takatsuka and zeng (2012)_trade liberalization and welfare differentiated-good

8/17/2019 Takatsuka and Zeng (2012)_Trade Liberalization and Welfare Differentiated-good

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Trade liberalization and welfare: Differentiated-good

versus homogeneous-good markets

Hajime Takatsuka a,⇑, Dao-Zhi Zeng b,c

a Graduate School of Management, Kagawa University, Saiwai-cho 2-1, Takamatsu, Kagawa 760-8523, Japanb Graduate School of Information Sciences, Tohoku University, Aoba 6-3-09, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japanc Center for Research of Private Economy, Zhejiang University, Zheda Road 38, Hangzhou, Zhejiang 310027, China

a r t i c l e i n f o

Article history:

Received 11 August 2011

Revised 14 April 2012

Available online 23 May 2012

JEL classification:F12

Q17

R1

Keywords:

Trade costs

Firm location

Home market effect

Trade liberalization

Welfare

a b s t r a c t

Takatsuka, Hajime, and Zeng, Dao-Zhi—Trade liberalization and

welfare: Differentiated-good versus homogeneous-good markets

In this paper, we examine the effects of liberalization on industrial

location and national welfare in a framework of new economic

geography. Specifically, we explicitly incorporate arbitrary tradecosts in both differentiated-good and homogeneous-good sectors

into a two-country model, and clarify the effects of trade-barrier

reduction in each sector. We show that their impacts on welfare

levels in the two countries are different, and, if an industry is liber-

alized while the other is protected, a conflict between the countries

might occur. Therefore, appropriate liberalization in both sectors is

effective to alleviate such a conflict. J. Japanese Int. Economies 26 (3)

(2012) 308–325. Graduate School of Management, Kagawa Univer-

sity, Saiwai-cho 2-1, Takamatsu, Kagawa 760-8523, Japan; Gradu-

ate School of Information Sciences, Tohoku University, Aoba 6-3-

09, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan; Center for

Research of Private Economy, Zhejiang University, Zheda Road

38, Hangzhou, Zhejiang 310027, China.

2012 Elsevier Inc. All rights reserved.

1. Introduction

In this paper, we examine the impacts of trade liberalization on industrial location and national

welfare in a framework of new economic geography (NEG) (Fujita et al., 1999; Baldwin et al., 2003).

0889-1583/$ - see front matter 2012 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/j.jjie.2012.05.003

⇑ Corresponding author. Fax: +81 87 832 1907.

E-mail addresses: [email protected] (H. Takatsuka), [email protected] (D.-Z. Zeng).

J. Japanese Int. Economies 26 (2012) 308–325

Contents lists available at SciVerse ScienceDirect

Journal of The Japanese and

International Economiesj o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j j i e

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Specifically, we explicitly incorporate arbitrary trade costs in both differentiated-good and homoge-

neous-good sectors into a two-country model, and clarify the effects of trade-barrier reduction in each

sector. We show that reducing the trade barrier in the homogeneous-good sector has a different impact

on the welfare levels in two countries from reducing the trade barrier in the differentiated-good sector.

According to Article XXIV of the General Agreement on Tariffs and Trade (GATT), all free trade

agreements (FTAs) should aim to eliminate duties and other restrictive regulations of commerce on

substantially all the trade among participating countries. However, in real FTAs, some industries are

often protected. For example, the United States excluded about 100 items (e.g., sugar and dairy prod-

ucts) from the liberalized list of a US–Australia FTA in 2005. In addition, Japan carefully protects the

agricultural market by imposing high tariffs and is very reluctant to join the Trans-Pacific Partnership

(TPP). These facts indicate the necessity to examine how a country’s welfare level changes if some indus-

tries are liberalized while others are protected.

Trade costs include various barriers to trade. In addition to formal regulations such as tariffs, the

technical barriers to trade (TBT) are also significantly restrictive. In particular, country-specific prod-

uct standards have the potential to keep foreign producers out of domestic markets by imposing adap-

tation costs (Fischer and Serra, 2000; Gandal and Shy, 2001), while internationally shared standards

(e.g., International Organization for Standardization (ISO)) are expected to promote trade (Swannet al., 1996). Interestingly, an empirical result of Moenius (2004) shows country-specific standards

having different impacts on the trade pattern. Although they tend to inhibit trade in non-manufac-

tured goods such as agriculture, they promote trade in manufactured goods.

Turning to theoretical trade studies, since Krugman (1980), the literature of NEG successfully clari-

fies that industrial location is strongly related to trade costs.1 However, most NEG papers focus on the

positive aspects, particularly the home market effect (HME), rather than the welfare issues (Davis,

1998; Head and Ries, 2001; Head et al., 2002; Ottaviano and Thisse, 2004; Yu, 2005; Crozet and Trionfetti,

2008; Zeng and Kikuchi, 2009). Some studies have focused on the gains and losses from trade; however,

the comparisons are limited to completely free-trade economies with entirely autarky economies

(Krugman, 1981; Venables, 1987). Furthermore, since Helpman and Krugman (1985), most NEG papers

(e.g., Krugman and Venables, 1990, 1995; Baldwin and Venables, 1995) imposean assumption of free tradeon the homogeneous good. Although this convenient assumption makes the analysis of the differentiated-

good sector much easier, it has two theoretical defects. First, if the two countries have identical technology

in the homogeneous-good sector, the wages in the two countries are equalized under this assumption,

failing to capture the wage gap between countries. Baldwin and Robert-Nicoud (2000) showed the reduc-

tion of frictional barriers between asymmetric-sized nations improving the welfare of both nations when

wages in the two countries are equalized by the free-trade assumption in the homogeneous-good sector. It

is uncertain if their result remains true when a wage gap is possible. Second, it becomes impossible to

examine the integration of the homogeneous-good markets under this assumption.

The importance of transport costs in the homogeneous-good sector was first recognized by Davis

(1998), who showed that the HME of Helpman and Krugman (1985) disappears if the homogeneous

good is transported with the same positive cost as the differentiated goods. Fortunately, their modelcan be used in our research. We maintained the structure of two asymmetric-sized countries, one pro-

duction factor (labor), and two sectors, in which arbitrary trade costs were allowed in both sectors.

This made it possible to compare the integration of the differentiated-good and homogeneous-good

markets. Furthermore, we were able to analyze the effects of integration on welfare at an arbitrary

level of trade costs. Thereby, we clarified when and which market integration produces (or does not

produce) a conflict between the two countries.

To the best of our knowledge, the equilibrium analysis of the Helpman–Krugman–Davis model is

incomplete. While Helpman and Krugman (1985) focused on the case of free trade in the homoge-

neous-good sector, Davis (1998) mainly considered the case of equal trade costs in the two sectors.

The case of arbitrary trade costs in the homogeneous-good sector remains unclear. Therefore, before

the welfare analysis, we rigorously re-examined the equilibrium of industrial location and wage forarbitrary trade costs in the two sectors.

1 Fujita and Thisse (1996) is a comprehensive review of theories of agglomeration economies.

H. Takatsuka, D.-Z. Zeng / J. Japanese Int. Economies 26 (2012) 308–325 309


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We obtained the following results. First, we found a necessary and sufficient condition for observ-

ing the HME. The condition is given as a relationship between the trade cost of the differentiated goods

and the trade cost of the homogeneous good. This result provides a comprehensive understanding of

some known results scattered in the literature. Second, when the differentiated-good markets are

more deeply integrated, the number of differentiated-good firms in the larger country (resp. the smal-

ler country) evolves as an inverted-U-shaped curve (resp. a U-shaped curve). Meanwhile, the smaller

country is definitely better off, whereas the larger one could be worse off. Third, when the homoge-

neous-good markets are more deeply integrated, the number of differentiated-good firms in the larger

country (resp. the smaller country) monotonically increases (resp. decreases). Meanwhile, the smaller

country is definitely worse off along the interior equilibrium path, whereas the welfare in the larger

country is definitely improved. In summary, if an industry is liberalized while the other is protected,

a conflict between the countries might happen. Therefore, appropriate liberalization in both sectors is

effective to alleviate such a conflict.

The remainder of this paper is organized as follows. Section 2 sets up the model of Helpman and

Krugman (1985) and Davis (1998). Section 3 is a detailed description of the relationship among trade

costs, firm location, and the HME. Section 4 is an analysis of the welfare, presenting the main results.

Section 5 is the conclusion.

2. The model

The economy consists of two countries (the north N and the south S), two sectors (modern M and

traditional A),2 and one production factor (labor). The amount of labor in country N is denoted as L, and

its counterpart in country S is denoted with an asterisk. The worldwide endowment Lw = L + L⁄ is fixed.

The share of labor in country N (L/Lw) is denoted as h. We assume that country N is larger: h 2 (1/2,1).

Sector M consists of a continuum of product varieties and is characterized by increasing returns to

scale (IRS) and monopolistic competition, whereas sector A produces a homogeneous good under con-

stant returns to scale (CRS) and perfect competition.

Workers are assumed to hold the same preference described by a Cobb–Douglas utility for the two

types of goods with a constant elasticity of substitution (CES) subutility on the varieties of good M :

U ¼ M l A1l

; ð1Þ

where

M

Z nw0

mðiÞr1

r di

" # rr1

;

nw is the number of varieties in sector M , and m(i) is the consumption of variety i. Parameter r > 1 isthe elasticity of substitution between any two varieties of good M , and l 2 (0,1) is the expenditure

share on good M .As in most related papers, we assume Samuelson’s iceberg trade costs. Specifically, sM (resp. s A)

units of the good M (resp. good A) must be shipped for one unit to reach the other country, where

sM 2 (1,1) and s AP 1 are assumed in the paper. The concept of trade costs here is rather general.In addition to transport costs, it contains adaptation costs if exporters have to adjust their goods to

the foreign market because of country-specific standards. Furthermore, as in Baldwin and Robert-

Nicoud (2000, p. 770), sM and s A also include tariffs.3

Labor is the only production factor. Each worker owns one unit of labor, which is immobile across

countries. In the production of good M , each firm needs a marginal cost of (r 1)/r units of labor anda fixed cost of f units of labor. Meanwhile, in the production of good A, one unit of labor produces one

unit of good A. Following Helpman and Krugman (1985) and Davis (1998), we assume that the con-

2 Many authors call them manufacturing sector and agricultural sector, respectively.3 However, even if such an interpretation is applied, in the following analysis, we assume that tariff revenue plays a negligible

role in national welfare calculations, as is the case of all nations of the Organization for Economic Co-operation and Development

(OECD) (Baldwin and Robert-Nicoud, 2000, p. 775).

310 H. Takatsuka, D.-Z. Zeng / J. Japanese Int. Economies 26 (2012) 308–325

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sumption share of good A is sufficiently large for both countries to constantly produce good A. We nor-

malize the wage in S as w⁄ = 1 and denote the wage in N as w. Then, the prices of good A in countries N

and S are

p A ¼ w; p A ¼ w

¼ 1; ð2Þ

respectively. Note that the wage is the only income of the workers. Therefore, the total expenditures in

N and S are

E ¼ Lw; E ¼ L; ð3Þ

respectively. Meanwhile, the total costs of producing x units of each variety of good M in N and S are

c ( x) = fw + (r 1) wx/r and c ⁄( x) = f + (r 1) x/r, respectively.Let p be the price of a variety of good M in country N made in country N, p⁄ be the price of a variety

in country S made in country S, p be the price of a variety in country N made in country S, and p be the

price of a variety in country S made in country N.4 Then, the monopolistic competition framework of

Dixit and Stiglitz (1977) suggests that

p ¼ w; p ¼ 1; p ¼ sM ; p ¼ wsM : ð4Þ

From (1), the demand (including iceberg costs) of each variety produced in N is

dM ¼ l pr

P 1r E þ sM l

ð pÞr

ðP Þ1r E

; ð5Þ

where P and P ⁄ are the price indices of good M in the two countries, respectively. They are defined by

P ¼ ½np1r þ nð pÞ1r

1

1r; P ¼ ½nð pÞ1r

þ nð pÞ1r

1

1r; ð6Þ

where n and n⁄ are the numbers of firms in the two countries, respectively. On the other hand, from (1)

to (3), the demands of good A in the two countries are

d A ¼ ð1 lÞE

p A; d

A ¼ ð1 lÞE

; ð7Þ

respectively.

In the model, free entry and exit of firms are assumed so that firms have zero profit. Therefore, the

output and input of each firm in the two countries are

x ¼ x ¼ f r; ð8Þ

l ¼ l

¼ f r; ð9Þ

respectively. Thus, from (3) to (6) and (8), the market-clearing conditions for each variety of good M

produced in N and S are

lwr hLww

nw1r þ n/M þ

ð1 hÞLw/M n þ n/M w

1r

¼ f r; ð10Þ

l ð1 hÞLw

n þ n/M w1r

þ hLww/M nw1r þ n/M

¼ f r; ð11Þ

where /M s1rM is the trade freeness of good M .

3. Trade costs, firm location, and the home market effect

In this section, we examine the equilibrium firm location. Following Krugman (1995, p. 1261) and

Davis (1998, p. 1271), we formally apply the following definition in this paper:

4 Because of symmetry among varieties, this price is independent of the variety name.



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Definition 1. The home market effect (HME) is the phenomenon that the larger country is a net

exporter of good M .

While the above definition is based on the trade pattern, many papers on the HME employ another

definition focusing on firm location: The larger country attracts more than proportionate share of

firms in the IRS sector. The following Lemma says that they are equivalent.

Lemma 1. The HME occurs iff

n

n þ n > h: ð12Þ

Proof. Denote the labor input in sector M in N and S as LM and LM . Since the labor input of each firm in

any country is the same given by (9), Eq. (12) is equivalent to

LM > h

1 hL

M

:

From the assumption L = hL⁄/(1 h), the above inequality is rewritten as

L LM < h

1 h L LM

;

which implies that the share of labor input in sector A (=the share of good A produced) in N is less than

h. On the other hand, according to Eqs. (2), (3) and (7),

d A

d A

¼ð1lÞwhLw

w

ð1 lÞð1 hÞLw ¼

h

1 h;

which implies that the share of good A consumed in N is h. Thus, we conclude that (12) is equivalent tothe fact that country N is an importer of good A. In other words, by the trade balance, this suggests that

country N is a net exporter of good M . h

If good A is not traded between the two countries, then the trade in good M is balanced and the

HME disappears. Meanwhile, the total output of good A is (1 l)L in country N and (1 l)L⁄ in coun-try S. Therefore, in this case, (9) gives

n ¼ lL f r

¼ lhLw

f r ; n ¼

lL

f r ¼

lð1 hÞLw

f r : ð13Þ

Substituting (13) into (11), we obtain

F ðwÞ ðw1r w/M Þh ðwr /M Þð1 hÞ ¼ 0 ð14Þ

after simplification. Therefore, the equilibrium wage is determined by (14) when A is not traded.

Clearly, F (w) decreases in w, and it holds that

F ð1Þ ¼ ð1 /M Þð2h 1Þ > 0;

F sr1

rM

¼

1

/M /M

ð1 hÞ < 0;

where the inequalities are from h 2 (1/2,1) and /M < 1. Thus, (14) has a unique solution that lies in

1; sr1r

M and will be denoted by ~w. On the other hand, when A is traded, Appendix A shows that itis impossible for country S to be the importer of good A. In other words, country N necessarily imports

A so that w = s A. Therefore, ~w is actually the highest value of trade costs for good A to be traded.Accordingly, we occasionally use ~s A to denote ~w, indicating the fact that good A is nontradable if and only if s A P ~s A.


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We have the following results on the HME and ~s A:

Proposition 1.

(i) Good A is tradable if and only if s A < ~

s A;(ii) the HME is observed if s A 0; @ ~s A@ h

> 0; @ ~s A@ r

< 0; limsM !1

~s A ¼ h

1 h

12r1

:

Proof. See Appendix A. h

As shown in Fig. 1, the above result is helpful to comprehensively understand some known results

scattered within the literature. Typically, good A is tradable when s A = 1. Helpman and Krugman(1985) examined the firms’ locations in this case and found the HME. Proposition 1 (ii) generalizes

their result and shows that the HME is observed in the whole shaded area of Fig. 1 (i.e., s A 1 holds for all h > h, which is neither sufficient

nor necessary for the HME.

In contrast, we found a necessary and sufficient condition for observing the HME. Thus, we couldinvestigate how some parameters affect the region of s A where the HME appears. Proposition 1 (iii)provides four results showing how ~s A depends on relative parameters. The first and the secondinequalities show that a larger trade cost of A is necessary to obscure the HME when sM or h is larger.This is because firms save more trade costs by locating in the larger country in such a situation. Mean-

while, a higher elasticity of substitution suggests smaller price cost markups and smaller economies of

scale in equilibrium and hence, it works against agglomeration of firms. This is captured by the third

inequality. Finally, the equality gives an upper bound of ~s A.

Fig. 1. The existence of the HME.


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Next, we consider how firms relocate when either sM or s A falls. We have the following result:

Proposition 2. At the interior equilibrium with tradable A,

(i) the firm number in the larger country (resp. the smaller country) monotonically increases (resp.

decreases) when s A falls;(ii) the firm number in the larger country (resp. the smaller country) evolves as an inverted-U-shaped

curve (resp. a U-shaped curve) when sM falls.

Proof. See Appendix B. h

To understand Proposition 2 (i), we note that the relative wage in N increases in s A as long as A istradable, since it holds that w = s A. The wage differential has two effects. On the one hand, it has animpact on the production side. As firms pay the wages as production costs, more firms are attracted

from S to N if w or s A falls. On the other hand, it also has an impact on the demand side. When w falls,the deducted wage income in N shrinks the market size of good M so that more firms of M are likely tomove out from the market to save transport costs. Proposition 2 (i) shows that the former production-

cost effect definitely dominates the latter income effect in our setup. Therefore, the firm number in N

(resp. S) monotonically increases (resp. decreases) for a falling s A. Such a change is shown by vector (I)in Fig. 1.

Helpman and Krugman (1985) concluded that a small country is de-industrialized when the good

M markets are more integrated. Proposition 2 (ii) shows that their result is not valid when the trade

costs of good A are positive. Specifically, there is a re-dispersion process whereby firms return to the

small country for a sufficiently small sM . This is because the dispersion force of a higher wage in thelarger country dominates the agglomeration force due to the market size.5 Such a change is shown by

vector (II) in Fig. 1. In summary, the argument of Helpman and Krugman (1985) is true for a falling s Arather than sM .

4. Welfare

In this section, we focus on welfare, which is the main concern of the paper. The indirect utility of

workers in N and S is expressed as

x ¼ wlP l; x ¼ ðP Þl;

respectively.6 Furthermore, from (4) and (6), the above equations are rewritten as

x ¼ ½n þ n/M wr1

lr1; x ¼ n/M

wr1 þ n

lr1

: ð15Þ

From the above equations, we know that the welfare in each country is determined by three fac-

tors: the trade freeness of good M (/M ), the number of firms (n,n⁄), and the wage in N (w). Clearly, if other

things are equal, the first two factors have positive effects on the welfare in both countries. Mean-

while, the third factor has a positive effect on local welfare and a negative one on foreign welfare.

For example, a higher wage w in N implies a higher price of differentiated goods produced there,

which lowers the welfare in S. Meanwhile, in country N, a higher wage also implies a higher income,

dominating the negative effect of higher prices and leading to a higher local welfare.

First, we derive the following result for the welfare comparison:

Proposition 3. The welfare in the larger country is always higher than that in the smaller country.

5 Zeng and Kikuchi (2009) analytically showed this fact with a model based on Ottaviano et al. (2002).6 For simplicity, a constant multiplier, ll(1 l)1l, is omitted in each equation.


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Proof. The previous section shows that w = s A if good A is tradable and w ¼ ~s A when A is nontradable.

In either case, we have w < sr1r

M < sM , which implies w1r > /M > /M w

1r. Therefore, it holds that

n

n > 1 >

w1r /M

w1r /M

ðw1rÞ2

¼ w1r /M

w1rð1 /M w1rÞ

; ð16Þ

where the first inequality is from Proposition 1 (ii). The inequalities of (16) imply

nw1rð1 /M w1rÞ > nðw1r /M Þ;

which derives x > x⁄ according to (15). h

Subsequently, we examine how the welfare in each country changes when either trade cost sM ors A decreases.

4.1. Falling sM

This subsection focuses on the decreasing sM , as illustrated by vector (II) in Fig. 1. We consider thecase of tradable A (the shaded area in Fig. 1) in Section 4.1.1 and the case of nontradable A in

Section 4.1.2.

4.1.1. The case of tradable good A

In this case, the large country imports good A from the small country (Appendix A (ii)), and thus, we

have w = p A = s A. Therefore, (15) could be rewritten as

x ¼ n þ n /M / A

lr1

; x ¼ ½n/M / A þ n

lr1; ð17Þ

where / A s1r

A is the trade freeness of good A. From the fact that w = s A, (10) and (11), we have

n ¼ s AlL

w

f rð1 hÞsr A /

2

M ½1 þ ðs A 1Þh/M þ h/ Að/ A s A/M Þðs A / A/M Þ

; ð18Þ

n ¼ s A/ AlL

w

f rhs A/

2

M ½1 þ ðs A 1Þhsr A /M þ ð1 hÞ

ð/ A s A/M Þðs A / A/M Þ : ð19Þ

Note that the above equations are true only if the RHSs of (18) and (19) are nonnegative. Otherwise,7

n ¼ lðhs A þ 1 hÞL

w

f rs A; n ¼ 0: ð20Þ

By (17)–(19), we have

@ xr1

l

@ /M ¼ l

hLws A /2M þ 1 2sr A/M

f r sr A /M 2

/ A

; ð21Þ

@ ðxÞr1

l

@ /M ¼

lð1 hÞLw sr A /2

M þ 1

2/M

f r sr A/M 1 2 > 0; ð22Þ

at the interior equilibrium. Inequality (22) implies that x⁄ increases in /M . Furthermore, it holds that

@

@ /M

xr1

l

ðxÞr1

l

" # ¼

hs A s2r A 1

ð1 hÞ sr A /M 2

/ A

< 0 ð23Þ

from (18) and (19). Thus, we know that x/x⁄ decreases in /M at the interior equilibrium.On the other hand, for a corner equilibrium with n⁄ = 0, we have

7 Appendix A shows that the corner equilibrium with n = 0 is impossible.


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9/18

@ xr1

l

@ /M ¼ 0;

@ ðxÞr1

l

@ /M ¼

lðhs A þ 1 hÞLw

f rs A/ A > 0;

from (17) and (20). These imply that x is independent of /M , while x⁄ must increase in /M .

Finally, from (21), we have

@ xr1

l

@ /M

/M ¼0

¼ lhLw

f rsr A> 0;

which implies that x increases in /M for a small /M at the interior equilibrium. However, for a large/M , x might increase or decrease in /M . For a further examination, let

T ðs AÞ 1 h

h

sr1 A 1 2s A 1 hh

sr1 A 1 þ 2ðsr A 1Þ; ð24Þwhich increases in s A because

T 0ðs AÞ ¼ 2ð1 hÞ

h2 s2r3 A ½hð2r 1Þs A ð1 hÞðr 1Þ > 0:

Meanwhile, it holds that

T ð1Þ ¼ 2 1

h

2< 0; T

h

1 h

1r1

! ¼ 2

h

1 h

rr1

1 > 0:

Therefore, T (s A) = 0 has a unique solution s]

A 2 ð1; ½h=ð1 hÞ1=ðr1ÞÞ, which is illustrated in Fig. 1. We

summarize the results as follows:

Proposition 4. If good A is costly tradable (i.e., s A 2 ð1; ~s AÞ),

(i) x⁄ increases in /M , and the ratio x / x⁄ decreases in /M ;

(ii) at the interior equilibrium, x increases in /M when s A > s]

A and has an inverted-U-shaped relation-

ship with /M when s A


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The model of Helpman and Krugman (1985) is the case of s A = 1. In a similar manner, we obtain thefollowing results for their case: (i) at the interior equilibrium, both x and x⁄ increase in /M , and theirratio x/x⁄ is independent of /M

8 and (ii) for a corner equilibrium, x is independent of /M , x⁄ increases

in /M , and their ratio x/x⁄ decreases in /M . Therefore, an integration of good M markets basically im-

proves the welfare of both countries, which is similar to the result of Baldwin and Robert-Nicoud

(2000, Section 3). This is because, in both papers, the assumption of costless trade of good A, which

equalizes wages in two countries and does not capture the U-shaped evolution of firm location, is

imposed.

4.1.2. The case of nontradable good A

In this case, firms in sector M are distributed in proportion to country size. The firm numbers in N

and S are expressed by (13) and the equilibrium wage in N is ~w, the unique solution of (14). Recall that

~w ¼ ~s A 2 1; sr1r

M

holds and ~w decreases in /M (see Fig. 1and Proposition 1 (iii)).

In this case, from (15), we have

x

r1

l ¼

lLw

r f ½h þ ð1 hÞ~wr1

/M ; ð25Þ

ðxÞr1

l ¼ lLw

r f ½h~w1r/M þ ð1 hÞ: ð26Þ

According to (26), x⁄ increases in /M since ~w decreases in /M .On the other hand,

@ ~wr1/M @ /M

¼ ðr 1Þ~wr2/M d ~w

d/M þ ~wr1

¼~w2rð1 hÞr þ ~whðr 1Þ þ /M ~w

r½ðr 1Þð1 hÞ ~whðr 2Þ~w2F 0ð~wÞ

; ð27Þ

where the second equality is obtained by the implicit function theorem. Since F 0(w) < 0, the denomi-

nator is positive. Then, if ðr 1Þð1 hÞ ~whðr 2ÞP 0, (27) is evidently positive. Otherwise, wehave

~whðr 1Þ þ /M ~wr½ðr 1Þð1 hÞ ~whðr 2Þ

> ~whðr 1Þ þ ½ðr 1Þð1 hÞ ~whðr 2Þ ¼ ~wh þ ðr 1Þð1 hÞ > 0;

where the first inequality is from ~w < sr1r

M . Therefore, (27) is always positive, which implies that x in-creases in /M .

Furthermore, from (25) and (26), we have

@

@ /M x

r1l

ðxÞr1

l

" # ¼ l

Lw

r f

ð1 hÞðxÞr1

l @ ~wr1 /M

@ /M

hxr1

l @ ~w1r/M

@ /M

ðxÞ2ðr1Þ

l 1/2,x > x⁄, and

@ ~w1r/M @ /M

> @ ~wr1/M

@ /M ;

where the last inequality is from the fact that ~w decreases in /M . Thus, we know that x/x⁄ decreases

in /M .

The above results are summarized as follows:

Proposition 5. If good A is nontradable (i.e., s A P ~s A), both x and x⁄ increase in /M , and their ratio x / x

⁄

decreases in /M .

8 For s A = 1, (23) becomes 0.


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11/18

Note that equilibrium wage ~w decreases in /M , while the number of firms in each country does not

change when A is nontradable. Thus, the welfare in S clearly increases, since the price of imported vari-

eties in country S (i.e., p ¼ ~wsM ) decreases. With respect to country N, the decreasing ~w reduces theincome as well as the price index of good M . Proposition 5 concludes that the positive effect dominates

the negative one and the welfare in N also increases.

Our model is adequately general to include the model of Krugman (1980, Section II) as a special

case of l = 1 (without sector A). Thus, Proposition 5 also holds for his setup.Fig. 2 provides simulation examples of r = 5, l = 0.4, and h = 0.7. From (24), we have s] A ¼ 1:04 in

this setting. The left side of the figure corresponds to the case with a smaller s A ¼ 1:02 < s]

A

, and

the right side is the case with a larger s A ¼ 1:05 > s]

A

. The upper graphs (a1) and (b1) show changes

of firm numbers for sector M with /M and the lower ones (a2) and (b2) show welfare changes with /M in each case. Note that, as in Fig. 1, good A is nontradable when /M is large (i.e., sM is small). The figureconfirms Propositions 4 and 5.

4.2. Falling s A

Next, we examine the effects of s A 2 ½1; ~s AÞ on the welfare.9 From (17) to (19), we have

@ xr1

l

@ s A ¼

lhLwsr1 A /M 1 /2

M f sr A /M

2 < 0;

Fig. 2. Effects of /M

on firm location and national welfare.

9 If s A P ~s A, good A is not traded, and, thus, decreasing s A does not change the equilibrium.



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@ ðxÞr1

l

@ s A¼

lð1 hÞLwsr1 A /M 1 /2

M

f sr A/M 1 2 > 0;

at the interior equilibrium. In other words,x increases in / A ¼ s1r

A

, while x⁄ decreases in / A. On the

other hand, for a corner equilibrium with n⁄ = 0, we have

@ xr1

l

@ s A¼

lð1 hÞLw

f rs2 A


13/18

When s A falls, w decreases, and n (resp. n⁄) increases (resp. decreases), while /M does not

change. Regarding the welfare in country N, Proposition 6 shows that the positive effect of increas-

ing n dominates the negative effect of decreasing w. In contrast, with respect to the welfare in S,

the negative effect of decreasing n⁄ dominates the positive effect of decreasing the price of im-

ported varieties in the country. At first glance, the above result (ii) might be counterintuitive be-

cause increasing / A improves country S’ export of A. However, our model captures the firm

relocation. A large sector A in S results in a small number of firms in M and finally, decreases

the welfare in S.

Fig. 3 provides simulation examples with the same parameter values as in Fig. 2 except for /M and

/ A, which confirms Proposition 6. The left side of the figure corresponds to the case with a smaller

/M (=0.2), and the right side is the case with a larger /M (=0.4). The upper graphs (a1) and (b1) show

changes of firm numbers of sector M with / A and the lower ones (a2) and (b2) show welfare changes

with / A in each case. Note that, from Proposition 1, good A is nontradable when / A is small (i.e., s A islarge). Furthermore, in the case with a larger /M , firms of sector M completely agglomerate in N for a

larger / A. This is consistent with Helpman and Krugman (1985), in which firms agglomerate in the lar-

ger country for a larger /M when / A = 1.

4.3. Discussion

For the interior equilibrium case, our results in Propositions 1–6 are summarized in Table 1, where

a falling sM is represented by ‘‘/M "’’and a falling s A is represented by ‘‘/ A".’’From the viewpoint of welfare, we find that the impact of integrating the homogeneous-good mar-

kets is contrastive to that of integrating the differentiated-good markets. In fact, the welfare in the

smaller country is improved, and the welfare differential (in terms of welfare ratio) becomes smaller

when the differentiated-good markets are more integrated. However, the welfare in the smaller coun-

try is lowered, and the welfare differential becomes larger when the homogeneous-good markets are

more integrated. In other words, while the integration of differentiated-good markets does not threa-

ten the smaller country, the integration of homogeneous-good markets does. This implies that increas-ing the trade freeness of differentiated varieties is beneficial to small countries even if it drives firms

from there to relocate to a larger country. Meanwhile, although increasing / A also contributes to

decreasing the price of imported varieties of the differentiated good via decreasing the wage in the

larger country, such a positive effect is not sufficiently large to dominate the negative effect of

decreasing firm share. On the other hand, the welfare in the larger country is improved when the

homogeneous-good markets are more integrated, while it might be lowered when the differentiated-

good markets are more integrated. In addition, this result shows that firm relocation is crucial for na-

tional welfare.

Table 1

Effets of globalization at the interior equilibrium.

Notes: +: Increase, : decrease, 0: no change.



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Table 1 reveals that x and x⁄ may change in different directions, suggesting possible conflicts(shown by two oval boxes) in free-trade policy. More specifically, integrating the differentiated-good

markets generates a conflict when trade costs of both sectors are small, whereas integrating the homo-

geneous-good markets definitely generates a conflict at the interior equilibrium. In both conflict cases,

firms producing differentiated varieties go out from the country where the welfare is lowered. Mean-

while, in the first conflict case, the price of imported varieties decreases in the country, which allevi-

ates the welfare loss and the liberalization can be beneficial to the country even if firms go out. On the

contrary, it is not true in the second conflict case of integrating the homogeneous-good markets. This

is one of the reasons why liberalization of agricultural products is delayed in some countries, as men-

tioned in the Introduction.

Consequently, liberalizing one sector may not be supported by both countries in a long-run equi-

librium with firm relocation due to a possible conflict. To alleviate such a conflict, appropriate liber-

alization in both sectors is effective. The larger (resp. smaller) country is definitely better off by

liberalizing the homogeneous-good (resp. differentiated-good) sector even if the country suffers a

welfare loss from the liberalization of the other sector. In other words, when the welfare in a country

is lowered by the integration of one sector, it is possible to reduce the welfare loss in the country by

slightly liberalizing the other sector, keeping the other country better off compared to its state beforeliberalization of both sectors.

Finally, our findings are consistent with some historical facts. Following the literature (e.g., Da-

vis, 1998; Fujita et al., 1999), we consider the differentiated and the homogeneous goods as the

manufactured and the agricultural goods, respectively. According to Kindleberger (1975, p. 33),

some political economists in Britain in the 19th Century sought free trade of agricultural goods

as a means of slowing down the development of manufacturing on the Continent. They believed

that other European countries could be diverted to invest more heavily in agriculture and to retard

the growth to manufacturing by the British repeal of the Corn Laws in 1846. This story is consistent

with our results of industrial relocation and welfare change accompanied by liberalizing the homo-

geneous-good sector. In fact, while the immediate impact of repealing the Corn Laws was not sig-

nificant (Grigg, 1989, p. 21), it paved the way for the agricultural depression after 1870 on the onehand, and increased industrial activities leading to the industrial agglomeration in the UK on the

other hand.

With respect to the recent FTA issue, the conflict occurs when manufacturing firms move from a

developed country to a developing country in order to save labor costs. To prevent the relocation of

firms, developed economies occasionally oppose the freer trade of manufacturing goods. For example,

the United States and Korea ratified a US–Korea FTA in November 2010. However, its negotiation was

long delayed due to the controversial issues regarding automobiles. By a US request, the agreement

finally allowed for the United States to retain a 2.5 percent tariff on vehicle imports until the fifth year.

This might be also consistent with our results of industrial location and national welfare.

5. Concluding remarks

This study is an examination of the effects of liberalization (i.e., falling trade costs) on industrial

location and national welfare. We use the Helpman–Krugman–Davis model with two countries, one

factor, and two industries, both of which incur trade costs. The following results were obtained.

First, we found a necessary and sufficient condition for the HME to be observed. The condition is in

regard to the trade costs of differentiated and homogeneous goods, and the result is helpful for a com-

prehensive understanding of some known results throughout the literature. Second, when the differ-

entiated-good markets are more integrated, the number of differentiated-good firms in the larger

country (resp. the smaller country) evolves as an inverted-U-shaped curve (resp. a U-shaped curve).

Meanwhile, the welfare in the smaller country must be better off, while the welfare in the larger coun-try could be worse off. Third, when the homogeneous-good markets are more integrated, the number

of differentiated-good firms in the larger country (resp. the smaller country) monotonically increases

(resp. decreases). Meanwhile, the welfare in the smaller country must be worse off at the interior equi-

librium while the welfare in the larger country must be improved.



15/18

In summary, if an industry is liberalized while the other is protected, a conflict between the coun-

tries might occur. Accordingly it is effective to appropriate liberalize trade in both sectors to alleviate

the conflict.

Acknowledgments

The authors are very grateful to an anonymous reviewer, Carlos Bacha, Taiji Furusawa, Salvador

Gil-Pareja, Tatsuo Hatta, Ryusuke Ihara, Jota Ishikawa, Edwin L.-C. Lai, Shin-Kun Peng, Kenmei Tsubota,

and Kazuhiro Yamamoto for their useful comments. The financial support from the Japanese Ministry

of Education, Culture, Sports, Science, and Technology and Japan Society for the Promotion of Science

through Grants-in-Aid for Scientific Research 20730183, 22330073, 24530303 for the first author, and

24243036, 24330072, 22330073, 21243021, and the Y. C. Tang disciplinary development fund of Zhe-

jiang University for the second author are acknowledged.

Appendix A. Proof of Proposition 1

The case of nontraded A is already considered in the text, so we analyze the case of traded A here.

First, we show that it is impossible that all firms agglomerate in country S. Otherwise, country N im-

ports good M , which implies that country N exports good A and w = 1/s A by the trade balance. Notingn = 0 and w = 1/s A, the market-clearing condition for good M (11) gives

n ¼ lLw

f r ð1 hÞ þ

h

s A

:

The number of workers of sector A in S is

ð1 hÞLw n f r ¼ ð1 hÞLw lLw ð1 hÞ þ h

s A

;

from (9), and, thus, the import of good A in S is

ð1 lÞð1 hÞLw ð1 hÞLw lLw ð1 hÞ þ h

s A

¼ lLw 2ð1 hÞ þ

h

s A

: ðA:1Þ

On the other hand, the export of good A from N is

hLw ð1 lÞhLw

s A¼

lhLw

s A;

which is always smaller than (A.1). Therefore, it is impossible that all firms agglomerate in country S.

Second, we show that it is impossible that all firms agglomerate in country N for s A P ~s A. Other-wise, country N imports good A, which implies w = s A. From (10), (11), n

⁄ = 0 and w = s A, the mar-ket-clearing condition for each variety of good M produced in N and the condition for no firms in S

are written as

lLw

n h þ

1 h

s A

¼ f r; ðA:2Þ

lLw

n

ð1 hÞ

/M / Aþ

s Ah/M / A

< f r; ðA:3Þ

respectively. From (A.2), we obtain

n ¼ lLw

f r h þ

1

s Að1 hÞ :

Substituting this into (A.3), we have

h s A/M s1r A

þ ð1 hÞ

1

/M sr A

< 0: ðA:4Þ


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16/18

The LHS is increasing in s A. On the other hand, when s A ¼ ~s A, the LHS of (A.4) is

h ~s A/M ~s1r A

þ ð1 hÞ

1

/M ~sr A

¼ ð1 hÞ ~sr A /M

þ ð1 hÞ

1

/M ~sr A

¼ ð1

hÞ sr1

M ~

sr

A

þ

1

sr1M

1

~sr A

¼ ð1 hÞ sr1M ~s

r A

sr1M ~s

r A 1

sr1M ~s

r A

> 0;

where the first equality is from F ð~s AÞ ¼ 0 and the last inequality is from ~s A 2 1; sr1r

M

. Therefore, the

LHS of (A.4) is positive for s A P ~s A, which implies that the agglomeration never occurs for s A P ~s A.Next, we consider an interior equilibrium. We first assume that the larger country N is the importer

of good A, so that p A = w = s A and E = wL = s AL hold. From (10) and (11), we have

l

hLw/ A

n/ A þ n/M þ

1

s A

ð1 hÞLw/M / A

n þ n/M / A

¼ f r; ðA:5

Þ

l ð1 hÞLw

n þ n/M / Aþ

s AhLw

/M n/ A þ n

/M

¼ f r: ðA:6Þ

The above equations immediately derive

hLw

n/ A þ n/M

¼ f rðs A / A/M Þ

ls A/ A 1 /2

M

; ð1 hÞLwn þ n/M / A

¼ f rð/ A s A/M Þ

l/ A 1 /2

M

:Since the above two terms are positive, we obtain a necessary condition for the interior equilibrium:

/ A s A/M > 0: ðA:7Þ

From (A.5) and (A.6), the numbers of firms in two countries are expressed as (18) and (19). Then,

using these equations, we have

n hðn þ nÞ ¼ lLw/M f r

½ðs A 1Þh þ 1F ðs AÞð/ A s A/M Þ s

r A /M

; ðA:8Þwhere F () is defined in (14). The denominator of (A.8) is positive from (A.7). Since F () is a decreasing

function and F ð~s AÞ ¼ 0, we have n h(n + n⁄) > 0 for all s A 2 ½1; ~s AÞ. According to Lemma 1, this implies

that the HME exists for all s A 2 ½1; ~s AÞ.On the other hand, whens A > ~s A, we have n h(n + n

⁄) < 0. By the same logic used above, country N

must be an exporter of good A, which contradicts the assumption that N is the importer of good A.

Thus, a necessary condition for N to be the importer of good A is that s A 0;

where the inequality is from the following facts: (a) sr A > /M , which can be derived similar to (A.7);

(b) F () is decreasing; and (c) F (1) > 0 and s A > 1. Therefore, country N must be an importer of good A,which contradicts the assumption that N is the exporter of good A.Summing up the above discussion, good A is not traded and the HME disappears if s A P ~s A. Other-

wise, the HME appears.

Finally, from (14), we have



17/18

@ F

@ w

w¼~w

¼ ~wrhðr 1Þ ~wr1ð1 hÞr h/M 1 and h > 1/2. By applying the implicit func-

tion theorem to (14) and noting ~w ¼ ~s A, we obtain three inequalities in Proposition 1 (iii). The equalityin (iii) is true because [h/(1 h)]1/(2r1)is the only solution of lim/M !0F ðwÞ ¼ 0. h

Appendix B. Proof of Proposition 2

(i) Noting / A s1r

A , we have

@ n

@ s A¼

lLw/M sr2 A

f rð1 hÞ sr A /M

2r 1 þ sr A/M

þ rhs A 1 sr A/M 2

1 þ s2r A

/M sr A 1 þ /

2

M

2 0

from (18) and (19). In other words, the firm number in the larger (resp. smaller) country mono-tonically increases (resp. decreases) when s A decreases.

(ii) Even if good A is traded initially, it becomes nontradable when /M increases and reaches a

threshold, as can be seen in Fig. 1. The threshold is obtained by solving F (s A) = 0 for /M , whereF () is defined by (14). Specifically, the threshold is expressed as

~/M sr A hs A ð1 hÞs

2r A

hs A ð1 hÞ

: ðB:1Þ

If s A < ~s A, it must hold that

hs A

> ð

1

hÞs

2r

A ;

ðB:2Þ

and, then, ~/M 2 ð0; 1Þ. From (18) and (19), we have

@ n

@ /M

/M ¼0

¼ lLwsr1 A hs A ð1 hÞs

2r A

f r

> 0;

@ n

@ /M

/M ¼0

¼ lLwsr A hs A ð1 hÞs

2r A

f r

< 0;

@ n

@ /M

/M ¼~/M

¼ lLwsr2 A ðhs A þ h 1Þ

2hs A ð1 hÞs2r A

f rhð1 hÞ s2r A 1

2

0;where all inequalities are from (B.2).



18/18

Furthermore, we know that both

@ n

@ /M ð/M Þ ¼ 0 and

@ n

@ /M ð/M Þ ¼ 0

have at most two roots. Thus, we conclude that @ n@ /

M

ð/M Þ (resp. @ n

@ /M

ð/M Þ) is concave (resp. convex) for

/M 2 [0,1]. h

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