Discussion Paper Series No.209
Globalization, Interregional and International Inequalities

Dao-Zhi ZENG
Laixun ZHAO

NovemberKagawa University
Kobe University

2007

The Discussion Papers are a series of research papers in their draft
form, circulated to encourage discussion and comment. Citation anduse of such a paper should take account of its provisional character.
In some cases, a written consent of the author may be required.

Globalization, Interregional and International
Inequalities
Dao-Zhi Zeng∗

Laixun Zhao†

November 2007

Abstract
This paper examines interregional and international inequalities in a setup of
two countries and four regions. Different from the existing literature, countries andregions are not required to be symmetric in size. Capital but not labor is mobile
across regions and countries. We find that the interregional and international inequalities are closely related to globalization and the efficiency of local governance.
In other words, they are jointly determined by the domestic transport costs (e.g., infrastructure, administrative barriers, etc) in the two countries and the international
trade cost. Particularly, the interregional inequality may be either a monotonicallyincreasing or an inverted U-curve function of its own domestic transport costs. Also,
the interregional inequality decreases with the national manufacturing share. These
results shed light on the so-called “deindustrialization” phenomenon.
Key Words: Regional Inequality, Firm Location, Infrastructure, Governance,
Deindustrialization
JEL Classification: R12∗

Graduate School of Management, Kagawa University, Saiwai-Cho 2-1, Kagawa 760-8523, Japan.
E-mail: zeng@gsm.kagawa-u.ac.jp.
†
Research Institute for Economics and Business, Kobe University, Kobe 657-8501, Japan. E-mail:zhao@rieb.kobe-u.ac.jp.

1

Introduction

There is deep concern that the recent wave of globalization has enlarged the inequality
between developed and developing countries, and between rich and poor regions withina country. Some developed countries as well as regions are concerned that globalization
might affect negatively their ability to sustain high living standards, while developing
countries and regions fear that a rise in the living standards of rich countries and regions
is at the expense of the poor.
Interregional and international inequalities are evidently related to interregional andinternational trade. For example, as a result of economic liberalization policies in thepast 30 years, China has narrowed its distance with advanced countries. However, theunequal development between the coastal regions and the inland is a major concern ofthe government. According to Fujita and Hu (2001), during the period between 1985 and1994, the absolute gap between coastal and interior China increased by 10 times (p.8).
They predicted that “as long as globalization and economic liberation continue in China,
production agglomeration toward the coastal area will continue” (p.31). In many cases,
such inequalities are complicated, and they usually do not change in a monotonic way
with economic policies. For example, Petrakos and Saratsis (2000) find that the regional
inequalities in Greece have a cyclical character: increasing in periods of economic expansion and decreasing in periods of economic recession. In addition, Sánchez-Reaza andRodrı́guez-Pose (2002) find that in the case of Mexico, the proximity to the US market
has been a determinant in the concentration of economic activity, and these forces haveinteracted with uneven distribution of infrastructure and public services to create very
different opportunities for different regions. They further observe that the end of the ISI(import substitution industrialization) period was characterized by regional convergence,
whereas economic liberalization and integration have been connected by regional divergence. As for the case of developed countries, Davis and Weinstein (2005) find that theuneven pattern of manufacturing activity in Japan contributes to overall efficiency—ifaggregate activity were to be spread evenly across all regions, output would be loweredby 5 percent.
The above phenomena have generated intense academic and policy debates as to theircauses and policy remedies. Existing studies basically take two approaches to the problem.
One is based on income/wage inequality, such as Feenstra and Hanson (1996), Freeman(1995) and Wood (1995), who highlight the role of import competition from develop1

ing countries, and Acemoglu (2002), Harrigan (1998), Krugman and Lawrence (1994),
Lawrence and Slaughter (1993) who focus on the role of technological changes. The otherapproach is based on industrial activities and adopts spatial-economy models (e.g., Krugman and Venables, 1995; Fujita et al, 1999; Puga, 1999). This literature attributes theincreasing inequality to increasing-returns-to-scale technology, monopolistic competition
and transport costs in product markets. The two approaches are closely related because
the latter one can be interpreted as the real wage inequality.
The present paper follows the second approach, which we believe is suitable for analyzing the so-called “deindustrialization” phenomenon, because it focuses on the concentration and relocation of industrial activities. The recent wave of globalization ischaracterized by freer mobility of goods as well as factors across countries, in the form oflower transportation costs, trade costs, easier access to foreign capital, etc. These are inturn driven by technological advances in transport and communications, and also partly
by deliberate policy designs such as those in China and Russia. Such factors must be
explicitly incorporated in order to address issues related to regional and international
inequalities, yet by and large they have been neglected in the literature. While in the realworld, one often hears loud cries of “deindustrialization”.1 Our analysis will highlightthe importance of capital mobility, which impacts both interregional and international
inequalities in complicated ways.
For this purpose, we examine a spatial economy of two asymmetric countries andfour asymmetric regions, with both domestic and international transport/trade costs.
We have in mind two countries with close economic ties such as Canada and the U.S.,
Germany and Poland, Japan and South Korea, Mexico and the U.S., etc. Each country has
its densely populated manufacturing centers and remote countryside, with interregional
administrative transport costs and international trade barriers. We wish to use this setup
to analyze how globalization in the form of higher capital mobility across countries aswell as improvements of domestic infrastructure and administrative barriers affect theinterregional and international income inequality. In particular, we ask the following
questions: Does globalization lead to agglomeration in the larger region in the larger
country? Will the remote countryside of the smaller country be deserted? Is the socalled ‘deindustrialization’ of some developed countries related to the domestic reduction
1

Also called ‘the giant sucking sound’ by former U.S. presidential candidate Ross Perot, referring to
U.S. firms moving out to Mexico, and ‘hollowing out’ in Japan, referring to Japanese firms’ outsourcing
activities to Southeastern Asian countries.

2

of adminstrative barriers and transport costs, or the international trade costs? If yes, inwhat way? Can one country’s efficiency of governance affect the regional inequalities ofthe other country?
With our setup, we obtain the following main results. I. If capital is not mobile
across countries, then i) the interregional inequality in a country is determined by its own
domestic transport costs which in turn depends on its administrative and infrastructure
efficiency, and by the international trade costs. It is independent of the transport costsin the other country; ii) regional inequality rises monotonically with globalization. Anda larger national manufacturing share brings a lower interregional inequality. This result
explains why many developing countries actively adopt various and systematic policies toattract foreign direct investment, especially in manufacturing.
II. In contrast, if capital is mobile across countries, i) the regional inequalities and theinternational inequality are jointly determined by the transport costs in both countries
and the international trade costs. A change in one country’s domestic transport cost (e.g.,
infrastructure, governance efficiency) affects the incentives of production, causing capitalto move not only domestically but also internationally, which further leads to changes ofindustrial relocation in both countries. If the domestic transport costs are equal in thetwo countries, then the regional inequality in the bigger country evolves as an inverted
U-curve, while that in the smaller country takes a monotonically increasing form withrespect to the trade costs; ii) A country’s national firm share rises (falls) with a lower
domestic transport cost of its own (the other country). Consequently, facing the wave ofglobalization (in contrast to the case of no international capital mobility), countries withpoor infrastructure or low governance efficiency may lose.
Earlier models consider two regions or countries, and analyze either (domestic) regional inequalities or international inequalities but not both simultaneously, see for instance Krugman and Venables (1995), Puga (1999) and Fujita et al. (1999). Meanwhile,
Krugman and Livas Elizondo (1996) and Paluzie (2001) employ three-location models
with two regions in one country and the rest of the world as the third region. Using land
rent and commuting costs as centrifugal forces, the first study shows that closed markets promote interregional agglomeration while open markets discourage it. The authors
predict that economic liberalization in developing countries will shrink the interregional
inequalities. To the contrary, based on immobile consumers as centrifugal forces, Monfort
and Nicolini (2000) and Paluzie (2001) predict that economic integration exacerbates the3interregional inequalities monotonically. The stark difference in their conclusions stimulated our interest in the present paper to examine more closely the inequality issue.
Mainly for the ease of tractability, all the existing two-country-four-region models assume that the two countries are of the same size, and the regions are also symmetric. In
Monfort and Nicolini (2000), the domestic transport costs in the two countries are also
kept the same. Consequently, an infrastructure improvement in one country automatically implies the same improvement in the other country. Symmetry also renders thesemodels unable to explore the relation between the national manufacturing share and theinterregional inequality. Thus they find that the domestic geographies of the two countries
are independent.
Our setup differs from the existing models in a number of important ways. First, neither the regions nor the countries are symmetric. Normally, the asymmetry would create
tremendous difficulty in solving the model. But we are able to obtain analytical solutionsin the present paper. More importantly, it enables us to analyze unequal development
between regions and across countries, which are absent in the existing literature. Second,
we allow capital to move across countries, an important characteristics of globalization.
That is, capital seeks the highest-profit opportunities, wherever they are. This assumption
enables us to exam issues related to the so-called ‘deindustrialization’ of manufacturingindustries, as often heard in the media. Third, while Behrens et al. (2006a, 2006b, 2007)
use a quasi-linear utility function, we adopt a standard Cobb-Douglas utility function,
as is often used in models of monopolistic competition. Monfort and Nicolini (2000) and
Paluzie (2001) also use Cobb-Douglas utility functions, but important results are obtainedwith simulations.
The rest of paper is structured as follows. Section 2 presents the basic model; Section
3 derives and discusses the location equilibria. The first part considers the case of nointernational capital mobility and the second part incorporates international mobility.
Section 4 concludes.

2

The Basic Model

We consider a spatial economy of two countries. In each country, there exist two regions:large and small. The two regions in the same country have the same physical geographicalconstraints except their population size, while regions in different countries may also differ

4

in transport costs. There are two sectors in each country: manufacturing and a numéraire
sector (e.g., agriculture). Two factors, labor and capital, are used in production. Capitalbut not labor is mobile across countries.
As an important feature of this paper, the two countries differ in size, i.e., theirendowments of capital and labor are both different. We assume Country 1 to be bigger
than Country 2, and region 1 to be bigger than region 2 in both countries. More precisely,
L1
=Θ
L

µ

¶
1
,
>
2

l11
= θ1 ,
L1

l21= θ2 ,L2µ¶
1,
θ1 , θ2 >2

where the first subscript denotes country, and the second one denotes region. Thus, L is
the world total endowment of labor, Li is that of country i, and lij is the labor endowmentof country i in region j. For short, we also call region j in country i by region ij. Finally,Θ, θ1 and θ2 are the respective shares of country 1, region 1 in country 1 and region 1 incountry 2. We assume them to lie within suitable values to ensure that every region is
involved in agricultural production.
The above definition implies
l11 = Θθ1 L,

l12 = Θ(1 − θ1 )L,

l21 = (1 − Θ)θ2 L,

l22 = (1 − Θ)(1 − θ2 )L.

For convenience, we subsequently use i0 to indicate the country other than i, and j 0 to
indicate the region other than j.

2.1

Preferences

Individuals in the two countries are identical and share the same Cobb-Douglas tastes forthe two types of goods expressed by utility function
U=

1
C µ C 1−µ ,µµ (1 − µ)1−µ M A

where CM represents a composite index of the consumption of the M -sector goods, CA
is the consumption of the A-sector good, and µ ∈ (0, 1) is a constant denoting the expenditure share of manufactured goods. The quantity index CM is defined by a constantelasticity-of substitution (CES) function over a continuum of varieties of manufactured

5goods

σ
µZ N
¶ σ−1
1− σ1
CM =
ci di
,

0

where N is the number of varieties, ci is the consumption of each available variety i.
Parameter σ > 1 is the constant elasticity of substitution between any two varieties and1 − 1/σ is the intensity of the preference for variety in manufactured goods.

2.2

Transportation

As in the standard literature of spatial economics, the agricultural product is freely transported between the two countries. We use it as the numéraire good and assume that nocountry alone has enough labor to satisfy the world demand for good A. Then the pricesof the agricultural good are equalized internationally: pA = p∗A = 1.
In the manufacturing sector, transaction costs across both regions and countries areformalized as Samuelson iceberg costs. Specifically, ti > 1 units of the manufactured goodmust be shipped for one unit to reach the other region in country i. In other words, afraction ti − 1 is lost in domestic transportation of country i. Similarly, τ units mustbe transported across countries for 1 unit to arrive, i.e., τ − 1 is lost in internationaltransportation. International transaction costs are assumed to be independent of theregions involved. The costs are shown in Figure 1.
Country 1
Country 2
l12 , c12l22 , c22

t1

τ

t2
l21 , c21

l11 , c11

Figure 1: Two countries and four regions
Following Behrens et al. (2006a, 2006b, 2007), we call t1 and t2 the (domestic) transport costs, and τ the (international) trade cost. Furthermore, we assume that interna6

tional transaction is more costly than domestic transaction because trade costs might
include a fraction of tariffs: τ ≥ ti (i = 1, 2).
Because of transaction costs, the price in region ij of a representative manufacturing
good produced in region i1 j1 is, where i identifies the country and j identifies the region,



 pij
pi1 j1 →ij =if i1 = i, j1 = j

pi1 j1 ti if i1 = i, j1 6= j
 p τ if i 6= i.
i1 j1
1Then the CES demand in region ij for the manufacturing good s produced in region i1 j1
is
di1 j1 →ij (s) =p−σi1 j1 →ij
Pij1−σµIij ,(1)

where Iij is the total income in region ij,
Pij =

2 X
2 µZ
X
i1 =1 j1 =11−σs∈ni1 j1

pi1 j1 →ij (s)

1
¶ 1−σ
ds
,

is the price index in region ij, and ni1 j1 is the number of varieties in region i1 j1 . The total
demand for a manufacturing good s produced in region ij is the following sum:
dij =

2 X
2
X

dij→i1 j1 .

i1 =1 j1 =1

2.3

Production

The representative consumer owns one unit of capital which can be invested, in either
country. The world total endowment of capital is thus L = L1 + L2 .
We have assumed no Ricardian comparative advantage in production across regions.
In other words, productivities are identical across countries and regions in either the
agricultural sector or the manufacturing sector. In particular, we assume one worker
can produce one unit of the agricultural good. Then the wages in the two countries areequalized at: w1 = w2 = 1.
Firms are monopolistically competitive in the manufacturing sector, under which eachfirm produces a single differentiated good. The production of manufactures features
economies of scale. Each firm in region ij requires one unit of capital as a fixed input

7and (σ − 1)/σ workers as a marginal input. The total number of firms is then N = L. To
produce q units of output, the total input of a firm in region ij is
rij +

σ−1
q,
σ

where rij is the unit return of capital (i.e., profits) in region ij.
A typical firm in region ij determines prices by maximizing profits
Πij =pij→ij dij→ij + pij→ij 0 dij→ij 0 + pij→i0 1 dij→i0 1 + pij→i0 2 dij→j 0 2
σ−1−
wi [dij→ij + tdij→ij 0 + τ (dij→i0 1 + dij→i0 2 )] − rij ,σ(2)where i0 6= i, j 0 6= j. According to (1), the first-order condition gives
 1 if i1 = i, j1 = j,pij→i1 j1 =ti if i1 = i, j1 6= j, τ if i =
i.
1 6

(3)

Therefore, the price index is simplified as
1

Pij = [kij + φti kij 0 + φτ (ki0 1 + ki0 2 )] 1−σ ,where kij is the number of firms in region ij, and φti = t1−σ∈ (0, 1] and φτ = τ 1−σ ∈ (0, 1]i
are the domestic and international trade ‘freeness’. That is, a larger φ means smaller costs.
Free entry in production ensures zero profits. Thus, (2) and (3) giverij =1
[dij→ij + ti dij→ij 0 + τ (dij→i0 1 + dij→i0 2 )].
σ(4)Meanwhile, given price (3), the CES demands of representative varieties are thendetermined asµIij,
kij + kij 0 φti + (ki0 1 + ki0 2 )φτt−σ
i µIij,dij 0 →ij =kij + kij 0 φti + (ki0 1 + ki0 2 )φττ −σ µIij
di0 j→ij =,kij + kij 0 φti + (ki0 1 + ki0 2 )φτdij→ij =8

di0 j 0 →ij =2.4

τ −σ µIij.
kij + kij 0 φti + (ki0 1 + ki0 2 )φτCapital mobility

Physical capital moves in search of the highest nominal reward.2 Denote the capital (firm)share of Country 1 by Λ, and that of region 1 inside Country 1 by λ1 and the counterpartof region 1 inside country 2 by λ2 . Then
k11 = λ1 ΛN,

k12 = (1 − λ1 )ΛN,

k21 = λ2 (1 − Λ)N,

k22 = (1 − λ2 )(1 − Λ)N.

Following established tradition in economic geography, we assume that markets forgoods adjust instantaneously, while international migration of capital is relatively slow,
implying that wages adjust much faster than the capital share. Also following the literature, we apply a standard dynamic system to describe the international factor flow:
λ̇i = (ri1 − ri2 )λi (1 − λi ),(5)Λ̇ = (r1 − r2 )Λ(1 − Λ).

(6)There are two phases. (5) describes the interregional mobility and (6) describes theinternational mobility. Both are adopted from replicator dynamics, routinely used inevolutionary game theory (Weibull, 1995, p. 73), and is also used in standard textbooks
such as Fujita et al. (1999, p. 62) and Baldwin et al. (2003, p. 72). We assume that theinternational adjustment in the second phase starts after the domestic adjustment in thefirst phase has finished so that r11 = r12 ≡ r1 and r21 = r22 ≡ r2 .

2

To simplify the calculation of the regional income, we make the following assumption: the capitalin each region originates uniformly from the four regions. That is, regardless of the spatial allocation ofindustry and the degree of openness, Θθ1 (resp. Θ(1 − θ1 ), (1 − Θ)θ2 , and (1 − Θ)(1 − θ2 )) of the capitalin each region originates from region 11 (resp. 12, 21, and 22). This is the four-region version of thestandard assumption imposed for two-region models (see Baldwin et al. (2003, p. 74). This assumption
does not change the equilibrium shares of capital but simplifies the mathematics a lot.

9

3

Equilibrium

3.1

Immobile capital across countries

We start with a benchmark case of no capital mobility across countries. This first phasedetermines domestic shares λ1 and λ2 , given r11 = r12 (≡ r1 ) and r21 = r22 (≡ r2 ).
Without international capital mobility, Country 1’s national share of capital/firms Λ
is fixed. If Λ = 1 or 0, then the model degenerates to the case of one country with tworegions, which is widely seen in the literature. Therefore, we assume that Λ ∈ (0, 1).
Equilibrium in Country 1 requires that r11 = r12 , which can be rewritten as
d11→11 + t1 d11→12 + τ (d11→21 + d11→22 ) = d12→12 + t1 d12→11 + τ (d12→21 + d12→22 ).
Because d11→21 + d11→22 = d12→21 + d12→22 , the above equation is simplified as
I11
I12
=
.
(k11 + φt1 k12 ) + φτ (k21 + k22 )(k12 + φt1 k11 ) + φτ (k21 + k22 )(7)

Denote the average return of capital by
2

r̄ =

2

1 XX
rij kij .
N i=1 j=1

According to the uniform assumption of footnote 2, we have I11 = θ1 ΘL(1 + r̄) andI12 = (1 − θ1 )ΘL(1 + r̄). Therefore, (7) yieldsµ¶
2θ1 − 1 1 − Λ
λ1 = θ 1 +φτ + φt1 .
1 − φ t1Λ

(8)

Since (8) is the only equilibrium, it is stable with respect to (5) according to Tabuchi
and Zeng (2004).
Obviously if Λ is close to 1, we have the case of a one-country-two-region model. In
particular, (8) degenerates to the firm share (16) of Ottaviano and Thisse (2004). The
property λ1 > θ1 says that a larger region attracts a more-than-proportionate share offirms in a monopolistically competitive industry with increasing returns technology. Thisis the so-called regional home market effect (HME) (see e.g., Krugman, 1980; Helpman
and Krugman, 1985).

10

Similarly, mobility of capital in country 2 requires that r21 = r22 , which implies

and derives

I22
I21
=
,
k21 + k22 φt2 + (k11 + k12 )φτ
k22 + k21 φt2 + (k11 + k12 )φτ

(9)

¶
µ
2θ2 − 1Λ
λ2 = θ 2 +φ + φt2 .
1 − φ t2 1 − Λ τ(10)This equilibrium is again stable due to its uniqueness. Since Λ ∈ (0, 1), firms in bothcountries produce positive outputs. And both [(1 − Λ)/Λ]φτ in (8) and [Λ/(1 − Λ)]φτ in(10) are positive; that is, the HME is strengthened due to international trade.
Proposition 1 When capital is immobile across countries,(i) a decrease in the domestic transport costs ti increases the regional inequality of countryi;(ii) a decrease in the international trade costs τ increases the regional inequality of bothcountries.
(iii) a larger firm-share in a country decreases the regional inequality of this country.
Proof : We only consider the case of Country 1. The conclusion stems from thefollowing facts∂λ1(2θ1 − 1)[Λ + (1 − Λ)φτ ]
=
> 0,
∂φt1
Λ(1 − φt1 )2∂λ1(2θ1 − 1)(1 − Λ)
=
> 0,
∂φτ
Λ(1 − φt1 )∂λ1
φ (2θ1 − 1)
= − τ2< 0.
∂ΛΛ (1 − φt1 )¤Part (i) of Proposition 1 is simply a restatement of the results obtained in the literaturefrom a one-country and two-region model. Our model of 2 asymmetric countries and 4
asymmetric regions further confirms that the regional HME is strengthened when trade
becomes freer.
Part (ii) shows the relationship between regional inequality and international trade
costs: the openness of a country to the world is accompanied by regional inequality. It
suggests that globalization is likely to lead to agglomeration in the larger region of the11larger country, and in the extreme, the remote countryside of the smaller country might
be deserted. This result is consistent with some empirical studies, such as Sánchez-Reaza
and Rodrı́guez-Pose (2002) and Rodrı́guez-Pose and Sánchez-Reaza (2005), who find unmistakable trends towards greater regional inequality and polarization, when Mexican
economic policy shifted from a closed-economy approach to trade liberalization since themid-1980s, and to economic integration since 1994. They explain that in Mexico, proximity to the US market has been a determinant in the concentration of economic activity,
and these forces have interacted with uneven distribution of infrastructure and public
services to create very different opportunities for different regions across Mexico.
Most importantly, part (iii) says that a larger national manufacturing share results
in a lower interregional inequality. Intuitively, when the national manufacturing share is
not too large, the competition effect in the bigger region is weak, then firms can benefit
from relocating in the bigger region. This results explains why many developing countries actively adopt various and systematic policies to attract foreign direct investment,
especially in manufacturing. Note that this result cannot be obtained if the countries are
exogenously assumed symmetric, as done in the literature.
Mathematically, results (i) and (ii) depend on the international immobility of capital,from which Λ in (8) and (10) becomes a constant. In subsequent analysis we shall see thatthe manufacturing share is jointly determined by various transport costs when capital isinternationally mobile. Therefore, according to (iii), the inequalities become much more
complicated.

3.2

Internationally mobile capital and international inequality

After the domestic adjustments in the first phase, we are now ready to endogeneize Country 1’s capital share Λ. To do so, we relax the assumption of no capital mobility acrosscountries and let capital move wherever nominal reward is the highest.
Previous equations (4), (7) and (9) give·¸
(1 + φt1 )θ1 ΘL(1 + r̄)µ
2φτ θ2 (1 − Θ)L(1 + r̄)r1 =+,σ (k11 + k12 φt1 ) + (k21 + k22 )φτ(k21 + k22 φt2 ) + (k11 + k12 )φτ·¸µ (1 + φt2 )θ2 (1 − Θ)L(1 + r̄)
2φτ θ1 ΘL(1 + r̄)r2 =+.
σ (k21 + k22 φt2 ) + (k11 + k12 )φτ(k11 + k12 φt1 ) + (k21 + k22 )φτ12At equilibrium, r1 = r2 ≡ r̄ must hold. Thenσr̄(1 + φt1 − 2φτ )µ(1 − Θ)(1 + r̄)Lθ2=[(1 + φt1 )(1 + φt2 ) − 4φ2τ ],(k11 + k12 φt1 ) + (k21 + k22 )φτσr̄(1 + φt2 − 2φτ )µΘ(1 + r̄)Lθ1[(1 + φt1 )(1 + φt2 ) − 4φ2τ ].
=(k21 + k22 φt2 ) + (k11 + k12 )φτSubstituting (8) and (10) into the above yields:σ(1 − Θ)(1 + r̄)r̄(1 + φt1 − 2φτ ) =[(1 + φt1 )(1 + φt2 ) − 4φ2τ ],µ2Λφτ + (1 − Λ)(1 + φt2 )σΘ(1 + r̄)r̄(1 + φt2 − 2φτ ) =[(1 + φt1 )(1 + φt2 ) − 4φ2τ ],µ2(1 − Λ)φτ + Λ(1 + φt1 )which imply the equilibrium share asΛ∗ =Θ[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2φτ (1 + φt2 − 2φτ )(1 + φt1 − 2φτ )(1 + φt2 − 2φτ )(11)

Due to uniqueness, this equilibrium is stable with respect to (5) according to Tabuchi and
Zeng (2004). At the equilibrium Λ∗ , the capital return is r∗ = µ/(σ − µ).
Expression (11) is independent of both θ1 and θ2 . This is due to the assumptionthat the (international) trade costs are identical for transactions between any two regions
across country borders.
If φt1 = φt2 = 1 (i.e., zero domestic trade cost), then the case degenerates to the
traditional model of two countries (regions) again. Also, expression (11) holds as aninterior equilibrium Λ ∈ (0, 1) only if
2φτ (1 + φt2 − 2φτ )(1 + φt1 )(1 + φt2 − 2φτ ).
2 < Θ <
(1 + φt1 )(1 + φt2 ) − 4φτ(1 + φt1 )(1 + φt2 ) − 4φ2τ

(12)

For Θ lying outside of this range, we have corner solutions. Specifically, for a larger Θ,Country 1’s capital share Λ becomes 1 (all firms agglomerate in Country 1), and for asmaller Θ, Λ becomes 0 (all firms agglomerate in Country 2).

13Now rewrite (11) asΛ∗ = Θ + Γ + Ω(Θ − 1/2).

(13)

where
(φt1 − φt2 )φτ,(1 + φt1 − 2φτ )(1 + φt2 − 2φτ )µ¶1
1Ω ≡ 2φτ
+.
1 + φt1 − 2φτ
1 + φt2 − 2φτΓ≡Equation (13) shows that the national manufacturing share is determined by two effects.
The expression Γ stems from domestic transport cost differences in the two countries,
which shows the importance of relative infrastructure construction and administrative
efficiency. We thus call it the infrastructure effect. Firms are likely to choose a country
with lower transport costs and higher administrative efficiency. If Country i has better
infrastructure, then φti > φtj and more firms move in. This effect disappears if the domestic transport costs are equalized between the two countries, as in the existing literature.
The third term in (13) is the international HME: the larger country is likely to hold amore-than-proportionate share of firms because of the increasing returns technology inmanufacturing.
We can further calculate the partial derivatives from (11) as follows:∂Λ∗2(1 − Θ)φτ=
> 0,
∂φt1 (1 + φt1 − 2φτ )2
∂Λ∗
2Θφτ
=−
< 0,
∂φt2
(1 + φt2 − 2φτ )2∂Λ∗ (2 + φt1 + φt2 )(2Θ − 1) + (φt1 − φt2 )=∂φτ(1 + φt1 − 2φτ )(1 + φt2 − 2φτ )4φ (φ − φt2 )[1 + Θφt1 + (1 − Θ)φt2 − 2φτ ]+ τ t1.
(1 + φt1 − 2φτ )2 (1 + φt2 − 2φτ )2(14)

They are summarized as:
Proposition 2 (i) Country 1’s equilibrium firm-share Λ∗ rises with a lower domestictransport cost t1 , but falls with a lower domestic transport cost t2 in the smaller Country2;(ii) The relationship between the national firm share Λ∗ and the international trade costτ depends on the domestic transport costs t1 and t2 . When t1 = t2 , lowering τ increases
14the national share Λ∗ .
Part (i) says that lowering the domestic transport costs in the two countries havecompletely different impacts on the international inequality. This arises because lowering
domestic transport costs attracts more firms into the country from the other country. This
result cannot be obtained when t1 = t2 is imposed exogenously, as in Monfort and Nicolini(2000). Part (ii) and expression (14) further show the importance of the infrastructure
effect. If the larger country is a developing country and the smaller one is a developed
country (like China and Japan), then φt1 < φt2 . In this case ∂Λ∗ /∂φτ might be negative
so that lowering τ decreases the international HME.
Davis and Weinstein (1999) explain the HME as a magnified impact of a high demandon production. Head and Ries (2001, p. 866) empirically examines the relationshipbetween such a magnified impact and trade barriers. They find that in a two-region
model, home market size matters more when trade barriers are lower, which is called
the secondary magnification effect (SME) in Head and Mayer (2004). Note that in ourmodel of two countries and four regions, there are three transport costs: t1 and t2 withincountries 1 and 2 respectively, and τ for international trade. The SME with respect tothose costs are as follows.
∂Ω
2φτ
=−
< 0,
∂φt1
(1 + φt1 − 2φτ )2
∂Ω
2φτ
=−
< 0,
∂φt2
(1 + φt2 − 2φτ )22(1 + φt1 )2(1 + φt2 )
∂Ω
=
+
> 0.
2
∂φτ
(1 + φt1 − 2φτ )(1 + φt2 − 2φτ )2Comparing with (14), we find that the SME and the infrastructure effect work in different
directions with respect to t1 . Result (i) in the above proposition shows that the latter
dominates the former. Meanwhile, the SME and the infrastructure effect work in thesame direction with respect to t2 .

3.3

Internationally mobile capital and regional inequality

To obtain the domestic industrial distribution in each country, we substitute (13) into (8)and (10). The equilibrium solution is obtained as follows.
λ∗1 = θ1 + Ω1 (2θ1 − 1),λ∗2 = θ2 + Ω2 (2θ2 − 1),
15

(15)

where1Ω1 =1 − φt1µ¶
φτ
+ φ t1 − φ τ ,
Λ∗

1
Ω2 =
1 − φt2µ¶
φτ
+ φt2 − φτ .
1 − Λ∗(16)

Proposition 3 Under capital mobility across countries, the regional HME in the bigger(smaller) country decreases (increases) with Θ.
Proof : The proposition holds from (16), because Λ∗ increases in Θ.

¤

Behrens et al. (2007, P.1829) find that the economic geography of a country i depends
on the domestic cost ti as well as international cost τ , but not on the domestic cost tj of
the other country. In the present, it is only true when capital is internationally immobileby (8) and (10). In contrast, when capital can move across countries, λ1 and λ2 evidently
depend on both t1 and t2 in (15). Intuitively, when the domestic transport cost in acountry changes, it changes the incentives of production, causing capital to move not only
domestically but also internationally. This further leads to changes of industrial locationin both countries.
We next explore the details by examining how the various transport costs impact on
the international and domestic industrial location. We find:
Proposition 4 (i) Ω1 increases in φt2 ;(ii) Ω1 increases in φt1 if φτ and φt2 satisfy
Θ[(1 + φt2 )(1 + φτ ) − 4φ2τ ]2 ≥ φτ (1 + φt2 − 2φτ )[(3 + φτ )(1 + φt2 ) − 8φ2τ ].

(17)

Otherwise, there exists φ̃t1 ∈ (φτ , 1) such that Ω1 increases in φt1 ∈ [τ , φ̃t1 ) and decreases
in φt1 ∈ [φ̃t1 , 1];(iii) The relationship between Ω1 and τ is related to the relative magnitude of the domestictransport costs t1 and t2 in the two countries. If t1 = t2 , then Ω1 increases in φτ if andonly if φτ < φ̃τ , whereφ̃τ =1 + φ t11−Θ√;2
Θ + 2Θ − 1(18)(iv) Ω2 increases in φt1 ;(v) Ω2 increases in φt2 if φt1 and φτ satisfy(1 − Θ)[(1 + φt1 )(1 + φτ ) − 4φ2τ ]2 ≥ φτ (1 + φt1 − 2φτ )[(3 + φτ )(1 + φt1 ) − 8φ2τ ].
16

(19)

Otherwise, there exists φ̃t2 ∈ (φτ , 1) such that Ω2 increases in φt2 ∈ [τ , t̃2 ) and decreases
in t1 ∈ [φ̃t2 , 1];(vi) The relationship between Ω2 and τ is related to the relative magnitude of the domestictransport costs t1 and t2 in the two countries. If t1 = t2 , then Ω2 increases in φτ .
Proof : See the Appendix.
Now we provide some intuition to the detailed results above. First, in the literature
it has been shown that the domestic geographies in the two countries are related if there
is a gated region with a lower transport cost than other regions (Behrens et al. 2006a),
and/or there are density economies with decreasing marginal transport cost (Behrens etal., 2006b). As a complement to their analysis, our results (i) and (iv) say that reducing
the transport cost in one country increases the inequality in the other country, undercapital mobility across country borders. It arises because this action attracts more firms
away from the smaller region in the latter country.
Next, while the inequality in one country has a simple relationship with the transport
costs of the other country, parts (ii) and (v) show that the relationship with its own transport cost is more complicated. The reason is, on the one hand, the foreign transport costs
only affect the national share Λ∗ , which has a monotonic relation with the interregional
inequality given by (iii) of Proposition 1; On the other hand, the domestic transport costs
have direct impacts on the interregional inequality, and this effect works in the opposite
direction to that of the increased national manufacturing share.
To gain more details on this complicated interaction, we now further examine (19).3
When the trade cost τ is large enough such that φτ = 0, then (19) is always true.
Therefore, Ω2 increases in φt1 . On the other hand, if t2 is small such that φt2 = 1, then(17) degenerates to 4φ2τ Θ + φτ (4Θ − 1) + Θ − 1 ≤ 0, or˜ ≡φτ ≤ φ̃t2√

1 + 8Θ + 1 − 4Θ.
8˜ and decreases if φ > φ̃
˜ . Similar conclusion
Therefore, Ω2 increases in φt2 if φt2 < φ̃t2
t2t2
holds when φτ or Θ is large. We thus obtain an inverted U-curve.

3

If we treat the other country as the rest of the world, then analyzing the smaller country is better,
since no country is larger than one half of the whole population in the real world. Therefore, we are moreinterested in (19) than in (17).

17The inverted U-shape curve is often called the Williamson hypothesis, or the Kuznet
hypothesis in development economics.4 Such an inverted U-curve has been shown within a
one-country-two-region model, by incorporating urban costs (Tabuchi, 1998), or workers’
immobility (Puga, 1999), or agricultural transport cost (Fujita, et al. 1999; Picard andZeng, 2005), and within a three-location model in Krugman and Livas Elizondo (1996).
However, in the two-country-four-region model of Monfort and Nicolini (2000) and thethree-location model of Paluzie (2001), the authors find that regional inequality increases
monotonically as international economic integration progresses. In contrast to all theabove, our results (ii), (iii) and (iv) show that, when production factors are mobile andheterogeneous domestic transport costs are allowed in the two countries, it is possible toobtain both the monotonically increasing form and the inverted U-curve, depending on
the parameter values.
Most existing literature also assumes
1
Θ= ,
2

t1 = t2 ≡ t.

(20)

In this case, Λ = 1/2 and Ω1 = (φt + φτ )/(1 − φt ). Therefore,∂Ω1
1 + φτ
=> 0,∂φt(1 − φt )2

∂Ω1
1
=
>0
∂φτ
1 − φt(21)

always hold. In contrast, our results of (ii) and (iii) reveal a more complicated relationshipbetween Ω1 and t1 , (also between Ω1 and τ ) in general situations. While (21) is consistent
with the conclusion of Monfort and Nicolini (2000), this limited result comes from two
respects of assumption (20). First, the assumption of identical domestic transport costs(t1 = t2 ≡ t) automatically implies that improvement in one country is accompanied by
improvement in the other country; Second, the assumption of no size difference in the twocountries implies no relative HME between them. Thus φτ ≤ φt1 < φ̃τ always holds when
Θ = 1/2.
Finally, (iii) and (iv) show that reducing the international trade cost τ have different
impacts on the regional inequalities in the two countries with t1 = t2 . The interregional
4

Empirical studies on China (Fujita and Hu, 2001), Mexico (Sánchez-Reaza and Rodrı́guez-Pose,
2002), Greece (Petrakos and Saratsis, 2000) and the EU–15 (Davies and Hallet, 2002) support the hypothesis. Williamson (1965) argues that catching-up countries enjoying a high national growth rate areoften associated with rising regional disparities. As growth proceeds, however, regional disparities arehypothesized to fall.

18

inequality in Country 1 behaves as an inverted U-curve while the interregional inequality
in Country 2 is monotonically increasing. Particularly, when Θ is large such that φτ > φ̃τ ,Ω1 is decreasing in φτ but Ω2 is increasing in φτ . Thus the inequality in the small country
becomes more severe than in the large country. This conclusion is consistent with (ii) of
Proposition 2 and (iii) of Proposition 1. It also suggests that as industries agglomerate in
the larger country, the larger region in it is not the single winner because the interregional
inequality does not increase in the larger country. Unfortunately, the situation in the
remote region of the smaller country is just the opposite. This result cannot be obtained
either with a one-country-two-region model, or with a symmetric two-country-four-region
model, as in the existing literature.

4

Conclusions

Based on a footloose-capital model of two countries and four regions, this paper examined
the interaction of interregional and international inequalities in the presence of domestictransport costs and international trade costs.
Different from the literature, we assumed countries as well as regions to be asymmetric,
and allowed capital to move across countries. These turned to be important because theygenerated richer and more realistic results than those found in the existing literature. We
find that the national manufacturing share is jointly determined by all transport costs,
domestic and international. Better infrastructure and governance increase production
incentives and attract more firms. A larger national manufacturing share leads to asmaller interregional inequality.
Consequently, the interregional inequality in a country is related to not only its own
domestic transport cost, but also the domestic transport cost in the other country. Furthermore, interregional inequality can exhibit a monotonically increasing relation or an
inverted-U shape under globalization, depending on each country’s infrastructure andgovernance efficiency, as well as the international trade cost, even though the present
model employed the standard centrifugal force (the immobile consumers), as in Monfort
and Nicolini (2000) and Paluzie (2001). These complement the existing literature andhopefully stimulate more research interests on related issues.
Acknowledgement: We wish to thank Hajime Takatsuka and seminar participants at
Kobe University for helpful comments. The usual disclaimer applies.
19Appendix(i) This is simply because
∂Ω1
2Θφ2τ
1
=
> 0.
2
∂φt2
(1 − φt1 )(1 + φt2 − 2φτ ) (Λ∗ )2(ii) The partial derivative of Ω1 with respect to φt1 is∂Ω1
Θ
=∂φt1 (1 − φt1 )2 {Θ[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt2 − 2φτ )φτ }2½
× Θ(1 − φτ )[(1 + φt1 )(1 + φt2 ) − 4φ2τ ]2− φτ (1 + φt2 − 2φτ )2 [4 − (1 − φt1 − φτ )2 − 3φ2τ ]¾
2− 2φτ (φt1 − φt2 )(1 + φt2 − 2φτ )(3 − φt1 − 2φτ ) .
The fraction outside the curly braces is positive because of (12). Let Ω10 denote the terms
inside the curly braces. Then we have∂Ω10
=2(1 + φt2 )∂φt1× {Θ(1 − φτ )[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − (1 − φt1 )(1 + φt2 − 2φτ )φτ }>2(1 + φt2 )[2(1 − φτ )φτ (1 + φt2 − 2φτ ) − (1 − φt1 )(1 + φt2 − 2φτ )φτ ]=2(1 + φt2 )φτ (1 + φt2 − 2φτ )(1 + φt1 − 2φτ )>0,where the first inequality is from (12), and the second inequality is from the assumptionof t1 ≤ τ and t2 ≤ τ . Our conclusion is true because¯Ω10 ¯φ =1 =4(1 − φτ )(1 + φt2 − 2φ2τ )[Θ(1 + φt2 − 2φ2τ ) − (1 + φt2 − 2φτ )φτ ]t1>4(1 − φτ )(1 + φt2 − 2φ2τ )½¾
12× Θ[(1 + φτ )(1 + φt2 ) − 4φτ ] − (1 + φt2 − 2φτ )φτ
2
>0

20

hold and¯
Ω10 ¯φ =φ =(1 − φτ ){Θ[(1 + φt2 )(1 + φτ ) − 4φ2τ ]2t1

τ− (1 + φt2 − 2φτ )φτ [(3 + φτ )(1 + φt2 ) − 8φ2τ ]}is nonnegative if and only if (17) holds.
(iii) The partial derivative of Ω1 with respect to φτ isΘ(1 + φt2 − 2φτ )2 [(1 + φt1 )2 + 4φ2τ − Θ(1 + φt1 + 2φτ )2 ]∂Ω1=∂φτ (1 − φt1 ){Θ[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt2 − 2φτ )φτ }24Θ(φt1 − φt2 )φτ {(φt1 − φt2 )φτ (1 − Θ) + Θ[(1 + φt1 )(1 + φt2 ) − 4φ2τ ]}−.
(1 − φt1 ){Θ[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt2 − 2φτ )φτ }2The second term has a factor of φt1 − φt2 , which is the differential of the trade freeness inthe two countries. The first term is positive if φτ < φ̃τ of (18) and negative if φτ > φ̃τ .
(iv) This is simply because∂Ω22(1 − Θ)φ2τ
1
=
> 0.
2
∂φt1
(1 − φt2 )(1 + φt1 − 2φτ ) (1 − Λ∗ )2(v) The partial derivative of Ω2 with respect to φt2 is
1−Θ
∂Ω2
=
2
∂φt2 (1 − φt2 ) {(1 − Θ)[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt1 − 2φτ )φτ }2½
× (1 − Θ)(1 − φτ )[(1 + φt1 )(1 + φt2 ) − 4φ2τ ]2− φτ (1 + φt1 − 2φτ )2 [4 − (1 − φt2 − φτ )2 − 3φ2τ ]¾
2− 2φτ (φt2 − φt1 )(1 + φt1 − 2φτ )(3 − φt2 − 2φτ ) .
The fraction outside the curly braces is positive because of (12). Let Ω20 denote the terms
inside the curly braces. Then we have∂Ω20
=2(1 + φt1 ){(1 − Θ)(1 − φτ )[(1 + φt1 )(1 + φt2 ) − 4φ2τ ]∂φt2− (1 − φt2 )(1 + φt1 − 2φτ )φτ }>2(1 + φt2 )[2(1 − φτ )(1 + φt1 − 2φτ )φτ − (1 − φt1 )(1 + φt2 − 2φτ )φτ ]21

=2(1 + φt2 )(1 + φt1 − 2φτ )(1 + φt2 − 2φτ )φτ>0,
where the first inequality is from (12), and the second inequality is from the assumptionof t1 ≤ τ and t2 ≤ τ . Our conclusion is true because¯Ω20 ¯φ =1 =4(1 − φτ )(1 + φt1 − 2φ2τ )[(1 − Θ)(1 + φt1 − 2φ2τ ) − (1 + φt1 − 2φτ )φτ ]t2>4(1 − φτ )(1 + φt1 − 2φ2τ )
½
¾
1−Θ
2
×
[(1 + φt1 )(1 + φt2 ) − 4φτ ] − (1 + φt1 − 2φτ )φτ2>0
always hold and¯Ω20 ¯φ =φ =(1 − φτ ){(1 − Θ)[(1 + φt1 )(1 + φτ ) − 4φ2τ ]2t2

τ− (1 + φt1 − 2φτ )φτ [(3 + φτ )(1 + φt1 ) − 8φ2τ ]}which is nonnegative if and only if (19) holds.
(vi) The partial derivative of Ω2 with respect to τ is∂Ω2 (1 − Θ)(1 + φt1 − 2φτ )2 [(1 + φt2 )2 + 4φ2τ − (1 − Θ)(1 + φt2 + 2φτ )2 ]=∂φτ
(1 − φt2 ){(1 − Θ)[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt1 − 2φτ )φτ }2−4(1 − Θ)(φt2 − φt1 )φτ {(φt2 − φt1 )φτ Θ + (1 − Θ)[(1 + φt1 )(1 + φt2 ) − 4φ2τ ]},(1 − φt2 ){(1 − Θ)[(1 + φt1 )(1 + φt2 ) − 4φ2τ ] − 2(1 + φt1 − 2φτ )φτ }2The second term has a factor of φt2 − φt1 , which is the differential of the trade freeness inthe two countries. Meanwhile, the first term is always positive according to (12).

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