local firm.
T < min[ T,It is counterintuitive that ROO may hurt the local firm because they only restrict the MNE’s actions. It contrasts with previous arguments, such as those of Krishna and Krueger (1995), who statethat ROO work as a “hidden protection” policy for both the domestic upstream and downstream
industries. In our model, although ROO induce the MNE to procure inputs inside an FTA country
where the production cost of inputs is higher, they also provoke the MNE to delegate its decisionright of final good production to the downstream affiliate. Then, the MNE uses its transfer price as acommitment device to make the downstream MNE more aggressive in the product market. In other19 We can derive the two cutoff levels of the tariff, τb holds for τbL ≤ τ < τ ∗ . Similarly,bL and τL∗ , such that T ∗ < TL ≤ T∗∗
e holds for τeL ≤ τ < τ .
we can derive τeL such that T < TL ≤ T

16words, our model indicates that ROO magnify the pro-competitive effect of an FTA by changing the
MNE’s allocation of the decision rights from centralization to decentralization. Note also that the
tax difference is a key to this result. If the tax difference is small, the MNE chooses the inshoring in
the pre-FTA equilibrium and the change from centralization to decentralization does not occur.
Another intriguing result is that FTA formation with ROO may hurt the MNE and firm L at thesame time, even though both comply with ROO and qualify for zero-tariff exports. As explained,
an FTA with ROO hurts the MNE if T > TM holds, whereas it hurts the local firm if T ∗ < T <b] holds. Thus, an FTA with ROO hurts both firms at the same time if TM < T < min[ TL , Tb]min[ TL , T
holds. Because an increase in τ increases TM and decreases TL , we have TM < TL for a sufficiently
low level of the initial tariff. Specifically, by (15) and (16), we have
TL > TM ⇐⇒ τ <

(2 −

√

2)( a − w)
.
4

(17)

Figure 3 illustrates the effects of FTA formation with ROO on the firms’ post-tax profits whenτ <√(2− 2)( a−w)
holds.
4

The red curves represent the equilibrium profits of the MNE whereas theblack curves represent those of the local firm. The solid curves depict the post-FTA profits whereas
the dashed curves depict the pre-FTA profits. We can confirm that an FTA with ROO hurts both
firms when TM < T < TL holds.
Proposition 2. FTA formation with ROO hurts both the MNE and the local firm if τ <√( a − w ) (2− 2 )and4TM < T < TL hold.
This result is novel because existing studies on FTAs suggest that FTA formation benefits at least
some exporting firms producing within the FTA. If we take into account the MNE’s location choice
and its manipulation of the transfer price, then FTA formation with ROO decreases the post-tax
profits of all exporting firms, even though they comply with ROO and all tariffs are eliminated.

4.3 The effect on consumers
Here, we investigate the effect on consumers in the country where the final good is imported andconsumed (country F). Because input relocation increases the MNE’s production cost of the final
good, it is not obvious whether FTA formation increases the total amount of exports to country F.
We can confirm, however, that FTA formation without ROO always benefits consumers because thepositive effect from the tariff elimination dominates the negative effect from the inefficiency in input
production.

17

Figure 3: The effects of FTA formation with ROO on the firms’ profits
Concerning FTA formation with ROO, the outcomes in the post-FTA equilibrium are the sameb holds. Therefore, consumers gain from FTA formation in thisas those without ROO when T ≤ T
b < T < T,e it is ambiguous whether ROO increase or decrease the exports of therange of T. For T
MNE. On the one hand, input relocation induced by ROO increases the MNE’s marginal cost andhas a negative impact on the volume of exports of the MNE. On the other hand, input relocationis accompanied by the MNE’s decentralization decision, which makes the MNE more aggressive inthe product market and has a positive impact on the volume of its exports. Note that the perceived
marginal cost of the MNE is lower and the outputs of the MNE in the pre-FTA equilibrium arelarger as the corporate tax in country H is higher. Larger total exports in the pre-FTA equilibrium
implies that consumer surplus is higher, which increases the likelihood of a consumer-hurting FTA
eCS , such that FTA formation with ROO
formation. Thus, we can derive a threshold denoted by TeCS holds. If the initial tariff is sufficiently low, we have Te<TeCSdecreases total exports when T > T
b Te). We can derive the threshold of theand FTA formation benefits consumers for all T in T ∈ ( T,e<TeCS holds if τ < τeCS . Otherwise, T
e>T
eCS holds, and FTA formation
initial tariff, τeCS , such that T
eCS < T < Te holds.
with ROO reduces total exports and hurts consumers when Te ≤ T, the MNE produces inputs in country O both before and after the formation of an
For T
18

FTA with ROO. In this case, the MNE does not comply with ROO, and the tariff is applied only to
the MNE. Although a part of the MNE’s exports are replaced by exports of the local firm that is lessefficient in output production, total exports always increase and the FTA benefits consumers. The
following proposition summarizes the results (see Appendix A.3 for the proof).
Proposition 3. FTA formation without ROO always benefits consumers in a foreign country. An FTA witheCS < T < Te hold. Otherwise, an FTA with ROO benefits consumers.
ROO hurts consumers if τ ≥ τeCS and T
Note that consumers may lose from FTA formation, even though all the exporters are eligible fortariff-free exports. The result is surprising because this happens when the initial tariff is large andthe gains from tariff elimination are large. Owing to ROO, a larger tariff induces the MNE’s input
relocation. Input relocation increases the production cost of the MNE, because input productionis less efficient in country H and the perceived marginal cost of the MNE in the pre-FTA situationeCS < T < T.
e Therefore,
is relatively large when the tax gap is in the middle range satisfying T
the negative effect of the increase in the marginal cost outweighs the positive effect from the tariffelimination in this case.20

4.4 The effect on the welfare of inside countries
We have shown that FTA formation may hurt exporters and consumers. FTA formation also changes
both tariff revenues and tax revenues of member countries. Thus, we next explore whether theseeffects are consistent with countries’ incentives to form an FTA.
We exclude the MNE’s profits from welfare in country H because the MNE is owned by residents
in country O. We denote the MNE’s taxable profits in country H in scheme s (s ∈ { I, O}) as

π sM =( pO − rO − λO τ ) xO = 0,
M

M

I
2


I τ ) x I = { a−w−(2λ M −λ L )τ } .
( p I − w − λ M
M

(18)

8

Then, the equilibrium welfare of country H and that of country F in scheme s is respectively givenbysWH≡ π Ls + Tπ sM

where CSsF ≡( xsL +xsM )2

2

and WFs ≡ CSsF + TRsF ,(19)

is the consumer surplus in country F and TRsF ≡ τ (λ L x sL + λsM x sM ) is thetariff revenue in country F. We suppose that member countries are able to arrange transfers of
20 We can confirm that an FTA with ROO never hurts consumers and all exporters at the same time. It hurts consumers

when τ is sufficiently large but hurts exporters when τ is sufficiently small and these ranges of τ do not overlap. Thus,
our model predicts that an FTA with ROO is more likely to hurt exporters as the initial tariff becomes lower and hurt
consumers as it becomes higher.

19welfare with the FTA formation, which can be done by making mutual concessions in other sectors,
for instance. This means that formation of an FTA is feasible if it improves the total welfare of thesmember countries, which is given by WFTA
≡ WHs + WFs .

We found that FTA formation without ROO can worsen the total welfare of the member countries. When T < T ∗ holds, the MNE produces inputs in country H, regardless of FTA formation.
In this case, although FTA formation increases the consumer surplus and the profit of the local
firm, the loss of tariff revenues exceeds these benefits if τ <2( a − w )holds.
13

This is because, underimperfect competition, a tariff has a strategic role to shift profits from the foreign firm to the welfareof the importing country as tariff revenue. The strategic effect tends to be relatively larger as thetariff becomes smaller. As the MNE pays a corporate tax in country H, the net negative effect on
I when T is large. Thus, under T < T ∗ ,π LI + CSFI + TR FI is covered by increases in tax payments, Tπ M

FTA formation without ROO decreases the total welfare of the member countries if τ <2( a − w )and
132( a−w)−13τ

I hold, where T I ≡I can be higher or
T < TWis the threshold level of T. Note that TWW
4{2( a−w)−τ }lower than T ∗ . If τ <2( a − w )I hold, FTA formation without ROO always worsens theand T ∗ ≤ TW
13

welfare of the FTA countries.
b < T holds and the MNE
Another possible effect of a welfare-reducing FTA occurs when T
produces inputs in country O, both before and after FTA formation. In this case, the MNE always
shifts all the taxable profits in country H to country O, and a higher T increases the profits of the
MNE due to a decrease in the perceived marginal cost. The resulting increase in the MNE’s sales is
e With a sufficiently large
more likely to reduce the total welfare inside the FTA as T approaches T.
T, however, the negative effect can be covered by a large increase in total exports because a partof the output supplies is shifted from the less productive local firm to the more productive MNE.
√
2( a−w)2 +10( a−w)∆+11∆2
holds such that consumer gains from tariff
Given that τ < ( a − w) + 2∆ −3Oelimination are not large, we can derive the two thresholds, TO
W and T W , such that FTA formation
O

without ROO decreases the total welfare of the member countries if TO
W < T < T W holds. We canbb < T W always holds, but it is ambiguous whether TO is higher or lower than T.
confirm that TWOb holds, FTA formation induces the input relocation of the MNE. It seems that
When T ∗ < T < T
FTA formation can be welfare-reducing because of the loss of tariff revenue and possible loss of thelocal firm. In the absence of ROO, however, we confirm that an FTA with input relocation improves
the total welfare because country H collects tax revenue from the MNE, and this positive revenue
effect outweighs possible negative effects. The following proposition summarizes the welfare effectfor FTA countries in the absence of ROO (see Appendix A.4 for the proof).

20

Proposition 4. In the absence of ROO, FTA formation worsens the total welfare of member countries when√2( a − w )2( a−w)2 +10( a−w)∆+11∆2I∗(i) τ <and T < min[ TW , T ] hold or (ii) τ < ( a − w) + 2∆ −
and
13
3
b
max[ TO
W , T ] < T < T W hold. Otherwise, an FTA improves the total welfare.
O

This result points out a new negative aspect of transfer pricing from the viewpoint of tradeliberalization. Due to tax avoidance, the MNE’s output decision becomes more aggressive, and its
market share of the export market is larger than the market equilibrium without transfer pricing.
However, increased operating profits due to the increased market share are not taxed inside theFTA. Therefore, transfer pricing makes FTA formation more likely to be welfare-reducing, which
implies that the FTA formation is infeasible.
ROO neither change the equilibrium outcome nor the welfare property of FTA formation whenb holds, but ROO change them when T
b < T holds. There are two sub-cases with T
b < T.
T ≤ T
e < T holds, the MNE’s input production takes place in country O irrespective of FTA
First, when T
formation, but an initial tariff is still applied to the MNE because the MNE does not comply with
ROO. In this case, country H cannot collect tax revenue from the MNE either before or after the FTA
formation. However, country F can collect tariff revenue from the MNE. Furthermore, because only
the MNE incurs the tariff after the FTA formation, the local firm earns more profits with the FTA,
which contributes to increasing the welfare of the member countries. Therefore, the MNE is treatedas if it produces the final good outside the FTA, and the rent-shifting effect makes FTA formation
welfare-improving for the member countries.
b<T<Te holds, an FTA induces the MNE to relocate its input production, andSecond, when T
the members of the FTA can collect tax revenue from the MNE. The tax revenue can cover the lossof consumer surplus owing to the reduced output of the MNE. Although the welfare effect of FTA
formation itself is ambiguous in this region of T, we can show that ROO make an infeasible FTA
without ROO a feasible one, if the MNE’s cost advantage of input production in country O is small√(7 2−8)( a−w).
32

enough to satisfy ∆ <This result is summarized as the following proposition (seeAppendix A.5 for the proof).
Proposition 5. If ∆ <√O(7 2−8)( a−w)
and TOW < T < T W hold, ROO transform an infeasible FTA into a
32

feasible one.
O

When TOW < T < T W holds, an FTA without ROO is infeasible because it reduces the total welfareof the member countries. With ROO, however, FTA formation either prevents tariff elimination to
the MNE owned by a non-member country or generates tax revenue by inducing input relocationof the MNE. These effects enhance the positive welfare effects of the FTA on the member countries,
21

Figure 4: The effect of FTA formation on the welfare of FTA countries
and the FTA becomes feasible if the relative production efficiency of the MNE, ∆, is small enough.
Figure 4 provides a numerical example that illustrates the welfare impacts of an FTA with andwithout ROO.21 The dotted curve depicts the change in total welfare without ROO whereas theb < T ≤ T,e the MNE relocates input production
solid curves represent the ones with ROO. For T
e < T, the MNE produces inputs outside the FTA
with ROO whereas it does not without ROO. For T
and it gives up utilizing an FTA tariff with ROO although the MNE is eligible for tariff elimination
O

without ROO. We can see that, for TO
W < T < T W , the welfare of FTA formation is positive for the
FTA countries with ROO whereas it is negative without ROO.

5 Discussion
Our analysis has provided new results that have not been explored in the extant literature. In thissection, we explain how the MNE allocates its decision rights, and also argue the robustness of theseresults by relaxing some assumptions made in the benchmark model.

21 In Figure 4, the parameters are set at a = 3, w = 1, t = 0.1 , ∆ = 1/32 and τ = 1/4.

22

5.1 The allocation of decision rights
In the baseline model, we suppose that the MNE chooses the centralization of its decision rights
when it chooses the offshoring scheme, while the MNE chooses the decentralization when it chooses
the inshoring scheme. Here, we explain the reason why the MNE makes these choices.
In the inshoring scheme, the MNE cannot use the transfer price to avoid a high tax in country
H. The MNE’s overall profit under the decentralized decision-makings is always larger than that
under the centralized decision-making, because the MNE is able to manipulate the transfer pricefor the strategic motive in the former case. Therefore, the MNE always chooses the decentralization
whenever it chooses the inshoring scheme.
In the offshoring scheme, if the MNE chooses the decentralization, it can use the transfer pricefor both the tax-avoidance motive and the strategic motive. Then, the MNE strikes the balance
between the two motives and sets the transfer price as
[
r

OD

I
= w − ∆ + { a − w + 2∆ − (2λ M− λ L )τ }]3( T − t )1−.
2{3(1 − t) − 2(1 − T )} 4

(20)

The first-term of the last parenthesis reflects the tax-avoidance motive, while the second-term
reflects the strategic motive. By using (20), we can calculate the overall profit of the MNE under
the offshoring scheme with decentralization, which is denoted by ΠOD
M . If the MNE chooses thecentralization under the offshoring scheme as in the benchmark model, it manipulates the transferO
price solely for the tax-avoidance motive, and its overall profit is given by ΠO
M . By comparing Π Mwith ΠOD
M , we haveODΠOM ≥ ΠM⇐⇒ T ≥ T

OD√
5(1 + t ) − 2(1 − t ) 5
.
≡
10

(21)

The MNE chooses the centralization in the offshoring scheme unless the tax gap is small enough.
We can confirm that there are a range of parameter values under which TOD is smaller than T M ,T̃CS , and TO
W . Therefore, the main results of the baseline model, such as an exporter-hurting FTA
and a consumer-hurting FTA , remain unchanged even if we consider a possibility that the MNE
can choose the decentralization under the offshoring scheme.

5.2 The timing of setting transfer priceIn the benchmark model, we assumed that the MNE’s decision to set the input price is earlier
than that of quantity setting. The pre-commitment of the input price along with the delegation of23

decision rights to the downstream affiliate generates more profits for the MNE under the inshoring
scheme because of the strategic effect. Under the offshoring scheme, however, the MNE may earnmore profits by setting quantity first and then adjusting its transfer price to avoid a high tax.
If the timing of setting the transfer price and that of setting quantity are reversed, the posttax profit is a standard duopoly profit taxed with a corporate tax rate in country O, ΠO,NC
=
M
(
)
2
a + c L − 2 ( w − ∆ + λO
M τ)
(1 − t ). Thus, we can derive the condition under which price commitment is3
more profitable than quantity commitment for the MNE:
O,NC
ΠO
≥ 0 ⇐⇒ T ≤M − ΠM

3−t
.
4

(22)

Hence, as long as the tax rate in the high-tax country, T, is sufficiently low, the MNE chooses
the timing of the game in the benchmark model, even if the timing of moves is endogenously
determined.

5.3 Home market
We assumed that the final product is consumed only in country F in the benchmark model. Here,
we discuss how the results are affected by considering the market in country H. For simplicity,
suppose that the market size of country H is the same as that of country F. We preserve the otherassumptions that the MNE establishes a single plant in either country O or H and cannot reportnegative profits in each country.
We also assume that the production process in one plant cannot be separated depending on thedestination of the products because it is highly costly for the MNE to adjust production processes
depending on the destination of the goods. Thus, it is not possible that the MNE procures local
inputs to comply with ROO and at the same time uses the inputs produced outside the FTA only
for the domestic supply of the product.
The optimal transfer price under offshoring is the one such that ( p H − r ) xO
MH + ( p F − r −OλOM τ ) x MF = 0 holds, whereas the first-order condition of profit maximization provides the opti-

mal internal price under inshoring. We put the subscript HM in the presence of the home market,
whereas no subscript corresponds to the benchmark case. We have the following rankings of the
input prices.
I
I∗
e
r HM
= er I < r HM
< r I∗,

(23)

O∗
∗
e
rO < e
rO
< rO
rO
rO ,
HM < r
HM < b
HM = b(24)

24

In the inshoring scheme, the pre-FTA level of the input price is lower with the home marketI∗(r HM< r I ∗ ). Because a tariff is incurred in supplying to country H, the strategic effect of input-

price adjustment is larger in the market of country H than that of country F. If the MNE could
discriminate its input prices across the markets, the input price set for the market of country H
would be lower with the home market. Thus, the uniform input price is lower with the homemarket. After FTA formation, the tariff is eliminated, and the market size of both countries becomesIthe same. Therefore, the input price with the home market is the same as that without it (erI = er HM).

In the offshoring scheme, the input price with the home market is the same as the benchmark
rO ). Because the effective market size is the samecase after FTA formation without ROO (brO
HM = bin the two countries, the transfer price that realizes zero profit in country H remains unchanged.
After FTA formation with ROO, the MNE faces a tariff in country F, and the effective market sizeis larger in country H. Therefore, even if the MNE’s profit from exporting to country F is zero at
r=e
rO , the overall profits of the downstream affiliate of the MNE are still positive because it earns
a positive profit from the home market in country H. Then, the MNE sets a higher transfer price(erO < erOHM ), such that a negative profit in country F is just covered by a positive profit in country∗
H. By the same reason, the MNE sets a higher transfer price before FTA formation (rO∗ < rO
HM ).

Thus, in both the inshoring and offshoring schemes, the MNE’s incentive to manipulate the input price gets stronger if we introduce home market competition. Nevertheless, the main results ofthe benchmark still hold. Because of the analytical complication, we present a numerical example toconfirm the existence of the main results. Figure 5 shows that we have the same welfare property as
the benchmark case shown in Figure 4, where the dotted curve depicts the change in total welfare
without ROO whereas the solid curves represent the ones with ROO. As in the benchmark model,O

22 Furthermore, two addiROO transform an infeasible FTA into a feasible one for T ∈ [ TO
W , T W ].

tional curves are depicted in Figure 5. The downward curve represents how FTA formation with
ROO changes the post-tax profits of the MNE, whereas the upward curve illustrates how it changes
the pre-tax profits of the local firm. Thus, even if we consider the home market, FTA formation with
ROO can hurt both the MNE and the local firm.

5.4 Concealment costs for transfer price manipulation
In the benchmark model, there is no cost of manipulating the transfer price. In practice, MNEs
need to explain the plausibility of transfer pricing in order to shift profits across country. This
concealment cost should increase as MNEs shift more profits because explaining the reasons for the
22 In Figure 5, the parameters are set at a = 3, w = 1, t = 0.05, ∆ = 1/32, and τ = 1/4.

25

Figure 5: The effects of FTA formation with home market competition
greater deviation from the “appropriate price” (or arm’s length price) becomes more difficult. Here,
we show that introducing a concealment cost of transfer pricing does not change the main results.
Following the literature on transfer pricing, we introduce the following quadratic concealment
cost in the case of offshoring:
C (rO ) =δ{rO − (w − ∆)}2
,
2

(25)

where δ is a parameter that captures the difficulty of concealing tax avoidance. A higher δ corresponds to a more difficult environment of profit shifting owing to a well-enforced tax code byauthorities, for example. In the case of inshoring, the MNE does not incur such a cost of profit
shifting. The introduction of the concealment cost does not influence the MNE’s actions under theinshoring scheme. Therefore, we only discuss the effect of introducing a concealment cost under
the offshoring scheme. The modified post-tax profits are given by
O
O
O
O
O
ΠO
M = (1 − t )[{r − ( w − ∆ )} x M ] + (1 − T )[( p − r − λ M τ ) x M ] − C (r )O
= (1 − T )( p − cOM ) xO
M − C (r ).

(26)

Unlike the benchmark case, the cost of profit shifting may prevent the MNE from shifting all the26

Figure 6: The effects of FTA formation with a concealment costprofits.23
Figure 6 illustrates a numerical example of the case with the concealment cost, where the dottedcurve again depicts the change in total welfare without ROO whereas the solid curves represent
the ones with ROO.24 We can again obtain qualitatively similar results as the benchmark analysis,Othough the upper bound of the thresholds, T W , disappears in this extension. Thus, the main findingsin the benchmark analysis are robust even if we consider the cost of profit shifting.

6 Conclusion
A recent proliferation of FTAs has played a key role in advancing trade liberalization between
countries. Trade liberalization usually increases the profits of firms via exporting and benefits
consumers in importing countries. Because FTAs entail ROO, however, the profits and the welfare
effects of FTAs are much more complicated than they seem. Specifically, ROO require exporting
firms to use inputs produced in FTA countries to be eligible for tariff elimination and thereby affect

23 As the amount of shifted profits depends on the parameter δ, a partial profit shifting occurs with the concealment
cost if the tax in country H, T, is less than the level that either makes the local firm’s supplies to be zero (xO
L = 0) or shifts
the entire tax base of the MNE to country O (πO=0).
M
24 The parameters are set at a = 3, w = 1, t = 0.1, ∆ = 1/32, τ = 1/8, and δ = 1 in Figure 6.

27

location choices of exporting firms for input production. In particular, if an exporting firm is avertically-integrated MNE that conducts both input and output production in different affiliates, it
is able to manipulate its transfer price to avoid a high corporate tax or to increase the downstream
affiliate’s competitiveness in the product market. The decision rights of the MNE are centralized in
the former case and decentralized in the latter case. Therefore, FTA formation that affects MNEs’
location choices also affects MNEs’ allocation of decision rights and strategies to manipulate theirtransfer prices. This study investigated the effects of an FTA with ROO when an MNE chooses its
location of input production and manipulates its transfer price set for intra-firm transactions.
If the tax gap between potential host countries of input production is wide, the MNE prefers
to locate its input production in a country outside an FTA in the pre-FTA equilibrium. In thiscase, the decision rights are centralized, and the MNE manipulates its transfer price to avoid ahigh corporate tax (i.e., the Lion is sleeping). If the tax gap is narrow, the MNE locates its input
production in the same country as the output production in the pre-FTA equilibrium. In this case,the decision rights are decentralized, and the MNE manipulates its transfer price to shift profits
from the local firm in the product market (i.e., the Lion is waking up). FTA formation can induce
the MNE to relocate input production to inside an FTA country and delegate its output decisions to
the downstream affiliate because the strategic motive of transfer pricing becomes more important
than the tax-avoidance motive. Thus, an FTA may wake the Lion and, in that case, the inducedchange in the nature of the product-market competition substantially affects the welfare properties
of FTA formation.
A remarkable result is that both the local firm and MNE can lose from FTA formation in thepresence of ROO, even if the tariffs imposed on them are eliminated. The local firm suffers fromthe FTA formation because the MNE relocates its input production and becomes more aggressive inthe product market. The MNE suffers from the FTA because it needs to pay a high tax with input
relocation. Nevertheless, the MNE chooses input relocation because it cannot comply with ROO,
and the tariff is imposed only on the MNE without the relocation.
FTA formation with ROO can also decrease total exports within the FTA and hurt consumers of
the importing country, even though all firms comply with ROO and all tariffs are eliminated. This isbecause input relocation increases the production cost of the MNE and the negative effect from theincrease in the marginal cost can outweigh the positive effect from the tariff elimination. Although
the presence of ROO tends to induce the inefficient relocation of input production, which can cause
unfavorable effects on the MNE and consumers, it can be a tool to improve the total welfare of the
FTA countries. An FTA without ROO may worsen the total welfare of the FTA countries because the28member countries collect no tax revenue from the MNE. With ROO, input relocation is necessary
for the MNE to be eligible for tariff elimination. With the induced input relocation, the member
countries of the FTA collect tax revenue from the MNE. Even without the input relocation, the FTA
countries are able to collect tariff revenue from the MNE because the MNE does not comply with
ROO. Because of these effects, ROO can transform an infeasible FTA into a feasible one. These
results point to a new role for FTA formation in the presence of the MNE’s tax avoidance throughtransfer pricing: An FTA works as a tool to prevent tax avoidance by the MNE, whose effectivenessis reinforced by the ROO.
These results provide important policy implications amid the real-world prevalence of intra-firmtrade and export-platform FDIs. Policy makers should note that, even if firms comply with ROO
and make tariff-free exports, an FTA does not always benefit these firms or consumers when the
MNEs manipulate their transfer prices. Besides that, although Felbermayr et al. (2019) conclude
that there is no rationale for having ROO because tariff circumvention is usually not profitable, ourmodel suggests that ROO work as a tool to prevent tax circumvention, if not tariff circumvention.
There remains scope for further research. We have assumed that tax rates and tariff rates are
exogenously given. It is intriguing to investigate how the formation of an FTA affects the outcomesof tax competition among countries and how it affects the optimal tariffs that FTA members set.
Examining the effects of regulations on transfer pricing, such as the arm’s length principle, in thissetting will also be a possible extension. Empirical investigations into the relationship between ROO
and transfer pricing will be essential to strengthen the real-world relevance of our results.

Appendix
A.1 Proof of Lemma 1
The comparison of supplies is equivalent to that of post-tax profits if the MNE’s input location isunaffected by FTA formation. The equilibrium supplies of firms are given by

x sM =

x sL =
 a−w−(2λ M −λ L )τwhen inshoring2 (1−t){a−w+2∆−(2λ M −λ L )τ }3−2T −t a−w−(3λ L −2λ M )τ ,

,

(a1)

when offshoring
when inshoring4
 (1−T )(a−w)−(1−t)∆−{(1−T )λ L −(1−t)(λ L −λ M )}τ
3−2T −t29

when offshoring

.

(a2)

When an FTA does not affect the MNE’s location of input production, tariff elimination clearly
increases these supplies, and equivalently, the post-tax profits of both firms. This means that theb holds, the MNE changes the country of input
total supply also increases. When T ∗ ≤ T ≤ T
production from country O to country H. The change in the MNE’s post-tax profits is computed byusing (a1), which is given byIIbM
Π− ΠOM∗ ∝ xbM−√

a − w (1 − t)( a − w + 2∆ − τ )
∗
2xO
−
M =

√

2

2
3 − 2T − t√
3 − t (1 − t)( a − w + 2∆ − τ ) 2−≡ TM ,⇐⇒ T ⋚
2a−w⋛0

b < TM always
Although the MNE’s post-tax profits would decrease if T > TM holds, because T
holds, FTA formation always benefits the MNE without ROO.

A.2 Proof of Lemma 2
Without ROO, the amount of supplies by the local firm decreases if and only if
xbLI =(1 − t)( a − w + 4∆)
a−w(1 − T )( a − w − τ ) − (1 − t)∆∗⇐⇒ T > 1 −
>
= xO
≡ TL
L
4
3 − 2T − t
2( a − w − 2τ )b we haveholds. By comparing TL with T ∗ and T,
{

√ }
2
a
−
w
−
τ
+
2∆
(
a
−
w
+
2∆
)
b − TL = (1 − t)T−≷0a − w − 2τa−w√
( 2 − 1)( a − w)( a − w + 2∆)√≡ τbL , and⇐⇒ τ ≷(2 2 − 1)( a − w) − 4∆
{
√ }
a
−
w
−
τ
+
2∆
(
a
−
w
+
2∆
−
τ
)
2
−
T ∗ − TL = (1 − t)≷0a − w − 2τ
a−w−τ
)
(√
2−1
√
⇐⇒ τ ≷( a − w) ≡ τL∗ .
2 2−1
We can confirm that τbL < τL∗ holds. Therefore, FTA formation hurts firm L when T ∗ ≤ T ≤ TL holds
b holds with τ ≤ τbL .
with τbL < τ < τ ∗ , or when T ∗ ≤ T ≤ TeWith ROO, (a2) suggests that FTA formation benefits the local firm. By subtracting TL from T,30

we have

√
a
−
w
−
τ
+
2∆
(
a
−
w
−
2τ
+
2∆
)
2
e − TL ∝−≥ 0 ⇐⇒ τ ≥ τeL ,T
a − w − 2τ
a−w
√(
( √
)
)
(
√
√
√ )
4 2 − 1 ( a − w) + 4∆ 2 −
8 2 + 1 ( a − w)2 + 8 4 + 3 2 ( a − w)∆ + 32∆2√
where τeL ≡.
8 2
e ≥ TL holds if and only if τ ≥ τeL holds.
Therefore, T

A.3 Proof of Proposition 3
First, we analyze the change in total exports in the absence of ROO. From (a1) and (a2), it is obviousthat total exports increase when an FTA does not change the MNE’s strategy. If the MNE changes
the production location owing to an FTA, the change in total exports is positive if() ()
3( a − w) (2 − T − t)( a − w − τ ) + (1 − t)∆
∗
O∗
I
+
x
=
−
>0
xbM
+ xbLI − xOML4
3 − 2T − t(1 − t){ a − w − 4(τ − ∆)}eCS⇐⇒ T < 1 −≡T
2( a − w + 2τ )eCS from T,bholds. By subtracting T(
eCS − Tb = (1 − t )T)√( a − w + 2∆) 2 a − w − τ + 2∆−
a−w
a − w + 2τeCS − Tb is minimized at τ = 0. At τ = 0,
is obtained. Because the second term is decreasing in τ, T√)(b < TCS always holds, which means that FTA
eCS − Tb = (1 − t)( 2 − 1) a−w+2∆ > 0. Therefore, TT
a−w
formation always benefits consumers in country F in the absence of ROO.
b holds, we investigate the case of Tb< T < Te and that of
As ROO are redundant when T < T
e < T, respectively. When Tb<T<Te holds, the FTA increases total exports under regime I if andTeCS holds. We have
only if T < T

√
a
−
w
−
τ
+
2∆
2
(
a
−
w
+
2∆
−
2τ
)
e − TCS =T−
a − w + 2τ
a−w
(
√ )
√
√
∝ −( 2 − 1)( a − w)( a − w + 2∆) − a − w + 4∆ 2 τ + 4τ 2 2.
√e − TCS takes the minimum value at τ = a−w+√4∆ 2 , which is negative. Furthermore, T
e − TCS isT
8 2( 1− t ) }{ a−w+2∆, a − w − 1−T ∆ . It is negative at τ = 0. Besides
maximized at either τ = 0 or τ = min231that, we have

√
(
) }
{
1−t
a − w + 2∆
a − w − 4∆ 2√,a−w−
∆ ≡ τ max .
< min
2
1
−
T
8 2
When T ≤a − w −2(2− t ) ∆holds, we have τ max = a−w2+2∆ , at which
a−w−∆

(

e−T
eCS
T

)
τ = a−w2+2∆=( a − w)( a − w + 2∆)
> 0.
2

e−T
eCS > 0 holds for τ > τeCS . By
This implies that there exists a unique threshold, τeCS , such that T)(
a − w −2(2− t ) ∆e− TeCSdefinition, a−w2+2∆ = a − w − 11−−Tt ∆ holds at T =, and thus T>0a−w−∆
τ = a−w−( 11−−Tt )∆a − w −2(2− t ) ∆. Specifically, the threshold is calculated asalso holds when T is close to T =
a−w−∆
e>T
eCS > 0 ⇐⇒ τ > τeCS ,
T
where

√
√
√
√
a − w + 4∆ 2 + (33 − 8 2)( a − w)2 + 8(8 − 3 2)( a − w)∆ + 32∆2√
τeCS =.
8 2

eCS < T < Te holds, which is the case when
Therefore, an FTA with ROO hurts consumers when T
τ > τeCS holds.
e < T holds, tariff elimination is applied only to the local firm. Then, we have
When T() ()(1 − T ) τ
O
O∗
O∗
e
xeO
+
x
−
x
+
x
=
> 0.
M
L
M
L
3 − 2T − t

In this case, FTA formation benefits consumers.

A.4 Proof of Proposition 4
Suppose that ROO are absent. When T < T ∗ holds, the effect of FTA formation on the total welfare
of member countries is given byb I − W I ∗ = τ ((11 + 4T )(2( a − w) − τ ) − 24( a − w − τ )) .
W
FTA
FTA
32
If τ ≥

2( a − w )I∗bIholds, we have W
FTA ≥ WFTA irrespective of the level of T.
13b I − W I ∗ depends on T. We can calculate that
however, the sign of W
FTAFTAb I ⋛ W I ∗ ⇐⇒ T ⋛ T I ≡ 2( a − w) − 13τ
W
FTA
FTA
W
4{2( a − w ) − τ }32

If τ <

2( a − w )holds,
13

I can be either higher or lower than T ∗ , FTA formation worsens the total welfare
holds. Because TW

if τ <

2( a − w )I , T ∗ ] hold.
and T < min[ TW13b < T holds, the welfare effect of FTA formation becomes
When Tτ
b O − W O∗ =
W
FTA
FTA

{

}
−2(1 − T ){( T − t)( a − w) + 3∆(1 − t)} + (t2 + T 2 + 4Tt − 6t − 6T + 6)τ
.
2{1 − t + 2(1 − T )}2

O
O∗
O∗
bO
bO
We can obtain the threshold level of T, TO
W and T W , by solving WFTA = WFTA . We have WFTA < WFTA

if

(1 − t){ a − w + 3∆ − 2τ +TO
W ≡ 1−√

2( a − w ) + τθ}(1 − t){ a − w + 3∆ − 2τ −< T < 1−
2( a − w ) + τ√

holds, where θ ≡ ( a − w)2 − 6(τ − ∆)( a − w) + 3(τ − ∆)(τ − 3∆). If τ < ( a − w) + 2∆ −

θ}

√

O

≡ TW

2( a−w)2 +10( a−w)∆+11∆2
3

O

holds, there is a real solution of TO
W and T W and an FTA becomes a welfare-reducing one if
O
O
O
O∗
bO
TO
W < T < T W holds. Otherwise, there is no real solution of T W and T W and WFTA ≥ WFTA alwaysObbholds. We can calculate that TO
W can be higher or lower than T whereas T < T W always holds.
√2( a−w)2 +10( a−w)∆+11∆2
Therefore, FTA formation worsens the total welfare if τ < ( a − w) + 2∆ −3band max[ TOW , T ] < T < T W hold.
Ob holds, the second derivative of the welfare effect of FTA formation is given
When T ∗ < T < T
by[]b I − W O∗ )∂ 2 (Wa − w + 3τ
6{( T − t)( a − w − τ ) + 3(1 − t)∆}
FTA
FTA
=−
+
< 0,
∂T 2
{1 − t + 2(1 − T )}3{1 − t + 2(1 − T )}4
b I − W O∗ takes the minimum value at either T = T ∗ or T = T.
b Furthermore,which implies that W
FTA
FTA
at T = T ∗ , we obtain(b I − W O∗
W
FTA
FTA

)

√
√
√
(8 − 5 2)( a − w)2 − 2(16 − 11 2)( a − w)τ + (5 2 + 24)τ 2 T ∗ ( a − w)2
√
=
+
,
8
T =T∗
64 2

whose first term takes the minimum value)(b I − W O∗
> 0 holds.
that W
FTA
FTA
∗

√
√
2
(1187 √2−1456√ )( a−w) > 0 at τ = (16−11√ 2)( a−w) . This means
16 2(5 2+24)2
5 2+24

T =T

At the other edge, we have(b I − W O∗
W
FTA
FTA

)

√
b ( a − w )2
(8 − 5 2)( a − w)2 ( a − w + 2∆)2 − 2( a − w)Γ1 τ + Γ2 τ 2 T
√
=
,
+
b
8
T =T
64 2( a − w + 2∆)2√√√√where Γ1 ≡ {(16 − 11 2)( a − w)2 + (56 − 38 2)( a − w)∆ + (48 − 32 2)∆2 > 0 and Γ2 ≡ {(5 2 +

33

√
√
( a − w ) Γ1
24)( a − w)2 + (48 + 32 2)( a − w)∆ + 32 2∆2 } > 0. It takes the minimum value at τ =,Γ2which is given by(b I − W O∗
W
FTA
FTA

)
Γ1 =

b =
T = T,τΓ

2b ( a − w )2
T
4( a − w )2 Γ3
+ √
> 0.
8
64 2( a − w + 2∆)2 Γ2√√√where Γ3 ≡ (68 2 − 89)( a − w)4 + (536 2 − 708)( a − w)3 ∆ + 4(396 2 − 529)( a − w)2 ∆2 + 25 (65 −√88)( a − w)∆3 + 27 (8 2 − 11)∆4 > 0. Thus, in the absence of ROO, FTA formation that induces
input relocation always improves the total welfare of member countries.

A.5 Proof of Proposition 5
e < T < T max , where the MNE procures inputs from country O bothFirst, consider the case of Te O − W O∗ be the welfare gains from an FTA with ROO. We
before and after FTA formation. Let W
FTA
FTA
obtaine O − W O∗ )∂ (W(1 − t)τ {2( a − w − τ ) + 5∆)t − (2( a − w + ∆) − 5τ ) T − 3(τ + ∆)}
FTA
FTA
=
∂T
{1 − t + 2(1 − T )}3(1 − t)τ {2( a − w − τ ) + 5∆) T − (2( a − w + ∆) − 5τ ) T − 3(τ + ∆)}<{1 − t + 2(1 − T )}3−3(1 − T )(τ + ∆)< 0.
=
{1 − t + 2(1 − T )}3
e O − W O∗ takes the minimum value at T = T max , which is given by
Therefore, W
FTAFTAe O − W O∗
W
FTA
FTA

T =T

=
max

∆τ {2( a − w − τ )2 + ∆(4( a − w) − τ )}> 0.
2( a − w + 2∆ − τ )2

Therefore, we havee O − W O∗
W
FTA
FTA

e
T =T

e O − W O∗
>W
FTA
FTA

T = T max> 0.

b < T < T,e where input relocation happens. As indicated in
Next, consider the case with T
b I − W O∗ may take the minimum value at T = T
e and be negative. Considering thisAppendix A.4, W
e O − W O∗ at T = T,e which is given bypossibility, we compare it with W
(

(
)
(
)
bI −W
eO
e O − W O∗
= W
− W
e
e
e
T =T
T =T
√
√T =T
( a − w)[(7 2 − 8)( a − w) − 32∆ + {4(4 − 2)( a − w) + 32(∆ − τ )}t]
√
=
.
64 2

b I − W O∗
W)

Note that FTA formation without ROO reduces the total welfare when τ < a − w + 2∆ −

34

√
(

2( a−w)2 +10( a−w)∆+11∆2
holds. Then, it is computed as3)√( a − w) √√ [(7 2 − 8)( a − w) − 32∆ + {4(4 − 2)( a − w) + 32(∆ − τ )}t]
e
T =T
64 2
{ √
}
√
√
2( a − w)2 + 10( a − w)∆ + 11∆2
∝ (7 2 − 8)( a − w) − 32∆ + 4 8− ((4 + 2)( a − w) + 8∆) t,
3

bI −W
eO
W

=

where the last bracketed expression is positive. Thus, if ∆ <O∗ > 0.
WFTA

35√(7 2−8)( a−w)
bI −holds, we obtain W
FTA
32

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