On the Emergence of Intra-Industry Trade
Toru Kikuchi∗

Koji Shimomura† Dao-Zhi Zeng‡
February 16, 2005

Abstract
This study explores the determinants of intra-industry trade by extending a Chamberlinian-Ricardian monopolistic competition trademodel to have a larger number of industries as did Dornbush, Fischer and Samuelson (1977). It will be shown that the degree of crosscountry technical diﬀerences among industries plays an important role
as a determinant of trade within each industry.

∗

Toru Kikuchi, Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho,Nada-ku, Kobe 657-8501, Japan; e-mail: kikuchi@econ.kobe-u.ac.jp†
Koji Shimomura, Research Institute for Economics and Business Administration, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan; e-mail:simomura@mail.rieb.kobe-u.ac.jp‡
Dao-Zhi Zeng, Graduate School of Management, Kagawa University, Saiwai-Cho 2-1,
Kagawa 760-8523, Japan; e-mail: zeng@ec.kagawa-u.ac.jp1

1

Introduction

Over the past several decades a vast literature has developed on the emergence of intra-industry trade (i.e., two-way trade of diﬀerentiated products).
Among several competing models of intra-industry trade, Chamberlinian monopolistic competition models of trade have been extensively studied since
the seminal work of Krugman (1979). Those models are very successful toexplain the emergence of intra-industry trade and the industrial agglomeration. To focus on the role of increasing returns and imperfect competition, astandard one-factor model assumes the cross-country technical homogeneity:each ﬁrm in the monopolistically competitive sector incurs an identical ﬁxed
cost (α) and a constant marginal cost (β), both expressed in terms of labor.
As a result, there has been little investigation of the role of technical heterogeneity among countries. However, the Ricardian comparative advantage,
which plays a basic role in traditional international-trade context, is worthyof more attention. To address this point, Kikuchi (2004) explored crosscountry technical heterogeneity in both ﬁxed costs and marginal costs as adeterminant of trade patterns. Within a two-country, two-industry framework, he showed that manufacturing sector is agglomerated in a country andthe intra-industry trade is very unlikely in a trading equilibrium.
The present study takes Kikuchi (2004) as its point of departure, andextends his analysis to include a large number of industries as did Dornbush, Fischer and Samuelson (1977). In each industry, both ﬁxed costs andmarginal costs can diﬀer between the countries. It will be shown that the2equilibrium specialization pattern is determined by the technology index. It
will also be shown that trade patterns, particularly the emergence of intraindustry trade, are crucially dependent on the shape of the technology index
schedule, which is taken from Dornbush, Fischer and Samuelson (1977). Thatis, if technical standardization occurs and the share of similar industries becomes larger between countries, the possibility of intra-industry trade rises.
This kind of extension is important since the standard model of monopolistic competition often assume only two (one diﬀerentiated-product and one
homogeneous good) industries and ignore interaction between diﬀerentiatedproduct (i. e., monopolistically competitive) industries. If there is only one
monopolistically competitive industry in the economy, intra-industry trade
is obtained as a result of identical technologies between countries and wage
rate equalization.1 In our multi-industry model, however, wage rates neednot be equalized to obtain intra-industry trade. This is more plausible forthe explanation of the intra-industry trade between developed and developing
countries.
This study is closely related to Venables (1999), which explores the division of industries between countries in a multi-industry framework. However,
he uses a framework in which there are both transport costs and linkages
through intermediate inputs.2 In contrast, in this study we assume away
1
2

Krugman (1979, p. 476).
Hanson and Xiang (2004) also develop a model of monopolistic competition with manyindustries to examine how home-market eﬀects vary with industry characteristics. Their
model, however, does not include any productivity diﬀerences between countries, which is
the main focus of our study.

3such aspects and focus on the interaction between cross-country technological diﬀerences and trade patterns.
The next section develops a Chamberlinian-Ricardian model with manyindustries. Section 3 deals with the determinants of trade patterns. Section
4 discusses some implications of the analysis.

2

The Model

Suppose that there are two countries in the world, Home and Foreign. Home
(Foreign) is endowed with L (L̃) units of labor and the only source of income
is the wage, w (w̃). We assume that there are M manufacturing industries.3
Industry speciﬁc variables will be indexed by industry label i. Consumers
have Cobb-Douglas preferences and purchase equal values of the output of
all industries.
Each industry is modelled as a Dixit-Stiglitz (1977) monopolistically competitive industry. The quantity index of industry i takes the form
i

X =


ni
k=1

θ
ñ

i θ
(dk̃ ),i(dik )θ +1

0 < θ < 1,

(1)

k̃=1

where ni (ñi ) is the number of products produced in industry i in Home
(Foreign), dik (dik̃ ) is the quantity of product k (k̃) in Home market, and1/(1 − θ) > 1 is the elasticity of substitution between every pair of products.

3

Although it is easier to set the model up with a ﬁnite number of manufacturingindustries, we will later think of there being a continuum of them.

4The price index of industry i can be obtained as:
Pi =


ni

θ−1

i

θ

(pik ) θ−1 +

ñ


k=1

θ

 θ

(pik̃ ) θ−1

,

(2)

k̃=1

where pik (pik̃ ) is the price of the k (k̃)-th diﬀerentiated product produced inindustry i in Home (Foreign). Note that the total revenue in Home is wL,
which will be equally expended in each industry due to the assumption of the
Cobb-Douglas preferences. Solving consumers’ maximization problem yields
the following demand functions for Home consumers:1

dik = in(pik ) θ−1θ(pij ) θ−1 +

ñi



j=1

j̃=1

dik̃ = n(pik̃ ) θ−1ñθ(pij̃ ) θ−1

1(pij )

θ
θ−1

+

j=1

(pij̃ )

θ
θ−1

wL
,
M

(3)

wL
.
M

(4)

j̃=1

Assuming that the products are transported free between countries, then theprices of each product in two countries are equal. Therefore, the demand
functions for Foreign consumers are1d˜ik =(pik ) θ−1
ni



θ

(pij ) θ−1 +

j=1

ñi



θ

w̃ L̃
,
M

θ

w̃ L̃
,
M

(pij̃ ) θ−1

j̃=1

and
1

d˜ik̃ =n(pik̃ ) θ−1θ(pij ) θ−1 +

j=1

ñ

j̃=1

5

(pij̃ ) θ−1

respectively.
Diﬀerentiated products are supplied by monopolistically competitive ﬁrms.
There is cross-country technical heterogeneity: each Home (Foreign) ﬁrm inindustry i has both αi (α̃i ) units of labor as a ﬁxed input and β i (β̃ i ) unitsof labor as a variable input. With the number of ﬁrms being very large, theelasticity of demand for each product becomes 1/(1 − θ). Thus, each productis priced at a markup over marginal cost:
pik =

β iw
β̃ iw̃
, pik̃ =.
θθUsing these pricing equations, the summation in equation (3) takes the formθθ
 i  θ−1
 i  θ−1
ni
ñi


θ
θ
i θ−1
i θ−1
i β w
i β̃ w̃
(pk )+(pk̃ )
=n
+ ñ
.
θ
θ
k=1
k̃=1

Substituting this into the demand function yields the proﬁt function of eachHome ﬁrm4
π i =(pi − β i w)x − αiw
1−θ i
β w(dik + d˜ik ) − αi wθθ
 i  θ−1βw
(1 − θ)wL + w̃L̃θ− αi w.
= 
θ
θ



i
i
M
θ−1
θ−1
βw
β̃ w̃
ni
+ ñi
θ
θ
=

Similarly, the proﬁt function of each Foreign ﬁrm isθ i  θ−1β̃ w̃(1 − θ)wL + w̃L̃θi− α̃i w̃.
π̃ = 
θ
θ



i
i
M
θ−1
θ−1
βw
β̃ w̃
ni
+ ñi
θ
θ
4

Hereafter, the subscript k is often dropped for simplicity.

6

(5)

(6)

Now turn to the specialization pattern of industry i. In the trading
equilibrium with zero transport costs, we need non-positive proﬁts in industry
i in each country, with proﬁts being equal to zero if production takes place.
Thus, by setting proﬁts equal to zero for both countries (π i = π̃ i = 0),
we would like to test whether the co-existence of both countries’ ﬁrms is
consistent with equilibrium.
First, let us draw attention to the condition that, if both countries’ ﬁrms
in industry i co-exist, proﬁts must be identical for each country’s ﬁrms, i.e.,
π i = π̃ i .

(7)This is the condition that must be satisﬁed if π i = π̃ i = 0 is to hold. Substituting (5) and (6) into (7), we obtainθ
wL + w̃L̃(1 − θ) θ 1−θ
αi w − α̃i w̃
M
=
θ
θ
θ
θ .
 i  θ−1
 i  θ−1i w) θ−1 − (β̃ i w̃) θ−1
(β
βw
β̃ w̃
ni
+ ñi
θ
θ

(8)

Inserting the RHS of (8) into the proﬁt function yields
θ

i

π =

(β i w) θ−1 (αi w − α̃i w̃)θθ(β i w) θ−1 − (β̃ iw̃) θ−1− αi w,

θ

i

π̃ =

(β̃ i w̃) θ−1 (αi w − α̃i w̃)θθ(β i w) θ−1 − (β̃ iw̃) θ−1− α̃i w̃.

It is important to note that proﬁts are independent of both the total numberof ﬁrms and market size.
Before turning to the case of co-existence, note that the equilibrium number of ﬁrms for the case in which only one country’s ﬁrms exist isniT{ñi =0} =(1 − θ)(wL + w̃ L̃)
,
Mαiw
7

ñiT
{ni =0} =(1 − θ)(wL + w̃ L̃),
M α̃iw̃where T denotes a trading equilibrium value.
Using these results, one can obtain the necessary condition for the coexistence of ﬁrms. Let us deﬁne a technology index for industry i: i 1−θ  i θ
α̃
β̃
i
.
A ≡
i
α
βi

(9)

In the free-trade equilibrium the proﬁt must be zero: π i = π̃ i = 0. Simple
calculations show that the equations are satisﬁed only if the technology index,
Ai , is equal to the relative wage rate ω ≡ w/w̃.
Proposition 1 If Ai > (<) ω, only Home (Foreign) firms produce the differentiated products in industry i. Intra-industry trade in industry i (i.e., theco-existence of both countries’ firms) occurs only if Ai = ω.
[Proof] Suppose that Ai > ω. In this case, both countries’ ﬁrms cannot coexist. To see that the case where only Home ﬁrms are active is an equilibrium,
note thatiπ̃{ni =niT , ñi =0} =β iw
β̃ i w̃

θ
 1−θ


i

i

i

α w − α̃ w̃ = α̃ w̃

ω
Ai

1
 1−θ


−1 .

This becomes negative if Ai > ω since θ ∈ (0, 1). Therefore, Foreign ﬁrms
have no incentive to enter given that niT Home ﬁrms are active. On the other
hand, the case in which only Foreign ﬁrms are active cannot support a free
trading equilibrium. This is because that
θ1
 i  1−θ i  1−θ

A
β̃ w̃
i
i
i
i
π{ni =0, ñi =ñiT } = iα̃ w̃ − α w = α w
−1
βw
ω
8

is positive, and hence, Home ﬁrms have an incentive to enter the world
market. Therefore, only Home ﬁrms produce the diﬀerentiated products inindustry i in the free trade equilibrium. The case of Ai < ω can be provenanalogously. [Q.E.D.]

3

Trade Patterns

To obtain the world trading equilibrium, we index industries in order ofdiminishing Home comparative advantage.5
dAi
≤ 0,
di
where Ai is deﬁned in (9). This schedule is drawn in Figure 1 as the downward
sloping locus AA. Now assume that there is ﬂat segment in the AA schedule: a partition of industries (from m to m̄) is assumed to have equal level oftechnology index. We can interpret this as, even ﬁrms in each industry produce diﬀerentiated products, production technologies of these industries havebecome standardized due to increased information ﬂow between industries.

5

See footnote 3.

9

A

B

B

ω

possibility of
intraindustry
trade
O

m

m

A

m̄

i

Figure 1: Intraindustry trade
Let m denote hypothetical dividing line between Home- and Foreignproduced commodities, equilibrium in the market for Home products requiresthat Home labor income wL equals world spending on Home-produced products:
wL =m(wL + w̃L̃).
M

This schedule is drawn in Figure 1 as the upward sloping locus OB and is
obtained by rewriting the equation in the form:
ω=

L̃
m
.
M −m LThe equilibrium relative wage is obtained as the intersection of schedules
AA and OB. Now assume that the intersection is obtained at the ﬂat segment
10

in the AA schedule. Thus, the following condition holds.
ω = Ai , m ≤ i ≤ m̄.
In this case, from Proposition 1, ﬁrms within these industries can be locatedin both countries. Therefore, intra-industry trade within these industries will
occur.
Proposition 2 Given that there is a flat segment in the AA schedule and the
OB schedule cuts that segment, intra-industry trade occurs between countries.
Using Figure 1, let us examine the eﬀect of an increase in the relative
size of Foreign. An increase in L̃/L shifts schedule OB upward. If the newintersection occurs in the ﬂat segment of AA, this shift only changes the portion of intra-industry trade and the relative wage remains unchanged. If the
upward shift is suﬃciently large (like OB  ) and the new intersection occurs in
the downward-sloping segment of AA, no intra-industry trade occurs in the
trading equilibrium and the Home relative wage rises. Our model suggeststhat the share of intra-industry trade is smaller between countries that are
dissimilar in size. This ﬁnding is consistent with empirical work by Helpman(1987).

4

Discussion

In the last section, we have shown, given that there is a ﬂat segment in
the AA schedule, intra-industry trade occurs between countries. Here, we
provide two cases in which there is a ﬂat segment.
11

4.1

Economic Integration and Technological Spillover
across Countries

In the literature of endogenous growth, it is often assumed that closer economic integration can be achieved by increasing trade in goods or increasing
ﬂow of ideas across borders.6 This implies that a ﬁrm in a given industry
acquire technical information from the activities of ﬁrms in its own industry operating in other countries. According to this line, suppose that, atleast some industries, production technologies have become standardized byincreased economic integration (see Figure 2).
Before closer integration occurs, cross-country information ﬂow is limited
and there are no ﬂat segment in the AA schedule: no intra-industry tradeoccurs between countries. Then, cross-country technological spillover changes
the shape of the technology index schedule: with some range, both α = α̃ andβ = β̃ hold, then the value of the technology index Ai becomes 1 over thoseindustries. This type of technological spillover due to integration gives rise to
intra-industry trade between countries: if intra-industry trade occurs, wage
rates are equalized between countries, which is consistent with the theoreticalﬁndings of Krugman (1979).

6

Rivera-Batiz and Romer (1991).

12

omega

A
B

1

A

O

^
m

m
_

possibility of
intraindustry
trade
FIGURE 2

13

_
m

m

4.2

Technological Spillover across Industries

There is another case for the existence of the ﬂat segment: inter-industry
technological spillover within each country.7 In this case, although products in diﬀerent industries are highly diﬀerentiated each other, production
technologies of these industries have become standardized due to increased
information ﬂow between industries. Thus, the followings hold:αi = αj , β i = β j ,α̃i = α̃j , β̃ i = β̃ j ,m ≤ i, j ≤ m̄.
Note that, in this case, the value of the technology index need not to be 1
(as Figure 1): even if standardization across industries occurs, productivity
diﬀerences between countries may remain. In this case, Ricardian productivity diﬀerences play an important role in determining relative wage. On theother hand, this case also emphasize that a rise in the number of standardisedindustries may also bring to the fore Chamberlinian determinants of trade.
If there is only one monopolistically competitive industry in the economy,
intra-industry trade is obtained as a result of identical technologies between
countries and wage rate equalization.8 In our multi-industry model, however,7

According to this point, most of the literature of learning by doing assumes thatﬁrms learn more from the experiences of other domestic producers than they do fromﬁrms located abroad. See, for example, Bardhan (1970). Martin and Ottaviano (1999)
also examines the case of local spillovers which occurs as the beneﬁt of interactions withproducers of other goods.
8
Krugman (1979, p. 476).

14

wage rates need not be equalized to obtain intra-industry trade. This is moreplausible for the explanation of the intra-industry trade between developed
and developing countries.
Krugman (1979, p. 479) argues that trade need not be a result of crosscountry diﬀerences in technology. We would like to emphasize that the degree of cross-country technical diﬀerences among industries plays a more
important role as a determinant of trade within each industry: if production
technologies are standardized among some industries within each country,
intra-industry trade between countries may occur.

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Trade, Wiley, New York.
[2] Davis, D. R. (1995) ‘Intra-industry Trade: A Heckscher-Ohlin-Ricardo
Approach,’ Journal of International Economics, Vol. 39, pp. 201–226.
[3] Dixit, A. K. and J. E. Stiglitz (1977) ‘Monopolistic Competition and
Optimum Product Diversity,’ American Economic Review, Vol. 67, pp.
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[4] Dornbush, R., S. Fischer, and P. Samuelson (1977) ‘Comparative Advantage, Trade and Payments in a Ricardian Model with a Continuum ofGoods,’ American Economic Review, Vol. 67, pp. 823–829.

15[5] Hanson, G. H., and C. Xiang (2004) ‘The Home-Market Eﬀect and Bilateral Trade Patterns,’ American Economic Review, Vol. 90, pp. 1108-1129.
[6] Helpman, E. (1987) ‘Imperfect Competition and International Trade: Evidence from Fourteen Industrial Countries,’ Journal of the Japanese andInternational Economies, Vol. 1, pp. 62–81.
[7] Kikuchi, T. (2004) ‘A Note on Chamberlinian-Ricardian Trade Patterns,’
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[8] Kikuchi, T., and D.-Z. Zeng (2004) ‘On Chamberlinian-Ricardian Trade
Patterns with Many Industries,’ Economics Bulletin, Vol. 6, No. 22, pp.
1–9.
[9] Krugman, P. (1979) ‘Increasing Returns, Monopolistic Competition, andInternational Trade,’ Journal of International Economics, Vol. 9, pp. 469–
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[10] Martin, P., and G. I. P. Ottaviano (1999) ‘Growing Locations: Industry
Location in a Model of Endogenous Growth,’ European Economic Review,Vol. 43, pp. 281-302.
[11] Rivera-Batiz, L. A., and P. Romer (1991) ‘Economic Integration andEndogenous Growth,’ Quarterly JOurnal of Economics, Vol. 106, pp.
531-555.

16

[12] Venables, A. J. (1987) ‘Trade and Trade Policy with Diﬀerentiated Products: A Chamberlinian-Ricardian Model,’ Economic Journal, Vol. 97, pp.
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[13] Venables, A. J. (1999) ‘The International Division of Industries: Clustering and Comparative Advantage in a Multi-industry Model,’ Scandinavian Journal of Economics, Vol. 101, pp. 495–513.

17