GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.197

Tariff Policy and Transport Costs under Reciprocal
Dumping

Jun Oshiro

May 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Tariﬀ Policy and Transport Costs under Reciprocal
Dumping∗
Jun Oshiro†
May, 2011

Abstract
This paper analyzes tariﬀ competition by investigating the strategic interactions amongfirms that are highly mobile across national boundaries. Although high transport costs
yield a geographic dispersion of the industry, suﬃciently low transport costs result in acore-periphery location where nobody bears tariﬀ burdens. In any case, the world economy would be in a much better position under an international coordination scheme. An
economy is only required to enforce a weak international trade agreement for improving
global welfare.
JEL classification: F12; F21; R38
Keywords: Tariﬀ competition; Transport costs; Reciprocal dumping; Trade agreement;
Factor mobility∗

An initial version of this paper was previously written as the author’s master thesis at Osaka University under

the title “Market size and tariﬀ policy under Cournot oligopoly.” We would like to extend our heartfelt gratitude
to Kazuhiro Yamamoto, Kenzo Abe, Kouichi Futagami, Noriaki Matsushima, Yasuhiro Sato Hiroshi Kitamura,
Takao Asano and Youichiro Higashi for their valuable comments and suggestions. The constructive comments by
Tomoya Mori, Se-il Mun, Hisaki Yamaga, and seminar participants at Kyoto University are highly appreciated.
We also significantly benefited from our discussions with conference participants in the autumn 2010 meetings of
the Japanese Economic Association. We would also like to extend our heartfelt gratitude to Takatoshi Tabuchi andthe participants of the 24th Meeting of the Applied Regional Science Conference at Nagoya University, December
4–5, 2010, for their valuable comments. All the errors and perspectives are the author’s alone.
†
Graduate School of Economics, Osaka University, 1–7, Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
E-mail address: jgp006oj@mail2.econ.osaka-u.ac.jp

1 Introduction
The significance of strategic relationships among governments has long been documented in
the literature on foreign direct investments (FDIs). This is because international mobility ofcapital creates fiscal externalities; a country’s taxation, public expenditures and trade policies
may cause a flow of capital to another country, which influence the economic welfare of theresidents in that country. In response to these international externalities, a coordinated international fiscal policy must be identified and evaluated with extreme prudence in order toimprove welfare. In this context, the example of governments independently competing for a
fixed amount of mobile capital stock through a tariﬀ policy may be considered. According to
the “tariﬀ-jumping” motivation1 , governments may have an incentive to over-protect domestic
firms in order to attract capital, despite a tariﬀ barrier that essentially restricts trade and distorts
the allocation of resources. Increased capital mobility engages governments in global tradenegotiations.
This paper focuses on the relationship between an optimal trade policy and trade costs.
“New economic geography” literature continually explains the matter in which changing trade
costs may endogenously lead to industrial agglomeration and geographical diﬀerentiation.
Trade policy influences the total trade costs, which are divided into transport costs and tariﬀs inthis paper. Although the former are exogenously given, the latter are strategically determinedby governments; therefore, transport costs are of consequence in both industrial locations aswell as for formulating trade strategies. This implies that the level of transport costs significantly impact the welfare implications of the non-cooperative trade policies.
This paper investigates an optimal tariﬀ policy in a strategic setting that considers the location choices of imperfectly competitive firms. We consider the tariﬀ competitions among thegovernments and establish a relationship between the strategic interactions in the trade policy
and the degree of market integration (as measured by exogenous transport costs). Tariﬀ rates
on import goods are established for maximizing a representative consumer’s indirect utility.
Tariﬀ competition involves international externalities associated with capital mobility.
Thus far, only a few attempts have been made to address the issues regarding tariﬀ competition in a new economic geography framework. A few important exceptions are Haufler andWooton (1999), Ludema (2002), and Mai, Peng, and Tabuchi (2008; hereafter MPT). Haufler
1

For example, Bhagwati (1987), Motta (1992), Belderbos and Sleuwaegen (1998), Dehejia and Weichenrieder(2001), and Blonigen, Tomlin and Wilson (2004).

1and Wooton (1999) considered a framework wherein two countries of diﬀerent sizes compete
for a foreign-owned monopolist location. They highlighted that a tariﬀ policy reinforces theimportance of selecting a large region for establishing a plant. Unfortunately, their study lacksa detailed welfare analysis. Since monopoly firms are owned by foreigners, their contributions
do not provide any insight into the distortions in the capital market. Therefore, the assumption of a single firm is disregarded and both spatial dispersion and industrial agglomeration arecomprehensively studied.
Ludema (2002) focused on the relationship between transport costs and trade agreements
under increasing returns and imperfect competition in a repeated game framework. In a oneshot game, each government’s dominant strategy is modeled to impose a tariﬀ that is highenough to attract multinational enterprises. However, one-shot tariﬀ competition does not necessarily result in such tariﬀ war, even taking into account the influence of tariﬀs on the location
decisions of firms. In the MPT model as well as ours, each country avoids a tariﬀ war. The
models exhibit asymmetry in the equilibrium tariﬀ strategies and location configurations. More
importantly, when asymmetric Nash equilibrium arises, it is diﬃcult to enforce cooperative
agreements in the absence of supranational political institutions despite the governments being
suﬃciently patient.
This paper extends and complements the MPT argument regarding the strategic tariﬀ policy,
wherein CES preferences and monopolistic competition have been introduced. We introduce
strategic interactions among firms that are Cournot competitors and encounter segmented markets. In our model, the relationship between an optimal tariﬀ policy and transport costs areanalogous to MPT’s model, wherein firms can freely enter and exit a monopolistic competitivemarket. High transport costs induce governments to set low trade barriers and lead to dispersion of production. Conversely, tariﬀ competition with suﬃciently low transport costs leads
to a core-periphery structure wherein the core government imposes a suﬃciently high tariﬀ
and the periphery government eliminates its trade barrier. As a result, nobody bears the tariﬀ
burden (i.e., de facto free trade becomes the equilibrium).
Our primary objective is to compare the welfare implications. Even if the equilibrium actions based on a theoretical model appear to be compatible with the evidence, we must nevertheless exercise caution while making political decisions. The economic welfare implications
presented in this paper are rather diﬀerent from those oﬀered by MPT. Although tariﬀ competition over large distances may reduce welfare, an internationally binding agreement is not2

necessary for free trade. In addition, de facto free trade between the core and the peripherygovernments will not be globally eﬃcient. In this paper, we propose a practical international
rule for improving world welfare.
The remainder of this paper is organized as follows: Section 2 presents the basic model.
Section 3 characterizes the tariﬀ competition for duopoly firms. Section 4 indicates the results for a more generalized case (i.e., oligopoly economy). Finally, Section 5 presents theconcluding remarks.

2 The Model
2.1 Production
Our model is a reciprocal dumping model à la Brander (1981) that considers footloose capital.
In this model, the economy is assumed to comprise two countries, that is, i ∈ {1, 2}, two factorsof production (capital and labor) and two sectors: manufacturing (M) and agriculture (A).
Further, capital is freely mobile between these two countries. The total endowments ofcapital, K, are evenly owned by identical consumers who inelastically supply one unit of laboreach.
The two countries have identical preferences, technologies, and populations. L denotes
the labor population in each country. Although labor is internationally immobile, it possesses
intersectoral mobility.
In the agricultural sector, a homogeneous good (A-good) is produced by employing only
labor according to the constant returns technology. A-good is traded with zero transaction costs
under perfect competition and is taken as a numéraire (the marginal cost is normalized to one).
The manufacturing sector employs both the factors of production in order to produce a homogeneous good (M-good) under imperfect competition and increasing returns to scale. Eachfirm requires one unit of capital for operations and a M units of labor per unit of output. Now, ni
denotes the number of firms located in country i; therefore, the total number of firms is given
by n = n1 + n2 = K. For the sake of simplicity, it is assumed that K = 2.2 In other words, firms
behave like Cournot duopolists.

2

This assumption will be relaxed in Section 4, wherein the qualitative nature of the analysis remains un-changed.

3

Shipping a unit of M-good from country i to country j requires positive specific tariﬀs34
θ j ≥ 0 and positive transport costs τ > 0. Therefore, the total access costs that need to be paidby firms for exporting goods to country j are τ+θ j units of the numéraire. Governments impose
specific import tariﬀs to maximize their objective functions and redistribute its tariﬀ revenue tothe consumers. The equilibrium condition in the tariﬀ policy of government i is given by
Lsi = θi n j q ji ,(1)where si denotes the per unit lump-sum transfer and q ji denotes the quantity of imports fromcountry j.
Now it is assumed that the markets are spatially segmented. Therefore, the profit of an
identical firm located in region i is given by
πi = (pi − wi a M )qii + (p j − wi a M − τ − θ j )qi j − ri ,(2)

where ri and wi represent the rewards to capital and labor, respectively, pi denotes the price ofM-good, and qii denotes country i’s consumption of the M-good produced in country i.
Because of the costless trade of the numéraire, the equilibrium wages of the workers in boththe countries are regarded as unity; that is, w1 = w2 = 1.

2.2 Preferences
We assume a quasi-linear utility with a quadratic subutility of a representative consumer incountry i, which is expressed as follows:γ
Ui = xi + αDi − D2i ,2(3)

where xi and Di represent the consumption of A-good and M-good respectively. α and γ areconstant parameters.
The budget constraint is given by
xi + pi Di = Yi + si + ω,
3

(4)

For the sake of simplicity, indeterminate locations have not been considered in this paper; therefore, negative

tariﬀs have been omitted. In addition, MPT assumed positive tariﬀs and emphasized that, in reality, negative tariﬀs
are rare. Even if negative tariﬀs are considered, the equilibrium location configuration remains unchanged in thecase of a duopoly.
4
It is assumed that the features of the model are independent of how transport costs are modeled — that is,whether they are per unit or ad valorem costs. See Behrens (2006).

4

where Yi denotes the income of an individual and ω denotes the initial endowment, which isassumed to be large enough to ensure a positive demand of the numéraire.
The utility function (3) yields the following inverse demand function for M-good:pi = α − γ(ni qii + n j q ji )
.
L

(5)

The utility maximization problem yields the following standard indirect utility function:Vi =(α − pi )2+ Yi + si + ω.
2γ

(6)The first term represents country i’s consumer surplus in the M-good market.

2.3 Structure of the Tariﬀ Game
The tariﬀ game comprises the following three stages, each of which is analyzed. In the firststage, both the national governments simultaneously and irreversibly5 select their specific tariﬀ
rates, where country i’s strategy is θi ∈ R+ . In the second stage, firms select the locationfor establishing their plant after observing both the tariﬀs. In the third stage, firms initiate
production in the international market.

3 Equilibrium
3.1 Trade Patterns
Here, the duopolistic market of sector M is discussed in detail.
Firms cannot always yield positive revenues from exports. As indicated below, the priceof M-good is endogenously determined as a function of tariﬀs. The threshold values of tariﬀs
at which a firm located in country j is not active in country i are defined as θi = θi (θ j ). If

5

The reason why governments can credibly make their short-run policy choices even before firms make their“long-run” choices (the mobility of capital is assumed to be costless here) may appear to be slightly confusing.
In Haufler and Wooton (1999), tariﬀs are selected only after the location decision has been made. However, theorder of play adopted here follows MPT to enable a comparison of results.

5θi ≥ θi (θ j ), then q ji = 0. The sets that represent trade patterns are defined as follows:
B ={(θ1 , θ2 ) ∈ R2+ | θ1 < θ1 (θ2 ) and θ2 < θ2 (θ1 )},U i j ={(θ1 , θ2 ) ∈ R2+ | θi ≥ θi (θ j ) and θ j < θ j (θi )} for i , j,
A ={(θ1 , θ2 ) ∈ R2+ | θ1 ≥ θ1 (θ2 ) and θ2 ≥ θ2 (θ1 )}.
The trade pattern sets B, U i j and A represent pairs of tariﬀs that characterize bilateral trade,
unilateral trade (only firms in country i can export to country j), and autarky, respectively.

3.2 Third-Stage Game: Cournot Competition
Given the tariﬀ rates and the location of the industries, each firm maximizes its operating profit
in the last stage.
The equilibrium price of M-good may be expressed as follows: α+nai Mif θi ≥ θi (θ j ),
ni + 1pi = α + 2a M + n j (τ + θi )
if θi < θi (θ j ).
3

(7)

Therefore, the no trade threshold is derived as follows:
θi =

a
− τ,
ni + 1(8)

where a ≡ α − a M is assumed to be constant and positive.6 As we will observe below, ni isdetermined as a function of the tariﬀs. Equation (7) implies that when all other things remain
constant, an increase in the number of firms located in the country result in lowering the pricesof the goods there.
The equilibrium reward to fixed costs is derived as follows:• If (θ1 , θ2 ) ∈ A,

(

a
ri =
ni + 1

)2

L
.
γ

(9)

• If (θ1 , θ2 ) ∈ U i j ,
(

)2
[
]
a − (n j + 1)(τ + θ j ) 2 L
a
L
ri =
+
,
ni + 1 γ
3γ[]
a + ni (τ + θ j ) 2 L
rj =
.
3
γ
6

(10)
(11)

This assumption ensures that the individual demand for M-good is positive for any positive access costs.

6• If (θ1 , θ2 ) ∈ B,[][]
a + n j (τ + θi ) 2 L
a − (n j + 1)(τ + θ j ) 2 L
ri =
+
.
3
γ
3
γ

(12)

3.3 Second-Stage Game: Equilibrium Distribution of Firms
In the second stage, firms can freely move to any location where they can earn a higher profit.
The strategic interactions regarding the location preferences of duopolists have been considered. In other words, each firm cannot disregard the decision made by the other.
Lemma 1. The location game possesses at least one Nash equilibrium for any given pair of
positive tariﬀs.
Proof. We consider an issue wherein two firms determine the locations for establishing theirbusinesses. Table 1 indicates the payoﬀ matrix of this location game.
[Table 1. HERE]
The term ri (n1 ) denotes the rent of return when a firm operates in country i, and is dependent
on the number of firms located in country 1. Here, it may be recalled that each firm possesses
the same technology. Subsequently, we are only required to evaluate the signs of the following:
r1 (2) − r2 (1) and r1 (1) − r2 (0). The signs of r1 (2) − r2 (1) and r1 (1) − r2 (0) indicate the ideal
locations for a company to establish its factory if the rival establishes its factory in country 1
and country 2, respectively. Since r1 (n1 ) and r2 (n1 ) take the real values for any (θ1 , θ2 ) ∈ R2+ at
all trade patterns, it is always possible to ascertain these signs. Therefore, Lemma 1 holds.



Table 2 summarizes the results of the location game.7 Both r1 (2) = r2 (1) and r1 (1) = r2 (0)are simultaneously satisfied only if θ1 = θ2 = −τ < 0. This implies that (θ1 , θ2 ) ∈ R2+ s.t.
r1 (2) > r2 (1) and r1 (1) < r2 (0) are empty sets. Therefore, both n1 = 2 and n1 = 0 are notsimultaneously supported in equilibrium.
[Table 2. HERE]

7

When r1 (2) = r2 (1) and r1 (1) > r2 (0), then both n1 = 2 and n1 = 1 are Nash equilibrium locations in thisgame. For the sake of simplicity, it is assumed that n1 = 1 if r1 (2) = r2 (1) and r1 (1) > r2 (0). Likewise, when
r1 (2) < r2 (1) and r1 (1) = r2 (0), the symmetric location is assumed to be n1 = 1, even though n1 = 0 is also a Nashequilibrium location.

7

The sets representing location configurations are defined as follows.
C 1 = {(θ1 , θ2 ) ∈ R2+ | n1 = 2},
I = {(θ1 , θ2 ) ∈ R2+ | n1 = 1},C 2 = {(θ1 , θ2 ) ∈ R2+ | n1 = 0}.

3.4 First-Stage Game: Tariﬀ Competition for Welfare
Before analyzing welfare, we must consider the per capita income, Yi . Yi consists of wages andcapital income. Wages are normalized to 1. The global reward to capital is given by n1 r1 + n2 r2 ,which is equally distributed among all the consumers. Therefore, the per capita income is givenbyYi = 1 +(n1 r1 + n2 r2 )
.
2L

(13)

The first-stage game considers tariﬀ competition. The welfare maximization problem may
be divided into the following two component parts. First, the “local” maxima within each of
the subsets may be identified from the first-order conditions (see Appendix 1). However, these
are not necessarily global solutions. Second, the welfare levels are compared and investigatedfor identifying whether or not either of the governments has any incentive to deviate.
National welfare can be altered by a tariﬀ increase through the following three channels.
First, in contrast to the monopolistic competition model, strategic interactions among firms play
an important role in welfare analysis. Protecting the domestic firm in one country increases domestic sales and lowers foreign sales in the market because domestic and foreign outputs are
strategic substitutes under Cournot competition. Such a production shift benefits the domestic
firm, and consequently enhances domestic welfare by saving on transport costs. At the sametime, domestic protection reduces the total supply in the domestic market, thereby increasing
the domestic price.8 As Brander and Krugman (1983) emphasized, each government encounters a trade-oﬀ between saving uneconomical transport costs as a result of trade and fostering
competition. The level of transport costs and the location configuration of the firms determine
which one of the two eﬀects, the production-shifting eﬀect or the anti-competitive eﬀect, ismore dominant.
8

Now firms can only partially transfer the marginal costs to foreign consumers (∂pi /∂θi ∈ [0, 2/3] if θi < θi ).

In other words, there exists “reciprocal dumping” which can be regarded as terms-of-trade gains (or losses). We
would like to emphasize that dumping will work even if firms co-locate.

8Second, a tariﬀ change generates a rent-shifting eﬀect that creates international externalities. Since the equities of firms are equally owned by domestic and foreign consumers, domestic consumers receive only half of the profits (or losses) from a change in rents. For example, if
a reduction in the operating profits earned by firms in the domestic market is exactly oﬀset by
an increase in the domestic consumers’ surplus and tariﬀ revenues, then the domestic welfare
must increase. Furthermore, both the production-shifting gains and the anti-competitive losses
influence foreign welfare.
The first-order conditions within each subset are indicated in Appendix 1 and represent thereactions of each of the countries to their rival’s tariﬀ without any changes in the trade patterns
and the locations of the firms. Keeping trade flow and capital allocation unchanged, the optimal
trade policy is to reduce the tariﬀ to zero.9
Third, trade barriers operate through a tariﬀ-jumping relocation of firms. Raising tariﬀ barriers above a certain level would attract additional capital into the region because suppliers want
to be protected by a high tariﬀ rate and export goods at a low tariﬀ rate. Spatial concentration
enhances the competitive pressure on the firms, and therefore a lower price of M-good benefits
consumers who incur no trade costs. Despite this, an increase in the number of firms locatedin a country will certainly lead to a reduction in this country’s tariﬀ revenue. We must notdisregard the fact that location configuration influences the impacts of both production-shifting
and anti-competitive eﬀects.
3.4.1 Benchmark Case: International Tariﬀ Coordination
We assume that there is a world-level benevolent planner who simultaneously establishes thetariﬀ levels in both countries, thereby maximizing the sum of indirect utilities, which is givenbymax L(V1 + V2 ).
θ1 ,θ2

Subsequently, the following proposition describes the optimal tariﬀ policy as a function of thetransport costs, τ.
Proposition 1. It is assumed that the economy is duopolistic. On the basis of this assumption,
tariﬀ coordination is obtained as follows:(i) For τ ≥ a/4, (θ1 , θ2 ) ∈ A ∩ I;
9This is largely owing to the assumption of symmetry in country size.

9

(ii) For a/5 < τ < a/4, (θ1 , θ2 ) ∈ B ∩ I and θ1 = θ2 = 5τ − a > 0;(iii) For τ ≤ a/5, (θ1 , θ2 ) = (0, 0) ∈ B ∩ I.


Proof. See Appendix 2.

When wasteful transport charges are suﬃciently higher than demand, international trade
becomes rather expensive. Therefore, it is more eﬀective to impose high tariﬀs that restrict theimport of products and promote domestic production. However, firms need to gradually adopt
an open trade policy when the transport costs become so low that the wastage of resources islesser than the loss from the anti-competitive eﬀect.
For any levels of transport costs, the benchmark policy requires dispersed locations. The
following is a straightforward corollary of Proposition 1.10
Corollary 1. If countries are symmetric with respect to their populations, agglomeration of the
manufacturing sector is ineﬃcient.
How are agglomeration diseconomies obtained? The strategic interactions among oligopolistic competitors play an important role in this analysis. When two firms are located in the same
country, there is no cost diﬀerence in the segmented markets. However, when the firms arelocated in diﬀerent countries, each firm enjoys an advantage of circumventing the payment oftrade costs in its own home market. Consequently, domestic production substitutes for importin both the country, thereby saving on transport costs.
3.4.2 Non-cooperative Equilibiria
We now investigate the case where governments select a tariﬀ rate within their jurisdictions for
maximizing the welfare of its citizens.
For τ ≥ a/4, the sets C 1 and C 2 are empty. All strategies induce a dispersed location.
This yields a unique free-trade11 equilibrium in this game; that is, θ1 = θ2 = 0. Furthermore,
reducing the tariﬀ rate is a dominant strategy. However, owing to the high transport costs inthe case of free trade, the closed economy yields more desirable trade patterns for both thecountries. The tariﬀ protection reduces transport costs.
10
11

In the case of K ≥ 2, we can also derive Corollary 1 (see Section 4).
This depends on the assumption of both symmetric countries and duopolistic markets. However, if we relax

even one of these assumptions, then the analytical description cannot be pursued over a broad range of parametervalues.

10

Proposition 2. When transport costs are higher than demand, free trade is a unique subgame
perfect Nash equilibrium of the tariﬀ competition for duopoly firms in identical countries. Thisequilibrium, wherein firms are geographically dispersed, is less eﬃcient than that obtained
under tariﬀ coordination.
Proof. See Appendix 3.

The reason for the diﬀerence in the result is that the benevolent planner internalizes therent-shifting eﬀect, which is counterbalanced by summing the welfare of the countries.
Subsequently, the case where τ < a/4 is considered. Figure 1 illustrates equilibrium tradeas well as location patterns as the functions of the countries’ tariﬀ oﬀers.
[Figure 1. HERE]
When transport costs are lower than demand, the game exhibits diﬀerent results. Thereexists no equilibrium on set I in this range.
Lemma 2. If transport costs are low enough to cause agglomeration, then a geographicallydispersed location is not achievable in equilibrium.
Proof. See Appendix 4.

Propositions 1 and 2 and Lemma 2 indicate that non-cooperative tariﬀ competition is unambiguously harmful for global welfare. Although the economy requires international policy
coordination, according to Lemma 2, mutual agreements among governments, which both facilitate and regulate trade, are diﬃcult to accomplish as the economy integrates.
We are now in a position to characterize the equilibrium of the game for τ < a/4.
Proposition 3. An equilibrium in pure strategies does not exist for intermediate transport costs.
When transport costs are suﬃciently lower than demand, there exists a subgame perfect Nashequilibrium such that one country sets its tariﬀ at zero and the other imposes a suﬃciently
high tariﬀ with industrial agglomeration. This tariﬀ competition deteriorates global welfare
whenever the transport costs are strictly positive.
Proof. See Appendix 5.

Even among symmetric countries, we arrived at the asymmetric distribution of capital inequilibrium. Tariﬀ competition with low transport costs leads to a core-periphery economy
11wherein the periphery country imposes a zero tariﬀ for importing goods. When transport costs
are suﬃciently low12 , it is rather economical for the periphery country to import goods. The
government has a weak incentive to attract firms by increasing the level of tariﬀ protection,
which exacerbates the anti-competitive eﬀect and reduces capital income. This is in sharp
contrast to Ludema (2002), wherein all the countries provide their domestic plants with theshield of tariﬀ protection regardless of the behavior of other governments in the static Nashequilibrium.
In this case, no country collects tariﬀ revenue in equilibrium for low transport costs. This
indicates the existence of a de facto free trade. This result may support Waugh (2007), whoargued that, as compared to rich countries, poor countries must bear higher costs in order toexport goods.
However, in our model, the governments cannot select a pure strategy for intermediatetransport costs. When the transport costs are not too low, the core-periphery structure is not an
equilibrium structure because the periphery country raises its tariﬀ rate in order to recapture
the firm.

3.5 Discussion
In terms of the relationship between equilibrium location configurations and the level of transport costs, our quasi-linear utility model with variable demand elasticity is partially consistent
with MPT, which assumed a constant markup pricing rule for firms. Both MPT’s and our results
indicate that although high transport costs yield a symmetric dispersed location, suﬃciently lowtransport costs lead to a core-periphery structure virtually without any tariﬀ burden.
However, the implications for welfare are contrary to those for transport costs. MPT suggested that suﬃciently high transport costs result in an equilibrium wherein both governments
establish excessive protection, which necessitates a mutually binding agreement for free trade.
However, our model implies that the non-cooperative equilibrium is ineﬃcient for very low tariﬀs but not for very high tariﬀs, because of a lack of “taste for variety.” In addition, de facto free
trade with suﬃciently low transport costs is optimal in MPT; this is contrary to Proposition 3.
Even without market-distorting tariﬀs, we find that distortions in the location of firms continue
12

The core-periphery equilibrium exists for τ < (9 −√78)a/12 ≈ 0.014a. This does not appear to be a broad

range. In MPT, the threshold iceberg transport costs that an agglomerated configuration can achieve in equilibrium
is given by 1 ≤ t < 1.28.

12

to exist because of the Nash policies. The political implication derived from the monopolisticcompetition setting may therefore be a model-specific result.
This diﬀerence in results is largely due to the diﬀerences in the assumed preferences. Since
this paper excludes the taste for variety, it was required to consider significant savings in transport costs and increased domestic production of homogeneous goods.
Here, we discuss the manner in which our model may be extended to a setting of selfenforcing agreements. In Section 3.4.1, we analyze the cooperative outcome that maximizes
the joint surplus of the two countries, and subsequently pose the following question: If international transfer payments are not available, how should agreements be designed so as to enable
their eﬀective implementation? For τ ≥ a/4, the outcome of international cooperation Pareto
dominates the Nash equilibrium. Therefore, cooperative self-enforcing agreements are wellcharacterized by certain repeated games.13 In other words, when the rate at which governments
discount the future is below a critical level, the tariﬀ coordination policy can be eﬀectively implemented without international transfers. However, for τ < a/4, the outcome of international
cooperation does not Pareto dominate the Nash equilibrium. In the absence of side payments,
international tariﬀ coordination leads to industrial delocation and welfare loss for households inthe core country. Both countries always have an incentive to deviate from the trade agreement
and impose a tariﬀ that is high enough to attract FDI. Therefore, it is diﬃcult to provide a useful and practical method to establish a self-enforcing agreement by considering circumstancessuch as the repeated game for suﬃciently low transport costs.
We note that a simple agreement that specifies tariﬀ ceilings will enable the establishmentof more eﬃcient tariﬀ levels. Our study, for example, requires only two conditions, which may
be expressed as follows: a lower limit on tariﬀs, i.e., θi ≥ 5τ − a, for τ ≥ a/5, and an upper()√
limit, i.e., θi < Φ2 ≡ 1 − 1 − 4τ/a a/2 − τ, for τ ≤ 5a/24. Under these constraints, noncooperative tariﬀ competition can eﬀectively implement the tariﬀ coordination results for any
level of transport costs. When governments need to save high transport costs, the lower limiton the tariﬀ is the relevant constraint. In contrast, when transport costs are low, it is desirable
to restrict the use of tariﬀs as an industry-grabbing policy. The upper limit on tariﬀs prompts
governments to lower their tariﬀs to a level below the limit in order to reduce the distortion in
prices.
This argument emphasizes the importance of a commitment by each government to prevent
13

See, for example, Friedman (1971), Bagwell and Staiger (1990) and Ludema (2002).

13

the deprivation of firms by imposing a prohibitive tariﬀ. In fact, the World Trade Organization(WTO) determines a bound rate, which is the maximum tariﬀ that the members can charge.
The tariﬀ ceilings may be of consequence in practice albeit they are much higher than theircorresponding applied rates.

4 Extension: OligopolyThis section discusses an extension of our model, that is, an oligopolistic economy, whereK = n ≥ 2. Consider the following two types of locational equilibria: interior equilibria wherer1 = r2 and n1 /n ∈ (0, 1), and corner solutions where ni = n and ri > r j .14
In this case, the marginal eﬀect of the tariﬀ on the firms’ location choices can be comprehensively studied. However, the analytical solution becomes uninformative because the formof the indirect utility function is highly non-linear and includes a flat range. Instead, we rely
on numerical simulation.
In order to enable a comparison with MPT, it is assumed that τ < a. This yields a relationship between optimal tariﬀs and transport costs that is similar to the relationship demonstrated
in MPT. In other words, a suﬃciently high transport cost gives θ1 = θ2 > 0 and n1 = n2 = K/2
at the equilibrium. In addition, a suﬃciently low transport cost provides a core-periphery location; that is, θi > θ j = 0 and ni = n. The symmetric equilibrium may be derived so long as√
the following inequality holds: τ ≥ a[−1 + 1 + (n − 1)/(n + 1)]/(n − 1) (see Appendix 6 fordetails).
Once again, the welfare implication in our study is diﬀerent from that in MPT. When transport costs are high, the equilibrium welfare in the oligopoly case can be further improvedby increasing the tariﬀ rates imposed by both the governments as indicated in the case of aduopoly. Besides, when transport costs are suﬃciently low, the free trade equilibrium rather
than the core-periphery equilibrium derived by the non-cooperative game is more beneficial for
global welfare; this result contradicts MPT’s finding. Our main results are remotely related tothe specifications of a duopoly.

14

This condition determines a finite number of firms, n1 and n2 (and n1 /n), which may not necessarily be an

integer. However, in this section, we will assume that the proportion of the firms located in country 1, n1 /n, is
continuously diﬀerentiable on (0, 1) with respect to tariﬀs.

14

5 Conclusion
In this paper, we have developed a strategic tariﬀ competition model with factor mobility.
Proposition 2 suggests that the tariﬀ competition between symmetric countries generate symmetric access costs and an ineﬃcient equilibrium when transport costs are higher than demand.
Consequently, mutual trade protection may improve welfare levels. On the other hand, tariﬀ
competition results in asymmetric access costs and spatial agglomeration of firms in the process of economic integration. In such a case, nobody bears tariﬀ burdens; however, industrial
distributions without free entry are ineﬃcient in such equilibria. Although these findings arecontrary to the findings of previous studies, both the models have indicated similar relationships between tariﬀ policy and trade freeness. Therefore, as is evident, this model must be
interpreted prudently.
We found that establishing constraints for tariﬀ rates and not negotiating these rigid tariﬀ
constraints may enhance global welfare. An international trade agreement that establishes alower limit on tariﬀs for high transport costs and an upper limit on tariﬀs for small transport
costs improves welfare. An agreement that prevents governments from engaging in a tariﬀ war
for attracting capital results in an accommodative trade policy. Horn, Maggi, and Staiger (2010)
argued that the presence of both uncertainty and contracting costs may explain a weakness ofthe trade agreement made under the General Agreement on Tariﬀs and Trade (GATT)/WTO.
Another explanation for the gap between the bound duty rate and the applied tariﬀ rate as itexists in reality was also oﬀered in this study. The strategy space available to players will be
an important component in a game.

Appendix
Appendix 1: First-order Conditions of Each Set
The following indicates the first-order conditions and all these conditions also satisfy the associated second-order conditions:• If (θ1 , θ2 ) ∈ B ∩ I, θ1 = θ2 = 0.
• If (θ1 , θ2 ) ∈ U i j ∩ I, θ j = 0.
• If (θ1 , θ2 ) ∈ C i , θ j = 0.
15

When country i does not import M-good, θi is indeterminate.

Appendix 2
Global welfare per capita may be calculated as follows:(V1 + V2 ) (θ ,θ )∈B∩I =12

1[16a2 + 22τ2 − θ12 − θ22 + 10τ(θ1 + θ2 ) − 2a(8τ + θ1 + θ2 )]18γ+ 2(1 + ω)

(V1 + V2 ) (θ ,θ )∈U i j ∩I =1

2

(V1 + V2 ) (θ ,θ )∈C i =12

1[59a2 + 44τ2 + 40τθ j − 4θ2j − 8a(4τ + θ j )] + 2(1 + ω)72γ

2
[4a2 + 2τ2 + τθ j − θ2j − a(4τ + θ j )] + 2(1 + ω)
9γ

Subsequently, the following are the first-order conditions:• If (θ1 , θ2 ) ∈ B ∩ I, θ1 = θ2 = 5τ − a. According to the non-negativity requirement on θi ,
θ1 = θ2 = 0 are global welfare maximizers for τ ≤ a/5.
• If (θ1 , θ2 ) ∈ U i j ∩I, θ j = 5τ−a. For 5a/24 < τ < a/4 and θi ≥ a/2−τ, (θi , 5τ−a) ∈ U i j ∩I.
• If (θ1 , θ2 ) ∈ C i , θ j = (τ − a)/2 < 0.
All the conditions also satisfy the second-order condition.
Substituting the optimal tariﬀs from above into global welfare yields the maximum welfare
levels within each of the subsets. We obtain Proposition 1 by comparing these maximum
welfare levels. Figure 2 summarizes these calculations.
[Figure 2. HERE]

Appendix 3
For τ ∈ [a/4, a/2), we haveV1 (0,0)∈B∩I − V1 (θ ,0)∈U 12 ∩I =(a − 2τ)2>0
12γ

V1 (0,θ )∈U 21 ∩I − V1 (θ ,θ )∈A =(a − 2τ)2
> 0.
12γ

1

and
2

1

2

A protected country always profits by opening up its import market. This discussion is completely pertinent for country 2 as well. Therefore, (θ1 , θ2 ) = (0, 0) ∈ B ∩ I is a unique Nashequilibrium. Proposition 1 indicates that free trade is ineﬃcient. This proves Proposition 2.
16

Appendix 4
We demonstrate that there exists no Nash equilibrium for τ < a/4 such that (i) (θ1 , θ2 ) ∈ B ∩ I,
(θ1 , θ2 ) ∈ A, and (θ1 , θ2 ) ∈ U i j ∩ I. The following proof relates to country 1 but is completely
pertinent to country 2.
For τ < a/4 and given θ j = 0, country i decides to deprive firms with θi ≥ θi .
V1 (0,0)∈B∩I − V1 (θ ,0)∈U 12 ∩C 1 = −1τ(4a − 9τ) < 0.
18γ

Therefore, free trade is no longer a global Nash equilibrium.
Likewise, for τ < a/4 and given that θ j ≥ a/2 − τ, country i continues to reduce its tariﬀ
until its consumers can import M-good.
V1 (a/4−τ,θ )∈U 21 ∩I − V1 (θ ,θ )∈A =212a(3a − 8τ)>048γ

In other words, autarky is also unachievable in equilibrium.
In addition, we can demonstrate that in the set U ji ∩ I, exporting country j has an incentive
to open up its market.
V1 (θ ,a/4−τ)∈U 12 ∩I − V1 (a/4−τ,a/4−τ)∈B∩I =1a(−3a + 8τ)
48γ

Therefore, for τ < a/4, the protected country will reduce its tariﬀ in the absence of the core.
There is no Nash equilibrium in U i j ∩ I for τ < a/4.

Appendix 5
Lemma 2 indicates that all Nash equilibria in pure strategies must belong to either C 1 or C 2 forτ < a/4 if they exist. We indicate that a periphery country has an incentive to increase its tariﬀ
and refuse to import rather than agree to be a periphery for at least τ ∈ (3a/16, a/4). Since
the two countries are assumed to be of the same size, this model is symmetric. Therefore, we
examine whether or not country 1 will be a core in equilibrium.
First, we consider θ1 ≥ θ1 (θ2 ) for any θ2 .
V2 (θ ,0)∈U 12 ∩C 1 − V2 (θ ,a/4−τ)∈U 12 ∩I =1

1This equation takes a negative value if τ > (9 −a2 − 72aτ + 48τ2144γ√78)a/12 ≈ 0.014a. Therefore, in the rangeτ ∈ (3a/16, a/4), a periphery country will deprive the protected core country of capital.
17

Second, we identify a range wherein a periphery country can become a core by increasing()√
its tariﬀ. When θ1 = Φ2 and θ2 = 0, then r1 (2) = r2 (1) where Φ2 = 1 − 1 − 4τ/a a/2 − τ. Φ2
is a horizontal intercept of r1 (2) = r2 (1) line. Here, (a/4 − τ) − Φ2 > 0 since τ < 3a/16. In otherwords, when τ > 3a/16, periphery country 2 never obtains the entire capital by increasing its
tariﬀ for a given θ1 ∈ [Φ2 , a/2 − τ) such that (θ1 , 0) ∈ C 1 .
()
a − 5τ − 5θ1∂ V2 (θ ,0)∈C 1 − V2 (θ ,θ )∈U 21 ∩I /∂θ1 =
<0
1 2
1
9γ
The diﬀerence decreases in θ1 for τ > 3a/16 and θ1 ≥ Φ2 . Therefore, if V2 C 1 − V2 U 21 ∩I < 0 in
the border between U 21 ∩ I and A, which is the point at which the diﬀerence is smallest, thenV2 C 1 < V2 U 21 ∩I holds for all θ1 ≥ Φ2 . The following equation is presented for τ > 3a/16:()
lim V2 (Φ +ϵ,0)∈C 1 − V2 (Φ +ϵ,θ )∈U 21 ∩I
2
2
2
ϵ→0
)
(
√
1
=−
14aτ − 12τ2 − 3a2 1 − 4τ/a < 036γ
Overall, periphery always endeavors to recover its capital share and unilaterally protect adomestic firm.
For the second result, we found Nash equilibria that belonged to the sets C 1 or C 2 for τ <√(9 − 78)a/12. In this range, we understand that V2 (θ ,0)∈U 12 ∩C 1 > V2 (θ ,a/4−τ)∈U 12 ∩I > V2 (θ ,θ )∈A
1

1

1

2

and V1 (0,0)∈B∩I < V1 (θ ,0)∈U 12 ∩C 1 . Therefore, θ1 > a/2 − τ and θ2 = 0 are subgame perfect Nash1equilibria. Subsequently, C 1 is obtained.
Although another equilibrium could exist, all equilibria resulted in the core-periphery location with “limit tax” owing to Lemma 2.
Corollary 1 indicates that the equilibria are trivially ineﬃcient.

Appendix 6: Simulations
Solving the systems of the first-order conditions in B ∩ I (i.e., n1 /n ∈ (0, 1) and θi < θi for
i ∈ {1, 2}) yields the following solution:
θ1 = θ2 = θ∗B∩I > 0
Symmetric property implies that when θ1 = θ2 = θ∗B∩I , n1 = n2 .
Here we examine whether or not θ1 = θ2 = θ∗B∩I is a global equilibrium or not. In otherwords, we investigate whether or not a country has an incentive to change its tariﬀ and moveout of B ∩ I. If V1 (θ∗B∩I ,θ∗B∩I )∈B∩I < V1 (0,θ∗B∩I )∈C 2 , then θ1 = θ2 = θ∗B∩I is not a Nash equilibrium.
18If (0, θ∗B∩I ) < C 2 , then θ1 = θ2 = θ∗B∩I is a unique Nash equilibrium.
If (0, θ∗B∩I ) belongs to the set C 2 , then V1 (θ∗B∩I ,θ∗B∩I )∈B∩I < V1 (0,θ∗B∩I )∈C 2 for any feasible
parameter settings with numerical calculations. We can also see that V2 (0,θ ) > V2 (0,θ′′ ) for any
2θ2 and θ2′′ such that (0, θ2 ) ∈ C 2 and (0, θ2′′ ) ∈ B ∩ I with numerical calculations.
Nash equilibria must belong to C j with θi = 0.
Since we derive a symmetric Nash equilibrium when C 2 = ∅ in R2+ ,√a 
n − 1 
τ≥
−1 + 1 +n − 1 (n + 1) is a necessary condition for a symmetric Nash equilibrium.

19

2

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23

Country 1

Country 2

Country 1

r1 (2), r1 (2) r1 (1), r2 (1)Country 2

r2 (1), r1 (1) r2 (0), r2 (0)Table 1: Payoﬀ matrix.

r1 (2) − r2 (1) r1 (1) − r2 (0)Equilibrium Location++

n1 = 2−+n1 = 1−−n1 = 00+n1 ≥ 1−0

n1 ≤ 1

Table 2: Equilibrium location.

24

θ2

U 21 ∩ I

A∩I

U 21 ∩ C 2

U 12 ∩ I
B∩I
B ∩ C 2´3́a4 −τB ∩PPC 1

U 12 ∩ C 1

q
P

0

Φ2

a
3 −τ

a
2 −τ

Figure 1: Trade and location configurations for τ < a/4.

25

θ1

V 1 + V2↓ U ij ∩ I

↓ B∩I
↓ A
τ
Ci →

Figure 2: Transport costs and maximized global welfare within each set.

26