Global COE Hi-Stat Discussion Paper Series 061

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Trade Liberalization, Economic Growth, andIncome Distribution ina Multiple-cone Neoclassical Growth Model

Hi-Stat Discussion Paper

Kozo Kiyota

April 2009

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Mar h 24, 2009

Trade Liberalization, E onomi

Growth, and In ome Distribution

in a Multiple- one Neo lassi al Growth Model

Kozo KiyotaFa ulty of Business Administration, Yokohama National University

Abstra t

The empiri al literature on trade liberalization ree ts two puzzles. First,
the effe t of trade liberalization on e onomi

growth is ambiguous. Se ond,

the effe t of trade liberalization by developing

ountries on their in ome dis-tribution is ambiguous. This paper attempts to explain these two puzzles atthe same time, based on a multiple- one neo lassi al growth model.
model shows thatThe

ountries that are labor abundant in a global sense may see

a rise in in ome inequality and a de line in per
onsumption with liberalization if they are
The results suggest that the two puzzles

apita GDP and perapita

apital abundant in a lo al sense.

an be explained by the existen e ofglobal and lo al fa tor abundan es.

Key words:

Trade

Liberalization;

Medium-run

Growth;In omeDistribution;

Multiple- one Model; StolperSamuelson Theorem

JEL lassi ation ode: F1, O41

 Spe ial thanks to Alan Deardorff and Robert Stern for many fruitful dis ussions and omments on earlier versions of this paper. Thanks as well to Ri hard Baldwin, Fumio Dei, Jota Ishikawa, Kaz Miyagiwa, James Rau h,Morihiro Yomogida, and seminar parti ipants at Hitotsubashi University, Kobe University, National Graduate Institute for Poli y Studies, and the Fall 2008 Midwest International E onomi s Meeting. The rst draft of this paper
was written while the author was visiting the Gerald R. Ford S hool of Publi Poli y, University of Mi higan, thehospitality of whi h is gratefully a knowledged. In addition, nan ial support from the Japan So iety for the Promotion of S ien e (JSPS) 2006 Postdo toral Fellowships for Resear h Abroad is gratefully a knowledged. The usual
dis laimer applies.
 Address: Fa ulty of Business Administration, Yokohama National University, 79-4 Tokiwadai, Hodogaya,
Yokohama 240-8501, Japan; Phone: +81-45-339-3770; Fax: +81-45-339-3707; E-mail: kiyota [at℄ ynu.a .jp

1 Introdu tion
The empiri al literature on trade liberalization ree ts two puzzles. First, the effe t of trade liberalization on e onomi

growth is ambiguous. A number of theoreti al studies su h as Baldwin(1992) have argued that trade liberalization leads to dynami

gains from greater

apital au-mulation as well as stati

ef ien y gains. This in turn implies that trade liberalization has apositive effe t on e onomi

growth.

1 However, empiri al studies have found that this theoreti al

predi tion does not ne essarily hold. Whereas some studies su h as Edwards (1998) and Frankel
and Romer (1999) stressed the positive relationship between trade liberalization and e onomi
growth, other studies su h as Rodriguez and Rodrik (2000) presented skepti al views about themethodologies and measurements used in previous studies.
tionship between trade poli y and e onomi

2 Therefore, the nature of the rela-

growth remains very mu h an open question. The

issue is far from having been settled on empiri al grounds (Rodriguez and Rodrik, 2000, p.
266).
The se ond puzzle is that the effe t of trade liberalization by developing

ountries on theirin ome distribution is ambiguous. The StolperSamuelson Theorem states that prote tion raises
the real fa tor pri e of aountry's s ar e fa tor and lowers that of its abundant fa tor (Stolper

and Samuelson, 1941). In other words, trade liberalization lowers the fa tor pri e of aountry'ss ar e fa tor and in reases that of its abundant fa tor. Given the fa t that developing ountries are
generally more labor abundant than are industrialized ountries, the StolperSamuelson Theorem
suggests that trade liberalization leads to a de rease in the rentalwage ratio with an in reasein the pri e of a labor-intensive good and a de rease in the pri e of a
Be ause the rentalwage ratio

apital-intensive good.

3

an be interpreted as a proxy for in ome inequality, a de rease in

the rentalwage ratio implies a de rease in in ome inequality between workers and the owners
ofapital. Contrary to the StolperSamuelson Theorem, however, there is a large amount ofeviden e from several developing

ountries regarding their exposure to globalization and the4parallel evolution of inequality (Goldberg and Pav nik, 2007, p. 39).

To solve the rst puzzle, a number of studies su h as Wa ziarg and Wel h (2003) attempt torene the empiri al framework. However, little attention has been paid to the theoreti al framework. The se ond puzzle is partly explained by Davis (1996), who fo used on multiple fa tor
pri e equalization (FPE) sets, or multiple ones of diversi ation. The key insight of his analysis
is in the distin tion between global and lo al fa tor abundan es. Global fa tor abundan e is dened as the relative fa tor abundan e ofountries in fa tor spa e. On the other hand, lo al fa tor

abundan e is dened as the relative fa tor abundan e within the
1 Note that, in his

ountry's

one of diversi a-riti al review of Baldwin (1992), Mazumdar (1996) showed that whether trade liberalization
leads to growth depends on the kind of good that is imported. Se tion 3 dis usses Mazumdar's laim in more detail.
2 Note that Edwards (1998) examined the effe ts of openness on total fa tor produ tivity growth whereas Frankel
and Romer (1999) and Rodriguez and Rodrik (2000) examined the effe ts on per apita gross domesti produ t(GDP) growth. Winters (2004) provided an ex ellent literature review of the issues.
3 See, for example, Jones (1975) and Davis (1996). In order to make the interpretation lear, this paper uses therentalwage ratio rather than the wagerental ratio.
4 A ording to Goldberg and Pav nik (2007, p. 40), while inequality has many different dimensions, all existingmeasures for inequality in developing ountries seem to point to an in rease in inequality.
1tion. Based on a stati

multiple- one model, Davis found that trade liberalizationin ome inequality. However, his analysis la ked dynami
trade liberalization, e onomi
question how the link

ould expand

aspe ts. Therefore, the link between

growth, and in ome distribution is un lear. It remains an open

an be modeled

omprehensively.

This paper attempts to explain these two puzzles at the same time, based on a multiple- one
neo lassi al growth model. The modelombines the elements of Davis's (1996) view of lo al

fa tor abundan e together with the elements of Deardorff's (2001) model of trade and growth.
Following previous studies su h as Mazumdar (1996), growth in this paper refers to medium-run
growth rather than long-run growth. Therefore, an in rease in per
positive effe t of trade poli y on medium-run e onomi

Before starting, some terminologi al matters need to be
paper
are

onsists of industrialized

ountries and developing

apital abundant whereas the developing

apita GDP is interpreted as a

growth.
laried. That is, the model of thisountries. The industrialized

ountries

ountries are labor abundant in a global sense. The

developing ountries are further divided into two groups. One omprises lo ally apital-abundantdeveloping

ountries that are labor abundant in a global sense but

sense. The otheromprises lo ally labor-abundant developingin both global and lo al senses. Table 1 summarizes theapital abundant in a lo al

ountries that are labor abundantountrylassi ation.

=== Table 1 ===Figure 1 illustrates the distin tion between the global and lo al fa tor abundan es, based on
the Lerner diagram of a three-good, two- one model.
The three goods are labor-, middle-, and

The two fa tors areapital and labor.

ones are [t1 ; t2 ℄ andapital-intensive goods. The two[t3 ; t4 ℄, where t j ( j = 1; :::; 4) represents the apitallabor ratio and t1 < t2 < t3 < t4 . Countries
that lo ate in theone [t3 ; t4 ℄ are more

apital abundant thanountries that lo ate in theone[t1 ; t2 ℄. To simplify the dis ussion, I assume that the world is even in the sense that there
are an equal number of fa tors and goods in ea hterminology, industrialized
abundant
in omeountries as middle-in ome
ountries.

lo ates in the
low-in omeone (S hott, 2003, p. 689). To simplify theountries are referred to as high-in ome

ountries, lo allyountries, and lo ally labor-abundant

apital-ountries as low-

I use EH to denote the fa tor endowments of a high-in ome

ountry thatone [t3 ; t4 ℄. I use EM , and EL to denote the fa tor endowments of middle- andountries, respe tively. Both EM and EL lo ate in theone [t1 ; t2 ℄.

=== Figure 1 ===The high-in ome ountry is globally apital abundant in the sense that it lo ates in the apitalabundant one [t3 ; t4 ℄ and thus it an produ e the apital-intensive as well as the middle-intensive
goods. On the other hand, the middle- and low-in ome
the sense that they lo ate in the labor-abundantountries are globally labor abundant in

one [t1 ; t2 ℄ and thus they

an produ e the labor-

as well as middle-intensive goods. Note, however, that the middle-in ome
apital abundant, whereas the low-in ome[t1 ; t2 ℄. Therefore, the middle-in ome
abundant, whereas the low-in ome

ountry is relatively

ountry is relatively labor abundant within theountry is globally labor abundant but lo allyone

apitalountry is labor abundant in both global and lo al senses.

This distin tion is explained in more detail in Se tion 3.
2

This paper fo uses on the trade poli y of developing
noted. The

ontribution of this paper is that it

ization on in ome distribution, perountries to explain the two puzzles

laries simultaneously the effe ts of trade liberal-

apita GDP, and per

apita

been explored in previous studies. The model shows thatonsumption, an issue that has not

ountries that are labor abundant in a

global sense may see a rise in in ome inequality and a de line in per
onsumption aompanying liberalization if they are

the two puzzles

an be attributed to the existen e of multiple

abundan e among

ountries within the sameapita GDP and perapita

apital abundant in a lo al sense. Therefore,
ones and the differen es in fa tor

one.

This paper is stru tured as follows. First, I present a three-good, two- one He ks herOhlin(HO) growth model in Se tion 2 and dis uss some impli ations for in ome distribution, e onomi
growth, and per

apita

onsumption. Se tion 3 introdu es theon ept of lo al fa tor abundan e

into the HO growth model and examines the effe ts of trade poli y by a developing

ountry.

Con luding remarks are provided in Se tion 4.

2 Model
2.1

Setup

The two-good HO growth and trade model was rst developed by Oniki and Uzawa (1965).
Deardorff (1974) developed a simplied version based on a single- one model, introdu ing asmall open e onomy assumption. Deardorff (2001) further extended the analysis from a twogood to a multiple-good model, introdu ing multiple

ones. Following Galor (1996), in whi hsavings result from wages rather than total in ome, Deardorff (2001) showed that the multipleone model be ame onsistent with the existen e of multiple steady states. My paper builds upon
Deardorff (2001).
This se tion fo uses on the basi

features of the model and dis usses some impli ations forin ome distribution, per apita GDP, and per apita onsumption. The impli ations of this se tion
hold irrespe tive of whether developing

ountries are lo ally

abundant. Therefore, this se tion fo uses on theapital abundant or lo ally laborase of global fa tor abundan e. The distin tion

between global and lo al fa tor abundan es is introdu ed in Se tion 3.
Suppose that there are three goods (a labor-intensive good Y1 , a middle-intensive good Y2 ,and aapital-intensive good Y3 ) and two fa tors (labor L andapital K). The

apital intensities of

the goods are k1 < k2 < k3 , where ki = Ki =Li . Assume that one of the three goods islassied as

an investment good used forapital alassied asonsumption goods used foronsumption. However, theumulation whereas the other two goods areis unknown. Therefore, the labor-, middle-, orapital intensity of the investment good

apital-intensive goods

ould be the investment

good.
I denote total

apital and labor in the e onomy as K and L, respe tively. I denote the produ -tion fun tion of industry i(= 1; 2; 3) as Yi = Fi (Ki ; Li ), where L1 + L2 + L3 = L and K1 + K2 + K3 =K. Let pi (> 0) denote the pri e of good Yi . Assume that the produ tion fun tion of good i is lin-

ear homogeneous: yi = Yi =Li = Fi (Ki ; Li )=Li = Fi (Ki =Li ; 1) = f i (ki ). Assume that the produ tion0

fun tions have the standard properties of a neo lassi al produ tion fun tion: limki !0 f i (ki ) =

3

¥,

0

0

00

¥ fi (ki ) = 0, fi (ki ) > 0, and fi (ki ) < 0.

limki !

I use W (> 0) and R(> 0) to denote the nominal wage and the nominal rental rate, respe tively.

Assume that apital aumulation omes from savings S. Note that both savings and apital must

be measured in the same units. If savings are measured differently from
andapital are notapital, then savings

omparable dire tly. In turn, this means that the pri e of the investment goodpI should be the numéraire. Let p
 i (= pi = pI ) be the pri e of good Yi normalized by the pri e ofthe investment good. Similarly, let w(= W = pI ) and r (= R= pI ) denote the wage and rental rate,

respe tively, normalized by the pri e of the investment good. Let zi (= p
 i yi ) denote the value of

produ tion per worker in industry i. In addition, assume that all markets are perfe tly ompetitive
and, thus, rms earn zero prot: p
 i yiw

rki = 0.

Based on this setup, Deardorff (2001) showed that the relationship between theratio and se toral output
tions z1 and z2 are

ould beonstru ted as in Figure 2. The peronne ted by theirapitallaborapita produ tion fun -ommon tangent AB. Similarly, the perapita produ tion

5
fun tions z2 and z3 are onne ted by their ommon tangent CD. Perpendi ulars At1 and Bt2 are

dropped from the points of tangen y to the horizontal axis. Similarly, let t3 ( p2 ; p3 ) and t4 ( p2 ; p3 )denote theapitallabor ratios dropped from the points of tangen ies for p2 f 2 (k ) and p3 f 3 (k ) to

the horizontal axis. Capitallabor ratios t1 ; :::t4 are referred to as knots. Both the labor- andthe middle-intensive goods are produ ed in the interval [t1 ; t2 ℄, whereas both the middle- and theapital-intensive goods are produ ed in the interval [t3 ; t4 ℄. The interval iswhi h is analogous to thealled an FPE set,

one of diversi ation, or  one in the Lerner Diagram.
=== Figure 2 ===Consider a small open e onomy where the pri e of goods is exogenously given and xed.
This in turn implies that ti

8i are also xed for given pri es. The maximized per apita GDPof this e onomy is des ribed as envelope OABCDE in Figure 2. I denote this per

apita GDPfun tion by z(k ) = ( p 1Y1 + p
2Y2 + p
 3Y3 )=L:8>p
 1 f 1 (k )>><w̄1 + r̄1 kz(k ) =p
 2 f 2 (k )>>w̄ + r̄ k>: p32 f3 (k2)

 k t1;if
t1  k  t2 ;
if

0

if

t2 < k < t3 ;t3  k  t4 ;k > t4 ;if
if

where w̄1 and r̄1 are the wage and rental rate within the<

one between t1 and t2 and thus are

onstant. Similarly, w̄2 and r̄2 are the wage and rental rates within theand are also

(1)

one between t3 and t4

onstant.

Some of the important properties of this model are summarized as follows. First, the slopeof the6ommon tangent indi ates the rental rate r, whereas its inter ept indi ates the wage w.

5 To simplify the dis ussion, this paper ex ludes the

6 See Hahn and Matthews (1964) for the proof.

ases of no ommon tangent or multiple ommon tangents.

4

Therefore, fa tor pri es are written as follows:

8 0>p 1 f 1 (k )>00>r̄1 = p
 1 f 1 (t1 ) = p
 2 f 2 (t2 )¶ z(k ) <0=r (k ) =p
 2 f 2 (k )
>
¶k
0
0
>
r̄2 = p
 2 f 2 (t3 ) = p
 3 f 3 (t4 )>: p3 f30 (k)and k t1 ;if
t1  k  t2 ;
if

0

if

t2 < k < t3 ;t3  k  t4 ;k > t4 ;

if
if

<

8
0
>
p
 1 f 1 (k )p
 1 k f 1 (k )>><w̄1 = p1 f1 (t1) p1t1 f10 (t1) = p2 f2 (t2) p2t2 f20 (t2)0w(k ) =p
 2 f 2 (k )p
 2 k f 2 (k )>00>w̄2 = p
 2 f 2 (t3 )p
 2 t3 f 2 (t3 ) = p
 3 f 3 (t4 )p
 3 t4 f 3 (t4 )>: p3 f3(k) p3k f30 (k)Se ond, per(2)

 k t1;if
t1  k  t2 ;

if

0

if

t2 < k < t3 ;t3  k  t4 ;k > t4 :

if
if

<

(3)

apita GDP is an in reasing fun tion of k. From equation (2), I have:¶ z(k )= r(k) > 0:¶kThat is, as an e onomy aumulates(4)

apital (relative to labor), perapita GDP also in reases.

Third, from equations (2) and (3), fa tor pri es take the following relationships:(¶ w(k)¶kand¶ r (k )¶k> 0

if k lo ates outside the=0

if k lo ates inside the

ones;

<0

if k lo ates outside the

ones;

=0

if k lo ates inside the

(

ones;

(5)

(6)

ones:

The rentalwage ratio r (k )=w(k ) is interpreted as a proxy for in ome inequality. Equations (5)and (6) imply the following general monotoni
apitallabor ratio (Jones, 1974):¶ fr(k)=w(k)g¶k(relationship between the rentalwage ratio and< 0

if k lo ates outside the=0

if k lo ates inside theones;

Figure 3 illustrates the relationship between the rentalwage ratio and thean e onomy lo ates outside theones,

apital a

(7)

ones:

apitallabor ratio. Ifumulation raises the wage, lowers the rental

ratio, and therefore lowers in ome inequality. On the other hand, if the e onomy lo ates inside
the

ones,

apital aumulation has no effe t on fa tor pri es or in ome inequality.

5=== Figure 3 ===2.2

Growth in the small open e onomy

 = nL(> 0), where L = dL=dt . Assume thatNow assume that population growth is La

 =Sumulation is K

Suppose that savings

apitald K, where K = dK =dt , S is savings, and d (> 0) is the depre iation rate.

ome from the wage: S = swL, where s (0 < s 1) is the savings rate.7

Savings are equal to the demand for the investment good that is used for
The rest of the in ome is used for theapital aumulation.

onsumption goods. The dynami s of theapitallaborratio are written as follows: = S=LkLet k(n + d )k = sw(k)(n + d )k

or


k
k

=s

w(k )

(n + d ):k(8) denote the apitallabor ratio at the steady state (i.e., k = 0).

Based on this setup, Deardorff (2001) has provided a geometri
oping

ountries

explanation whereby devel-

onverge to a low steady state, whereas industrialized

high steady state, whi h is shown in Figure 4. If the (n + d )k line

ountries

rosses the wage

onverge to aurve inside 
8
the two ones, there exist three steady states: k1 , k2 , and k3 . If the initial endowment of an e on
omy is in the interval (0; k2 ), the e onomy onverges to a low steady state k1 . Therefore, its wage
and per apita GDP will be w̄1 and z1 , respe tively. If, on the other hand, the initial endowment

of an e onomy is greater than k2 , the e onomy onverges to a high steady state k3 . Its wage and
per apita GDP will be w̄2 and z3 , respe tively. Be ause k2 is an unstable equilibrium, it is not
examined in this paper.
=== Figure 4 ===Note that the failure of a single FPE set is regarded as one of the important reasons why the
HO model sometimes performs poorly in empiri al analysis (e.g., Davis, Weinstein, Bradford,
and Shimpo (1997)). Thus, the present paper does not assume that all
FPE set. In other words, as in Figure 4, I

onsider theountries are in a single

ase where someountries are in a low

steady state whereas others are in a high steady state. Countries in a high steady state k3 arereferred to as industrialized

ountries be ause they have a high perapita GDP z3 . Similarly,

ountries in a low steady state k1 are referred to as developing ountries be ause they have a low
per apita GDP z1 .

7 This assumption was introdu ed by Galor (1996) to explain the existen e of multiple steady states and extended
by Deardorff (2001) to in orporate international trade. Overlapping generations an be one possible justi ation forthis assumption. For more detail, see Deardorff (2001).
8 The multiple equilibria arise be ause savings ome from wages rather than in ome. If savings are proportional
to in ome, the per apita savings urve is a urve involving a proportional downward shift of the per apita GDP
fun tion. Be ause of the on avity of the GDP fun tion, as in the Solow one-se tor model, the savings urve rosses
the wage urve only on e. With Galor's assumption of savings resulting from wages, the wage urve be omes
onstant within the ones, whi h auses the multiple interse tions with the (n + d )k line. In addition, it is possible
to obtain multiple equilibria from the savings out of the rental rate. However, note that in this ase the savings urve
will be a de reasing fun tion of apital a umulation.

6

This paper fo uses on
omplete spe ialization: t1

ountries whose

apitallabor ratios lo ate within theones (i.e., in- k  t2 or t3  k  t4). From equations (3) and (8):sw̄ jTherefore:(n + d )k = 0

j = 1; 2:

w̄ j
¶ k
=
> 0
¶s
n+d

Savings have positive effe ts on

apital a(9)

j = 1; 2:(10)umulation if the e onomy lo ates inside one of the denote per apita onsumption at the steady state. Be ause the in ome is used forones. Leteitheronsumption or savings:

This in turn means:¶  (k  ) ¶ z(k  )
=
¶ k
¶ k







(k ) = z(k )(n + d )k :S=L = z(k )8>< 0(n + d ) = r̄ j (n + d ) = 0
>
: 0
>

<

(11)

if

r̄ j > n + d ;ifr̄ j = n + d ;ifr̄ j < n + d

j = 1; 2:(12)

The relationship between steady-state per apita onsumption and the apitallabor ratio depends
upon the relationship between r̄ j and n + d .

2.3

Trade patterns

Assume that the preferen es of the e onomy are homotheti . Let di and ti denote the value of perapita domesti

demand for good i (either a

net export of good i, respe tively: ti = ziperapita net export of theis ti = zionsumption good or an investment good) and the

di . Assume that trade is balan ed: t1 + t2 + t3 = 0. The

onsumption good is ti = zii whereas that of the investment good

S=L.

Deardorff (2000) showed that trade patterns for the three-good, two- one model
sented as in Figure 5. The steady state of developing
and, therefore, theseountries export the labor-intensive good and import the

good. The steady state of industrialized
fore, they export theountries is lo ated inside theountries is lo ated inside theone [t1 ; t2 ℄apital-intensive

one [t3 ; t4 ℄ and, there-

apital-intensive good and import the labor-intensive good. Whether the

middle-intensive good is exported by industrialized or developing
steady-state

an be pre-ountries depends upon theirapitallabor ratios.
=== Figure 5 ===2.4

Changes in the pri e of goods

For a small open e onomy, a prote tive tariffauses ahange in the domesti

Therefore, to examine the effe ts of trade poli y, it is important to7

pri e of imports.

larify the effe ts of pri ehanges on the steady state. Be ause developing
intensive good, theountries are not able to produ e thehanges in its pri e do not have any effe ts on the domesti

apital-pri es of thelabor- and middle-intensive goods or on fa tor pri es in developing ountries. Thus, the following
analysis examines thehanges in the pri es of the labor- and middle-intensive goods.

Note that Uzawa (1961) found that if the investment good se tor was more
sive than theinitialonsumption good se tor, the steady state

apitallabor ratio may notexist multiple steady-state

apital inten-

ould be unstable in the sense that theonverge to the steady-state

apitallabor ratio or there may

apitallabor ratios. However, this paper would not rule them out toexamine multiple equilibria.
Suppose that the pri e of the middle-intensive good in reases while holding the pri e of thelabor- andapital-intensive goods

onstant. Assume that this in rease is not large enough toause a single FPE in the world. In other words, the world
after theonsists of two FPE sets before andhange in the pri e. Regardless of whether the labor-(orapital-)intensive good is theinvestment good, however, the following lemmas are obtained at the steady state.

LEMMA 1: An in rease in the pri e of the middle-intensive good de reases per apita GDP
and in reases in ome inequality for developing

ountries.

PROOF. See Appendix A1.

LEMMA 2: An in rease in the pri e of the middle-intensive good 1) de reases per apita
onsumption if r̄1 > n + d ; 2) in reases per apita onsumption if r̄1 < n + d ; and 3) has noeffe t on per apita onsumption if r̄1 = n + d for developing ountries.
PROOF: See Appendix A1.
Next, suppose that the pri e of the labor-intensive good in reases, holding the pri e of the
middle- andapital-intensive goods

onstant. Similarly to thease of the pri ehange in the

middle-intensive good, the following lemmas are obtained at the steady state.

LEMMA 3: An in rease in the pri e of the labor-intensive good in reases per apita GDP andde reases in ome inequality for developing

ountries.

PROOF: See Appendix A2.

LEMMA 4: An in rease in the pri e of the labor-intensive good 1) in reases per apita
onsumption if r̄1 > n + d ; 2) de reases per apita onsumption if r̄1 < n + d ; and 3) has noeffe t on per apita onsumption if r̄1 = n + d for developing ountries. PROOF: See Appendix
A2.

3 Lo al Fa tor Abundan e and Trade Poli y
3.1

Lo al fa tor abundan e and trade patterns

This se tion introdu es the lo al fa tor abundan e into the model. As dis ussed in Se tion 1,
the lo al fa tor abundan e means that developing
8

ountries lo ate in the same

one but havedifferent steady-state

apitallabor ratios be ause, for example, they have different savings rates.

Suppose that the developing ountries are divided into two groups. One group has a high savings
rate.

Countries in this group have a relatively high steady-state

are lo ally

apitallabor ratio (i.e., theyapital abundant) and, therefore, have a relatively high steady-state perapita GDP

among the developing ountries. The other group has a low savings rate. Countries in this group
have a relatively low steady-state

apitallabor ratio (i.e., they are lo ally labor abundant) and,

therefore, have a relatively low steady-state perapita GDP among the developing

ountries.

To simplify the terminology, industrialized ountries are referred to as high-in ome ountries.
The lo ally

apital-abundantlabor-abundantountries are referred to as middle-in ome

ountries are referred to as low-in ome

is summarized in Table 1.

ountries. The

ountries. The lo allylassi ation of

ountries

I denote the savings rates of the high-, middle-, and low-in ome

ountries by sH , sM , and sL , respe tively. I denote the steady-state apitallabor ratios of the high, middle-, and low-in ome



assume that the high- and middle-in ome

ountries have the same savings rates (sH = sM = s).

This, in turn, means that the middle-in ome
the high-in omeountries by kH , kM , and kL , respe tively. For analyti al simpli ity,
ountries have the same behavioral parameters as

ountries.

Figure 6 presents the global and lo al fa tor abundan es in the three-good, two- one model.
Be ause savings ome from wages, the high-in ome ountries onverge to the higher steady statekH , whereas the middle-in ome

ountriesonverge to the lower steady state kM . In addition,owing to the different savings rates, the low-in omestate kL . These are dynami

ountries

equilibria analogous to the stati

onverge to further lower steadyequilibria in Figure 1.

=== Figure 6 ===Assume that the differen e in savings rates between the middle- and low-in ome
is large enough to generate the different trade patterns between theseountries

ountries. Figure 7 showsthese patterns. The low-in ome ountries export the labor-intensive good and import the middleintensive andapital-intensive goods. The middle-in ome

good and import the labor-intensive andexport theountries export the middle-intensive

apital-intensive goods.

The high-in ome

ountries

apital-intensive good and import the labor-intensive and middle-intensive goods.
=== Figure 7 ===3.2

Effe ts of trade poli y

In this model, there are three types of prote tion utilized by a developing
and middle-in ome
in omeountries restri t the imports of theountries. Se ond, the low-in ome

good from the middle-in ome

ountry. First, the low-

apital-intensive good from the high-ountries restri t the imports of the middle-intensive

ountries. Third, the middle-in omeof the labor-intensive good from the low-in ome

ountries restri t the imports

ountries. For analyti al simpli ity, following

Deardorff (2001), I assume that tariff revenue is used for9onsumption.

9 This assumption implies that the tariff revenue is not saved su h that the savings are a onstant fra tion of
the wages. If tariff revenue is used for savings, trade poli y auses hanges in pri es and savings. The in rease in9

First, onsider the ase where the middle- and low-in ome ountries restri t the imports of theapital-intensive good from the high-in ome ountries. At the steady state, I obtain the following
propositions.

PROPOSITION 1: The imposition of prote tion by a low- or middle-in ome ountry on theimports of theperapital-intensive good from high-in ome

apita GDP if theprote tion lowers per

apital-intensive good is theapita GDP if theountries has no effe t on the former's

onsumption good. On the other hand,apital-intensive good is the investment good.

PROOF: See Appendix A3.

PROPOSITION 2: The imposition of prote tion by a low- or middle-in ome ountry on theimports of the
per

apita

apital-intensive good from high-in ome

onsumption if a

apital-intensive good is theapital-intensive good is the investment good, perapitar̄1 > n + d ; 2) in reases when r̄1 < n + d ; and 3) isountries has no effe t on the former's
onsumption good. If theonsumption: 1) de reases when

onstant when r̄1 = n + d .

PROOF: See Appendix A3.

PROPOSITION 3: The imposition of prote tion by a low- or middle-in ome ountry on theimports of theapital-intensive good from high-in ome

in ome inequality irrespe tive of whether theountries has no effe t on the former's

apital-intensive good is theonsumption good or

the investment good.
PROOF: See Appendix A3.
The intuition behind Proposition 3 is that the pri e of theno effe t on the pri e of other goods orapital-intensive good p3 either has

auses proportional in reases in fa tor pri es. The pro-portional in reases do not affe t the rentalwage ratio and, therefore, in ome inequality is notaffe ted.
Note that trade liberalization has the opposite effe t to prote tion. Three ndings stand out
from Propositions 13. First, trade liberalization by a developingperapita GDP growth. If thetion raises per

ountry is not harmful to its

apital-intensive good is the investment good, trade liberaliza-

apita GDP. If theliberalization has no effe t on perapital-intensive good is not the investment good, then trade
apita GDP.

Se ond, the effe t of trade liberalization by a developing

ountry on its

onsumption is am-

biguous in the sense that the effe t depends upon the relationship between r̄1 and n + d .
r̄1 > n + d , trade liberalization has a positive effe t on perr̄1 < n + d , trade liberalization has a negative effe t on perplies that the effe t on per
If theperapita

onsumption.

However, if

onsumption. This in turn im-

onsumption is different from the effe t on e onomi

growth.

apital-intensive good is the investment good and if r̄1 > n + d , trade liberalization raises

apita GDP and per
Finally, aapita

onsumption at the same time.

hange in the pri e of theapital-intensive good does not have any effe ts on therentalwage ratio in the low- and middle-in ome
ized

apita

apita

If

ountries operate in different

ountries. Be ause developing and industrial-

ones, developing

ountries import theapital-intensive goodsavings auses the in rease in per apita GDP. The effe t on onsumption be omes more omplex. However, in ome
inequality is not affe ted by the hanges in savings so long as the steady state lo ates in the one of diversi ation.
10

that is produ ed outside the developingtheountries'

one. Therefore, an in rease in the pri e ofapital-intensive good either has no effe t on the pri e of goods produ ed in the developing

ountries or it

auses proportional

hange in the pri e of thehanges. Thus, the rentalwage ratio is not affe ted by theapital-intensive good.

Next, onsider the ase where a low-in ome ountry restri ts imports from the middle-in ome
ountries. At the steady state, the following propositions are obtained.

PROPOSITION 4: The imposition of prote tion by a low-in ome ountry on imports of the
middle-intensive good from the middle-in ome
in ome inequality and lowers its per

ountries raises the low-in ome

PROOF: The imposition of prote tion by a low-in ome
middle-intensive good from the middle-in ome
middle-intensive good in the low-in omefrom Lemma 1.

ountry's

apita GDP.



ountry on the imports of theountries results in in reases in the pri e of theountry. Then, Proposition 4 is immediately derived

PROPOSITION 5: The imposition of prote tion by a low-in ome ountry on the imports of the
middle-intensive good from the middle-in ome
per

apita

ountries: 1) lowers the low-in ome

onsumption if r̄1 > n + d ; 2) raises its per

has no effe t on per

apita

apita

onsumption if r̄1 = n + d .

ountry's

onsumption if r̄1 < n + d ; and 3)

PROOF: As for the proof of Proposition 4, the imposition of prote tion by a low-in ome
ountry on the imports from the middle-in ome
the middle-intensive good in the low-in ome
derived from Lemma 2.
Finally,in ome

onsider theountries results in an in rease in the pri e ofountry. Thus, Proposition 5 is immediately

ase where a middle-in ome

ountry restri ts imports from the low-ountries. At the steady state, the following propositions are obtained.

PROPOSITION 6: The imposition of prote tion by a middle-in ome ountry on the imports of
the labor-intensive good from the low-in ome
in ome inequality and raises its per

ountries lowers the middle-in ome

ountry's

apita GDP.

PROOF: The imposition of prote tion by a middle-in ome

ountry on the imports of thelabor-intensive good from the low-in ome

ountries results in an in rease in the pri e of thelabor-intensive good in the middle-in ome

ountry. Then, Proposition 6 is immediately derived

from Lemma 3.



PROPOSITION 7: The imposition of prote tion by a middle-in ome ountry on the imports of
the labor-intensive good from the low-in ome
per

apita

ountries: 1) raises the middle-in ome

onsumption if r̄1 > n + d ; 2) lowers its per

has no effe t on perapita

onsumption if r̄1 = n + d .

apita

ountry's

onsumption if r̄1 < n + d ; and 3)

PROOF: As for the proof of Proposition 6, the imposition of prote tion by a middle-in ome
ountry on imports from low-in ome

ountries results in an in rease in the pri e of thelabor-intensive good in the middle-in omefrom Lemma 4.

ountry. Thus, Proposition 7 is immediately derived

11

Figure 8 presents the imposition of prote tion by a middle-in omeof the labor-intensive good from the low-in ome
assumes that s is unity so that the wage
An in rease in p1

urve

ountry on the imports

ountries. For illustrative purposes, Figure 8

an be treated as the perauses an upward shift of the se toral per

apita savings

urve.

apita produ tion fun tion of thelabor-intensive good z1 if Y1 is not the investment good (Figure 8 (a)). If Y1 is the investment
good, an in rease in p1

auses a downward shift of the se toral perof the middle-intensive good z2 and thein rease in the steady-statefrom z to z .

ABapita produ tion fun tions

apital-intensive good z3 (Figure 8 (b)). Thisapitallabor ratio from kA to kB and thus raises the perauses anapita GDP=== Figure 8 ===In addition, the in rease in p1 results in a downwardright shift of the rentalwage ratio
urve, whi h de reases the steady-state rentalwage ratio from r̄1A =w̄1A to r̄1B =w̄1B . Althoughboth low- and middle-in ome
on e onomi

ountries are globally labor abundant, the effe ts of trade poli y

growth and in ome distribution between theseountries differ be ause of the lo al

fa tor abundan e.
Trade liberalization has the opposite effe ts to prote tion. Therefore, Proposition 6 states that
trade liberalization by a middle-in ome ountry in relation to imports from the low-in ome ountries in reases the middle-in ome

ountry's in ome inequality while de reasing its per

apita

GDP. Moreover, Propositions 5 and 7 states that the effe t of trade liberalization by a developing

ountry (either the middle- or the low-in ome

ountry) on its per

apita

onsumption is

ambiguous.
Note that Propositions 47 hold irrespe tive of whether the imported good is the onsumption
or investment good.

This result is different from Mazumdar (1996), who showed that tradeliberalization would in rease growth only if it lowered the pri e of the investment good. Thisis for the following two reasons.

First, Mazumdar (1996)

onsidered an e onomy in whi h

fa tor intensities were the same between two se tors, whereas this paper

onsiders an e onomy

in whi h fa tor intensities are different. Se ond, Mazumdar (1996) assumed that savings
from in ome rather than wages, whereas the model in this paper assumes that savings
wages. If two se tors have different fa tor intensities and savingsin the pri e of theome

ome from

ome from wages, thehange

onsumption and investment goods have the same effe ts on fa tor pri es

regardless of the type of goods. The results of this paper do not depend upon what kinds of goods
are imported.
Table 2 summarizes the effe t of trade liberalization by a developing

ountry. Propositions

17 together imply that the effe ts of trade liberalization by a developing

ountry on e onomi

growth and inequality depend upon whi h goods theimported. If aountry imports and from where they areross- ountry regression study does not take into aount su h differen es, it is

not surprising that the effe ts of trade liberalization by developing

ountries on their e onomi

growth and in ome distribution be ome ambiguous.
=== Table 2 ===12In addition, Table 2 indi ates that these propositions are robust in the sense that the effe ts
on in ome inequality depend upon neither the relationship between r̄1 and n + d nor the kind ofgood, that is, whether the import is a numéraire good. The effe t on e onomi

growth does notdepend upon the relationship between r̄1 and n + d . Thus, it is not surprising that
regressions generate ambiguous results. The existen e of multiple
fa tor endowments within the sameone

ross- ountry

ones and the differen e inould be a possible explanation of these puzzles.

4 Con luding Remarks
The empiri al literature on trade liberalization ree ts two puzzles.
liberalization on e onomi
developing

First, the effe t of trade

growth is ambiguous. Se ond, the effe t of trade liberalization by

ountries on their in ome distribution is ambiguous. This paper attempts to explain

the two puzzles at the same time, based on a multiple- one neo lassi al growth model.
My model ombines the elements of Davis's (1996) view of stati multiple equilibria together
with the elements of Deardorff's (2001) model of trade and growth.

I fo us on new aspe ts

that are not explored in these previous studies: in ome distribution, perapita GDP, and perapita onsumption. My model shows that if developing ountries lo ate in different steady states
within the same FPE set, or the same diversi ation
ountryone, trade liberalization by a developing

ould in rease its in ome inequality while de reasing its per

onsumption. My results suggest that the existen e of multiple
states within the sameapita GDP and per

apita

ones and the multiple steadyone, or the existen e of global and lo al fa tor abundan es,

an be apossible explanation of these puzzles.
Note that although my paper

laries the two empiri al puzzles at the same time, it does

not examine the welfare effe ts involved. In addition, identifying the lo al fa tor abundan e ofdeveloping

ountries is an important empiri al question. These issues will be explored in thenext stage of my resear h.

Referen es
Baldwin, Ri hard E. (1992) Measurable Dynami Gains from Trade, Journal of Politi al E onomy, 100(1): 162-174.
Davis, Donald R. (1996) Trade Liberalization and In ome Distribution, NBER Working Paper,
No. 5693.
Davis, Donald R., David E. Weinstein, S ott C. Bradford, and Kazushige Shimpo (1997) Using International and Japanese Regional Data to Determine When the Fa tor Abundan e
Theory of Trade Works, Ameri an E onomi

Review, 87(3): 421-446.

Deardorff, Alan V. (1973) The Gains from Trade In and Out of Steady-State Growth, Oxford
E onomiPapers, 25(2): 173-191.

Deardorff, Alan V. (1974) A Geometry of Growth and Trade, Canadian Journal of E onomi s,
7(2): 295-306.

13

Deardorff, Alan V. (2000) Patterns of Trade and Growth a ross Cones, De E onomist, 148(2):141-166.
Deardorff, Alan V. (2001) Ri h and Poor Countries in Neo lassi al Trade and Growth, E onomi

Journal, 111(470): 277-294.

Edwards, Sebastian (1998) Openess, Produ tivity and Growth: What Do We Really Know?
E onomiJournal, 108(447): 383-398.

Frankel, Jeffrey A. and David Romer (1999) Does Trade Cause Growth? Ameri an E onomi
Review, 89(3): 379-399.
Galor, Oded (1996) Convergen e? Inferen es from Theoreti al Models, E onomi

Journal,106(437): 1056-69.
Goldberg, Pinelopi Koujianou and Nina Pav nik (2007) Distributional Effe ts of Globalizationin Developing Countries, Journal of E onomi

Literature, 45(1): 39-82.

Hahn, F.H. and R.C.O. Matthews (1964) The Theory of E onomi
nomi

Growth: A Survey, E o-

Journal, 74(296): 779-902.

Jones, Ronald W. (1974) The Small Country in A Many-Commodity World, Australian E onomi

Papers, 13(23): 225-236.

Jones, Ronald W. (1975) In ome Distribution and Effe tive Prote tion in a Multi-Commodity
Trade Model, Journal of E onomi

Theory, 11(1): 1-15.

Kiyota, Kozo (2007) Paths of Development and Wage Variations, RSIE Dis ussion Paper, No.
572, University of Mi higan.
Mazumdar, Joy (1996) Do Stati

Gains from Trade Lead to Medium-Run Growth? Journal of

Politi al E onomy, 104(6): 1328-1337.
Oniki, Hajime and Hirofumi Uzawa (1965) Patterns of Trade and Investment in a Dynami
Model of International Trade, Review of E onomi

Studies, 32(1): 15-38.

Rodriguez, Fran is o and Dani Rodrik (2000) Trade Poli y and E onomi Growth: A Skepti 's
Guide to the Cross-National Eviden e, NBER Ma roe onomi s Annual, 15: 261-325.
S hott, Peter K. (2003) One Size Fits All? He ks her-Ohlin Spe ialization in Global Produ tion, Ameri an E onomi

Review, 93(3): 686-708.

Stolper, Wolfgang F. and Paul A. Samuelson (1941) Prote tion and Real Wages, Review of
E onomiStudies, 9(1): 58-73.

Uzawa, Hirofumi (1961) On a Two-Se tor Model of E onomi

Growth, Review of E onomi

Studies, 29(1): 40-47.
Wa ziarg, Romain and Karen Horn Wel h (2003) Trade Liberalization and Growth: New Eviden e, NBER Working Paper, No. 10152.
Winters, Alan L. (2004) Trade Liberalization and E onomi
nomi

Journal, 114(493): F4-F21.

14

Performan e: An Overview, E o-

Table 1. Country Classification

Global factor abundance Local factor abundance

Trade

Export capital-intensive
good and import middleHigh-income countries
and labor-intensive
goods
Export middle-intensive
good and import capitalLocally capital abundant Middle-income countries
and labor-intensive
goods
Globally labor abundant
Export labor-intensive
good and import middleLocally labor abundant Low-income countries
and capital-intensive
goods

Globally capitalIndustrialized countries
abundant

Developing countries

Classification(Not examined in thispaper)

Table 2. Effects of Trade Liberalization
Trade liberalization

Income inequality

Per-capita GDP

Per-capita consumption

SourceLiberalization by thelow- and middle-income
countries on imports
from the high-income
countries

No effect

Liberalization by the
low-income countries onimports from the
middle-income
countries

Decrease

Increase

1) Decrease if r > n +δ2) Increase if r < n +δ3) No change if r = n +δPropositions 4 and 5

Liberalization by the
middle-income
countries on imports
from the low-income
countries

Increase

Decrease

1) Increase if r > n +δ2) Decrease if r < n +δ3) No change if r = n +δPropositions 6 and 7

1) Increase if the import 1) Increase if r > n +δis the numeraire good2) Decrease if r < n +δ2) No effect otherwise 3) No change if r = n +δPropositions 1-3

Figure 1. Global and Local Factor AbundanceIndustrialized country (high-income country)

Locally capital-abundant developing country(middle-income country)

Locally labor-abundant developing country(low-income country)

Figure 2. Relationship between Per-capita GDP and Capital-labor Ratio in the Three-good Two-cone Model

Figure 3. Relationship between Rental-Wage Ratio and Capital-labor Ratio in the Three-good Two-cone ModelFigure 4. Multiple Equilibria in the Three-good Two-cone Model

Figure 5. Patterns of Trade for the Three-good Two-cone Model
Developing countries

Industrialized countries

Figure 6. Global and Local Factor Abundances in the Three-good Two-cone Multiple-cone Model

Figure 7. Patterns of Trade for the Three-good Two-cone Model: Global and Local Factor AbundancesFigure 8. Protection by A Middle-income Country on Imports from Low-income Countries(a) Y 1 is not the investment good

Note: For illustrative purposes, s = 1 is assumed.

Figure 8. Protection by A Middle-income Country on Imports from Low-income Countries(b) Y 1 is the investment good

Note: For illustrative purposes, s = 1 is assumed.