Discussion Papers In Economics
And Business

The Effect of Technology Choice on Specializationand Welfare in a Two-Country Model

Yukiko Sawada
Discussion Paper 15-10

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Effect of Technology Choice on Specializationand Welfare in a Two-Country Model

Yukiko Sawada
Discussion Paper 15-10

May 2015

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Eﬀect of Technology Choice on Specializationand Welfare in a Two-Country Model∗
Yukiko Sawada†

Abstract
This study presents a simple two-country model in which firms in the
manufacturing sector can choose a technology level (high or low). We show
how trade costs and productivity levels aﬀect technology choices by the firms
in each country, where the fixed cost of adopting high technology diﬀers. Thisdepends on the productivity level of the high technology. In particular, if
productivity is medium and trade costs are not too low, then a technology
gap between the countries arises. In this case, improving the productivityof the high-technology country reduces the welfare level of consumers in the
country in which low technology is adopted. To compensate for the welfare
loss of the country from the technological improvement, trade costs should be
reduced.

JEL Classification: F10; F12
Key words: Specialization, Technology Choice, Technology Gap∗

We are especially grateful to Koichi Futagami, Tadashi Morita and Kazuhiro Yamamoto forbeneficial discussions and suggestions. We would also like to thank Ryo Horii, Jota Ishikawa,
Tatsuro Iwaisako, Kozo Kiyota, Tomoya Mori, Se-il Mun, Yasusada Murata, Yuka Ohno, andYoshimasa Shirai for useful suggestions and Comments. We gratefully acknowledge financial support from the Japan Society for the Promotion of Science through a Grant-in-Aid for JSPS Fellows.
†
Graduate
Schoolof
Economics,
Osaka
University,
E-mailaddress:
nge012sy@student.econ.osaka-u.ac.jp1

1

Introduction

Production technologies have evolved significantly over a long period of time. Consequently, industries are able to choose various technologies to produce goods. Highly
productive technologies have been developed in some industrialized countries andmay be available in other countries. At the same time, technology gaps exist between countries through the technology choices of each firm, especially where technology is highly developed. It is sometimes said that one of the main reasons forthe existence of such technology gaps is that production circumstances diﬀer among
countries. When a country whose productivity is not developed attempts to adopt
a new technology, the country tends to incur more adoption costs than a country
whose productivity is developed. To adopt the new technology, the following are
required: absorption of costs, development of laws, and developed infrastructure,including financial systems and major railways; moreover, additional costs diﬀer
among developing countries. In addition to such technology issues, we must consider the eﬀect of trade costs, which are a key determinant of international trade.
In the context of the new trade theory of Krugman(1980), trade costs determine
whether full agglomeration or partial agglomeration arises; in addition, such costs
aﬀect welfare levels. Hence, we must analyze the eﬀects of technology advances on
economic performance by considering trade costs. Such an analysis enables discussion of the manner of technology improvement in an economy with international
trade.
In this study, we incorporate technology choice by firms in a two-country model.
In each country, there are two sectors: the manufacturing sector, whose firms compete via monopolistic competition, and the agricultural sector, which is perfectlycompetitive. Labor is the only production factor. We assume that firms can choose
a production technology to produce manufacturing goods from two types of technology: high or low. By adopting high technology, firms can produce manufacturing
goods at a lower marginal cost and however, need a higher fixed cost than firms that
adopt low technology. A theoretical feature of our model is that such a fixed-costlevel depends on the location in which the firm adopts high technology. We cananalyze how the trade costs and productivity levels of technology determine firms’
agglomeration patterns and technology choices by examining firms in equilibrium.
In addition, we can analyze how exogenous changes of trade costs and productivity
levels aﬀect welfare levels of consumers in each country and obtain the implicationsof the reduction in trade costs for each country in the case of a technology gap. In
equilibrium, the model shows that a technology gap arises when the trade cost is not
too low and the productivity level of high technology is medium. In addition, we findthat an increase in the productivity level of the high technology always decreases
the welfare level in a country in which low technology us adopted, while it increases
the welfare level of a country in which high technology is adopted. These results
indicate that technology needs to improve with decreasing trade costs in order not
to decrease the welfare level of the low-technology country.
Our model is based mainly on Martin and Rogers (1991), although they assume
that all firms face an identical technology. We incorporate technology choice into2

their model. There are many theoretical studies that focus on diﬀerences in production technology in trade theory.1 There is far less research on technology choicein the new trade theory. Yeaple (2005) and Bustos (2011) incorporate technology
choice into their trade models in a similar way to ours. However, both of the previous studies focus on the technology gap within a country, which is generated fromthe heterogeneity of labor skills or a firm’s ex ante productivity.2 In our model,
we analyze the eﬀect of the technology gap between countries, while the previous
studies are unable to discuss. Furthermore, we can discuss the eﬀects of technological improvement on welfare levels, while mentioning the policy implications of tradeliberalization.
The key to generate the technology gap between countries is that we represent
the diﬀerence in productivity circumstances of adopting high technology on the fixed
costs of increasing-return technology. Although fixed costs are identical in previous
studies, in our model, there is a diﬀerence in the ease of entry because each country
varies in terms of entry regulations, financial support, or the absorption costs ofadopting new technology. By assuming such diﬀerences, we can focus on the relationship between adopted technology and the productivity environment represented
by the degree of fixed-cost levels and we can obtain additional implications about
the eﬀects on economic performance.
The remainder of the paper is organized into four sections as follows. In Section
2, we present the model. In Section 3, we characterize equilibrium. In Section 4,
we analyze the eﬀects of a reduction in international trade costs and an increasein productivity on the welfare level of consumers, and derive the implications fortechnology innovation and trade liberalization. Section 5 concludes.

2

The model

There are two countries, called country 1 and 2. Variables referring to country 1
have the subscript 1, and those referring to country 2 have the subscript 2. Eachcountry is endowed with a fixed amount of labor, L1 and L2 , respectively.
We assume that agents in both countries obtain their utility from consumptionof homogeneous agricultural goods and diﬀerentiated manufactured goods. Labor
can be used to produce agricultural goods and diﬀerentiated manufactured goods.
While labor can be mobile between sectors in the same country, it cannot be mobile
between the two countries.
1

Melitz’s (2003) model, in which each firm faces uncertain productivity determined by its distribution, provides rationale for the widely observed phenomenon that only high-productivity firms
export to foreign markets. Since then, many subsequent studies have accumulated: Baldwin andOkubo (2006), Bernard et al. (2003, 2007), and Melitz and Ottaviano (2008).They assume thatthe technology gap between firms is given by the distribution function.
2
In Yeaple’s (2005) model, firms choose both their individual production technologies and types
of workers, which are explained as giving rise to the diﬀerence between exporters and non-exporters.
Hence, the technology choices of firms change by the distribution of labor skills in equilibrium.
Bustos (2013) incorporates technology choice into the trade model with heterogeneity of firms totest consistency empirically. The model explains that the technology gap within a country arises
from firm heterogeneity.

3

2.1

DemandThe utility function of agents in country i (i = 1, 2) is given by
Ui = Ai + µ ln Mi ,

(1)

where
[∫ n iMi =mii (j)

σ−1
σ

∫ ni′
dj +

0

′

mi′ i (j )

σ−1
σ

dj

′

σ
] σ−1

, σ > 1, i, i′ ∈ {1, 2} , i ̸= i′ . (2)0Here, Ai is consumption of the agricultural goods in country i, Mi is consumptionof a composite of the manufactured goods in country i, and µ is a weight on theutility from consumption of the manufactured goods. mii′ (j) denotes consumptionof a variety j of the manufactured good in country i′ produced in country i. ni is
the number of varieties produced by a firm in country i. σ represents the elasticity
of substitution among diﬀerentiated goods.
The budget constraint of the agent in country i becomesyi ≥2 ∫ n′∑
ii′ =1

pi′ i (j)mi′ i (j)dj + Ai ,(3)0where pii′ (j) denotes the price of a variety j of the manufactured goods in countryi′ produced in country i and yi denotes the income level in country i. We takehomogeneous agricultural goods as the numeraire. Then, we can obtain the following
demand functions
pi′ i (j)−σmi ′ i =
µ,
(4)
Pi1−σ
Ai = yi − µ,

Pi =

[ 2 ∫
∑ ni
i=1

pi′ i (j)1−σ dj

(5)
]

1
1−σ

,

(6)

0

where Pi stands for the “price index” in country i.

2.2

Production

Each good is produced by using only labor and each worker has one unit of labor.
We describe the production structure of the agricultural sector. The agricultural
goods market is perfectly competitive and taken as a numeraire. We assume that inboth countries, one unit of agricultural goods is produced with one unit of labor andthat the international trade of homogeneous goods incurs no trade costs. Therefore,
the equilibrium wages in the two countries are w1 = w2 = 1. Because we assume freeentry into the manufacturing sector, profits in the sector become zero, and therefore,
income is equal to the wage, that is, yi = wi = 1.

4

2.2.1

Manufacturing sector and technology choice

In the manufacturing sector, monopolistic competition prevails and each firm produces a diﬀerentiated good. There are two types of technologies for producing eachvariety of manufacturing goods. The amount of goods a worker can produce is given
by az , z ∈ {H, L}. z is an index to indicate the adopted technology for production.
z = H refers to high technology for producing manufacturing goods, and z = L
refers to low technology for producing the same goods. High technology is moreproductive than low technology, that is, aH > aL = 1.
To produce with technology z ∈ {H, L} in country i, a firm in country i is
required to pay a fixed cost fiz . Since we consider low technology to be old or wellknown, the fixed cost of adopting it is assumed to be
f1L = f2L ≡ fL .

(7)

That is, the firms in both countries incur the same level of fixed cost if they adopt
the technology L. On the other hand, for high technology, we assume that thelevel of such a fixed cost depends on which technology the firm employs and whichcountry it locates in, as follows
f L < f1H < f2H .

(8)

The first inequality means that high technology is more costly. The firms bear alarge cost to adopt the high technology because it incurs large equipment investment,
payment of license fees, and so on. The second inequality represents diﬀerences in
productivity circumstances for high technology between the countries because of
diﬀerences in support systems by governments, such as subsidies to adopt hightechnology, infrastructure development, and absorption of costs in a skill-abundant
country versus one with scarce skills. In other words, we assume that country 1
has an advantage in introducing technology H over country 2. This assumption
represents a diﬀering degree-of-entry barrier between one country and another andis key for generating a technology gap between the countries.
Potential firms can enter production activities freely as long as their profits are
positive and they can choose to employ a more profitable technology. Each manufacturing firm faces the demand function, (4) and thus sets the following constantmarkup priceσpz11 = pz22 =,(9)(σ − 1)az
where pzii denotes the price of the manufactured good in country i produced incountry i by technology z. The international trade of manufactured goods incurs“iceberg”-type trade costs. If a firm in one country sends one unit of its good to theother country, it must dispatch τ units of the good. τ − 1 > 0 represents the trade
costs. Thus, the price of imported manufactured goods in country i becomes τ pii′
and i ̸= i′ . Thus, the price index in country i can be written as
Pi =

] 1
σ [ H
L 1−σ
αni + nLi + φ(αnH, i, i′ ∈ {1, 2} , i ̸= i′ ,
i′ + ni′ )
σ−1
5

(10)

where φ ≡ τ 1−σ and α ≡ aσ−1
H . φ represents the freeness of trade. φ = 0 corresponds
to the case of autarky, whereas φ = 1 implies free trade. In other words, increasing
φ means trade liberalization. α corresponds to the gap of productivity between
technologies and α ≥ 1. From Eqs. (4) to (9), profits of a firm in countries 1 and 2
can be expressed as follows

3

πiH =

)
µσ −σ α (
σ−1
σ−1
′P ′
L
P
+
φL
− fiH
i
i
i
i
(σ − 1)1−σ

(11)

πiL =

)
µσ −σ (
− f L.
Li Piσ−1 + φLi′ Piσ−1′
1−σ(σ − 1)(12)

Equilibrium

In equilibrium, agglomeration patterns and technology choices are determined by
the two parameters, α and φ. In this section, we analyze how firms choose thetechnologies and derive the equilibrium number of firms, with close attention to theexisting conditions of firms in both countries.
Although in practice firms in the same country can choose either technology
for production, in our model, each firm in a country chooses the same technology
in equilibrium because of the homogeneity of firms. Which technology it chooses
mainly depends on the productivity level of the high technology relative to the fixed
costs of the high technology adopted in the country. Specifically, technology choiceby firms in country i depends on whether the productivity level α is greater than thefH
relative fixed costs of the technologies, fiL . We can summarize this as the following
lemma
Lemma 1L.
fH

fH

1. If α < f1L , then all firms in countries 1 and 2 choose technology
fH

2. If f1L < α < f2L , firms in country 1 adopt technology H whereas firms incountry 2 adopt technology L.
fH

3. If f2L < α, then all firms choose technology H.
Proof. See Appendix A.
We can categorize specialization of technology into three cases according to α
fH
from Lemma 1. When α is suﬃciently low( f1L > α), all firms choose technology
L (low technology case). This case is consistent with the results of Helpman andKrugman (1985). On the other hand, when α takes moderate value, firms in country
1 adopt technology H whereas firms in country 2 adopt technology L. In this case,a technology gap exists between the countries (technology gap case). When α is
suﬃciently high, all firms in both countries choose technology H since adopting
technology H is profitable in both countries (high technology case).

6

In what follows, we derive the equilibrium number of manufactured goods (firms)
fH
fH
when f1L < α < f2L .3 To focus on a clear and interesting case, we consider L1 > L2 .4
As in the previous literature, the freeness of trade determines whether partial
agglomeration equilibrium or full agglomeration occurs. Partial agglomeration arises
when the following holds
π1H = π2L = 0.
(13)
The price index in this case becomes
P1 =

1
σ
L 1−σ
(αnH
1 + φn2 )
σ−1

1
σ
1−σ .
(nL2 + φαnH1 )σ−1Thus, free-entry condition (13) can be rewritten as

P2 =

φL2
µα
L1
+ L
) = f1H( H
L
H
σ αn1 + φn2n2 + φαn1

(14)

µ
L2
φL2
( L
+
) = f L.
H
H
L
σ n2 + φαn1
αn1 + φn2

(15)

L
Dividing (14) by (15), we obtain the relationship between nH
1 and n2 as followsnH
1 =µ[φ(L1 + L2 )f1H − (L1 + φ2 L2 )f L α] Ln .
α[φ(L1 + L2 )f L α − (φ2 L1 + L2 )f1H )] 2

(16)

The numerator of Eq. (16) is always negative but the sign of the denominator
depends on φ. Therefore, the denominator must be negative in equilibrium; that is,
the following inequality must hold5
φ(L1 + L2 )f L α < (φ2 L1 + L2 )f1H .

(17)

We define φ(α) as follows,φ(α)(L1 + L2 )f L α = (φ2 L1 + L2 )f1H .

(18)

φ(α) defines a relationship between α and φ that is satisfied when (17) holds as anequality. If φ < φ(α), Eq. (17) can hold and the manufacturing firms locate in bothcountries in equilibrium.6 From Eq. (16) and the free-entry condition π1 = 0, we
can obtain the number of manufacturing firms locating in country 2 as follows
nL2 =µα[φ(L1 + L2 )F L α − (φ2 L1 + L2 )f1H ].
σ(f L α − f1H φ)(f L αφ − f1H )

3

(19)

Similarly, we can derive other cases. See Appendix B.
Similarly, we can discuss the other cases, in which L1 ≤ L2 .
5
If Eq. (17) does not hold, that is π1H > π2L , then the firms agglomerate to country 1 inequilibrium. In other words, when φ is too high, the full agglomeration arises.
6
When φ ≤ φ(α), all manufacturing firms locate in country 1.
4

7

Figure 1: The patterns of location and technology choice
Hence, we obtain the Eq. (20) of manufacturing firms locating in country 1 asfollows,nH
1 =µ[φ(L1 + L2 )f1H − (L1 + φ2 L2 )f L α].
σ(f L α − f1H φ)(f L αφ − f1H )(20)

We can summarize the preceding arguments as follows
Proposition 1 A technology gap exists between countries if the following inequalities are satisfied
f1H
f2H
<
α
<
fL
fL
φ < φ(α)
In this case, partial agglomeration equilibrium arises and firms locating in country
1 employ technology H and firms in country 2 employ technology L.
This proposition indicates that when the productivity of high technology is not
suﬃciently high and it is costly to trade goods, a technology gap exists.
As mentioned before, the type of technology that firms in each country adopt
and whether full agglomeration arises depend on the relationship between φ and α.
Hence, this can be summarized as shown in Figure 1. The vertical axis represents
the productivity level α of technology H (α > 1). The horizontal axis represents
the freeness of trade, φ (0 < φ < 1). Figure 1 shows how these parameters aﬀect
equilibrium and how the technology choice and agglomeration of firms depend on α8and φ. From Proposition 1, the technology gap case arises when the combination of
α and φ is in the domain (II).
As φ becomes larger, full agglomeration tends to arise. Two factors aﬀect theagglomeration pattern: the diﬀerence in market size and the fixed costs of adopting
high technology in each country. In the low productivity case, only the diﬀerence inmarket size generates agglomeration power since firms face the same level of fixed
costs. However, we start from the point at which both α and φ are low enough to
be in (III). Increasing the productivity level α from the starting point to a medium
level, only firms in country 1 change to the high-technology type. When α reaches
a high level in (I), firms in country 2 catch up with the high-technology type.
Next, we analyze the eﬀects of a change in the productivity level of high technolLogy on the number of manufacturing firms. Diﬀerentiating nH
1 and n2 with respect
to α, we can obtain the following derivatives[]∂ ln nH(φ2 − 1)L2 f1H
φ
1
L
=f φ
−
>0
H
∂α
[φ(L1 + L2 )f1H − (L1 + φ2 L2 )f L α][f L α − f1H φ] f L aσ−1
H φ − f1,
∂ ln nL2
φ(f L α + f1H )(f L α − f1H )φ(L1 + L2 )f L
+
< 0.
=
∂α
φ(L1 + L2 )f L α − (φ2 L1 + L2 )f1H α(f1H − f L αφ)(f L α − f1H φ)
Therefore, the following proposition can be obtained
Proposition 2 Productivity improvement of technology H increases the number ofmanufacturing firms locating in country 1 that adopt high technology but decreases
the number of manufacturing firms in country 2 that adopt low technology.
We provide an intuition as follows. Technology improvement increases the profit offirms locating in country 1 because improvement can reduce the marginal cost of
adopting high technology; then, more manufacturing firms enter country 1.

4

Welfare Analysis

In this section, we examine the welfare eﬀects of trade liberalization and technology
improvement, which correspond to increases in φ and α. In addition, we analyze
the comparative statics of these parameters. We focus on the case in which thetechnology adopted diﬀers between countries.
First, substituting Eq. (4) into Eq. (1), we obtain the following indirect utility
functions in the countries
V1 = 1 − µ + µ[ln1µα(1 − φ2 )L1µ(σ − 1)]+ln
σσ − 1 σ(f1H − f L αφ)(21)

V2 = 1 − µ + µ[lnµ(σ − 1)1µα(1 − φ2 )L2
]+
ln
.
σ
σ − 1 σ(f L α − f1H φ)(22)

We can conduct the welfare analysis based on these indirect utility functions.
94.1

The eﬀect of trade liberalization

Trade liberalization signals falling trade costs τ (increasing φ). By diﬀerentiating
Eq. (21) and (22) with respect to φ, we can obtain the following equations∂V1µ[(φ2 + 1)f L α − 2φf1H ]=>0∂φ(σ − 1)(1 − φ2 )(f1H − f L αφ)∂V2µ[(φ2 + 1)f1H − 2φf L α]
=
> 0.
∂φ
(σ − 1)(1 − φ2 )(f L α − f1H φ)
The second equation is satisfied because the following inequality must be satisfied
in the equilibrium,(φ2 + 1)f1H
α<
.
2φf L
In addition, we analyze the eﬀect on the welfare gap between countries. By
taking the diﬀerence between Eqs. (21) and (22) and diﬀerentiating it with respect
to φ, we obtain(f L α)2 − (f1H )2∂(V1H − V2L )
= L
> 0.
∂φ
(f α − f1H φ)(f1H − f L αφ)
Therefore, the result can be summarized as follows.
Proposition 3 Falling trade costs increase the welfare levels in both countries andwiden the welfare gap between the countries
This is because falling trade costs decrease the prices of all imported manufacturing
goods, which increases their consumption. Hence, this increases the welfare level of
all consumers.

4.2

The eﬀect of technology improvement

Next, we analyze the eﬀects of technology improvement in the case of a technology
gap. We assume that technology improvement increases the productivity of thehigh-technology type, which corresponds to increasing α. Diﬀerentiating Eqs. (21)and (22) with respect to α, we obtain the following

fH

∂V1
µ
f Lφ
=
[α−1 + H]>0∂ασ−1f1 − f L αφ

(23)

∂V2
−µf1H φ<0=∂αα(f L α − f1H φ)

(24)

fH

because f1L < α < f2L and (17) hold.
Proposition 4 In the technology-gap case, by increasing the productivity of thehigh-technology type, the welfare of a consumer in country 1 increases and that of aconsumer in country 2 decreases.
10Figure 2: relationship between welfare and productivity
As well as the technology-gap case, we derive the welfare eﬀect of the other casesin the Appendix. Hence, we present the relationship between productivity and theindirect utility for any α as shown in Figure 2.
Figure 2(a) shows that improving the productivity of technology H always increases the welfare level of consumers in country 1. On the other hand, Figure 2(b)shows that the welfare level of consumers in country 2 decreases when the productivity level of technology H is at medium levels. In this case, the welfare of country
2 is always lower than the case when productivity is low. Why does this occur? The
reason is because increasing α has positive and negative eﬀects on the consumption
level of goods produced in each country. The positive eﬀect arises from an increaseof total demand of manufacturing goods produced in country 1. The negative eﬀect
rises from a decrease of total demand of manufacturing goods produced in country
2. Whether technology improvement increases welfare depends on which eﬀect islarger for consumers in each country. For consumers in country 2, an increase of α
decreases the total demand of domestic goods, which are consumed without incurring trade costs, and increases the total demand of imported goods, which do incur
trade costs. Hence, the former (negative) eﬀect is larger than the latter (positive)
one. Conversely, country 1 has more benefits from an increase of domestic goods
than a decrease of imported goods. Comparing the welfare level in country 2 between specialization patterns, Figure 2(b) also shows that the welfare level of the
fH
technology-gap case is always lower than that of the low-technology case (α < f1L ).
Even if productivity becomes so high that firms in country 2 can employ technology
H(high technology case), there exists an area in which the welfare level in country 2
fH
is still lower than that of the low-technology case(α is slightly larger than f2L ). This11

implies that technology innovation works better for consumers in a high-technology
country, but if the technology level is medium, then, a small improvement of thehigh-technology type makes those in low-technology country poorer by the presenceof trade cost. From Proposition 1 and 2, we show that increasing α has a negativeeﬀect on welfare in country 2, which is opposite to decreasing trade costs. Therefore, decreasing trade costs can avoid the formation of U-shaped indirect utility incountry 2. By total diﬀerentiation of (22), we obtain the following proposition.
Proposition 5 To compensate for the welfare loss in country 2 from technology
improvement, trade costs have to be reduced by the following amountdφ
φ(1 − φ2 )=(< 0).
dα
α[α(1 + φ2 )f L − 2φf1H )]This proposition implies the importance of trade liberalization to keep the welfare
level in country 2 high. In particular, trade costs need to be reduced more if α isfHslightly larger than f1L , which is the threshold at which firms in country 1 change thetechnology into a high type, since the above equation decreases with α. In addition,
this result indicates that the low-technology country has a stronger incentive topromote trade liberalization in order to keep the welfare level when its technology
is less developed. From Proposition 3, trade liberalization always works better for
the welfare of both the countries. Thus, with regard to the policy impacts onsocial welfare, we should consider not only technology innovation but also tradeliberalization.

5

Concluding remarks

In this study, we explain the relationship between the productivity level of technology and technology choice when fixed costs diﬀer between countries. In addition, we
examine how technology innovation aﬀects the technology choice of firms and thewelfare levels of consumers. Furthermore, we consider the eﬀects of trade liberalization on location choice and welfare levels. We develop a simple two-country trademodel with technology choice. Firms can choose a technology from two types (highor low) and the number of firms is determined through free entry. The productivityof the high-technology type is higher than that of the low-technology type, and hightechnology is more costly than low technology. Moreover, we assume that there
is a large country and a small country, and that high technology employed in thelarge country is made available at a lower cost than the same technology type in thesmall country. The latter assumption means that a large country has an advantage
in adopting high technology.
We find that in the equilibrium, firms locating in the developed country employ
higher technology and firms locating in the developing country employ lower technology. In addition, we find that improving the productivity of higher technology
does not always improve consumer welfare in both counties. In particular, when the
productivity level of the high-technology type is medium, the welfare of a consumer
in the small country decreases with a small technological improvement.
12

Finally, we comment on directions for future work. In this study, we analyze astatic trade model. In the future, we will extend this model to a dynamic model inwhich the productivity of technology varies through time. In this paper, the eﬀect ofinvestment on R&D is not considered, but such an extension should be investigated.

AppendixA

Proof of Lemma 1

Assume a case in which firms in country 1 employ technology H. Then, π1H = 0
must be satisfied, that is, Eq. (11) is rewritten as followsµσ σ−1(L1 P1σ−1 + φL2 P2σ−1 )α = f1H .
σ−1

(25)

Substituting (25) into (12), we can rewrite Eq. (12) as follows
π1L =

f1H
− f L.
α(26)

fH

If α ≤ f1L , the right-hand side of (26) is always positive, which induces firms toemploy technology L. Hence, this contradicts the case in which all firms employ
fH
technology H. Therefore, f1L < α must be satisfied. Next, assuming that π1L = 0,
the following equation is satisfiedµσ σ−1(L1 P1σ−1 + φL2 P2σ−1 ) = f L .
σ−1

(27)

Substituting (27), we can rewrite Eq. (11) as follows
π1H = f L α − f1H .

(28)
fH

Employing the same argument above, we can show that α < f1L must be satisfied.
Similarly, the same fact for country 2 can be shown in the same way.

B

fH

fH

Cases other than f1L < α < f2L
fH

When α < f1L holds, any firm employs technology L because the productivity oftechnology is not high enough to recover the fixed cost of technology H. Therefore,
fH
this case is consistent with Helpman and Krugman (1985). When f2L < α holds, any
firm employs technology H because the productivity of technology H is high enoughH
to recover its fixed cost. If π1H > π2H , nH
1 > 0 and n2 = 0 are in equilibrium. From
Eq. (11),µnH(L1 + L2 )
1 =
σf1H
13

holds. Substituting it into Eq. (12), T must satisfy the following equation
π2H =(φ2 L1 + L2 )f1H − φ(L1 + L2 )f2H
< 0.
φ(L1 + L2 )(29)

Let φ̄ satisfy the left-hand side of Eq. (29) is equal to zero. When φ > φ̄, nH
1 > 0
Hand n2 = 0 is the equilibrium. Hence, we assume that φ < φ̄. From free-entry
conditions, we consider the following equations
π1H = π2H = 0.
H
The relationship between nH
1 and n2 is given bynH
1 =φ(L1 + L2 )f1H − (L1 + φ2 L2 )f2H Hn .
φ(L1 + L2 )f2H − (φ2 L1 + L2 )f1H 2(30)

Then, substituting (30) into the free-entry condition π1H = 0, we can obtain thenumber of manufacturing firms locating in country 1 and country 2 byµφ(L1 + L2 )f1H − (L1 + φ2 L2 )f2H
H
n1 =σ(f2H − f1H φ)(f2H φ − f1H ),µφ(L1 + L2 )f2H − (φ2 L1 + L2 )f1H.
σ(f2H − f1H φ)(f2H φ − f1H )In this case, the number of firms is independent from a.
nH
2 =

C

(31)

(32)

Derivation of Figure 2
fH

When α < f1L holds, all firms employ L technology. Then, indirect utility is obtained
as followsµ(σ − 1)1µ(1 + φ)L1V1 = 1 − µ + µ[ln
+
ln
],
(33)
σ
σ−1
σf L
µ(σ − 1)1µ(1 + φ)L2V2 = 1 − µ + µ[ln
+
ln
].
(34)
σ
σ−1
σf L
This implies that the welfare level is independent from α because no firm employsfH
fH
H technology. When f1L < α < f2L , firms locating in country 1 employ H technology and firms locating in country 2 employ L technology. Then, indirect utility is
obtained as followsµ(σ − 1)1µ(1 − φ2 )L1 α],(35)
V1 = 1 − µ + µ[ln+lnσσ − 1 σ(f1H − f2H φ)µ(σ − 1)1µ(1 − φ2 )L2 α
V2 = 1 − µ + µ[ln
+
ln
].
σ
σ − 1 σ(f2H − f1H φ)Considering the eﬀect of an increase in α, we derive the following equations
∂V1
∂V2
=
= µα−1 > 0,∂α∂α
∂ 2 V2∂ 2 V1== −µα−2 < 0.
∂α2
∂α2
14

(36)

(37)
(38)

References[1] Baldwin, R.E., and Okubo, T., 2006. Heterogeneous firms, agglomeration andeconomic geography: Spatial selection and sorting. Journal of Economic Geography 6 (3). 323-346.
[2] Bernard, A.B., Redding, S., Schott, P.K., 2007. Comparative advantage andheterogeneous firms. Review Economic Studies 74, 31-66.
[3] Bustos, P., 2011. Trade liberalization, Exports, and Technology Upgrading: Evidence on the impact of MERCOSUR on Argentinian Firms. American Economic
Review 101, 304-340.
[4] Helpman, E. and P. Krugman., 1985. Market Structure and Foreign Trade: Increasing Returns, Imperfect Competition, and the International Economy, Cambridge, MA: MIT Press.
[5] Krugman, P. (1980) Scale Economies, Product Diﬀerentiation, and the Patternof Trade. American Economic Review 70, 950-959.
[6] Melitz, M., 2003. The impact of trade on intra-industry reallocations and aggregate industry productivity.Econometrica 71, 1695-1725.
[7] Yeaple, S. R., 2005. A Simple Model of Firm Heterogeneity, International Trade,and Wages. Journal of International Economics 65, 1-20.

15