DP2010-36

On the devel opment strategy ofcountries of intermediate size ‒An analysis of heterogenous fir ms
in a multiregion framework
Ri k ard FORSLID
Toshihiro OKUBO
December 22, 2010

On the development strategy of countries of intermediate size An analysis of heterogenous …rms in a multiregion framework
Rikard Forslidy

Toshihiro Okuboz

December 2010

Abstract
This paper compares two policies: trade cost reduction and …rm relocation cost reduction
using a three-country version of a heterogeneous-…rms economic geography model, where thethree countries have di¤erent market (population) size. We show how the e¤ects of the twopolicies di¤er, in particular, for the country of intermediate size. Unless the intermediate
country is very small, it will gain industry when relocation costs are reduced, but lose
industry when trade costs are reduced. The smallest country loses industry in both cases,
but only experiences lower welfare in the case of lower relocation costs. Thus, the rankingof the policies from the point of view of the two small and intermediate countries tends tobe the opposite.

JEL Classi…cation: F12, F15, F21, R12
Keywords: agglomeration, …rm heterogeneity, multi-country model, trade liberalisation,
relocation costs

1

Introduction

World-wide economic integration, often called globalisation, makes it easier to trade goods and,in many cases, makes it easier to set up plants and establishments in foreign countries. Models
of economic geography and trade have focused on the e¤ects of lower trade costs. They show
how industries agglomerate to large core countries as trade costs are reduced (see e.g. Baldwin
et al. (2003) and Fujita and Thisse (2002) for a survey). The analysis is generally performed
in a two-country setting, but similar conclusions apply in a multi-country setting.1
This reseach is partly …nanced by Grant-in-Aid for Scienti…c Research (JSPS).
y

Stockholm University and CEPR; email: rf@ne.su.se.

z

Kobe University; email:okubo@rieb.kobe-u.ac.jp.

1

For a multiregion analysis, see e.g. Baldwin et al. (2003, ch. 14), Forslid (2010), Krugman and Livas (1996)

and Puga and Venables (1996).
Ago et al. (2006) and Okubo and Thisse (2008) show how industry may relocate towards the smallest region
because of severe price competition in the larger markets when using the linear-demand monopolistic competition
model of Ottaviano et al. (2002).

1

An important example of far reaching economic integration is the European Union. The
focus here has been as much on lower barriers to the free mobility of production factors, such as
labour and capital, as on lower trade costs for goods.2 The economic integration in Europe hasin‡uenced the geographical patterns of industries, but unlike what models of trade and economic
geography tells us, there is no strong empirical evidence of an emerging core-periphery patternin Europe, as shown by Midelfart-Knarvik et al. (2000) and Midelfart-Knarvik and Overman(2002). The location pattern in Europe is therefore better described by a multi-country than a
two country framework, and by an framework where the reduction of relocation costs of factorsof production are analysed together with reduction of trade costs.3
The current research on …rm location patterns focuses not only on geographical concentration, as mentioned above, but also on …rm heterogeneity in productivity. The emergenceof this literature is closely related to micro-econometric results based on …rm level data sets.
More precisely, the current theoretical advancement concerns how spatial location patterns are
related to …rm heterogeneity in labour productivity, and how …rms are selected or sorted tomarkets of di¤erent size according their productivity. Baldwin and Okubo (2006) show how themost productive …rms have the strongest incentives to move to the larger countries leading tospatial sorting, with the less productive …rms left in the periphery when there is a fall in trade
costs. On the empirical side Combes et. al. (2009) show how …rm heterogeneity in‡uences the
productivity of French cities.4
To analyse these issues, the present paper studies the e¤ects of lower relocation costs of…rms (capital) as well as lower trade costs and presents a three-country economic geographymodel with heterogeneous …rms. Relocation costs in our model are any costs associated withthe geographical movement of a production facility, such as e.g. regulatory barriers.5 Our
analysis shows how the collapse of all industry to the core may be speci…c to two-country
models analysing economic integration in the form of lower trade costs only. Here, we use amodel with large, intermediate and small countries. In addition to lower trade costs, we analyse
economic integration in the form of lower relocation costs. We show that, contrary to tradeliberalisation, lower relocation costs can lead to …rm relocation into both the large and theintermediate country.
The framework we use is a multi-country version of the heterogeneous …rms trade andlocation model by Baldwin and Okubo (2006). We …nd several new results. Lower trade costs
2

The …rst ’pillar’of the Maastricht Treaty includes the the Internal Market with its four freedoms: free move-

ment of goods, services, workers and capital, as well as the Single Market Programme including harmonisationof standards.
3

Okubo and Rebeyrol (2005) analyse a fall in relocation costs but use a two country framework. .

4

There is also a body of literature showing that workers and …rms on average are more productive in larger

markets (Head and Mayer, 2004; Redding and Venables, 2004; Syverson, 2004, 2006; and Amiti and Cameron,2007).
5

Relocations costs could also encompass such phenomena as a malfunctioning housing market that makes itdi¢ cult to establish a factory in a new location.

2

tend to produce the usual concentration of economic activity to the core (large) country in
our model. That is, industry from all countries moves towards the core. Despite this, welfare
increases for all countries as a result of trade liberalisation.6 Lower relocation costs also leadto an increased concentration to the core but, unless the intermediate country is very small,
it is only …rms from the smallest country that move there. The intermediate country actually
gains industry as a consequence of lower relocation costs. Welfare increases for the large andintermediate countries, whereas the small country that loses industry experiences declining
welfare in this case.
A policy implication of our analysis is that European countries of intermediate size, in particular, may bene…t from free mobility of production factors within EU. Turning to development
strategies of poor countries, our analysis indicates that intermediate size developing countries
may be better served by focusing on FDI than on trade. Lower barriers to FDI would lead toan in‡ow of industry, whereas lower trade costs could lead to the opposite. Our model could
also be applied to a regional context within a country, where trade costs are interpreted astransportation costs only. An interpretation of our results, from a regional perspective, is thatthe long-run prospects of regional centers outside the largest core regions could be upgraded asa result of lower relocation costs.

2

The Model

We use a multi-country version of the Baldwin and Okubo (2006) model, which combines the
Melitz (2003) heterogenous …rms model with the ’footloose capital’ new economic geographymodel by Martin and Rogers (1995).

2.1

BasicsThere are n countries with an asymmetric population (market size). Countries are ordered sothat Country 1 is the largest and Country n the smallest. There are two types of factors of
production, capital and labour. Capital, which is sector speci…c, can move between countries
but capital owners do not. Workers can move freely between sectors but are immobile between
countries. A homogeneous good is produced with a constant-returns technology only using
labour. Di¤erentiated manufactures are produced with increasing-returns technologies using
both capital and labour. The mass of di¤erentiated …rms is normalised to one, N

1:

All individuals have the utility function
1
U = CM CA
;

where

2

CM = 4

Z

l2

6

(
cl

1)=

3 =(

dk 5

1)

(1)

Our results on trade liberalisation are related to those of Gopinath and Saito (2011) who analyse the e¤ects

of preferential trade liberalisation in a setting with two domestic regions trading with the outside world. They use
a model with heterogeneous …rms in a linear demand setting, and do not analyse the e¤ects of lower relocation
costs.

3

where2 (0; 1);

> 1 are constants andis the set of consumed variety. CM is a consumption

index of manufacturing goods and CA is consumption of the homogenous good. cl is the amountconsumed of variety l: Country subscripts are suppressed when possible for ease of notation.
Each consumer spends a shareof his income on manufactures. Total demand for a do-

mestically produced variety i is
xi = R

pi

l2

p1l

Y;

(2)

dk

where pl is the price of variety l and Y income in the country.
Ownership of capital is assumed to be fully internationally diversi…ed; that is, if one country
owns X-percent of the world capital stock, it will own X-percent of the capital in each country.
The income of each country is therefore constant and independent of the location of capital.
World expenditure equals world factor income E W = wLW + E W = : Without loss of generality,
we choose units so that LW

1; which gives E W = 1 1 = : Income of country j is equal to its

share of world expenditures given by
Yj = sj E W = sj:(3)

Yj is thus constant irrespective of the location of capital; i.e. also out of long-run equilibrium.
Turning to the supply side, the homogeneous good sector is a constant returns and perfectcompetition sector. The unit factor requirement of the homogeneous good is one unit of labour.
The good is freely traded and since it is also chosen as the numeraire, we havepA = w = 1;

(4)

w being the wage of workers in all countries.
In the production of di¤erentiated goods, …rms have a …rm speci…c unit labour input coe¢ cient (a) and uses one unit of capital, as in the standard footloose capital model. Fixed amountof capital endowments in the world leads to no entry and exit of …rms, whilst international
capital mobility allows …rms to move between countries. Total costs for …rm i are speci…ed as
T Ci =

i + ai xi ;(5)where the …xed cost consists of capital, whereas the variable cost consists of labour. Importantly…rms are heterogeneous and their …rm-speci…c marginal production costs ai are distributed
according to the cumulative distribution function F (a).
Geographical distance is represented by trading costs. Shipping the manufactured good
involves a frictional trade cost of the “iceberg” form: for one unit of good from country j toarrive in country k,
countries

jk =jk > 1 units must be shipped.

Trade costs are symmetric between all

8 j; k:

Pro…t maximisation by manufacturing …rms leads to a constant mark-up over marginal cost
pi =

1
4

ai ;

(6)

s1F(a)

s1

0

1

a

a

s2F(a)

s2

a
0

a

1

s3F(a)

s3

a
0

a

1

Figure 1: The distribution of …rms in autarky
and the export price is pi jk ; taking the iceberg trade costs into account.

2.2

Short-run equilibrium

In the short run equilibrium, the allocation of capital in each country is taken to be …xed.
Capital owners hold capital in their country of origin. sj denotes the share of capital and thenumber (mass) of …rms in Country j since one unit of capital corresponds to one …rm, andsince N W = 1:
Firm heterogeneity in labour requirements, ai ; is probabalistically allocated among …rms. In
order to analytically solve the model, we follow Helpman, Melitz and Yeaple (2004) and assume
a Pareto cumulative density function of a:
F (a) =
where

> 1 is a shape parameter and a0

a
a0

a

;

(7)

a is a scaling factor. We assume the distribution to

be truncated at 0 < a < a0 so that the productivity of …rms is bounded, and we normalise sothat a0 = 1: Figure 1 illustrates the distribution of …rms in the three economies before capitalcan move.

5The return to capital of a …rm in a country j is the …rm’s operating pro…t,
!
X
ai1
sj
sk
+
;
j (ai ) =
jk
(
)
j
k

(8)

k

where the right-hand side follows from the demand functions in (2) and

j

sj

Z1

a1i

dF (a) +

1
jk

jk

jk sk

k

a

The object

X

Z1

a1i

dF (a):(9)a, ranging between 0 and 1, stands for "free-ness" of trade between

countries j and k (0 is autarky and 1 is zero trade costs). It is assumed that the labour stock
is su¢ ciently large so that the agricultural sector, which pins down the wage, is active in all
countries.
Consider now what would happen if …rms were allowed to move between countries. From
(8) the …rms’ return to capital is convex and falling in ai . Firms with the highest labour
productivity (the lowest ai ) have the largest pro…ts and will be the most sensitive to market
size and thus have the strongest incentives to move to the large market. Under reasonableassumptions of moving costs, this would lead to sorting with the most productive …rms in thelarger market, as shown by Baldwin and Okubo (2006).
More formally, a …rm will move from k to j whenj (ai )

wherek (ai )

=

a1i
(

)

(1

)

sj

sk

j

k

> 0;

(10)

is a per-unit of capital …xed relocation cost.7

In the following we proceed with a three-country analysis, which is the simplest structurethat enables us to focus on countries of intermediate size. Country 1 has the largest population, Country 2 is of intermediate size and Country 3 has the smallest population (s1 > s2 > s3 ).

2.3

Relocation tendencies

Before moving to the full long-run solution of the model, we consider the relocation incentives
faced by …rms starting out from the initial equilibrium. Figure 2 showsj (ai )k (ai ) for all

country pairs.
Note that we rule out that …rms have in…nite productivity by assuming a to be boundedfrom below at a:8 The incentive to relocate increases in …rm size as well as in the market sizedi¤erence between two countries. Higher productivity …rms are more sensitive to market sizedi¤erence and have stronger incentives to move to large markets. The largest size di¤erence
7This speci…cation di¤ers from that of Baldwin and Okubo (2006), where the relocation cost is a function of

the migration pressure.
8

No bounded …xed moving cost per unit of capital would be su¢ ciently high to prevent the in…nitely productive…rms to move.

6π (a) − π (a)χ0
π 1 (a) − π 3 (a)π 2 (a) − π 3 (a)π 1 (a) − π 2 (a)

a

a

1

Figure 2: Pro…t di¤erentials between countries
corresponding to the highest curve in Figure 2 is always between the largest and the smallest
country. Then, the curves will be ordered depending on the relative size of countries.
The e¤ects of relocation costs can be seen from Figure 2. For a high moving cost, as
illustrated by line

0 in the …gure, only the most productive …rms from the smallest country

will migrate to Country 1. As relocation costs are reduced, relocation will take place between
more countries. The extent of relocation between di¤erent countries will depend on their relative
size.
When turning to the long run equilibrium, …rms start to move and we need to explicitly
model the dynamics. With many countries, there will in general be a simultaneous relocation
between several country pairs.

2.4Long-run equilibrium

In the long run equilibrium, capital is fully mobile between countries and responsive to the
incentives provided by the relative returns that can be obtained in the two countries. 9 Thus,…rms are mobile internationally. However, note that capital owners are bound to their countryof origin, and capital rewards are therefore repatriated to the country of origin. The value of
relocation to a larger market is highest for the most productive …rms since they have higher sales
and are better equipped to cope with the higher competition in the large market. Relocation
9

Pro…t maximisation ensures that capital is located where its return is maximised.

7therefore starts from the high end of the productivity distribution. Generally, the value of
migrating for a …rm depends on its own marginal cost and the mass of …rms that have alreadymigrated, aR : The value of migrating from smaller market (Country k) to the larger market(Country j) at a point in time is therefore
vjk (aR ) =j (aR )

j (aR )ZaRk (aR )

=

a1R
(

)

(1

) (Bj

Bk )

;

(11)

where

sj
;
j (aR )

Bj

sj

a

1

dF (a) + (1

sj )

a

Z1

aR

1

a

dF (a) + sk (1

)

ZaR

a1

dF (a);a(12)
and where B is a measure of the average per-…rm market size that is independent of the …rm’s
productivity, ai . The long-run equilibrium is determined by solving vjk (aR ) = 0 for aR :The relative size of countries will be of key importance in any multiple country setting. As
mentioned above, we assume that s1 > s2 > s3 , which implies that relocation will start fromCountry 3 to Country 1. The long-run implications for the intermediate country, Country 2,
will depend on its relative size. To highlight market size di¤erences, we assume thatis thesame between all country pairs.

3

The e¤ect of reduced trade costs

Trade liberalisation (an increase in ) a¤ects the value of relocation. A di¢ culty, when analysing
trade liberalisation with many countries, is that it may be that …rms from one country move totwo other countries simultaneously or that …rms from two countries simultaneously move to athird country. When …rms are heterogeneous, it becomes di¢ cult to keep track of the sortingof …rms when this happens. To simplify the analysis, we assume in this section that, insteadof a …xed relocation cost, there is a …rm relocation cost à la Baldwin and Okubo (2006) thatis related to the migration pressure. The relocation cost is high when many …rms move outof a country at the same time, or when many …rms move in to a country at the same time,
but gradually declines as the migration pressure falls when we approach equilibrium. This
assumption implies that the most productive …rm is the …rst to relocate and that it moves tothe location with the highest return. It will likewise be the …rms with the highest gains that are
the …rst to move into a country. This implies that as long as the gains from moving between
country pairs are di¤erent, out-migration of …rms from a country will go to one destination
country at a time, while …rms migrating into a country will come from one source country at a
time.

8

3.1

The equilibrium path

Using the above logic, starting from autarchy the productive …rms in the smallest country moveto the other countries. Section 6.1 in the Appendix shows thatdv31 (a)d>=0dv21 (a)
d

> 0:

(13)

=0

This implies that relocation starts by …rms in Country 3 relocating to Country 1; as tradeliberalisation starts from autarky. Further trade liberalisation implies that there is a fall in1,

as …rms move into Country 1. Would it then be the case that after a while, …rms instead moveto Country 2? The answer is no as long as

B<; whereB

stands for bifurcation point tradecost. Section 6.1 in the Appendix shows thatdv31 (aR )dv32 (aR )>> 0 for
d
d
where

B

<

B

;

(14)

2

= (13s2s2 1) : This implies that starting from any equilibrium aR when<B

; it ismore pro…table for a Country 3 …rm to relocate to Country 1 than to Country 2. (Note thatv31 (aR ) = v32 (aR ) in equilibrium, since the relocation costs related to congestion go to zero as
the relocation of …rms stops.)
This relocation pattern is illustrated in the left-hand part of Figure 3. However, successive
trade liberalisations reduce the pro…t gap between Country 1 and 3 more than between Country
2

2

R)
R)
2 and 3: d vd31 (a< d vd32 (a< 0 as shown in section 6.1 in the Appendix. When we reach
2
2

=

B

; we have dv31d(aR ) = dv32d(aR ) , and here relocation also starts from Country 3 to Country

2. This is illustrated in Figure 3 by the hump-shape for Country 2.
2

2

Further liberalisation a¤ects the pro…t di¤erentials according to: d vd312(a) < d vd212(a) < 0; andat the level of0(a)> 0 (for aR > a) relocation also starts from Country
where dv31d(aR ) = dv21
d2 to 1 (See section 6.1 in the appendix).10
At the sustainpoint for Country 3,

03= 1 s2s; all …rms have left Country 3, and migration
3

continues from Country 2 to Country 1 only. Country 2 thereafter gradually loses its industry
as illustrated in Figure 3.
The end result is always that all …rms concentrate in Country 1 for su¢ ciently low trade
costs, as illustrated in the …gure. This relocation pattern is, in a qualitative sense, very similar
to the standard footloose capital model with three countries.11
10

It may be the case thatexact condition for
11

0

>

B

0

<

if Country 3 is very small, in which case there no hump for Country 2. The22)
is s3 > 1(1s s+2s2:22

See e.g. Forslid (2010).

9

Share of Firms
1
Country 1

Country 2

s1
s2
s3

Country 3
0

φB

φ'

φ''

1

φ

Figure 3: The e¤ect of trade liberalisation

3.2

Welfare e¤ects of reduced trade costs

In the case of homogenous …rms, the small and intermediate countries will always gain fromtrade liberalisation despite losing their entire manufacturing industry.12 Here, we consider
heterogeneous …rms and the welfare consequences are therefore potentially di¤erent because of
the sorting of the least productive …rms to the periphery.
The welfare of country j could be measured by real income,

w
P p1A

. The trade cost reduction

has two e¤ects on welfare. It reduces the price of imports, which is always positive for welfare,but it also leads to an out‡ow of …rms for the smaller countries, which is negative for welfare
since these varieties must now be imported.
Since w = pA = 1 and capital is fully internationally diversi…ed, it su¢ ces to study the11; to compare welfare between countries. As shown in section 6.2 in thej@ 3
Appendix, @ > 0, implying that the small country will always gain from trade liberalisation
price index, Pj =in spite of losing its industry. That is, the e¤ect of cheaper imports always outweighs the e¤ectof the out‡ow of industry. The same logic applies for the country of intermediate size, which
will gain from trade liberalisation even during the …nal phase of trade liberalisation when it
loses its industry to the core country.
We next turn to the e¤ects of reduced relocation costs. As will be seen, these e¤ects can bevery di¤erent than for reduced trade costs.
12

See e.g. Forslid (2010).

10

4

The e¤ect of reduced relocation costs

Here, we discus the general e¤ects of reduced relocation costs keeping trade costs …xed. In thefollowing subsections, we derive the critical levels of relocation costs where relocation changes
nature (the sustain and bifurcation points).

4.1

The equilibrium path

Starting from a hypothetical situation with a given
theand with high relocation costs ; whereline does not intersect with any of the pro…t di¤erential curves in Figure 2, there will be

no relocation. Gradually reducing

we reach a point where theline reaches the …rst pro…t-di¤erential curve and relocation starts. The …rst …rms to move are the most productive …rms
in the smallest country, which move to the largest country; thus, from Country 3 to Country 1.
Further reductions in

imply that successively less productive …rms move. The relocation of…rms into Country 1 reduces B1 and thereby the incentives to move to Country 1. Despite this,…rms from Country 3 will never prefer to move to Country 2 instead of Country 1, as shown insection 6.3 in the Appendix.
The marginal …rm at equilibrium, aR ; is de…ned by the condition that
a1R
(

)

(1

) (B1

B3 ) = :(15)

The relocation of …rms from Country 3 to Country 1, as relocation costs are reduced, will
reduce B1 as competition increases in Country 1 and for the same reasons, it will increase B3 :However, B2 and the pro…t of …rms in Country 2 remain constant since the price index isuna¤ected when no …rms relocate to or from Country 2 and when trade costs are unchanged.
That is, prices of import goods in Country 2 are unchanged, even if …rms relocate from Country
3 to Country 1, since the cost of import, determined by ; is the same from both countries. Thisis illustrated in Figure 4, where the B1 line falls and B3 rises as successively as less productive…rms relocate.
In the case illustrated in Figure 4, B1 converges to B2 while B3 < B1 = B2 . A su¢ cientcondition for this to happen is that s1

s2 < s 2

s3 as shown in section 6.3 in the Appendix.

At the point where B1 = B2 , we have that
3 =

1

2

(16)

3

since
a1R
(

)

(1

) (B1

B3 ) =

1
aR

(

)

(1

) (B2

B3 )

f or

B1 = B2 :(17)Countries 1 and 2 are then equally attractive for a potential relocater from Country 3; andrelocation from Country 3 therefore goes to both Country 1 and Country 2 from this point on.
Successively lower relocation costs will lead to a gradual relocation from Country 3 until no
11

B

B1

B1 = B2

B2

B3

a

1

aB

aR

Phase 2Phase 1Figure 4: The e¤ect of a lower relocation cost when the intermediate region is relatively large.

12Firm share
1
Country 1

s1
s2
s3

0

Country 2
Country 3
1/ χS

1/ χ B

1/ χ

Phase 2Phase 1Figure 5: The e¤ect of lower relocation costs.
…rms are left in that country. Further reductions in

do not a¤ect the location of …rms as longas the relocation costs are positive since B1 = B2 . The location pattern of …rms as relocation
costs, ; are reduced is illustrated in Figure 5, where

decreases along the x-axis.13

The e¤ects of lower relocation costs are thus very di¤erent from the e¤ects of reduced trade
costs in the case where the intermediate country is not too small (s1s2 < s 2s3 ): The

main di¤erence lies in the outcome for the country of intermediate size. Lower trade costs
lead to a concentration of industry from all countries to the largest country, whereas reduced
relocation costs lead to deindustrialisation of the smallest country only. Here, both the large
and the intermediate country gain industry. The fundamental reason for this di¤erence is that
trade liberalisation always a¤ects the price index of all countries, and therefore the relative
attractiveness of the countries. In contrast, reduced relocation costs only a¤ect the price index
of countries where …rms move in and out.
Our interest lies in the case where s1
13

s2 < s2

When the intermediate country is smaller so that s1

s3 , as illustrated in Figure 5. There are twos2 > s2s3 ; it will instead be the case that the systemreaches a point where B3 = B2 < B1 as relocation costs are reduced. At this point, relocation starts from bothCountry 2 and 3 towards Country 1. Thus, this case resembles the core-periphery outcome that is the result oftrade liberalisation, and this case will not be further analysed here.

13

s1F(a)s1
s3F(a)0a1as2F(a)

s2

a
0

a

1

s3F(a)

s3

a
0

a

aB

1

Figure 6: Phase 1 relocation
phases in the relocation of …rms to Country 1. In the …rst phase, …rms from the small country
relocate to the largest country only. Thereafter, in phase 2, when the point where B2 = B1
has been reached, relocation from Country 3 goes to both Country 1 and Country 2. We now
turn to the calculation of the "bifurcation point" at which relocation switches from the …rst
to the second phase and the "sustain point" at which all industry has left Country 3. From
this point onwards, there is no more reallocation since there are positive reallocation costs, andsince B2 = B1 with constant trade costs (constant ):4.2

Phase 1 (relocation from Country 3 to Country 1)

We here analyse relocation under phase 1 when …rms in Country 3 only relocate to Country 1.
This phase continues until B1 = B2 .
As noted above, the cut-o¤, aR , is determined by the following equation:
a1R
(

)

(1

) B11

B31 =

where B11 = s11 ; B21 = s21 and B31 = s31 . Superscript "1 " indicates phase 1.
1

2

3

are given by

14

(18)
1;
1

1
2

and

1
3

where

1 a
+ 1 a

1

1
1

=

fs1 + (1s1 ) + (112=

fs2 + (1

s2 )g

1
3

=

fs3 + (1

s3 )

1

+

;

and

)s3

(1

1

)s3

(aR

a )

(aR

a )

g

g

(19)

a . Note that …rm relocation never a¤ects

d 13
d 11
dB3
2 and B2 in phase 1. Using these de…nitions, we get daR < 0 and daR > 0. Thus, daR > 0,
daR
dB1
1
3
< 0: Due to dB> 0 and dB< 0,
daR < 0: As a result of total di¤erentiation, we get ddda decline in relocation costs promotes relocation, which decreases B1 but increases B3 . This
relocation phase …nishes when B1 = B2 . The cut-o¤ at the bifurcation point is
aB =

(s1
(1

s2 )
+a ;
)s2 s3

a1B

(1

)

(20)

and the level of relocation costs is
B =

(

)

s1 ) +

s1

s3

B
1

B
3

;

(21)

where

4.3

B
1

=

fs1 + (1

B
2

=

1
2 =

B
3

=

fs3 + (1fs2 + (1s3 )(s1 s2 )(1 s2 )
g = s1 f1 +
g;
s2
s2
s2 )g
(s1 s2 )
g:
s2

(22)

Phase 2 (Relocation from Country 3 to Country 1 and Country 2)

When relocation costs are lower thanB , B1 = B2 and relocation from Country 3 goes to bothCountry 2 and Country 1. Relocation will now keep B1 = B2 for all levels of : This will imply
that a fraction

1= s1s+sof the moving …rms moves to Country 1 and a fraction (12) movesto Country 2.
The cut-o¤, aR ; is determined by the condition that
a1R
(

)

(1

) B12

B32 =

a1R
(

)

(1

) B22

B32 = ;

where B12 = s12 ; B22 = s22 and B32 = s32 . Superscript "2" indicates phase 2 .
123phase 2 are given by

15

2;
1

2 and
2

2 in
3

δs3F(a)s1s1F(a)

01aa(1- δ)s3F(a)s2F(a)

s2

a

0

a

0

a

1

s3

a
1

aB

Figure 7: Phase 2 relocation

16

2
1

=

fs1 + (1s1 ) + (1

)s3

=

fs1 +

2
2

=

fs2 + (1s2 ) + (1

)(1

2
3

=

fs3 + (1

s3 )

)s3

s1 (1 s2 )
+ (1
s2

(1

(aB
)s3

a )
(aR
)s3

(aR

+ (1
aB )

(aR

a )

)s3

(aR

aB )

2

d

g

g

aB )

g

g:

d

2

d

2

Note that B12 = B22 . Using these expressions, we get daR3 < 0 and daR1 = daR2 > 0. Thus,
dB1
dB2
dB3
dB3
R
< 0: As a result of total di¤erentiation, we can derive da> 0.
daR > 0, daR < daR < 0; dd

The relocation cost at the sustain point when all …rms have left Country 3 is given by

S

1

=

(

)
1

=

(

)

(1
(1

) (B2
0
)@

B3 )
s2
s2 + (1s2 ) + (1

)(1

)s3 1

(s1 s2 )(1 )s2 s3

1

s3 A: (23)All …rms are concentrated in Country 1 and Country 2 when relocation costs are lower thanS.

Importantly, when=S ; the relocation process …nishes.

Even if relocation costs are0
S , no …rms relocate from Country 2 to Country 1 since the B s are not directly. From the sustain point and onwards, we have B1S = B2S , where

reduced froma¤ected bys1 (1 s2 )
+ (1
s2

S
1

=

fs1 +

S
2

=

fs2 + (1

S
3

=

;

s2 ) + (1

)s3
)(1

(1
)s3

aB )
(1

g;

aB )

g; and(24)

where superscript "S" indicates the sustain point. This di¤ers starkly from the usual coreperiphery outcome. Full agglomeration never occurs as a result of reduced relocation costs in
our model. Both Country 1 and Country 2 experience an in‡ow of industry.

4.4

Welfare e¤ects of reduced relocation costs
1

Once more, the price index, Pj =1

j; can be used for welfare comparisons. The welfare

analysis is simple in this case, since …rm location is the sole factor a¤ecting welfare with constanttrade costs. The welfare e¤ects of lower

are di¤erent in the two phases. Starting with phase

1 when B1 > B2 > B3 ; …rms relocate from Country 3 to Country 1, resulting in dd 3 > 0 andd 1< 0: This implies that welfare increases in Country 1 and decreases in Country 3. Duringdphase 2, when B1 = B2 ; …rms move from Country 3 to both Country 1 and Country 2, resulting17

in dd 3 > 0, dd 1 < 0 and dd 2 < 0: This implies that welfare increases in both Country 1 and 2
and decreases in Country 3.
The welfare implication of lower trade costs and lower relocation costs are thus very di¤erent
for the smaller countries. The smallest country loses its industry in both cases, but experiences
increased welfare as trade costs are reduced, while a lower relocation cost leads to lower welfare
as industry relocates. The intermediate country has increasing welfare in both cases, but gains
industry as relocation costs are reduced, while it loses industry as trade costs are reduced.

5

Concluding Discussion

This paper analyses a three-country trade and location model with heterogenous …rms, where
the e¤ects of trade liberalisation and a reduction of …rm relocation costs are compared. Tradeliberalisation eventually leads to the usual core periphery outcome with all …rms in the core,also in our case of multiple (three) countries and heterogeneous …rms. However, this is no longer
the case when considering the e¤ect of lower relocation costs and multiple (three) countries.
Unless the intermediate country is too small, it will grow (as will the largest country) as a resultof reduced relocation costs.
The welfare implications of trade liberalisation and reduced relocation costs also di¤er.
Trade liberalisation leads to welfare gains for all countries even if both smaller countries lose
their industrial base to the core. Reduced relocation costs instead imply loss of welfare andindustry for the smallest country, but gains in welfare for the intermediate country, as longas it is su¢ ciently large to gain industry. This means that the interests of intermediate andsmall countries may be very di¤erent when it comes to these two types of economic integration
policies.
Our model may be applied in a national context, where the policy experiments are regional
policies, or it may be applied in an international context where the policy experiments pertain
to di¤erent aspects of globalisation. First, from a regional policy perspective, the above experiments imply that it is of great importance how the integration of di¤erent regions in a country
is achieved. Regional policy may involve policies that make it easier for individuals and …rms tomove between regions, such as subsidies for movers or a better functioning real estate market,
as well as policies that decrease transportation costs, such as better roads and trains. The …rstof these policies corresponds to a lower relocation cost in the model and the second to lower
trade costs. From the perspective of the largest core region, these policies are both attractive as
they lead to an increased concentration to the core and higher welfare. However, the interests ofthe two smaller regions di¤er. Lower relocation costs lead to higher welfare and more industry
in the intermediate region (unless it is very small), whereas it leads to a loss of industry andwelfare for the smallest region. Lower transportation costs lead to a deindustrialisation of theintermediate region along with the smallest one, while both regions gain in welfare.
Second, from an international perspective, our policy experiments imply that the development strategies of countries di¤er. In particular, the strategy may be di¤erent for very small
18

countries and for countries of intermediate size. Intermediate size countries, as e.g. some of
the fast growing Asian countries, may be best served by focusing on policies that facilitate
the relocation of capital to the country, e.g. policies that promote inward FDI. The smallest
developing countries should instead focus on trade liberalisation according to our model.

19

6

Appendix

6.1

The trade liberalisation experiment

6.1.1

(a)
(a)
Proof that dv31
> dv21>0ddFirst, we prove that, starting from autarky, …rms in Country 3 always relocate to Country 1
rather than to Country 2:
dv21 (a)dv31 (a)>> 0:dddv31 (a)d=(B1B3 )a1

+ (1

)

=

(B1

B3 )a1+ (1)

dB1 d 1
d 1 d
s1
2 ((1

dB3 d 3
d 3 d

a1

s1 )

s3 ) +s1 )s3 ) +

s3

2 ((1
3

1

=

(B1

B3 )a1

+ (1

B1

)

((1

B3

1

= a1
= a1
= a1

B1

where

1

1
+ 1 a ;s3 ) + s3 ) a1

3

(1 s1 )s3
1 + (1)s1 + (1 s1 ) + s3 (11B1 +
s1 + (1 s1 ) + s3 (1
)
1
1
+
>0
1

((1

s3 ) + s3 ) a1

B1 + 1 + (1)

s3 + (1

1
s3 )

s3

(1
+ (1

s3 (1

)

)

3

a and

aR

1

a :

Note that, in the trade cost reduction case, B1 = B3 in equilibrium since there are nocongestion related relocation costs in equilibrium as migration stops (see Baldwin and Okubo(2006)).
Likewisedv21 (a)
= a1
d
Since
6.1.2

1 >

1

B1 +

1

1

B2

2

2 and B1 = B2 , we have that1

= a1R B1

+

1

1

> 0:

2

dv31 (a)(a)> dv21> 0.
ddProof that dv31d(aR ) > dv32d(aR ) > 0

Second, we prove that …rms in Country 3 always relocate to Country 1 rather than to Country
2 for a range of trade costs:
dv31 (aR )dv32 (aR )>> 0 fordddv32 (aR )
= a1R
d
Since

1 >

2 , we have that

1
2

B2 +

1

B3

3

1
= aR
B1

dv31 (aR )> dv32d(aR ) > 0.
d

20

<

B

1
2

+

1
3

> 0:

s3 ) + s3
s3 )
s3 (1
B3

6.1.3222

d2 v32 (a)<0d 2Proof that d vd312(a) < d vd212(a) < 0, and that d vd312(a)(a)(a)
We here derive the relative size of the second derivatives dv31
and dv21
.
d
d

B1

(

1

B1

(

dB1
< 0; and dd 3 =
3; d

f(1

dB1
d

1
1

3

d2 v21 (a)
= a1
d 2

dB1
d

1

1

1

2

d2 v32 (a)
= a1
2
d

dB1
d

1

1

because of
d 1
=
d

B1

(

d2 v31 (a)
= a1
d 2

f(1

1 >

s1 )

2 >

1

+

+

+

2

+ a1

+ a1

+a

3

s3 g > 0.

1

d 3
2 d
( 3)

)

<0

1

d 2
2 d
( 2)

)

<0

1

d 2
2 d
( 3)

)

<0

d 1
2 d
( 1)

d 1
2 d
( 1)

d 1
2 d
( 2)

1

1

1

s3 ) + s3 g > dd 2 =f(1s2 ) g >Furthermore, using these two derivatives, we can get

d2 v31 (a)d 2

d2 v21 (a)
= a1
d 2

dB1
d

2

1

1

3

2

+ a1

1

B1

d 3
2 d
( 3)

2

d2 v32 (a)
< 0:
d 2

2

Thus, we can derive d vd312(a) < d vd212(a) < 0. Likewise we get d vd312(a)
6.1.4

!

d 2
2 d
( 2)
1

< 0:

(a)
Proof that dv31d(aR ) > dv21
>0d

We here derive the point of the top of the hump-shaped …rms’location in Country 2. Because of
the congestion cost when entering Country 1, there is no movement from Country 2 to Country
1 as long as
dv31 (aR )dv21 (a)>> 0;ddwhere dv31d(aR ) = a1R B1

1
1

+ 1

3

(a)
and dv21
= a1
d

1

B1

1

+ 1

2

.

Straightforward calculation shows that this condition holds foraR < ac
R =

s1
s1

s3
s2

s2
s3

1
1

a:

When acR = aR , the most productive …rms in Country 2 will start to relocate to Country 1 since(a)dv31 (aR )= dv21
> 0.
d
d

21

6.2

The welfare e¤ect of trade liberalisation for the small country

Here, we prove that trade liberalisation always improves the per-capita welfare of the smallest
country (Country 3). Once Country 3 has been completely deindustrialised, it will obviously
gain from further reductions in trade costs, since lower trade costs reduce the price index due
to cheaper imports. However, we need to be shown the welfare consequences during the phasewhen Country 3 loses industry due to trade liberalisation.
In the long-run equilibrium, B1 = B3 always holds as long as there is a manufacturingindustry in both countries. The following equation must therefore be satis…ed in the equilibrium:
s1

3

s3

1 = 0 () F

where

1 =

[fs1 + (1

s3 (1

) ].

1

a ,

(s1

s3 )

s1 s3 (1s1 ) g + s3 (1aR31) + s2 (1a ands23 (1)s3 s2 (1

) = 0;) ]; and3 =[fs3 + (1s3 ) g)a . Note that aR21 denotes the cut-o¤aR21level of …rms in Country 1 which were relocated from Country 2 to Country 1. When there is
no relocation from Country 2 to Country 1 (with su¢ ciently high trade costs), then

= 0. But

here we more generally consider the case of the …rm relocation from Country 3 to Country 1 as
well as from Country 2 to Country 1. We note that

only in‡uences

1.

There is no relocation from Country 3 to Country 2. The reason for this is that B1 > B2 >
1 (aB3 , which implies that

3 (a ) >
R

R)

2 (a

3 (a ) for all a .
R
RR)

This means that …rms

in Country 3 would always relocate to Country 1 rather than Country 2.
Next, di¤erentiating F w.r.t.

and aR31 gives

dF
= (s1
d

s3 ) + s3 (s1 + s3 ) + s2 s3 > 0

anddF= s3 (s1 + s3 )(1daR31
Using these two di¤erentials, we get) aR311 < 0:daR31
(s1 s3 ) + s3 (s1 + s3 ) + s2 s3=> 0:d
s3 (s1 + s3 )(1) aR311d 3
Since da
=
R31

s3 (1

) aR311and dd 3 = f(1s3 ) + s3 g , we haved 3
d 3 @ 3 daR
=
+
d
d
@aR d
= f(1

s3 ) + s3 g

f (s1

= f(1

s1 ) + s3 (1

s1

= f(1

s1 ) + s3 s2

s2 s3 g

> f(1

s1

s3 )

s3 ) + s3 (s1 + s3 ) + s2 s3 g
s2 s3 gs2 s3 ) + s3 s2 g > 022where>and 1

Thus, a rise ofs1

s2 s3 > 1s1

s2 = s3 > 0.
d 3> 0). Hence, trade liberalisation always improves3 ( dalways increases

per-capita welfare in the smallest country.

6.3

Reduced relocation costs

This Appendix proves the following inequality:
v31 (aR ) > v21 (a);which may be rewritten as
1B3 )aR(B1
In the following, (B1B3 )a1RB2 )a1> (B1:B2 )a1is called LHS and (B1

is called RHS. Note that

because of the …xed per capital relocation cost, it will here typically not be the case that B 0 s
are the same in equilibrium.
1) First we check whether it always holds at the initial short-run equilibrium, i.e. with norelocation. When aR = a, it will always be the case that LHS>RHS because B2 > B3 .
2) Second we show that LHS and RHS are both decreasing (continuous) functions of aR .
LHS:

dLHS
=
daR

dB1
daR

dB3
daR

1
aR

+ (1

)(B1

B3 )aR < 0

since
B1 > B3 ;
dB1
daR
dB3
daR

=
=

dB1 d
B1 d
=
< 0;
d daR
daR
1
dB3 d
B3 d
=
> 0;
d daR
daR
3

where
(1
(1

)
(a
a ) R

a );

and

d
(1
)
a 1 > 0:=daR
(1 a ) R
Turning to RHS, we get
dRHS
=
daR

dB1
daR

a1

=

23

B1 d
a1
1 daR

< 0:

3) No crossing point property: We here show that RHS and LHS never cross in terms of aR .
This means that there does not exist any aR (>a) for 1 >> 0 such that RHS and LHS areequal.
First we assume that there is an aR such that RHS and LHS are equal. To equalise RHS
and LHS, we need B1 = B2 = B3 . This happens only when

= 0; since s1 > s2 > s3 . However,this is a contradiction to our setting.
4) We show that for aR = aB , which implies B1 = B2 , we have LHS larger than RHS. RHS
is zero sinceB2 )a1(B1Since B1 = B2 ; we have

=

= 0:

s1 s2
s2 : LHS can be written as (B11
B3 )aR= (B21
B3 )aR:

The di¤erence in B 0 s is
B1

=
=
=

=
=
Therefore, for s1
then s3 < 2s2

s3
fs3 + (1 s3 )g
s2 =s2 s3 =
s2 + (1 s2 ) s2 s3 + s2 (1 s3 )(s1 s2 )s2 s3 =s2 =s2 + (1 s2 ) s2 s3 + s2 (1 s3 )(s1 s2 )s2 fs2 s3
s2 s3(s1 2s2 ) s2 s3
s3(1 s2 )g
fs2 + (1 s2 )g fs2 s3
s2 s 3s1 + 2s2 )g
s2 fs2 s3
s2 s3(s1 2s2 ) s2 s3
s3 (1 s2 )g
fs2 + (1 s2 )g fs2 s3 (1) + (2s2 s1 ))g
s2 f (s1 2s2 )s3 g
fs2 + (1 s2 )g fs2 s3 (1) + (2s2 s1 ))g
s2 f (s1 s2 ) + (s2 s3 )g:
fs2 + (1 s2 )g fs2 s3 (1) + (2s2 s1 ))g

B3 = B2B3 =s2 < s2

s1 : Hence 2s2

s2
fs2 + (1s 3 , B1s2 )gB3 > 0 always holds. Note that if s1

s3 ,s1 > 0 always holds, which indicates that the denominator isalways positive.
From 1) to 4),(1(s2 < s2)(B1)

1
B3 )aR>holds for any aR 2 (a; aB ).

24

(1
(

)
(B1
)

B2 )a1References[1] Ago, T., I. Isono, and T. Tabuchi (2006) "Locational Disadvantage of the Hub," Annals ofRegional Science, Vol. 40, pp. 819-848.
[2] Amiti, M., and L. Cameron (2007): “Economic Geography and Wages, Review of Economics and Statistics, 89(1), 15–29.
[3] Baldwin, R.E., R.Forslid, P.Martin, G.Ottaviano and F. Robert-Nicoud, (2003). Economic
geography and public policy, Princeton University Press.
[4] Baldwin R.E. and T.Okubo, (2006). Heterogenous Firms, Agglomeration and Economic
Geography: Spatial Selection and Sorting, Journal of Economic Geography 6(3), pp.323346.
[5] Combes P-P, Duranton G., Gobillon L., Puga D. and S.Roux, (2009). "The Productivity
Advantages of large Cities: Distinguishing Agglomeration from Firm Selection", CEPR
Discussion Paper 7191.
[6] Forslid, R. (2010). "Regional Policy, Integration and the Location of Industry”, Handbookof Regional Economics, forthcoming.
[7] Fujita, M. and J.-F. Thisse (2002) Economics of Agglomeration, Cambridge University
Press, Cambridge.
[8] Gopinath M. and H. Saito, (2011). "Heterogeneous Firms, Trade Liberalization and Agglomeration", Canadian Journal of Economics, forthcoming.
[9] Head, K., and T. Mayer (2004): “Market Potential and the Location of Japanese Firms in
the European Union,” Review of Economics and Statistics, 86, 959–972.
[10] Helpman, E., M. J. Melitz, and S. R. Yeaple (2004). “Export versus FDI with HeterogeneousFirms,”American Economic Review, 94(1), 300–316.
[11] Krugman P. and R.E. Livas (1996). "Trade Policy and the Third World Metropolis", Journal of Development Economics 49:1, pp.137-50.
[12] Martin, P. and C.A. Rogers, (1995). "Industrial location and public infrastructure", Journalof International Economics 39, 335-351.
[13] Melitz, M. J. (2003). “The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity”, Econometrica, 71(6), 1695–1725.
[14] Melitz, M. J., and G. I. P. Ottaviano (2005). “Market Size, Trade and Productivity,”NBER
Working Paper No. 11393.

25

[15] Midelfart-Knarvik, K.H. and H.Overman (2002). “Delocation and European integration:is structural spending justi…ed?” Economic Policy 17 (35), 321-359.
[16] Midelfart-Knarvik, K.H., H Overman, S Redding and A Venables (2000) “The Locationof European Industry”, European Commission, D-G for Economic and Financial A¤airs,
Brussels. Economic Papers no 142.
[17] Okubo, T, Picard, P.M., and Thisse, J-F. (2010). “The spatial selection of heterogeneous…rms,” Journal of International Economics, forthcoming.
[18] Okubo, T and V.Rebeyrol, (2006). "Home Market E¤ect, Regulation Costs and Heterogeneous Firms", Cahiers de la MSE, Universite Paris 1.
[19] Okubo, T and Thisse, J-F. (2008), "Market Size and Distance across Countries", mimeo.,
Kobe University.
[20] Ottaviano G.I.P., T. Tabuchi and J-F Thisse (2002). "Agglomeration and Trade Revisited",
International Economic Review 43, 409-36.
[21] Puga D. and T.Venables (1996). The Spread of Industry; Spatial Agglomeration and Economic Development", Journal of the Japanese and International Economies 10:4, pp.44064.
[22] Redding, S., and A. J. Venables (2004): “Economic Geography and International Inequality,” Journal of International Economics, 62, 53–82.
[23] Syverson, C. (2004): “Market Structure and Productivity: A Concrete Example,”Journalof Political Economy, 112(6).
[24] Syverson, C. (2007): “Prices, Spatial Competition, and Heterogeneous Producers: An
Empirical Test," Journal of Industrial Economics 55, 197–222.

26