Firm Heterogeneity, Financial Imperfection, andInternational Trade
Taiji Furusawa∗

Noriyuki Yanagawa†

Hitotsubashi University

University of Tokyo

November 2008

Abstract
The paper investigates the role of wealth distributions and financial institutions of an
economy on within-industry firm heterogeneity in productivity. If there is no financial
imperfection so that entrepreneurs are not constrained in borrowing, all of them makethe same, optimal, productivity-enhancing investment. As a result, the industry will
be composed of many homogeneous firms. If there exists financial imperfection, on theother hand, borrowing is constrained so the initial wealth of an entrepreneur becomes
important. Given that the individuals of the economy are endowed with heterogeneous
wealth, entrepreneurs with different wealth levels may choose different investment levels, resulting in the firm heterogeneity in productivity. The paper examines the impactsof the goods and capital trade on the market structure of the differentiated good sector.
Preliminary and incomplete∗

Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601 Japan. Email:furusawa@econ.hit-u.ac.jp†
Graduate School of Economics, University of Tokyo. Email: yanagawa@e.u-tokyo.ac.jp

1

Introduction

Recent empirical studies provide ample evidences that firms are very different in their productivities, size, and export and import activities, even within an industry (see, for example,
Bernard, et al., 2007). Inspired by these empirical evidences, Bernard, et al. (2003) and
Melitz (2003) develop theoretical frameworks, in which heterogeneous firms engage in export
activities differently in an industry under monopolistic competition. In their frameworks,
productivity of each firm is drawn from a probability distribution, and once drawn it is fixed
for the entire lifetime of the firm. As expected, high-productivity firms both export theirproducts and sell them domestically, whereas low-productivity firms only sell domestically.
If the export is profitable for productive firms, however, why do low-productivity firms
upgrade production technology to enjoy export profits? To answer this question, Bustos(2005), Atkeson and Burnstein (2007), and Constantini and Melitz (2007) allow firms to
upgrade their production technologies with a fixed amount of investment. They show that
inherently productive firms have more incentives than others to upgrade their technology
and engage in the export. However, their studies do not address questions as to why firms
are inherently different in their productivities in the first place.
Indeed, in principle, any firm can hire necessary human capital and purchase the up-todate technology. Firm heterogeneity in the ability to adopt the up-to-date technology may
be minimal in recent years of knowledge spillover. Even if entrepreneurs need to borrow theentire amount of investment when they establish new firms, they can do so under the perfectfinancial institution. In reality, of course, this is not the case. Not all entrepreneurs canborrow as much as they need to install up-to-date production facilities. This is especially
so in less-developed countries which are often financially less developed. In this paper, weanalyze how financial imperfection affects the firm heterogeneity and market structure of
an industry. We also examine the effects of international trade of capital and goods underfinancial imperfection.1
1Antràs and Caballero (2007) examine the relationship between financial imperfection and substitutability
between goods and capital trade. They show that in a Heckscher-Ohlin-type model with financial imperfection, goods trade and capital mobility are complements, rather than substitutes, in less financially developed1

We consider countries in which individuals with different wealth levels choose whether
or not they become entrepreneurs, producing varieties in a differentiated good sector. Ifthey become entrepreneurs, they choose whether they produce with a more-costly, highproductive production technology or with a less-costly, low-productive technology. Under
perfect financial institution, all entrepreneurs invest on the high-productive technology, since
they all can borrow the entire amount of investment if necessary. As a consequence, theindustry is composed of many homogeneous firms. If there exists financial imperfection, on
the other hand, borrowing is constrained so the initial wealth of an entrepreneur becomes
important. Given that the individuals of the economy are endowed with heterogeneous
wealth, entrepreneurs with different wealth levels may choose different investment levels,
resulting in the firm heterogeneity in productivity.2
Manova (2008) also develops a model with credit-constrained heterogeneous firms. In
her model, firms are faced with credit constraint in financing trade costs. Efficient firms
are less financially constrained, so efficient firms in financially developed countries are more
likely to engage in the export. Our model is quite different from hers in that financial
imperfection leads to firm heterogeneity in not just their attitudes toward exporting but
their productivities themselves (which of course affect export activities). We also investigate
the impact of international trade of capital and goods on the market structure.

2

Model

In the basic model, we consider a country in which the mass m of individuals resides. Eachindividual owns one unit of labor and a wealth of ω that is uniformly distributed on [0, ω̄];thus the density of individuals whose wealth is ω ∈ [0, ω̄] equals m/ω̄. All individuals sharethe same utility function over the two goods, a differentiated good X and numeraire goodcountries.
2
Although the interests and aims of the papers are quite different, the model structure of this paper issimilar to the ones developed by Matsuyama (2004, 2005). Matsuyama (2004) shows that financial market
globalization may widen the inequality of nations in the existence of financial imperfection. Matsuyama(2005) demonstrates that the difference in the financial development between countries may lead to thesystem of comparative advantage in international trade.

2

Y , characterized byu = log ux + y,

(1)

where
Z

ux =

x(i)

σ−1
σ

 σ

di

σ−1

; σ > 1.

(2)Ω

denotes the subutility derived from the consumption of continuum varieties of good X,{x(i)}i∈Ω , and y denotes the consumption level of good Y . The numeraire good is competitively produced such that one unit of labor produces one unit of good, so the wage rateequals one.
Each individual chooses a consumption profile of good X to maximize ux subject toRi∈Ω p(i)x(i)di ≤ E, where p(i) and E denote the price for variety i and the total expenditureon all varieties of good X, respectively. It is immediate to obtain x(i) = p(i)−σ E/P 1−σ ,1where P ≡ [ i∈Ω p(i)1−σ di] 1−σ denotes the price index of good X. We substitute this result
R

into (2) to obtain ux = E/P . Therefore, an individual’s utility function can be written as
u = log E − log P + y. Maximizing this with the constraint E + y ≤ I, where I denotethe individual’s income (which is at least as large as one, the labor income of hers), we
obtain E = 1. That is, each individual spends E = 1 on good X, so the country’s aggregate
expenditure on good X is m.
Good X industry is characterized by a monopolistic competition with free-entry and freeexit. When a firm enters, however, it incurs an R&D (or setup) cost. There are two typesof production technology (or facility). The higher the investment, the lower is the marginal
cost of production. More specifically, if a firm invests gh (gl ) units of the numeraire good,its marginal cost becomes c/ϕh (c/ϕl ). We assume that ϕl < ϕh and gl < gh < ω̄. To obtaineach firm i’s profits, we define the “aggregate” productivity
ϕ̃ ≡

Z

σ−1

ϕ(i)

 1

di

σ−1

.

(3)

i∈Ω

We make a standard assumption that each firm ignores the impact of its pricing on the priceindex, so that firms select prices that are σ/(σ − 1) times their individual marginal costs. It

3

is easy to see that firm k’s profits equalmπ(ϕ(k)) =
σ

ϕ(i)
ϕ̃

!σ−1

.

(4)

Individuals decide whether or not they become entrepreneurs who can borrow money ata gross interest rate of R to finance their investments if necessary. However, entrepreneurs
are faced with a financial constraint: entrepreneur i can borrow only up to θπ(ϕ(i)), thefraction θ ∈ (0, 1] of the profits that her firm will earn.3

3

Equilibrium under perfect financial institution

This section shows that if there is no financial constraint, all entrepreneurs choose the same
production technology and hence all firms in the differentiated good sector are homogeneous.
Each individual chooses one of the following three options: (i) she becomes an entrepreneur and invests gh , (ii) she becomes an entrepreneur and invests gl , and (iii) she
lends her money to entrepreneurs. Consider an individual with the wealth ω. If she invests
gh , she would obtain π(ϕh ) − R(gh − ω). If ω < gh , she borrows gh − ω to earn π(ϕh ) and
pay R(gh − ω) back to the lenders. If ω ≥ gh , she obtains π(ϕh ) from the production of goodX (by investing gh ) and −R(gh − ω) from lending out. Similarly, if she invests gl , she would
obtain π(ϕl ) − R(gl − ω). Finally, if she lends out her wealth, she would get Rω.
An entrepreneur chooses the high-productivity technology rather than the low-productivity
technology if
π(ϕh ) − R(gh − ω) > π(ϕl ) − R(gl − ω),which can be written asϕlπ(ϕh ) 1 −ϕh!σ−1 
 > R(gh − gl ).

(5)Note that this inequality does not depend on ω, so all entrepreneurs choose the same technology. Whether or not the inequality (5) holds depends on the productivity and investment
cost parameters. In this paper, we focus on the natural case in which entrepreneurs choose
3

Matsuyama (2005, footnote 1) lists various possible causes for financial imperfection of this kind.

4the high-productivity technology if they are not financially constrained, so the inequality(5) holds. In equilibrium, some individuals lend money to entrepreneurs, and hence the net
benefit of being an entrepreneur and that of lending money must be the same. That is,π(ϕh ) − R(gh − ω) = Rω,which is reduced toπ(ϕh ) = Rgh .

(6)

Substituting this equality into (5) and rearranging terms, we obtain gl /gh > (ϕl /ϕh )σ−1 .
Assumption 1
gl
>
gh

ϕl
ϕh

!σ−1

.

Under this assumption, all entrepreneurs choose the high-productivity technology while someindividuals lend their wealth to those entrepreneurs. Moreover, it is easy to check that
under this assumption, there does not exist equilibrium in which entrepreneurs choose thelow-productivity technology.
To find the details of the equilibrium, we first investigate the credit market. Letting ndenote the mass of firms (or equivalently the number of entrepreneurs) in equilibrium, thetotal investment demands equal ngh under Assumption 1. The total supply of assets, on theother hand, equalsmω̄m Z ω̄
ωdω =
.
ω̄ 0
2
By equating the asset demands and supplies, we find that the mass of firms is given by
n=

mω̄
.
2gh

(7)

Recall that the decision as to whether or not an individual becomes an entrepreneur does
not depend on her wealth. This means that despite that the number of entrepreneurs isunambiguously determined, who become entrepreneurs is indeterminate. Now, we calculateϕ̃ from (3) using (7) to obtain
ϕ̃ =

mω̄
2gh
5

! 1

σ−1

ϕh .

Substituting this into (4), we haveπ(ϕ) =

2gh
.
σ ω̄

(8)

Then, it follows from (6) that
R=

2
.
σ ω̄

We record our findings in the following proposition.
Proposition 1 Under perfect financial institution, all entrepreneurs in the differentiatedgood sector choose the same production technology upon entry, and hence firm heterogeneity
will not arise.

4

Financial Imperfection and Firm Heterogeneity

We have shown that under perfect financial institution, an individual’s wealth is irrelevantin her decision as to whether or not she becomes an entrepreneur. As expected, individual’s
wealth will be an important factor under financial imperfection. Moreover, since individuals
are heterogeneous in their wealth, their choice of technology may be heterogeneous leading
to the firm heterogeneity in productivity.
Under financial imperfection, in addition to the profitability constraint
π(ϕh ) − Rgh ≥ 0,π(ϕl ) − Rgl ≥ 0,
the following borrowing constraints must be satisfied for both types of firm selecting thehigh-productivity technology and low-productivity technology:θπ(ϕh ) ≥ R(gh − ω),(9)θπ(ϕl ) ≥ R(gl − ω).

(10)

It is easy to see that for each type of firm, the profitability constraint is tighter than the
borrowing constraint if θ is large, whereas the borrowing constraint is tighter than the
profitability constraint if θ is small.
6If θ is less than one but is large enough, the borrowing constraint does not bind forany entrepreneur. All of them still choose the high-productivity technology earning zeroprofits. To find the threshold value of θ at which the borrowing constraint starts binding,we substitute (6) into (9) to obtainω ≥ (1 − θ)gh .

(11)

In the case where all entrepreneurs choose the high-productivity technology, the borrowing
constraint binds for all individuals with the wealth less than or equal to (1 − θ)gh . Supposethat all individuals with the wealth higher than or equal to ωh become entrepreneurs choosing
the high-productivity technology. Then, it follows from (7) thatmmω̄(ω̄ − ωh ) =,ω̄2ghwhich can be rewritten asωh = ω̄ −

ω̄ 2
.
2gh

(12)

Therefore, the equilibrium derived in the previous section continues to exist as long as thiscritical entrepreneur derived in (12) is free from the borrowing constraint, i.e.,
ω̄ −

ω̄ 2
≥ (1 − θ)gh
2gh
!
ω̄
ω̄
θ ≥ 1−
1−
.
gh
2gh

(13)

Notice that all firms adopt the high-productivity technology and earn zero profits in thiscase (i.e., π(ϕh ) − Rgh = 0), and as a consequence no firm chooses the low-productivity
technology (i.e., π(ϕl ) − Rgl < 0) under Assumption 1.
If θ is so small that the inequality (13) is violated, the borrowing constraint binds forentrepreneurs whose wealth is the smallest among them. Only wealthy individuals become
entrepreneurs and relatively poor individuals lend their money. The borrowing constraint isbinding for the critical individuals whose wealth is ωh , i.e.,θπ(ϕh ) = R(gh − ωh ).
7(14)

In addition, the credit market clearing condition can be written asmmω̄(ω̄ − ωh )gh =.
ω̄
2
Since the number of firms, n, equals m(ω̄ − ωh )/ω̄, this gives us n = mω̄/(2gh ). Somewhat
surprisingly, the number of firms is the same as that under the perfect financial institution(see (7)). Total wealth of the economy completely determines the number of firms. Since
the environment surrounding the differentiated good sector is the same as before, every
firm earns the same profits (shown in (8)) as in the case of perfect financial institution.
Furthermore, we substitute (8) into (14) to obtain
4θgh2
R=
.
σ ω̄[2gh (gh − ω̄) + ω̄ 2 ](15)

The gross interest rate R is linearly increasing in θ. As θ decreases, it becomes more difficult
to borrow money for the individuals with relatively small ω. The gross interest rate R
decreases to completely offset this negative impact of θ for the critical individuals so that they
continue to be critical entrepreneurs (recall that the number of entrepreneurs are completely
determined by the availability of credit).
Proposition 2 Under mild financial imperfection, the same number of individuals as in
the case of perfect financial institution become entrepreneurs. As the degree of financial
imperfection becomes severe, the gross interest rate falls proportionately so the firms’ profits
and the number of firms do not change.
As θ falls further and R falls accordingly, the net profit from entering the good X sector(when all incumbent firms adopt the high-productivity technology), π(ϕl ) − Rgl , becomes
non-negative at some point. The zero-profit condition for a firm with the low-productivity
technology, π(ϕl ) = Rgl , gives us the critical θ. Using (8) and (15), we can reduce thisequality to obtain
2gh (gh − ω̄) + ω̄ 2
θ=2gh gl

ϕl
ϕh

!σ−1

.

(16)

Thus, if θ is smaller than this critical value, an entrepreneur has an incentive to enter thedifferentiated good sector with the low-productivity technology. If gl is so small that it is8less than ωh given in (12), an individual whose wealth is gl indeed enters the sector. In thiscase, therefore, the equilibrium described above will not exist. Henceforth, we focus on sucha case in which the gap between gh and gl is so large that firms with different productivities
coexist when θ is smaller than the critical value given in (16).
If θ is smaller than the one given in (16) but close enough to that critical value, theprofitability constraint is binding while the borrowing constraint is slack. Indeed, we canrewrite the borrowing constraint (10) using π(ϕl ) = Rgl to obtain ω ≥ (1 − θ)gl , which issimilar to (11). This inequality is satisfied with strict inequality if ω (< gl ) is close enoughto gl .
As θ falls further, the borrowing constraint for the low-productivity firms starts binding,as well as that for the high-productivity firms. In the rest of the paper, we assume that θis small enough that for either type of firm, it is the borrowing constraint that is binding.
Before proceeding, we record one of our main findings.
Proposition 3 Firm heterogeneity within the differentiated good sector arises if and only if
the economy is faced with relatively severe financial imperfection.
Now, we derive equilibrium in which θ is small enough that the borrowing constraint
is binding for either type of firm. We define ωl such that all individuals with ω ∈ [ωl , ωh ]become entrepreneurs choosing the low-productivity technology while all individuals withω ∈ [ωh , ω̄] become entrepreneurs choosing the high-productivity technology. Defining β > 1
by ϕh = βϕl , we have
σ−1 m



ϕ̃ =

(βϕl )


= ϕl

m
ω̄

ω̄
 1

σ−1

 1

m
(ω̄ − ωh ) + ϕσ−1
(ωh − ωl )
l

σ−1

ω̄

1

[β σ−1 (ω̄ − ωh ) + ωh − ωh ] σ−1 .

(17)

We first derive from the two borrowing constraints a condition for ωh and ωl to satisfy.
It follows from (9) and (10) thatgh − ωh=gl − ωl

9

ϕh
ϕl

!σ−1

,

which can be rewritten asωl = gl − β 1−σ (gh − ωh ).

(18)

We call this condition the market structure (MS) condition, since this condition determines
the relative size of the groups of firms (the high-productivity firms and low-productivity
firms) which simultaneously satisfies the two borrowing constraints.
The next condition for ωh and ωl to satisfy is the credit market (CM) clearing condition.
It is written asmmω̄m(ω̄ − ωh )gh + (ωh − ωl )gl =
,
ω̄
ω̄
2

(19)

which can be reduced toωl =2gh ω̄ − ω̄ 2 gh − gl
−
ωh .
2gl
gl

(20)

The lower panel of Figure 1 illustrates the market structure and credit market clearing
conditions. It is easy to verify that the market structure schedule is upward-sloping while
credit market clearing schedule is downward-sloping, as the figure shows. We immediately
find from the figure (or from (18) and (20)) that the critical asset levels, ωh and ωl , are solely
determined from these conditions.
To determine the gross interest rate, we consider the high-productivity firms’ borrowing
constraint (BCh ). To derive the condition, we use (17) to rewrite the high-productivity firm’s
profits asm
π(ϕh ) =
σ
=

ϕh
ϕ̃

!σ−1

ω̄β σ−1.
σ[β σ−1 (ω̄ − ωh ) + ωh − ωl ]It follows from (18) thatωh − ωl = β 1−σ gh − gl + (1 − β 1−σ )ωh .
Substituting this into (21) gives us
π(ϕh ) =ω̄β σ−1.
σ[β σ−1 ω̄ + β 1−σ gh − gl − (β σ−1 + β 1−σ − 1)ωh ]
10

(21)

Thus, we can rewrite θπ(ϕh ) = R(gh − ωh ) to obtain the condition that determines R:R=θω̄β σ−1.
σ(gh − ωh )[β σ−1 ω̄ + β 1−σ gh − gl − (β σ−1 + β 1−σ − 1)ωh ](22)

As the upper panel of Figure 1 shows, the right-hand side of (22) increases in ωh . The autarkic
equilibrium rate of R is determined so that firms’ borrowing constraints are binding, onceωh and ωl are determined by the credit and product markets.
Having derived the equilibrium in which the borrowing constraints are binding for bothtypes of firm, we investigate the effect of an increase in θ on the equilibrium. Since θ does
not appear in (18) and (20), an increase in θ only shifts up the BCh schedule in the upper
panel of Figure 1. As a result, R increases proportionately as (22) suggests. An increasein θ would not affect the market structure at all. As θ increases, credit demands increase
accordingly, which is completely offset by an increase in R to meet the fixed supply of credit.
Proposition 4 When financial imperfection is severe so that the borrowing constraints arebinding for both high-productivity and low-productivity firms, an improvement of financial
institution would only increase the interest rate leaving the market structure of the differentiated good sector unchanged.

5Opening to International Trade and Capital Mobility

This section extends the model to a two-country setting in which countries trade goods
and/or capital (credit) to each other.
There are two countries, North and South, which differ only in the degree of financial
imperfection such that θN > θS . There is no trade barriers in goods and capital trade, if they
trade them at all. Thus, if the goods are traded, the worldwide “aggregate” productivity insector X becomes
 1



ϕ̃

T

X m
m
(ω̄ − ωhi ) + ϕσ−1(ωhi − ωli )
= (βϕl )σ−1
l
ω̄
ω̄
i=N,S
i=N,S
X

=

i 1
mϕl X h σ−1β (ω̄ − ωhi ) + ωhi − ωli σ−1 .
ω̄ i=N,S11

σ−1

Then, it follows from the fact that the total expenditure on good X in the world equals 2mthat firm k’s profit, whether it is Northern or Southern, is given by2m
π (ϕ(k)) =
σ
T

ϕ(k)
ϕ̃T

!σ−1

.

Whereas the profit for firm k in country i = N, S when goods are not traded can be written,
similarly to (4) asmπ (ϕ(k)) =
σ
i

ϕ(k)
ϕ̃i

!σ−1

,

where ϕ̃i is defined as country i’s ϕ expressed in (17).
The market structure condition under free trade of goods is derived from the set ofborrowing conditions:θi π T (ϕh ) − Ri (gh − ωhi ) = 0,θi π T (ϕl ) − Ri (gl − ωli ) = 0,
for i = N, S. Consequently, we haveβ σ−1 =

gh − ωhi.
gl − ωli

Note that this market structure condition is the same as that in the closed-economy model
expressed in (18). This condition also serves as the market structure condition when goods
are not traded, since the same condition obtains even if we replace π T with π i , for i = N, S
in the above set of equations. Also note that the market structure condition is not affectedby capital mobility. The market structure condition is depicted as the MS schedule in Figure
2.
In contrast, the credit market clearing condition critically depends on capital mobility
between the countries. When capital is immobile between the countries, it can be written as(ω̄ − ωhi )gh + (ωhi − ωli )gl =

ω̄ 2
,
2

for i = N, S, similarly to (18). The CM schedule, common to both countries, in Figure 2
illustrates this condition. Without capital mobility, goods trade does not affect the condition.
12

Under perfect capital mobility, the credit market is integrated, so the worldwide credit
market clearing condition together with the interest parity, i.e., RN = RS , must hold. The
worldwide credit market clearing condition can be written as
i
X mω̄
mh
(ω̄ − ωhi )gh + (ωhi − ωli )gl =,i=N,S ω̄
i=N,S 2X

which is reduced toω N + ωhSω̄ − h2!

ωhN + ωhS
ω N + ωlS
gh +
− l
2
2

!

gl =

ω̄ 2
.
2

(23)

The condition under which RN = RS can be expressed differently depending on whether
or not goods are traded. If goods are not traded, the borrowing constraint for the highproductivity firms in country i can be rewritten as Ri = θi π i (ϕh )/(gh − ωhi ) for i = N, S.
Consequently, RN = RS can be reduced toθSωhS = 1 − N
θ

ϕ̃N
ϕ̃S

!σ−1 

ϕ̃N
ϕ̃S!σ−1 

θS
 gh +
θN

ϕ̃N
ϕ̃S

!σ−1

ϕ̃N
ϕ̃S

!σ−1

ωhN .

(24)

Similarly, we haveθSωlS = 1 − NθθS gl +
θN

ωlN ,for the low-productivity firms. Substituting these relationships into (23) gives us the condition for ωhN and ωlN to be satisfied in order to clear the worldwide credit market. Thiscondition is depicted as the CMT schedule in Figure 2. As the figure shows, it is located to
the left of the CM schedule if
θS
θN

ϕ̃N
ϕ̃S

!σ−1

≡

θS β σ−1 (ω̄ − ωhN ) + ωhN − ωlN< 1.
θN β σ−1 (ω̄ − ωhS ) + ωhS − ωlS

If goods are traded, on the other hand, RN = RS is reduced toθN π T (ϕh )θS π T (ϕh )=,gh − ωhN
gh − ωhS
so we have
ωhS =

θS
1− N
θ

!

13

gh +

θS N
ω .
θN h

(25)

˜ T schedule that
The weight on ωhN is smaller in (25) than in (24), which implies that the CM
depicts (23) with (25) is located to the left of the CMT schedule.
Turning to the BCh schedule, it is readily verified that the borrowing constraint for thehigh-productivity firms in country i can be written asRi =θi ω̄β σ−1σ(gh − ωhi ) [β σ−1 ω̄ + β 1−σ gh − gl − (β σ−1 + β 1−σ − 1)ωhi ](26)

if goods are not traded, while it is written asθi ω̄β σ−1

Ri =σ(gh − ωhi )ω N +ω S
β σ−1 ω̄ + β 1−σ gh − gl − (β σ−1 + β 1−σ − 1) h 2 h

(27)



if goods are not traded.
Without capital mobility, both (ωhN , ωlN ) and (ωhS , ωlS ) are determined as a common intersection between the MS and CM schedules in the lower panel of Figure 2. Threshold values
of wealth are the same between the countries because the market structure is constrainedby the limited wealth endowment, so conditions (26) and (27) are equivalent. Even if capital is mobile between the countries, the BCih schedules are the same as before when goodS
are not traded. But as goods trade is allowed, the BCN
h schedule shifts up while the BChschedule shifts down. To see this, we first note that ωhN < (ωhN + ωhS )/2 < ωhS as we can write(ωhN + ωhS )/2 in two different ways:1
ωhN + ωhS
=
2
2

"

θS
1− N
θ

!

θS
gh + 1 + N
θ

!

#

ωhN

1
=
2

"

θN
1+ S
θ

!

θN
ωhS −
− 1 gh .
θS

N

!

#

S

˜ h schedule is located above the BCN
˜Consequently, the BC
h schedule, while the BCh schedule
is located below the BCSh schedule.
Figure 2 shows the equilibrium points for four different scenarios. Points 1 show theautarkic equilibrium. Point 2 shows the equilibrium when only goods are traded, while
point 3 shows the one when only capital moves between the countries. Finally, point 4 showsthe equilibrium when both goods and capital are internationally traded.
As the figure shows, the market structures and interest rates will not change if countries
start engaging in goods trade. Consumers benefit from trade because they become able14

to consume more varieties of good X. But the market structure does not change since
the individual countries’ credit markets are constrained by their own wealth endowments.
Capital mobility changes the environment surrounding sector X. Capital moves from North(with a higher autarkic interest rate) to South, expanding sector X in North (by both
lowering ωhN and ωlN ) and shrinking sector X in South. This change in the market structures
is amplified if goods trade is also allowed. Interestingly, goods trade affect the market
structure only when it is accompanied by international capital mobility. Capital mobility
leads to heterogeneity in market structure between the two countries. Sector X in North
enjoys trade benefits only when this heterogeneity exist.
Proposition 5 The equilibrium market structures in both countries will not change if only
goods trade is opened. Capital mobility, on the other hand, will expand the differentiatedgood sector in North and shrink the sector in South. International trade of goods amplifies
this impact of capital mobility. Indeed, goods trade affect the market structures only when it
is accompanied by international capital mobility.

6

Concluding Remarks

In the model where entrepreneurs with different wealth levels choose technology levels when
they enter a differentiated good sector, we have shown that the firm heterogeneity in productivity arises only if there exists financial imperfection. We have examined the impact
of international trade of goods and capital between two countries with different degree offinancial imperfection. We have found that (i) goods trade alone will not affect the market
structure, (ii) capital movement induces the financially constrained sector to expand in North
with a smaller degree of financial imperfection, (iii) goods trade will amplify this impact of
capital movement, and (iv) goods trade will affect the market structures only when it isaccompanied by capital mobility.
Capital would move between two countries if the countries are asymmetric also in their
population size, average wealth level, and so forth. It would be interesting to examine thecomplementarity between goods trade and capital trade in such contexts.
15References
Antràs, Pol and Ricardo J. Caballero (2007), “Trade and Capital Flows: A Financial
Frictions Perspective,” unpublished manuscript, Harvard University.
Atkeson, Andrew and Ariel Burstein (2007), “Innovation, Firm Dynamics, and International
Trade,” NBER Working Paper 13326.
Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum (2003),“Plants and Productivity in International Trade,” American Economic Review, 93,
1268-1290.
Bernard, Andrew B., J. Bradford Jensen, Stephen J. Redding, and Peter K. Schott (2007),“Firms in International Trade,” Journal of Economic Perspective, 21, 105-130.
Bustos, Paula (2005), “The Impact of Trade on Technology and Skill Upgrading: Evidence
from Argentina,” unpublished manuscript, Universitat Pompeu Fabra.
Costantini, James A. and Marc J. Melitz (2007), “The Dynamics of Firm-Level Adjustment
to Trade Liberalization,” unpublished manuscript, Princeton University.
Manova, Kalina (2008), “Credit Constraints, Heterogeneous Firms, and International Trade,”Unpublished manuscript, Stanford University.
Matsuyama, Kiminori (2004), “Financial Market Globalization, Symmetry-Breaking, andEndogenous Inequality of Nations,” Econometrica, 72, 853-884.
Matsuyama, Kiminori (2005), “Credit Market Imperfections and Patterns of International
Trade and Capital Flows,” Journal of the European Economic Association, 3, 714-723.
Melitz, Marc J. (2003), “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 71, 1695-1725.

16

R

BCh '
BCh

A

R '
RA

ωh

ωhA

ωl

MS

ωlA
CM

ωhA

Figure 1. Autarkic Equilibrium

ωh

R
BChN
1,2

4

3

~
BChN

3

4

~
BChS

1,2

BChS

ωh
ωl

MS

4

3

1,2

3

~
CM T

4

CM
CM T

ωh

Figure 2. Trade Equilibrium