Discussion Papers In Economics
And Business

Does globalization foster economic growth?
Tadashi Morita, Hajime Takatsuka and Kazuhiro Yamamoto

Discussion Paper 12-11

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDoes globalization foster economic growth?
Tadashi Morita, Hajime Takatsuka and Kazuhiro Yamamoto

Discussion Paper 12-11

June 2012

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDoes globalization foster economic growth?∗
Tadashi Morita† Hajime Takatsuka‡ Kazuhiro Yamamoto§
June 6, 2012

Abstract
This article focuses on two distinct faces of globalization: the decreasein trade costs of goods and the decline of aﬃliation costs of joint venturesby foreign ﬁrms with local ﬁrms. The decrease of aﬃliation costs drives
relocation of ﬁrms from the North to the South. When the market size of
the North is relatively small (resp. large), the growth rate monotonously
decreases (resp. ﬁrst decreases and rises after this) with a decline ofaﬃliation costs. In the case of lowering trade costs, the ﬁrm share in the
North evolves as a U-shaped curve (resp. monotonously increases) whenthe market size of the North is relatively small (resp. large). Growth
rates are raised with agglomeration in the North. Finally, we present
some welfare implications.

JEL Classiﬁcation: F0, O31.
Key words: trade costs, aﬃliation costs, growth rates, innovation sector.

∗ The ﬁrst author acknowledges the ﬁnancial support by the Japan Society for the Promotion of Science. The second and third authors acknowledge the ﬁnancial support by JSPS
Grants-in-Aid for Scientiﬁc Research (A, B, and C) and a MEXT Grant-in-Aid for Young
Scientists (B).
† Faculty of Economics, Osaka Gakuin University, E-mail address: t-morita@ogu.ac.jp‡ Graduate
SchoolofManagement,
KagawaUniversity,
E-mailaddress:
takatsuka@gsm.kagawa-u.ac.jp§ Graduate School of Economics, Osaka University, E-mail address: yamamoto@econ.osakau.ac.jp1

1

Introduction

When ﬁrms operate in foreign countries, they aﬃliate and share their proﬁts
with local ﬁrms in many cases. For foreign ﬁrms, there are many reasons which
induce them to aﬃliate with local ﬁrms to construct their own plants. We canclassify these reasons into two: environmental and political. Regarding the environmental reasons, foreign ﬁrms face legal, cultural, and climatic diﬀerences
between their host and home countries. Aﬃliation with local ﬁrms helps foreign
investors ﬁll those types of gaps. Foreign ﬁrms may require a large and uncertain
number of permits in order to do business. Foreign ﬁrms may also be systematically subjected to greater pressures to directly or indirectly pay oﬀ local oﬃcials.
Foreign ﬁrms may have much higher costs of acquiring information about local production conditions, legal systems, and local consumers.1 In those cases,
aﬃliation with local ﬁrms enables foreign ﬁrms to overcome country- speciﬁc
diﬃculties. On the other hand, we can point out political reasons. There are
equity share regulations for foreign investment in some countries. For example,
in China, there is an equity share regulation in the automobile industry. There
are also equity share regulations in Russia (insurance industry), Brazil (ﬁnanceand transportation), and India (ﬁnance, insurance, and telecommunications)(JETRO 2012).
For example, in China, most foreign automobile ﬁrms aﬃliate with local
ﬁrms and share proﬁts when they start to operate in China. Wang (2003)
reported that, between 1991-1998, of 604 foreign investment companies, 567(or 93.8 percent) were joint ventures with local ﬁrms. The dominance of joint
ventures is partly explained by the mandatory equity share regulations. In addition, foreign investors often ﬁnd that, even without the institutional restraint,
the joint venture is essential. In order to accomplish the goals of the Chinesesystem, Chinese partners are essential to help understand the functioning of
the local market and the business norms. Managing the cross-cultural aspectsof relationships is diﬃcult if foreign ﬁrms want to exploit the market independently. This pattern of investment can also reduce initial risks. Wang (2003)
pointed out that these reasons enhance joint ventures in the Chinese automobile
industry.
In this paper, we study the inﬂuences of two types of ”globalization.” Thedecrease in trade costs of goods is the one aspect of globalization. The other aspect of globalization is the decline of ”aﬃliation costs” which are associated withthe operation of North ﬁrms in the South. In our paper, we assume that Northﬁrms should aﬃliate with local ﬁrms when they operate in the South. Whenthey construct joint ventures in the South, North ﬁrms should share proﬁts withlocal ﬁrms, which we call ”aﬃliation costs.” These two types of globalization,
decline in trade costs and aﬃliation costs, inﬂuence ﬁrms’ location and economic
growth. For example, as shown in the present paper, a decline of aﬃliation costs
drives the hollowing out of industries from the North to the South. Meanwhile,
a suﬃcient decrease of trade costs manifests the agglomeration of manufactur1 Baldwin et al. (2002: Chapter 12) and Yamamoto (2008) constructed static models inwhich location shifts of ﬁrms incur costs.

2

ing ﬁrms in the North. Such location behavior of ﬁrms has large impacts on
economic growth.
Multilateral negotiations under General Agreement on Tariﬀs and Trade(GATT)/World Trade Organization (WTO) have fostered the liberalization of
the trade in goods, and many countries have committed to maintain low levelsof tariﬀ rates. Although the General Agreements on Trade in Services (GATS)
have been contributing toward expanding trade in services, the progress of expanding trade in services is still limited. Then, ﬁrms which operate in foreigncountries should incur substantial extra costs, i.e., aﬃliation costs. However,
the aﬃliation costs of foreign ﬁrms have decreased in recent years. The TPP(Trans-Paciﬁc Strategic Economic Partnership) aims to standardize patent systems and copyrights among signatory countries. The standardization of the legal
system (patents and copyrights) will lower the aﬃliation costs of multinationalﬁrms.
The decrease in aﬃliation costs raises the operation of ﬁrms in foreign countries. Fujita and Ishii (1998) reported that, from 1975 to 1994, the number ofoverseas plants of Japanese electronics ﬁrms located in East Asia increased from40 to 143. Furthermore, Toyota (2011) reported that, in 2001, 9,777,191 vehicles
were produced in Japan, 11,424,689 were produced in the U.S., and 2,334,440,
were produced in China. In 2001, the U.S. was the largest producer of automobiles. In 2006, Japan produced 11,484,233 vehicles, the largest number in theworld. On the other hand, in 2009, China became the largest producer of automobiles, producing 10,383,831, while Japan produced 7,934,057. In China, thenumber of vehicle products has monotonously increased year by year. In 2001,
China entered the WTO, which lowers the aﬃliation costs in China, and foreign
investments have progressed since then. For example, in 2008, over 80 percent
of vehicles were produced by foreign-owned joint ventures (Kwan, 2009). Thissuggests that, in China, foreign-owned joint venture ﬁrms have increased withthe decline in aﬃliation costs.
In this paper, a Grossman-Helpman (1991) and Romer (1990)-type endogenous growth model with two countries is developed, in which the operation of
manufacturing ﬁrms in the South incurs some aﬃliation costs. This means that,when a manufacturing ﬁrm operates in the South, this ﬁrm should consign someof the product line to a local ﬁrm. Without local ﬁrms, manufacturing ﬁrms
cannot produce their products in the South. Manufacturing ﬁrms should share
their proﬁts with local ﬁrms. Those proﬁt sharing with local ﬁrms are aﬃliation
costs for North manufacturing ﬁrms.
Intuitively, a decline in aﬃliation costs raises the proﬁts of foreign ﬁrms in theSouth and, thus, encourages ﬁrms to relocate in the South. Then, manufactured
goods market in the North becomes less competitive and the proﬁts gained in the
North increases. However, manufactured goods market in the South becomescompetitive and the proﬁts gained in the South decreases. If ﬁrms’ proﬁts
are raised with this movement, innovation activities that produce patents toobtain proﬁts are manifested, which results in higher growth rates. Meanwhile,
if ﬁrms’ proﬁts are lowered, innovation activities are reduced and growth rates
are lowered.
3

In fact, the present paper shows that a decline in aﬃliation costs can monotonously
reduce the growth rates of the economy. In this case, the negative eﬀect of decline in aﬃliation costs on growth rates overcomes the positive eﬀect. On theother hand, growth rates may ﬁrst decrease and increase after this, with a decline in a ﬁrm’s aﬃliation costs. This suggests that the positive eﬀect of adecline in aﬃliation costs on growth rates might overcome the negative eﬀect
when aﬃliation costs are small. The pattern that emerges depends on the relative market size. When the market size of the North is relatively small, a decline
in aﬃliation costs reduces growth rates of the economy. Meanwhile, when themarket size of the North is relatively large, the growth rate follows a U-shaped
curve as aﬃliation costs decrease. Thus, our paper oﬀers richer implications
about the relationship between economic growth and globalization.
We also study the eﬀect of trade costs. A decline in trade costs aﬀects
industrial location by changing the balance of the eﬀects of market size andaﬃliation costs. Generally, a large market country attracts more ﬁrms than asmall market country. This tendency is manifested by a decline in trade costs
when trade costs are high. However, the tendency is weakened when trade costs
are suﬃciently low. Instead, the eﬀect of aﬃliation costs becomes dominant,and, thus, ﬁrms avoid operating in the South.
If the population of the North is small enough relative to that of the South,
the number of ﬁrms in the North ﬁrst decreases and then increases after a decline
in trade costs. On the other hand, if the population in the North is relatively
large, the number of ﬁrms in the North monotonously increases with a decline
in trade costs since the two eﬀects reported above work for agglomeration in
the North and are manifested by a decline in trade costs. In the former case,the growth rate follows a U-shaped curve, while, in the latter case, the growthrate monotonously increases with a decline in trade costs.
We also present the welfare implications of the model. In a case in which
the population in the North is small enough relative to the South, the welfare ofboth countries would follow U-shaped curves with a decline of aﬃliation costs.
In this case, the value of patents increases with a decline of aﬃliation costs, since
the market size of the South is large. This asset value eﬀect raises the welfareof the North. On the other hand, growth rates monotonously decrease with adecline in aﬃliation costs, which reduces the welfare of both countries. These
two eﬀects (asset value and growth rate) create a U-shaped curve of welfare
movements.
In a case in which the population in the North is relatively large, the welfareof the North would monotonously decrease, and the welfare of the country would
follow a U-shaped curve. In this case, the asset value eﬀect is weak, which makes
the welfare decrease monotonously. On the other hand, since growth rates
increase when aﬃliation costs become low, the welfare in the South follows a
U-shaped curve. In both cases, the welfare of the whole economy also follows
a U-shaped curve. Thus, our research shows that globalization in terms of aﬁrm’s aﬃliation costs reduces the welfare of the economy in many cases, since
the eﬀect of a reduction in growth rates is large.
Finally, our numerical simulations show that a decline in trade costs raises
4

growth rates in a wide range of parameters. With this movement, the welfareof the North, the South, and the whole economy improves. Thus, our study
shows that globalization of international goods trade raises the welfare of theeconomy.
According to Gao (2007), the recent global shifting of manufacturing fromthe North to the South received signiﬁcant attention from researchers. In addition, Hatch and Yamamura (1996) reported that many manufacturing goods
in East Asia were developed in Japan. The ﬁrms that produce manufactured
goods agglomerated in Japan, which support the rapid growth of Japan. In
recent years, manufacturing ﬁrms relocated from Japan to other countries, suchas Korea, Chinese Taipei, Singapore, Hong Kong, and China, and the growth
rates of Japan decreased with these movements. Our model explains the mechanism behind the spread of ﬁrms to some countries near Japan. Furthermore, in
our paper, we emphasize the importance of studying the parameters of market
size, trade costs, and aﬃliation costs of ﬁrms in the analysis of the eﬀects ofglobalization on the growth rates.
The literature makes evident the many aspects of the relationship of economic geography, international trade, and growth.2 Baldwin, Martin, and Ottaviano (2001), Martin and Ottaviano (1999, 2001), Yamamoto (2003), andGao (2007) are studies in which the endogenous growth model of Grossman
and Helpman (1991) and Romer (1991) (GHR) is integrated with New Economic Geography (NEG) models à la Fujita, Krugman, and Venables (1999).
These researchers studied the relationship between growth and agglomerationand show that agglomeration raises economic growth as trade costs decrease.
Minitti and Parello (2011) constructed a model of GHR with NEG in which
trade integration has no eﬀects on economic growth. Our model in this paper isalso a GHR-type model with NEG, which involves the aﬃliation costs of ﬁrms.
In our paper, we show that aﬃliation costs inﬂuence the relationship between
growth and economic geography.
Section 2 is a presentation of the model and some propositions derived fromthe analysis. An analysis of the welfare levels in both countries is presented in
Section 3. Section 4 is the conclusion of the paper.

2

The model

There are two countries, the North and the South. We assume that patents canbe produced exclusively in the North. Variables referring to the North have thesubscript N , and those referring to the South, S. Each country is endowed with
a ﬁxed amount of labor, LN and LS , respectively. Labor can be used to produce
homogeneous agricultural goods and diﬀerentiated manufactured goods. Whilelabor can be mobile between sectors in the same country, it cannot be mobile
between diﬀerent countries.
The intertemporal utility function of the consumer in country i (i = N, S)
2 See Kuznets (1966) and Long and Wong (1997).

5

∫ ∞

is as follows:e−ρt (Yit + µ log Mit ) dt,

Ui =

(1)

0

where
[∫ nN tMit =mN it (ω)

σ−1
σ

∫ nS
dω +

0

σ
] σ−1
( 0 ) σ−10
σmSit ωdω, σ > 1.

(2)0Here, Yit is the consumption of agricultural goods at time t in country i, Mit is
the consumption of the composite of manufactured goods at time t in country i, ρ
is the subjective discount rate, and µ is a positive parameter. mjit (ω) denotes
the consumption of manufactured variety ω produced by a ﬁrm in country j(j = N, S). njt is the number of varieties produced by a ﬁrm in country j
at time t. njt is also the number of operating ﬁrms in country j at time t.
nt ≡ nN t + nSt denotes the total number of varieties at time t. σ represents
the elasticity of substitution among diﬀerentiated goods. Following Grossman
and Helpman (1991), the market is characterized by free ﬁnancial movements
between two countries. Thus, the interest rate of both countries is the sameat all times (rN t = rSt = rt ). The intertemporal optimization behavior of theconsumer results in the next equation
rt = ρ.

(3)

We derive the following instantaneous demand functions (we take homogeneous goods as the numeraire),
µ
,
Pit
∫ nSt

Mit =
(∫ nN t1−σPit =pN it (ω)

dω +

0

(4)
0

pSit (ω )

1−σ

dω

0

1
) 1−σ

,

(5)

0

Yit = Eit − µ,mjit (ω) =µPit σ−1,
pjit (ω) σ

(6)
(7)

where Pit is called the ‘price index’ in country i at time t. pjit (v) is the consumer
price of variety ω, which is produced in j and consumed in i, and Eit represents
the instantaneous expenditure of a consumer in country i at time t.
Here, we describe the production structure of the agricultural sector. The
agricultural good market is perfectly competitive. We assume that in bothcountries, one unit of agricultural goods is produced with one unit of labor.
We assume that the international trade of homogeneous goods incurs no trade
costs. Therefore, the equilibrium wages in the two countries are both one:wN = wS = 1.3
3 If (EN t − µ) LN + (ESt − µ) LS ≥ LN , agricultural goods are produced in both countries
at the equilibrium. Here, Est ≥ 1, in this model. We, then, assume that (1 − µ) LN +(1 − µ) LS ≥ LN to ensure that the agricultural sector exists in both countries.

6

In the manufacturing sector, manufacturing ﬁrms operate under a DixitStiglitz (1977)-type monopolistic competition. Each ﬁrm produces diﬀerentiatedgoods, and each variety is produced by one ﬁrm. To start a production activity,
a ﬁrm in country j is required to buy one unit of patent produced by theinnovation sector at market price Vjt , which plays the role of ﬁxed costs for theﬁrms. Moreover, a ﬁrm locating in a country uses one unit of labor in its country
as the marginal input to produce one unit of manufactured goods. Potential
ﬁrms can freely enter a production activity as long as the pure proﬁts are positiveand can choose to locate in a country where proﬁts are higher. We assume that,when a manufacturing ﬁrm produces in the North, it does not incur aﬃliation
costs. When a manufacturing ﬁrm operates in the South, the ﬁrm should consign
some of its product line to a local ﬁrm. Without local ﬁrms, manufacturingﬁrms cannot produce their products in the South. Manufacturing ﬁrms shouldshare their proﬁts with local ﬁrms. Consignation costs would then represent
aﬃliation costs for manufacturing ﬁrms. Under this production structure, eachmanufacturing ﬁrm sets the following constant markup (mill) price:
pN = pS =

σ
.
σ−1

(8)

The international trade of manufactured goods incurs ‘iceberg’-type trade costs.
If a ﬁrm sends one unit of its good to a foreign country, it must dispatch T unitsof the good. T − 1 > 0 represents the trade costs. Thus, consumer prices arepji = pj if j = i, and pji = T pj if j 6= i. The price index in country i can be
written as,
Pit =

1
σ
· (nit + njt τ ) 1−σ , i, j ∈ {N, S} , i 6= j,
σ−1

(9)

where τ ≡ T −(σ−1) and τ represent the freeness of trade. τ = 0 describes thecase of autarky, whereas τ = 1 implies free trade. From (7) and (8), instantaneous proﬁts of ﬁrms in the North and South can be expressed as follows:
]
(µ) [
LN
LS τ
πN t =+,(10)σnN t + nSt τ
nN t τ + nSt
]
(µ) [
LN τ
LS
πSt =
+
.
(11)
σ
nN t + nSt τ
nN t τ + nSt
Furthermore, the output of a ﬁrm in country i is expressed as
qit = (σ − 1)πit .

(12)

We assume that innovation activities occur exclusively in the North. In theinnovation sector, we assume that lR units of labor for R&D activities for a timeinterval dt produce a new variety of ﬁnal goods according to the following:4
4 If we assume local knowledge spillovers and dn = l (nt
R N t + φnSt )dt/η, where 0 < φ < 1,
all results in this paper are qualitatively unchanged.

7lR n tdt.
(13)
ηThe cost of the R&D activities is wN lR dt because the R&D sector is locatedonly in the North. Producing the patent creates a value for the manufacturingﬁrms in country i of Vit dnt . We assume that there is free entry into the R&D
race. Therefore, the following free-entry condition must hold:
dnt =

η
dnt
> 0, i ∈ {N, S} .
(14)
, with equality whenever ṅt ≡ntdt
A patent used in the North generates returns πN t , while a patent used in
the South generates returns θπSt , where 0 < θ < 1. When a manufacturing
ﬁrm operates in the South, it should consign some parts of the productionlines to a local ﬁrm and share proﬁts with the local ﬁrm. Without local ﬁrms,
manufacturing ﬁrms cannot produce any manufactured goods in the South.
Here, θ is the share of proﬁts that a manufacturing ﬁrm obtains when it producesin the South. The aﬃliated local ﬁrm obtains the share of 1 − θ in proﬁts. As isshown later, manufacturing ﬁrms determine θ endogenously to maximize their
proﬁts. We assume that there are risk-free assets and the interest rate is rt .
The value of the ﬁrm, which is the market price of the patent, is equalized tothe present value of the sum of the discounted proﬁt over time. ¿From (10) and(11), the values of the patent used in the North and the South are represented
by
∫
Vit ≤

∞

VN t =
t
∫ ∞

VSt =

e−r(τ −t) · πN τ dτ,(15)e−r(τ −t) · θπSτ dτ,

(16)

t

respectively. Diﬀerentiating (15) and (16) with respect to t, we can obtain the
no-arbitrage conditions for capital investment as follows:
πN t + V̇N t = rVN t .

(17)

θπSt + V̇St = rVSt .

(18)

Next, we describe the behavior of local ﬁrms in the South. In the South,
starting up a local production ﬁrm requires κ/nt units of southern labor. Whena local ﬁrm cooperates with a manufacturing ﬁrm, the cost at time interval dt
is (wS κ/nt ) dt. We assume that the beneﬁt of the local ﬁrm at time interval
dt is VLt dt. The condition, then, that local ﬁrms in the South cooperate with
manufacturing ﬁrms is as follows:κ.
nt
Meanwhile, the value of an aﬃliated local ﬁrm is as follows:
∫ ∞
VLt =
e−r(τ −t) · (1 − θ)πSτ dτ.
VLt ≥

t

8

(19)

(20)

Diﬀerentiating (20) with respect to t, we obtain the no-arbitrage condition of a
local ﬁrm as follows:(1 − θ)πSt + V̇Lt = rVLt .

(21)

Manufacturing ﬁrms that operate in the South must consign some parts of
their production lines to local ﬁrms and share their proﬁts. Without local ﬁrms,
manufacturing ﬁrms operating in the South cannot produce any manufactured
goods. A manufacturing ﬁrm presents a take-it-or-leave-it oﬀer of θ to a local
ﬁrm. If a local ﬁrm accepts this oﬀer, the local ﬁrm and the manufacturing ﬁrm
cooperate to produce their products. A manufacturing ﬁrm oﬀers the share of
θ, in which the beneﬁt of a local ﬁrms equals the cost of theirs. Therefore, thevalue of the local ﬁrm satisﬁes the next equation:5
VLt =

κ
.
nt

(22)

If nSt > 0, from the free-entry conditions of manufacturing goods ﬁrms producing in the South, VSt = η/nt must be satisﬁed. Equations (16) and (20) mean
that
θ
VSt =
VLt .
(23)
1−θ
Then, substituting (22) and (23) into (14), we obtain the following equation:
θ κ
η
≤ .
1 − θ nt
nt

(24)

Manufacturing ﬁrms that operate in the South must determine θ, which satisﬁes(24). The left-hand side (LHS) of (24) represents the beneﬁt of manufacturing
goods ﬁrms locating in the South. The right-hand side (RHS) of (24) represents
the cost of R&D investment. If LHS of (24) is smaller than RHS of (24), theoperation of manufacturing ﬁrms in the South is not proﬁtable, and the numberof manufacturing ﬁrms locating in the South becomes zero. Therefore, when
there are manufacturing ﬁrms locating in the South, the following equationmust hold:
θ=

η
.
κ+η

(25)

Equation (25) shows that, when aﬃliation costs are high, θ becomes low. If
κ = ∞, θ = 0. If κ = 0, θ = 1. When (25) is satisﬁed, (21) becomes thesame equation to the (18). Thus, equilibrium conditions in the asset market aresatisﬁed.

5 We assume that the value of the outside option for local ﬁrms is zero. If a local ﬁrm
requires a larger share than 1 − θ, this ﬁrm is rejected by a manufacturing ﬁrm, and the
manufacturing ﬁrm oﬀers 1 − θ to other potential local ﬁrms.

9

3

Equilibrium

Let us deﬁne st ≡ nN t /(nN t + nSt ) as the share of manufacturing ﬁrms in the
North. In equilibrium, if 0 < st < 1 holds, the following equation must hold:πN t = θπSt .

(26)This is because capital returns are equalized in equilibrium. From (10), (11),and (26), the equilibrium share of manufacturing ﬁrms in the North iss∗ =(1 − θτ )LN + (τ − θ)τ LS.
(1 − τ ) [(1 − θτ )LN − (τ − θ)LS ](27)

Note that (27) is true only if the RHS is in [0, 1]. Otherwise, s∗ is either 0 or
1. Diﬀerentiating s∗ with respect to θ,6 we can obtain the following proposition(See Appendix B for the proof):
Proposition 1 For the interior equilibrium (i.e., s∗ ∈ (0, 1)), an increase in θ
decreases the share of manufacturing ﬁrms in the North.
When st = 1 and πN t ≥ θπSt are satisﬁed, it holds that s∗ = 1. From (10)and (11), whenθ ≤ θN ≡τ (LN + LS ),
τ 2 LN + LS(28)

we have s∗ = 1. In the case that LN /LS ≤ 1/τ , we have 0 < τ < θN ≤ 1. On
the other hand, when st = 0 and πN t ≤ θπSt are satisﬁed, it holds that s∗ = 0.
From (10) and (11), whenθ ≥ θS ≡LN + τ 2 LS,
τ (LN + LS )(29)s∗ = 0. In the case that LN /LS ≤ τ , we have 0 < θS ≤ 1. Simple calculations
show that θN < θS (See Appendix A). For an interior equilibrium to exist forθ ∈ (0, 1), we present the following assumption:
Assumption 1 It holds that LN /LS ≤ 1/τ .
This suggests that the population in the North is not as large as that in theSouth. Under that assumption, we have θN ≤ 1, and, if θ ∈ (θN , min{θS , 1}),
it holds that s∗ ∈ (0, 1).
Because the share of manufacturing ﬁrms in the North, s∗ , is constant from(27), we diﬀerentiate s with respect to t as follows:
ṅt
ṅN t
ṅSt
=
=
≡ g.
nt
nN t
nSt

(30)

6 From (25), a higher θ corresponds to a lower {, which implies lower aﬃliation costs in
the South.

10If ṅt > 0, diﬀerentiating (14) with respect to t, we can obtain the following
equation:
V̇it
ṅt
(31)
= − = −g.
Vit
nt
Substituting (31) into (17), we obtain the value of a patent that is used in
the North as follows:πN t
VN t =.
(32)
ρ+gThen, substituting (10), (31), and (32) into (14), the growth rate is given by

g=

3.1

[
]
µ
τ LS
LN
+
− ρ.
ησ (1 − τ )s + τ
1 − (1 − τ )s

(33)

Eﬀects of aﬃliation costs

Diﬀerentiating (33) with respect to θ, we can obtain the following equation:
[
]
ησ ∂g
(1 − τ )LN(1 − τ )τ LS
∂s
= −
+
,
(34)
2
2
µ ∂θ
((1 − τ )s + τ )(1 − (1 − τ )s) ∂θwhere ∂s/∂θ < 0 from Proposition 1. The ﬁrst term in the square bracketof (34) represents the eﬀect of s on proﬁts gained in the North. This eﬀect
is negative because an increase in the share of ﬁrms in the North exacerbates
the market competition in the North and decreases the proﬁts gained in the
North. The second term in the square bracket of (34) represents the eﬀect of son proﬁts gained in the South. This eﬀect is positive because an increase in theshare of ﬁrms in the North ameliorates the market competition in the South andincreases the proﬁts gained in the South. When LN is very small (resp. large)
relative to LS , the absolute value of −(1 − τ )LN /((1 − τ )s + τ )2 is small (resp.
large) relative to the absolute value of (1 − τ )τ LS /(1 − (1 − τ )s)2 . Then, when
LN is very small (resp. large) relative to LS , the term in the square bracket
becomes positive, and, thus, an increase in θ decelerates (resp. accelerates) thegrowth rates.
Substituting (27) into (34), we can obtain the following equation:2µ ∂g(1 − τ ) [(1 − θτ )LN − (τ − θ)LS ]∂s=−
F (θ) ,ησ ∂θ(1 + τ )2 (1 − θτ )2 (τ − θ)2 LN LS
∂θ

(35)

F (θ) = (τ − θ)2 LS − τ (1 − θτ )2 LN .

(36)

where
From Proposition 1 (i.e., ∂s/∂θ < 0), we know that ∂g/∂θ R 0 is equivalent toF (θ) R 0. We denote that θ̂ is the unique solution of F (θ) = 0 in (τ, ∞). To
investigate the sign of F (θ), we have the following proposition (See Appendix
C for the proof).

11

Proposition 2 (Eﬀects of aﬃliation costs on growth rates).
i) When LN /LS < τ 3 , it holds that ∂g/∂θ < 0 for θ ∈ (θN , θS ).
ii) When LN /LS ∈ (τ 3 , τ ), it holds that ∂g/∂θ < 0 for θ ∈ (θN , θ̂) and ∂g/∂θ >0 for θ ∈ (θ̂, θS ).
iii) When LN /LS ∈ (τ, 1/τ ), it holds that ∂g/∂θ < 0 for θ ∈ (θN , θ̂) and∂g/∂θ > 0 for θ ∈ (θ̂, 1).
We can see the eﬀect of θ on the growth rate in Figures 1, 2, and 3. In
Figure 1, when LN /LS < τ 3 , a decrease in the aﬃliation costs decreases thegrowth rate. In Figures 2 and 3, when LN /LS ∈ (τ 3 , 1/τ ), the relationshipbetween the aﬃliation costs and the growth rate follows a U-shaped curve.
We explain Proposition 2 intuitively. From Proposition 1, a decrease in theaﬃliation costs lowers the share of manufacturing ﬁrms in the North. From(34), the manufactured goods market in the North becomes less competitive,
and its market in the South becomes competitive. The proﬁts gained in the
North, then, increase, and proﬁts gained in the South decrease. If an increasein proﬁts gained in the North is larger than a decrease in proﬁts gained in theSouth, the proﬁts of manufacturing ﬁrms increase. An increase in the proﬁt
pushes up the value of R&D investment, and the growth rate increases.
When LN is small relative to LS , the South has a large market relative to
the North. The proﬁts gained in the North are then smaller than proﬁt losses
in the South. Therefore, in this case, an increase in θ depresses the growth rate.
It is noteworthy that the reverse could occur when LN is relatively large. If
the aﬃliation costs are suﬃciently high, the manufactured goods market in the
North is still competitive. Thus, the proﬁts gained in the North are smaller
than proﬁt losses in the South, which lowers the growth rate again. However, if
the aﬃliation costs are suﬃciently low, the manufactured goods market in the
North is less competitive. In this case, the proﬁts gained in the North could
dominate proﬁt losses in the South, and, thus, the growth rate could be higher.

3.2

Eﬀects of trade costs

Next, we study the eﬀects of trade costs on growth rates. Before analyzing theeﬀects of trade costs on growth rates, we investigate the relationship between
trade costs and the share of manufacturing ﬁrms. From (27), we can rewrite
the equilibrium share of manufacturing ﬁrms in the North as follows:s∗ =f0 (τ ),f0 (τ ) − f1 (τ )

(37)

where
f0 (τ ) = (1 − θτ )LN + (τ − θ)τ LS ,(38)

f1 (τ ) = τ (1 − θτ )LN + (τ − θ)LS .

(39)

and
The denominator of (27) or (37) is positive for any interior equilibrium (i.e.,s∗ ∈ (0, 1)) since the numerator of (37), f0 (τ ), is positive because of θ > θN > τ .
12

Thus, we know that f1 (τ ) ≥ 0 is equivalent to s∗ = 1. Substituting τ = 0 andτ = 1 into (39), we havef1 (0) = −θLS < 0,
f1 (1) = (1 − θ)(LN + LS ) > 0.
Since f1 (τ ) is a concave function of τ , we obtain the boundary of τ , where allﬁrms agglomerate in the North:Lemma 3 There is a threshold value τ1 ∈ (0, 1) of the trade freeness of manufactured varieties so that s∗ = 1 if and only if τ ∈ [τ1 , 1).
This lemma suggests that all ﬁrms agglomerate in the North if trade costs
are suﬃciently small. The reason is as follows. In our model, two primaryeﬀects determine ﬁrm location, namely, market size and aﬃliation cost. The
market size eﬀect refers to the tendency in which manufacturing ﬁrms prefer tolocate in the larger country to save trade costs. Meanwhile, the aﬃliation costeﬀect refers to the tendency in which manufacturing ﬁrms prefer to locate in
the North to avoid aﬃliation costs. When trade costs are suﬃciently small, theformer eﬀect is negligible, since ﬁrms can export their products cheaply. Thus,
the aﬃliation cost eﬀect dominates, which suggests that ﬁrms agglomerate in
the North, where aﬃliation costs are not required.
From (27) or (37), we know that f0 (τ ) > 0 is equivalent to s∗ > 0. If
equation f0 (τ ) = 0 has two roots, they are denoted as τ01 and τ02 (> τ01 ).
We then have the following lemma, which gives the conditions for all ﬁrms toagglomerate in the South (see Appendix D for the proof):
Lemma 4 There is a threshold value λ ∈ (0, θ2 ) so that s∗ > 0 for any τ
if LN /LS > λ; otherwise, s∗ = 0 (resp. s∗ > 0) for τ ∈ [τ01 , τ02 ] (resp.
τ∈/ [τ01 , τ02 ]), where 0 < τ01 < τ02 < τ1 .
This lemma suggests that all ﬁrms agglomerate in the South if the North
is suﬃciently small and trade costs are intermediate. The reason is as follows.
From Lemma 3, we know that all ﬁrms agglomerate in the North if trade costs
are suﬃciently small. On the other hand, if trade costs are suﬃciently large,
ﬁrms are necessarily dispersed, since it is very costly for ﬁrms to export. In
the case of intermediate trade costs, ﬁrm distribution depends on the balance ofthe market size eﬀect and the aﬃliation cost eﬀect. If the North is suﬃciently
small, the market size eﬀect dominates the aﬃliation cost eﬀect, which resultsin attracting all ﬁrms to the large country, the South.
For any interior equilibrium, Appendix E gives another expression of thegrowth rate:7µθ(LN + LS )
− ρ.
(40)
g=
ησ(θs + 1 − s)
7 Substituting the equilibrium value of s (27) into (33) and (40), we know that the two
expressions of g are equivalent.

13

Thus, we know that∂g∂g
> 0 and
> 0,
(41)
∂s
∂θ
which suggests that the growth rate increases if the ﬁrm share in the North
increases (and aﬃliation costs are ﬁxed) or if aﬃliation costs decrease. The
reason is as follows. First, if ﬁrms locate in the South, they have to produce
more than ﬁrms in the North, since they must pay aﬃliation costs. Since theworld output of manufactured goods is constant due to (E.1) in Appendix E,
this suggests that both the output and the proﬁt of a ﬁrm in the North decrease.
Thus, if s increases or θ increases, the reverse occurs, i.e., the proﬁt in the North
becomes higher. From (32), a higher proﬁt in the North implies a higher growth
rate.
From (27), we obtain(LN + LS )h(τ )
∂s
=
,
2
∂τ
(1 − τ ) (1 + θLS − (θLN + LS )τ )2
where
h(τ ) ≡ (θ2 LN − LS )τ 2 − 2(LN − LS )τ + (LN − θ2 LS ).
Thus, from (40) and (41), we have
( )
( )
∂g
∂s
sgn
= sgn
= sgn [h(τ )] ,
∂τ
∂τ

(42)

(43)

If equation h(τ ) = 0 has two roots in (0, 1), the smaller root is denoted as τ2 .
The next proposition is then derived (see Appendix E for the proof):
Proposition 5 (Eﬀects of trade costs on growth rates).
i) When LN /LS > θ2 , it holds that ∂g/∂τ > 0 for τ ∈ (0, τ1 ).
ii) When LN /LS ∈ (λ, θ2 ), it holds that ∂g/∂τ < 0 for τ ∈ (0, τ2 ) and ∂g/∂τ > 0
for τ ∈ (τ2 , τ1 ).
iii) When LN /LS < λ, it holds that ∂g/∂τ < 0 for τ ∈ (0, τ01 ) and ∂g/∂τ > 0
for τ ∈ (τ02 , τ1 ).
Figures 4, 5, and 6 correspond to the case of i), ii), and iii) in Proposition
5, respectively. This proposition suggests that the growth rate monotonously
increases in τ if the North is large relative to the South; otherwise, the growthrate evolves in a U-shaped pattern when trade costs decline. From (43), we
know that the growth rate and the ﬁrm share of the North co-evolve in thesame direction. From Lemmas 3 and 4, if the North is suﬃciently smaller thanthe South, ﬁrms ﬁrst disperse and then agglomerate in the South and, ﬁnally, in
the North when trade costs decline. This suggests that the growth rate follows
a U-shaped curve. On the other hand, if the North is relatively large, the net
eﬀect of the two primary factors, the market size eﬀect and the aﬃliation costeﬀect, accelerates agglomeration in the North when trade costs decline. Thus,
the growth rate monotonously increases in τ .
14

4

Welfare analysis

In this section, we investigate the welfare level in both countries. From r = ρ
and wit = 1, we can rewrite the intertemporal budget constraint as follows:
∫ ∞
∫ ∞
−ρt
e Eit dt = ai0 +e−ρt dt,(44)00where ai0 is the present value of assets owned by a worker in country i. Because the expenditure levels in both countries are constant in equilibrium, theexpenditure level in each country is given by
Eit = 1 + ρai0 .

(45)

The total value of assets at the initial time is [nN VN 0 + nS (VS0 + VL0 )]. We
assume that the ratio of assets held in the North at the initial time is ζ and theratio of assets held in the South at the initial time is 1 − ζ. The assets held in
both countries are represented byaN 0 =

ζ[η + (1 − s)χ] ,LN1−ζ[η + (1 − s)χ] .
LS
Therefore, the expenditure levels in both countries are given by
aS0 =EN t = 1 + ρζ[η + (1 − s)χ] ,
LN

(46)
(47)

(48)

1−ζ
[η + (1 − s)χ] .
(49)
LSThen, substituting (4), (5), (6), (48), and (49) into (1), we obtain the welfare
levels in both countries as follows:
∫ ∞
ρζ
UN =
e−ρt {1 +[η + (1 − s)χ] + µ(log µ − 1)LN0µσ − 1 1−σ+log[()(nN + τ nS )]}dt, (50)σ−1σESt = 1 + ρ

∫ ∞
US =

e−ρt {1 +0ρ(1 − ζ)[η + (1 − s)χ] + µ(log µ − 1)LSµσ − 1 1−σ+log[()(nN τ + nS )]}dt.
σ−1
σ

(51)

Then, from nt = n0 egt , the welfare levels in both countries are given by
ρUN = 1 +µρζ[η + (1 − s)χ] + µ(log µ − 1) +log n0
LN
σ−1
σ−1
µ
g
− µ log()+
log[(1 − τ )s + τ ] + , (52)
σ
σ−1
ρ
15

ρUS = 1 +µρ(1 − ζ)[η + (1 − s)χ] + µ(log µ − 1) +log n0
LS
σ−1
σ−1
µ
g
− µ log()+
log[1 − (1 − τ )s] + . (53)σσ−1ρThen, diﬀerentiating UN and US with respect to θ, we obtain the following
equations:[]∂UNρζχ ∂sµ1−τ∂s 1 ∂g
ρ
=−
+
+
.
(54)
∂θ
LN ∂θ σ − 1 (1 − τ )s + τ ∂θ ρ ∂θ[]∂USρ(1 − ζ)χ ∂sµ1−τ∂s 1 ∂g
ρ
=−
+
+
−
.
(55)
∂θ
LS
∂θ σ − 1
1 − (1 − τ )s ∂θ ρ ∂θWe explain the relationship between θ and the welfare level in the North. The
sign of the ﬁrst term is positive. The sign of the ﬁrst term in the square bracket
is negative, and the sign of the second term in the square bracket is ambiguous.
The ﬁrst term is a positive eﬀect in which a decrease in the aﬃliation costs
increases the total value of the assets and increases the expenditure level. Thiseﬀect then increases the welfare level in the North. The ﬁrst term in the square
bracket is a negative eﬀect: when there is an increase in θ, the number of ﬁrms
producing in the South increases, and the price level in the North increases.
The welfare level in the North then decreases. At last, the second term in thesquare bracket is an ambiguous eﬀect because the relationship between θ andthe growth rates is ambiguous. In the same way, we explain the relationshipbetween θ and the welfare level in the South.
In order to get some clear results, we present numerical examples. In thisexample, the number of population in both countries are LN = 0.3 and LS = 1
respectively. The subjective discount rate is ρ = 0.05 and the elasticity of
substitution is σ = 1.5. The eﬃciency of R&D investment is η = 1.3. The
initial number of the manufactured goods is n0 = 1. The ratio of asset holdingin the North at initial time is ζ = 1. Figures 7, 8 and 9 represent the eﬀect of
θ on the welfare of the North and the welfare of the South. Figure 7 depicts
the case that LN /LS < τ 3 , Figure 8 depicts the case that τ 3 < LN /LS < τ ,and Figure 9 depicts the case that LN /LS > τ . In Figure 7, from Proposition
2, a decline in aﬃliation costs lowers the growth rates monotonously and thewelfare level in both countries are also lowered by a decline in aﬃliation costs.
In Figures 8 and 9, from Proposition 2, the relationship between growth rates
and the aﬃliation costs follows the U-shaped curve. Therefore, the welfare levelof the South follows the U-shaped curve.
We study the eﬀect of trade costs on welfare. Diﬀerentiating UN and US
with respect to τ , we can obtain the following equation:[]ρζχ ∂s
µ
1−τ
∂s
1 ∂g
1−s
∂UN
=−
+
+
+
. (56)
ρ∂τLN ∂τ
σ − 1 (1 − τ )s + τ ∂τρ ∂τ
1 − (1 − τ )s[]∂USρ(1 − ζ)χ ∂s
µ
τ −1
∂s
1 ∂g
s
ρ
=−
+
+
+
.
∂τ
LS
∂τ
σ − 1 1 − (1 − τ )s ∂τρ ∂τ
1 − (1 − τ )s
(57)
16

The ﬁrst three terms in RHS of (56) and (57) are the same with respect tothe eﬀect of θ on UN and US , which are expressed in (54) and (55). The lastterms in RHS in both equations are positive, which represents the direct eﬀectof decline in trade costs. Figures 10 , 11 and 12 depict the eﬀect of trade costs on
the welfare of the North and the welfare of the South. Figure 10 depicts the casethat LN /LS > θ2 . From Proposition 3, trade liberalization raises the growth
rates monotonously. Then, trade liberalization raises the welfare level in bothcountries for τ < 0.4 in Figure 10. On the other hand, when τ > 0.4, all of ﬁrms
locate in the North. Therefore, trade liberalization does not aﬀect the welfare of
the North and raises the welfare of the South monotonously. Figure 11 depicts
the case that λ̄ < LN /LS < θ2 . From Proposition 3, the relationship between
trade liberalization and the growth rate follows the U-shaped curve. However,when trade costs are suﬃciently high, the direct eﬀect is larger than the indirect
eﬀect and trade liberalization raises welfare level of both countries. Figure 12
depicts the case that LN /LS < λ̄. From Proposition 3, when τ01 < τ < τ02 , thenumber of ﬁrms locating in the North is zero. Then, trade liberalization does
not aﬀect the welfare of the South and raises the welfare of North monotonously.

5

Conclusion

Throughout this paper, we constructed a model introducing aﬃliation costsof ﬁrms into the Grossman-Helpman-Romer-type growth theory with a New
Economic Geography model. This paper focuses on two distinct faces of globalization: the decline of aﬃliation costs and the decrease in trade costs of goods.
We investigated the eﬀects of aﬁlliation costs on growth rates. When the market
size of the North is relatively small, a decline in aﬃliation costs reduces growth
rates of the economy. On the other hand, when the market size of the Northis relatively large, the growth rate follows a U-shaped curve as aﬃliation costs
decrease.
We also studied the eﬀects of trade costs on growth rates. If the populationof the North is small enough relative to that of the South, the number of ﬁrms
in the North ﬁrst decreases and then increases after a decline in trade costs. On
the other hand, if the population in the North is relatively large, the number ofﬁrms in the North monotonously increases with a decline in trade costs. In theformer case, the growth rate follows a U-shaped curve, while, in the latter case,the growth rate monotonously increases with a decline in trade costs.
In this paper, we assume that equilibrium wages in two countries are constantand the same. We can construct a model in which wages are endogenously
determined. We assume that innovation activities can be done in one country.
We can extend the model to one in which innovation activities can be operated
in both countries. These are problems for additional research.

17

References[1] Baldwin, R., Forslid, R., Martin, P., Ottaviano, G.I.P., and Robert-Nicoud,F. (2001) Economic Geography and Public Policy, Princeton University
Press, NJ.
[2] Baldwin, R., Martin, P., and Ottaviano, G.I.P. (2001) Global income divergence, trade, and industrialization: The geography of growth takeoﬀs,
Journal of Economic Growth 6, 5-37.
[3] Kwan, C.H. (2009) China in Transition, (In Japanese) Research Institute of
Economy, Trade & Industry (RIETI), http://www.rieti.go.jp/users/chinatr/jp/090601sangyokigyo.htm.
[4] Dixit, A., and Stigliz, J. (1977) Monopolistic competition and optimum
product diversity, American Economic Review 67, 297-308.
[5] Fujita, M., and Ishii, R. (1998) Global location behavior and organizational dynamics of Japanese electronics ﬁrms and their impact on regional
economies, in A.D. Chandler, P. Hagström, and Ö. Sölvell, eds., The Dynamic Firm, Oxford University Press, Oxford.
[6] Fujita, M., Krugman, P., and Venables, A. (1999) The Spatial Economy:
Cities, Regions, and International Trade, MIT Press, Cambridge, MA.
[7] Gao, T. (2007) Trade costs, international production shifting, and growth,
European Economic Review 51, 317-335.
[8] Grossman, G., and Helpman, E. (1991) Innovation and Growth in theWorld Economy, MIT Press, Cambridge, MA.
[9] Hatch, W., and Yamamura, K. (1996) Asia in Japan’s Embrace-Building a
Regional Alliance. Cambridge University Press, Cambridge.
[10] JETRO(2012)
Reports
http://www.jetro.go.jp/en/reports/.

andStatistics,[11] Kuznets, S. (1966) Modern Economic Growth, Rate Structure, and Spread.
Yale University Press, New Haven.
[12] Minniti, A., and Parello, C.P. (2011) Trade integration and regional disparity in a model of scale-invariant growth, Regional Science and Urban
Economics 41, 20-31.
[13] Martin, P., and Ottaviano, G.I.P. (1999) Growing locations: Industry location in a model of endogenous growth, European Economic Review 43,
281-302.
[14] Romer, P. (1990) Endogenous technological change, Journal of Political
Economy 98, 71-102.

18

[15] Toyota(2011)
Toyotanogaikyou
2011(In
Japanese),
http://www.toyota.co.jp/jpn/company/about toyota/gaikyo/pdf2011/world V2.pdf.
[16] Yamamoto, K. (2003) Agglomeration and growth with innovation in theintermediate goods sector, Regional Science and Urban Economics 33, 335360.
[17] Yamamoto, K. (2008) Location of industry, market size, and imperfectinternational capital mobility, Regional Science and Urban Economics 38,
518-532.
[18] Wang, H. (2003) Policy reforms and foreign direct investment: The caseof the Chinese automobile industry, East-West Journal of Economics andBusiness, 1, 287-314.

19

Appendix
A

Proof of Proposition 1

Differentiating (16) with respect to θ, we can obtain the following equation:∂s∗−τ (LN + LS )[(1 − θτ )LN − (τ − θ)LS ] − (−τ LN + LS )[(1 − θτ )LN + (τ − θ)τ LS ]=∂θ
(1 − τ )[(1 − θτ )LN − (τ − θ)LS ]2(τ LN − LS − τ LN − τ LS )(1 − θτ )LN + [τ (τ LN − LS ) + τ (LN + LS )](τ − θ)LS=
(1 − τ )[(1 − θτ )LN − (τ − θ)LS ]2(1 + τ ) [(1 − θτ ) + (θ − τ )] LN LS
< 0,
(A.1)
=−
(1 − τ )[(1 − θτ )LN − (τ − θ)LS ]2
because θ > τ .

B

Deviation of θN < θS

Subtracting θN from θS , we can obtain the following equation:
LN + τ 2 LS
τ (LN + LS )(LN + τ 2 LS )(τ 2 LN + LS ) − τ 2 (LN + LS )2− 2=
τ (LN + LS )
τ LN + LS
τ (LN + LS )(τ 2 LN + LS )(τ 2 − 1)2 LN LS
=
> 0.
(B.1)
τ (LN + LS )(τ 2 LN + LS )Then, θS is larger than θN .

C

Proof of Proposition 2

From Proposition 1 and (35), we know that the sign of ∂g/∂θ is equivalent tothe sign of F (θ). Then, we investigate the sign of F (θ). F 0 (θ) and F 00 (θ) are
given byF 0 (θ) = −2(τ − θ)LS + 2τ 2 (1 − θτ )LN ,(C.1)
F 00 (θ) = 2(LS − τ 3 LN ) > 0,

(C.2)
00

where the last inequality is from Assumption 1. From θ > τ and F (θ) > 0,0
the sign of F (θ) is given by
F 0 (θ) > F 0 (τ ) = 2τ 2 (1 − τ 2 )LN > 0(C.3)

Therefore, F 0 (θ) > 0 for θ ≥ τ . Then, the value of F (1), F (θN ), and F (θS ) canbe obtained as follows:
F (1) = (1 − τ )2 (LS − τ LN ),F (θN ) =(1 − τ 2 )2 τ LN LS(τ LN − LS ),(τ 2 LN + LS )2
20

(C.4)
(C.5)

F(µ)
F(µ)

µN

µS

F(µ)

µ
µN
µ^

µ
µS

µN
µ^

µ

1 µS

Figure C.1: LN < τ 3 LS Figure C.2: τ 3 LS < LN < Figure C.3: τ LS < LN <
τ LS
LS /τ

F (θS ) =(1 − τ 2 )2 LN LS(LN − τ 3 LS ).
τ 2 (LN + LS )2(C.6)

Then, we have F (θN ) < 0 from Assumption 1, while F (θS ) R 0 holds when
LN R τ 3 LS .
When LN < τ 3 LS , we have 0 < θS < 1, F (θN ) < 0, and F (θS ) < 0. Then,
we can depict F (θ) in Figure C.1. Because F 0 (θ) > 0 for θ > τ , F (θN ) < 0,and F (θS ) < 0, we know that F (θ) is negative for θN < θ < θS . Therefore,∂g/∂θ < 0 holds.
When τ 3 LS < LN < τ LS , we have 0 < θS < 1, F (θN ) < 0, and F (θS ) > 0.
Then, we can depict F (θ) in Figure C.2. Because F (θN ) < 0 and F (θS ) > 0,
there exists the unique solution of F (θ̂) = 0. Then, F (θ) is negative for θN <
θ < θ̂ and F (θ) is positive for θ̂ < θ < θS . Therefore, ∂g/∂θ < 0 holds forθN < θ < θ̂ and ∂g/∂θ > 0 holds for θ̂ < θ < θS .
When τ LS < LN < LS /τ , we have θS > 1, F (θN ) < 0, and F (1) > 0. Then,
we can depict F (θ) in Figure C.3. Because F (θN ) < 0 and F (1) > 0, there
exists the unique solution of F (θ̂) = 0. Then, F (θ) is negative for θN < θ < θ̂and F (θ) is positive for θ̂ < θ < 1. Therefore, ∂g/∂θ < 0 holds for θN < θ < θ̂and ∂g/∂θ > 0 holds for θ̂ < θ < 1.

D

Proof of Lemma 2

We investigate the value of f0 (τ ). We have s∗ > 0 if f0 (τ ) > 0; otherwise s∗ = 0. From (38), we know that if LN > [τ (θ − τ )/ (1 − θτ )] LS , thenf0 (τ ) > 0. In the following, we investigate the condition which holds LN >21

[τ (θ − τ )/ (1 − θτ )] LS . Since·¸∂ τ (θ − τ )θτ 2 − 2τ + θ=
2 ,∂τ 1 − θτ(1 − θτ )θτ 2 − 2τ + θ|τ =0 = θ > 0,
θτ 2 − 2τ + θ|τ =θ = θ3 − θ < 0,
θτ 2 − 2τ + θ|τ =1 = 2(θ − 1) < 0,
we know that [τ (θ − τ )/ (1 − θτ )] LS is maximized (and positive) at τ ∈ (0, θ),which is the smaller root of θτ 2 − 2τ + θ = 0. Let λ ≡ [τ (θ − τ )/ (1 − θτ )].
Thus, if LN > λLS , then f0 (τ ) > 0, which is equivalent to s∗ > 0 for any τ
because of (37). Furthermore, sincef0 (0) = LN > 0,f0 (1) = (1 − θ)(LN + LS ) > 0,
the equation f0 (τ ) = 0 has two roots, τ01 , τ02 , in (0, 1) if LN < λLS . Thus, if
LN < λLS , it holds that s∗ = 0 for τ ∈ [τ01 , τ02 ] because of (37).
The difference of θ2 and λ isτ (θ − τ )θ2 −1 − θτ
2τ − θ(1 + θ2 )τ + θ2
=
.
(D.1)
1 − θτ
We know that the numerator of (D.1) is positive since the discriminant is£¤2£¤
θ(1 + θ2 ) − 4θ2 = θ2 (1 + θ2 )2 − 4 < 0.
This implies that λ < θ2 . Finally, if τ02 ≥ τ1 , it holds that s∗ = 1 in [τ1 , τ02 ]from Lemma 1, which contradicts the last result. Thus, τ02 < τ1 .

E

Proof of Proposition 3

For the interior equilibrium (i.e., s∗ ∈ (0, 1)), from the market clearing conditionof manufacutured goods, we have
³
σ
nSt ´
µ(LN + LS ) =(nN t qN t + nSt qSt ) = σ nN t +πN t ,(E.1)
σ−1θ
where the second equality is from (12) and (26). Thus, we have
πN t =µθ(LN + LS ).
σ(θnN t + nSt )From this equation and (32), we have another expression of the growth rate:g=µθ(LN + LS )− ρ.
ησ(θs + 1 − s)In addition, the next lemma holds concerning the function h(τ ) defined by (42):22

Lemma E.1 It holds that h(τ1 ) ≥ 0. Furthermore, if LN < LN , it holds thath(τ01 ) ≤ 0 and h(τ02 ) ≥ 0.
Proof. If h(τ1 ) < 0, we have ∂s/∂τ < 0 at τ = τ1 from (43). It evidently
contradicts Lemma 1. If h(τ01 ) > 0, we have ∂s/∂τ > 0 at τ = τ01 from (43).
It evidently contradicts Lemma 2. Finally, we can show that h(τ02 ) ≥ 0 in asimilar way.
From (42), we know thath(0) = LN − θ2 LS ,h(1) = (LN − LS )(1 − θ)2 ,and the vertex of h(τ ) isτ∗ ≡LN − LS.
θ 2 LN − LS

We consider the following four cases separately: (a) θ2 LS < LS < θ2 LN < LN ,(b) θ2 LS < θ2 LN < LS < LN , (c) θ2 LN < θ2 LS < LN < LS , and (d)θ2 LN < LN < θ2 LS < LS . We know that τ ∗ > 1, h(0) > 0, h(1) > 0, and h(τ )is convex in case (a), while τ ∗ < 0, h(0) > 0, h(1) > 0, and h(τ ) is concavein case (b). Thus, we conclude that h(τ ) > 0 for τ ∈ (0, 1) in these two cases.
In case (c), we know that τ ∗ ∈ (0, 1), h(0) > 0, h(1) < 0, and h(τ ) is concave.
From Lemma E.1, we conclude that h(τ ) > 0 for τ ∈ (0, τ1 ). Summarizing theresults of (a)-(c), we have i) in Proposition 3 by (43).
In case (d), we know that τ ∗ ∈ (0, 1), h(0) < 0, h(1) < 0, and h(τ ) is
concave. From Lemma E.1 and the definition of τ2 (i.e., the smaller root ofh(τ ) = 0), we conclude that τ2 < τ1 , h(τ ) < 0 for τ ∈ (0, τ2 ) and h(τ ) > 0 forτ ∈ (τ2 , τ1 ). Therefore, from Lemmas 2, E.1, and Equation (43), we obtain ii)
and iii) in Proposition 3.

23

g



θN

θS



θ

Figure 1: The relationship between transaction costs and growth rate when
LN /LS < τ 3

24

g



θˆ

θN

θS



θ

Figure 2: The relationship between transaction costs and growth rate when
LN /LS ∈ (τ 3 , τ )

25

g



θN

θ̂



θ

Figure 3: The relationship between transaction costs and growth rate when
LN /LS ∈ (τ, 1/τ )

26

g



τ



τ

Figure 4: The relationship between trade costs and growth rate when LN /LS >
θ2

27

g



τ

τ



τ

Figure 5: The relationship between trade costs and growth rate when LN /LS ∈(λ̄, θ2 )28

g τ 

τ 

τ



τ

Figure 6: The relationship between trade costs and growth rate when LN /LS <
λ̄

29

130

122

128

121

htuoS fo eraflew

123

htroN fo eraflew

132

126

120

124

119

122

118

120

117

118

116

116

115

114
0.87

0.88

0.89
θ

0.9

0.91

114
0.87

Figure 7: τ = 0.8

30

0.88

0.89
θ

0.9

0.91

135

118

130

116

htuoS fo eraflew

htroN fo eraflew

125

114

120

112

115

110

110

108

105
100
0.7

106

0.75

0.8
θ

0.85

0.9

104
0.7

Figure 8: when τ = 0.6

31

0.75

0.8
θ

0.85

0.9

135

115

130
110

htuoS fo eraflew

htroN fo eraflew

125
120

105

115

100

110
105

95

100

90
95
90

0.4

0.5

0.6

0.7

0.8

0.9

85

0.4

θ

0.5

0.6

0.7

θ
Figure 9: when τ = 0.4

32

0.8

0.9

140

130

130

120

htuoS fo eraflew

htroN fo eraflew

120

110

110

100

100

90

90

80

80

70

70
60

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

τFigure 10: when θ = 0.5

33

60

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

τ

140

125
120

130

htuoS fo eraflew

htroN fo eraflew

115

120

110

110

105

100

100

90

95

80

70

90

0

0.2

0.4

0.6

0.8

1

τ

85

0

0.2

0.4

0.6

τ
Figure 11: when θ = 0.7

34

0.8

1

128

130

126

125

124

htuoS fo eraflew

htroN fo eraflew

135

120

122

115

120

110

118

105

116

100

114

95

112

90

0

0.2

0.4

τ

0.6

0.8

1

Figure 12: when θ = 0.9

35

110

0

0.2

0.4

τ

0.6

0.8

1