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TEXTO PARA DISCUSSO N

141

THE RICARDIAN THEORY OF INTERNATIONAL TRADE:

A CRITICISM

Cludio Goni!o

S""#$%o d" &'''

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Ficha Catalogrfica

339.5

G641r

2000

Gontijo, Cludio.

The icardian Theor! of "nternational Trade# $

Critici%& ' (or Cludio Gontijo. )elo *ori+onte#

F-G'Cede(lar, 2000.

26(. Te/to (ara i%cu%%o, 141

1. elae% econ&ica% internacionai% -odelo%

&ate&tico%. 2. Co&7rcio internacional -odelo%

&ate&tico%. ". ni8er%idade Federal de -ina% Gerai%.Centro de e%en8ol8i&ento e laneja&ento egional.

"". T:tulo. """. ;7rie.

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UNI(ERSIDADE FEDERAL DE MINAS GERAIS

FACULDADE DE CI)NCIAS ECON*MICAS

CENTRO DE DESEN(OL(IMENTO E PLANE+AMENTO REGIONAL

THE RICARDIAN THEORY OF INTERNATIONAL TRADE:

A CRITICISM

Cludio Goni!o

rofe%%or do e(arta&ento de Ci

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SUM-RIO

1. ">T?CT"?> ............................................................................................................................... @

2. $ ;"-A= -?=A ?F A?>GB> ="A")"- "C=; F? T*= G?A ;T$>$ .. D 3. $ ;"-A= -?=A F? )$A$>C= G?ET* $A"T ................................................... 12

4. C?-$$T"= $$>T$G= $> ?F"T$)"A"T ............................................................ 13

5. C?-$$T"= $$>T$G=, )$A$>C= ?F T$=, $> G?ET* .............................. 16

6. C?-$$T"= $$>T$G=; $> ?F"T $T= =$A"H$T"?> ................................ 16

@. C?-$$T"= ? $);?AT= $$>T$G=;I .................................................................... 1@

D. C?-$$T"= $$>T$G=; $> T*= =JC*$>G= $T= ............................................. 19

9. $ >-="C$A =J$-A= ............................................................................................................ 20

10. C?>CA;"?>; ............................................................................................................................... 23

)")A"?G$* .................................................................................................................................... 24

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1. INTRODUCTION

For al&o%t tKo centurie%, the theor! of international trade ha% Leen entirel! do&inated L! the

(rinci(le of co&(arati8e ad8antage. ?riginall! for&ulated L! icardo or Torren% La%ed on the laLor

theor! of 8alue,1 thi% (rinci(le Ka% incor(orated into the %u((l!BandBde&and a((roach, through the

*ecM%cherB?hlin &odel.2=8en the neoBicardian or ;raffian %chool, Khich critici+ed the *ecM%cherB

?hlin &odel on the ground% that it i% incon%i%tent Khen (roduced ca(ital good% are introduced a&ong a

countr!N% in(ut%,3ha% al%o (re%er8ed the (rinci(le of co&(arati8e ad8antage,4Khich ha% thu% found onl!

a feK critic% %o far, liMe ;haiMh 19@9a and 19@9L, Kho ne8erthele%% ha% not (re%ented a full!

for&ali+ed alternati8e &odel.

*oKe8er, a% Kill Le %hoKn later, neither icardoN% (rinci(le of co&(arati8e co%t% nor it% neoB

icardian 8er%ion %ee& to Le co&(atiLle Kith the conce(t of longBrun eOuiliLriu& (rice% icardoN%

Pnatural (rice%Q Khen &one! i% a co&&odit! liMe gold. The rea%on i% that neither laLor i% traded again%t

laLor nor co&&oditie% are traded again%t co&&oditie%. Co&&oditie% are traded again%t &one! %o that

co&(aring relati8e (rice% in different countrie% do not &aMe %en%e. Ehat &atter% are (rice% in ter&% of

gold, that i%, aL%olute (rice%. =8en in an econo&! Khere fiat &one! taMe% the (lace of co&&odit!

&one!, although the e/change rate can indeed &aMe roo& for a co&&odit! that Ka% (re8iou%l!

e/cluded fro& the international &arMet, there i% little roo& for the (rinci(le of co&(arati8e ad8antage.

The oLjecti8e of thi% article i% to addre%% the Oue%tion of international trade under the light of the

theor! of long run eOuiliLriu& (rice%. articular attention i% gi8en to the (rinci(le of co&(arati8e

ad8antage and the relation%hi( LetKeen free trade and efficienc!. To a8oid a long di%cu%%ion o8er i%%ue%

that are not the &ain concern of thi% article, the financial a%(ect% of international trade Kill Le ignored.

Thi% article i% co&(o%ed L! ten %ection% and one a((endi/. ;ection 2 (re%ent% a %i&(le &odel of

longBrun eOuiliLriu& (rice% for the gold %tandard, that i%, an econo&! Kith co&&odit!B&one! gold.

;ection 3 di%cu%%e% the dual of the (rice %!%te&, Khich i% the %!%te& of %ectorall! Lalanced groKth.

;ection% 4 to 6 (re%ent the argu&ent in fa8or of the (rinci(le co&(arati8e ad8antage and di%cu%% the

relation%hi( LetKeen free trade, (rofitaLilit!, Lalance of trade and econo&ic groKth. The critici%& on the

(rinci(le of co&(arati8e ad8antage% i% (re%ented in %ection @. ;ection D di%cu%%e% the relation%hi( LetKeen

trade and the e/change rate. $ nu&erical e/a&(le i% %hoKn in %ection 9 and the conclu%ion% are li%ted in

%ection 10. The $((endi/ di%cu%%e% -ori%hi&aN% contention that the laLor theor! of 8alue ha% no relation to

deter&ining the co&(arati8e ad8antage LetKeen tKo countrie%.

1

Chi(&an 1966, (. 4D2 argue% that Pit Kould Le fair to %a! that Loth Torren% and icardo contriLuted in e%%ential Ka!% to thede8elo(&ent of the laK of co&(arati8e ad8antageR and that credit for the (rinci(al di%co8er! %hould go to Torre%Q.

2 ;ee ;a&uel%on, 194D and 1949R Aerner, 1952R Sone%, 1956R Sohn%on, 195@R )hagKati and ;rini8a%an, 19D4.

3 ;ee -etcalfe and ;teed&an, 19@2 and 19@3R =8an%, 19D9a.

4 The ;raffian author% recogni+e the (o%%iLilit! of lo%%e% fro& free trade arri8ing fro& the nonBo(ti&alit! of the choice of

%(eciali+ation or fro& a te&(orar! fall in e&(lo!&ent in an econo&! that ado(t% the free trade regi&e. *oKe8er, Khen theecono&! groK% at it% &a/i&u& rate, the longBrun effect% of international trade are (o%iti8e, leading to an outKard %hift in theKageB(rofit and the con%u&(tionBgroKth frontier%. ;ee -ainKaring, 19@3R arrinello, 19@3R -etcalfe and ;teed&an, 19@4,;teed&an, 19@9R =8an%, 19D9R and a%inetti, 1993.

@

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&. A SIMPLE MODEL OF LONG/RUN E0UILIRIUM PRICES FOR THE GOLD

STANDARD

The fir%t (reci%e definition of longBrun eOuiliLriu& (rice% can Le found in Cha(ter @ of )ooM " of

The Wealth of Nations, Khere ;&ith di%tingui%he% naturalQ (rice% fro& &arMet (rice%. Ehile the for&er%

are defined a% (rice% that alloK laLor, ca(ital, and land to Le re&unerated according to their ordinar! or

a8erage rate% ;&ith, 19@6 (. 62, the latter are concei8ed a% actual (rice% that de(end on the Lalance

LetKeen the Ouantit! %u((lied and the le8el of effectual de&and, the Ouantit! that Kould Le de&anded if

longBrun eOuiliLriu& (rice% (re8ailed in the &arMet. -arMet (rice% &a! either Le aLo8e, or LeloK, or

e/actl! the %a&e a% the natural (rice% ;&ith, 19@6 (. 63.

;&ith i% al%o clear regarding natural (rice% a% the (rice% that enca(%ulate the (er%i%tent force% in the

econo&ic %!%te&, in o((o%ition to &arMet (rice%, Khich de(end on te&(orar! and accidental factor%. The

central (o%ition of the natural (rice% i% a%%ured L! the (re%ence of econo&ic force% that are unlea%hed a%

%oon a% actual (rice% di8erge fro& natural (rice%. The%e force% co&(ri%e the adju%t&ent &echani%&, Khich

KorM% a% folloK%. "f the Ouantit! of a co&&odit! Lrought to the &arMet e/ceed% the effectual de&and, %o&e

co&(onent (art% of it% (rice &u%t Le (aid LeloK their natural rate, Khich &aMe% %o&e factor% of (roduction

to KithdraK fro& thi% e&(lo!&ent. The con%eOuence i% that the Ouantit! Lrought to &arMet decrea%e% until it

i% ju%t %ufficient to %u((l! the effectual de&and. Then, the &arMet (rice a% Kell a% the re&uneration of the

different factor% of (roduction ri%e u( to their eOuiliLriu& le8el%. The o((o%ite taMe% (lace Khen the Ouantit!

Lrought to &arMet fall% %hort of the le8el of effectual de&and ;&ith, 19@6, (. 65.

;&ith conclude% L! con%idering natural (rice% a% centers of gravity of &arMet (rice%# The natural

(rice, therefore, i%, a% it Kere, the central (rice, to Khich the (rice% of all co&&oditie% are continuall!

gra8itating. ifferent accident% &a! %o&eti&e% Mee( the& %u%(ended a good deal aLo8e it, and %o&eti&e%

force the& doKn e8en %o&eKhat LeloK it. )ut Khate8er &a! Le the oL%tacle% Khich hinder the& fro&

%ettling in thi% center of re(o%e and continuance, the! are con%tantl! tending toKard% it ;&ith, 19@6, (.

65.

icardo doe% not add an!thing neK to ;&ithU% anal!%i%, %ince he recogni+e% that in the @th cha(ter

of the Eealth of >ation%, all that concern% thi% Oue%tion VB the difference LetKeen &arMet (rice% and natural

(rice% and the gra8itation of the for&er% around the latter B W i% &o%t aLl! treated icardo, 1951, (. 101.

>e8erthele%%, icardo %hift% the e&(ha%i% toKard the fact that it i% the tendenc! to an unifor& rate of (rofit%

acro%% %ector% that Lring% aLout the (roce%% of gra8itation of &arMet (rice% around natural (rice%. *e

conclude%, thu%, that "t i% then the de%ire, Khich e8er! ca(itali%t ha%, of di8erting hi% fund% fro& a le%% to a

&ore (rofitaLle e&(lo!&ent, that (re8ent% the &arMet (rice of co&&oditie% fro& continuing for an! length

of ti&e either &uch aLo8e, or &uch LeloK their natural (rice icardo, 1951, (. 91.5

$ &odern e/(re%%ion of the ;&ithianBicardian conce(t of PnaturalQ (rice% &a! Le oLtained L!

u%ing &atri/ algeLra. To a8oid unnece%%ar! difficultie% not related to the Oue%tion under e/a&, it i% a%%u&ed

5 The %a&e conce(tion i% held L! -ar/, Kho (oint% out that it i% co&(etition of ca(ital% in different %(here%, Khich fir%t Lring% out

the (rice of (roduction eOuali+ing the rate% of (rofit in the different %(here% -ar/, 1D94, (. 1D0.

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a %i&(le econo&! %uLject to con%tant return% to %cale, Kithout joint (roduction and fi/ed ca(ital. The

turno8er ti&e of circulating ca(ital i% %u((o%ed to Le unitar!.6

"f thi% econo&! (roduce% n co&&oditie%, the %!%te& of longBrun eOuiliLriu& (rice% can Le

e/(re%%ed a%#@

2 X 2 AY K 3'Yr2 AYK 3' X 1 Yr2 AYK 3' 2.1

Khere 2i% the roK 8ector of longBrun eOuiliLriu& (rice%R Athe n L! n &atri/ of technical coefficient%R 3'the roK 8ector of laLor coefficient%R Kthe Kage rate and r the rate of (rofit%, Khich &ean% that 2Are(re%ent

raK &aterial unitar! co%t%, K3'%tand% for laLor unitar! co%t% and r2A Y K3' are (rofit% (er unit of (roduct

%ince 2A Y K3' re(re%ent% the a&ount of circulating ca(ital (er unit! of out(ut.

Con%idering 2.1 a% a %!%te& of %"l3i"(rice%, it can Le %een that it ha% n inde(endent eOuation%

and nY1 unMnoKn% %uch that it ha% one degree of freedo&. )ut icardo %u%tain% that the tKin conce(t% of

co&(etition and nor&al (rice% al%o hold in the laLor &arMet %o that the (rice of laLor (oKer con%idered a%an ordinar! co&&odit! %hould Le eOual to it% co%t% of (roduction. Thi% idea can Le for&all! e/(re%%ed

through the Kage eOuation#

K X2 d 2.2

Khere di% the colu&n 8ector re(re%enting the gi8en Kage La%Met, Khich i% the real Kage deter&ined L!

the P%uL%i%tenceQ reOuire&ent% of the laLor force.

;uL%tituting 2.2 into 2.1 gi8e% a %!%te& of ho&ogeneou% eOuation%, Khich %olution reOuire%#

det V

B A Yd3'W X 0

2.3

Khere

X1'1Yr 2.4

>ote that %ince the technical (ro(ertie% of the econo&ic %!%te& &u%t Le %uch a% to (er&it the

(roduction of at lea%t %o&e (roduct in addition to tho%e needed for the re(lace&ent of the &ean% of(roduction u%ed u( in the (roduction (roce%% and to tho%e nece%%ar! to %ati%f! KorMer%U need%, the %(ectral

radiu% of the &atri/ A Y d3', &a/, %hould Le le%% than unit!. >oK, if in addition A Y d3' i% a%%u&ed to Le

6 The %!%te& (re%ented LeloK i% the %a&e a% -ori%hi&aN% 1990, ((. 126B146.

7 Aand i% e/cluded Lecau%e icardo con%ider% ground rent alKa!% a% differential rent %o that it doe% not enter (rice deter&ination the

Pnatural (riceQ of agricultural (roduct% are deter&ined in the land of higher co%t%.

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irreduciLle, it folloK% fro& the erronBFroLeniu% theore& that it% eigen8ector 2 a%%ociated Kith it%

&a/i&u& eigen8alue, &a/, and defined in the identit!

2V&a/ A Y d3'W X 0 2.5

i% (o%iti8e %ee Graha&, 19D@, ((. 112B6DR a%inetti, 19@@, ((. 26@B@6. >ote that thi% eigen8ector i% uniOue

Kith the onl! Oualification that it% length i% undefined# an! other 8ector of the for& M2Khere M i% a con%tant

different fro& +ero i% al%o a %olution of the aLo8e characteri%tic eOuation. "n other Kord%, once the

technolog! and the real Kage are MnoKn, the cla%%ical %!%te& of longBrun (rice% !ield% a %olution that e/i%t%

and i% uniOue Lut for a (ro(ortional factor.

?nce the e/i%tence and uniOuene%% of eOuiliLriu& ha8e Leen e%taLli%hed, it i% (o%%iLle to %hoK the

in8er%e relation%hi( LetKeen the (rofit rate and the real Kage. Fir%t, a%%u&e that the co&(o%ition of the real

Kage i% fi/ed Lut it% le8el i% 8ariaLle#

d 5 d 2.6

Khere 0 &a/. The &a/i&u& real Kage &a/dcorre%(ond% to that %ituation Khere the econo&ic

%!%te& doe% not (roduce an! %ur(lu%, %uch that all the (roduct i% reOuired to re(lace the &ean% of

(roduction u%ed u( in the (roduction (roce%% and to %ati%f! KorMer%U need%. Then the folloKing condition

hold%#

det V

A Y &a/d3'W X 0

Khich &ean% that

&a/X 1

$%%u&ing then a gi8en technolog! Khich corre%(ond% to a &atri/ of technical coefficient% Aand a

8ector of laLor coefficient% 3', the ele&ent% of the &atri/ A Y d3' Kill Le a cre%cent function of the real

Kage le8el . )ut Lecau%e the erronBFroLeniu% Theore& %tate% that the %(ectral radiu% &a/of a nonB

negati8e &atri/ i% a cre%cent function of it% ele&ent%, it folloK% fro& 2.4 that the (rofit rate i% an in8er%e

function of the ele&ent% of the real Kage %ee Figure 1.

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Fi6u%" 1: 736"/P%o8i Cu%"

r

0

*a8ing e/a&ined the deter&ination of the (rofit rate and the eOuiliLriu& (rice% La%ed on a gi8en

technological %et, A, 3', and the real Kage, d, the onl! Oue%tion that re&ain% regarding the e/i%tence of

eOuiliLriu& i% then the choice of technolog!, Khich &ean% the choice of the ele&ent% of &atri/ A and

8ector 3'.

?Mi%hioU% Theore& ?Mi%hio, 1961R oe&er, 19DD, ((. 9@B9D &a! Le u%ed to addre%% thi% Oue%tion.

$%%u&ing a gi8en real Kage d, co&(etition force% the entre(reneur% of each %ector to u%e the a8ailaLle

technolog! a%%ociated Kith the loKe%t co%t of (roduction. ?Mi%hioU% Theore& en%ure% that the re%ulting

technological %et, A, 3', Kill Le a%%ociated Kith the highe%t (rofit rate r %o that the %olution of the (roLle&

of techniOueN% choice i% eOui8alent to the choice of the (articular technological %et a%%ociated Kith the

loKe%t &a/.

$% %een, the ;&ithianBicardian theor! of 8alue and di%triLution de8elo(ed aLo8e i% %ufficient to

deter&ine all relati8e (rice% and the %hare% of the different factor% of (roduction in the (roduct. *oKe8er,

the %!%te& i% o(en %ince the (rice le8el re&ain% undeter&ined. To clo%e it Loth ;&ith 19@6, ((. 25B26 and

icardo 1D11, (. @4 a%criLe to a %(ecific co&&odit! the role of &one!.D$% *aKtre! 1950, (. 1@ a%%ert%,

according to the cla%%ical theor! of &one! ..., &one! i% a %elected co&&odit! %ee al%o icMer%, 19@5, (.

4D3. $ unit! of thi% co&&odit! B %a!, a gold coin B i%, then, the %tandard of 8alue of the (rice %!%te 9

8 -ar/ al%o KorM% Kith co&&odit!B&one!. ;ee -ar/, 1D6@, 8ol. ", (. @4.

9 >ote that (rice% in ter&% of gold coin% &a! di8erge fro& (rice% in ter&% of Lullion in the long run due to tKo cau%e% ;&ith,

1996, (. 52. Fir%t, the (rice of Lullion differ% fro& the (rice of (roduction of gold coin% L! the co%t% of coinage, if noadditional %tate %eignorage i% charged. ;econd, the Kear and tear of coin% due to the circulation (roce%% &a! cau%e their realKeight to Le different fro& their no&inal Keight. To a8oid additional and unnece%%ar! difficultie%, it i% %u((o%ed in thi%%tud! that the co%t of coinage i% co8ered L! the %tate and that the coin% re&ain in full Keight L! an efficient &anage&ent,Khich &ean% that there i% no di8ergence LetKeen (rice% in ter&% of coin% and (rice% in ter&% of gold in the long run.

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(oX 1 2.@

=Ouation 2.@ clo%e% the ;&ithianBicardian (rice %!%te& alloKing the deter&ination of (rice

le8el. Therefore, eOuation% 2.1, 2.2, and 2.@ con%titute the ;&ithianBicardian (rice &odel, Khich

deter&ine% the di%triLuti8e 8ariaLle% K and r and aL%olute (rice% 2X 2'(o. "t %hoK% that (rice le8el de(end%

in the long run u(on the (urcha%ing (oKer of the co&&odit!B&one!, i.e., on it% (rice of (roduction 8i%BaB8i%

the (rice of (roduction of the other co&&oditie%.

9. A SIMPLE MODEL FOR ALANCED GRO7TH DUALITY;

$lthough the &odel outlined in %ection 2 alloK% to e/a& the i&(act% of international trade u(on

econo&ic efficienc! &ea%ured L! the rate of (rofit%, it doe% not ha8e the ele&ent% to %tud! the relation%hi(

LetKeen international trade and econo&ic groKth.

To addre%% thi% Oue%tion, it i% nece%%ar! to con%ider the Lalance LetKeen %u((l! and de&and for all

co&&oditie%. $%%u&ing that there i% no technical (rogre%%, that con%u&er%N (reference% are con%tant o8er

ti&e,10that KorMer% do not %a8e and that, a% in ue%na!N% Tableau Economique or in -ar/N% %che&e% of

re(roduction, (roduction in one (eriod i% con%u&ed in the ne/t one, the Lalance LetKeen %u((l! and

de&and in all %ector &a! Le de%criLed a%

1i% the 8ector of ca(itali%tic de&and for

con%u&(tion good%.

$%%u&ing that groKth i% %ectorall! Lalanced i.e., that all %ector% groK at the %a&e rh!th& 11, it

folloK% that#

1 X 1 Y g

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V 1 Y gA Yd3'W

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X 1'&a/ 1 4.2

the h!(othe%i% that ortugal i% le%% de8elo(ed that the re%t of the Korld &a! Le e/(re%%ed a%

&a/ZAY d 3'[ \ &a/ZA Y d3'[.

Khere &a/ZAYd3'[ i% the %(ectral radiu% of &atri/ A Y d 3' and &a/ZAYd3'[ i% the %(ectral

radiu% of AYd3'.

Co&(aring 2.4 and 4.2 and con%idering that X &a/, it i% clear that the %ur(lu% rate i% eOual to

the (rofit rate#

X r 4.3

Khich &ean% that the %u((o%ition that ortugal i% le%% de8elo(ed than the re%t of the Korld i% eOui8alent to

the h!(othe%i% that the re%t of the KorldN% econo&! ha% a higher (rofit rate than the ortugue%e econo&!

rR\ rP.

"f thi% i% the ca%e, it Kould not Le not difficult to (ro8e that at lea%t one (rice in the re%t of the Korld

i% loKer than in ortugal.12 Thi% i&(lie% that, if it (re8ail% a free trade regi&e and if tran%(ortation co%t% are

null, ortugue%e &erchant% Kill i&(ort tho%e co&&oditie% that are chea(er in the re%t of the Korld Khile

&erchant% fro& the re%t of the Korld Kill (urcha%e tho%e co&&oditie% that are chea(erl! (roduced in

ortugal. "&(ort% Kill then taMe the (lace of do&e%tic (roduction for tho%e co&&oditie% that are chea(erl!

(roduced in the re%t of the Korld %o that the corre%(onding colu&n% in the ortugue%e &atri/ A Kill

Leco&e null and %o the corre%(onding entrie% in the ortugue%e do&e%tic (rice 8ector 2. $fterBtrade (riceeOuation Kill then a%%u&e the for&

2X 1 Y rT 2AY 2AY K3' 4.4

Khere rTP re(re%ent% afterBtrade ortugue%e rate of (rofit, A i% the ortugue%e afterBtrade &atri/ of

technical coefficient% of do&e%ticall! (roduced good%R A i% the ortugue%e &atri/ of technical

coefficient% of i&(orted good%R Ki% the ortugue%e Kage rateR and 3'%tand% for the ortugue%e roK

8ector of laLor coefficient%.

)ut %ince the Kage La%Met &a! include i&(orted good% a% Kell, the Kage eOuation Leco&e%

KX 2dY 2d 4.5

12 $%%u&e that 22. -ulti(l!ing Loth %ide% L! AY d3' X M!ield% 2RM 2M, or 2M.j'(j2M.j'(j.)ecau%e 2M.j'(jX, it folloK% that2M.j'(j. )ut %ince 22it folloK% that &inj2M.j'(j ]] &inj2M.j'(j, Khich i% a contradiction.

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Khere d and d %tand for the colu&n 8ector% of ortugue%e do&e%tic and i&(orted Kage good%

re%(ecti8el!.

;uL%tituting 4.5 into 4.4 !ield%

2X 1 Y rT V2AY 2AY 2dY 2d 3'W 4.6

>oK, a%%u&ing that &atri/ V

1 Y rTAY d3'W i% nonB%ingular, it folloK% that#

2X 1 Y rT 2AY d3'V 1 Y rTAY d3'WB1 4.@

The nece%%ar! and %ufficient condition to ha8e a nonB%ingular &atri/ V

1 Y rTAY d

3'W and a nonBnegati8e V 1Y rTAY dP3'WB1, Khich i% reOuired to oLtain a nonBnegati8e (rice

8ector 2, i% gi8en L!

rT\ rP 4.D

To %ee Kh!, reKrite eOuation 4.@ a%

2X 2AY d3'V AY d3'WB1

Khere X 1'1 Y rT. ;ince 2and AY d3' are nonBnegati8e, it folloK% that &atri/ V APY

d3'WB1&u%t e/i%t and Le nonBnegati8e to en%ure the nonBnegati8ene%% of 2. )ut thi% douLle condition

can Le %ati%fied onl! if \ &a/ZAYd 3'[. "n thi% ca%e, V AP Y d 3'W Leco&e% a

-aiaMo8%M! &atri/, Khich i% nonB%ingular and nonBnegati8e L! definition Graha&, 19D@, ((. 169B@0.

>oK, %ince i% a &onotonicall! increa%ing function of the ele&ent% of it% corre%(onding &atri/ and the

difference LetKeen AYd3' and AYd3' i% that the for&er include% %o&e colu&n% that are null

in the latter, it folloK% that &a/ZAYd3'[ &a/ZAYd3'[. Condition 4.D folloK% then fro& the

fact that, according to 2.4, rTPX 1'&a/AYd3'1 and rPX1'&a/AYd3'1.

Condition 4.D i% %triMing, Lecau%e it %hoK% that %(eciali+ation re%ult% in a higher rate of (rofit%,

confir&ing the co&(arati8e ad8antage (rinci(le. 13

13 "n thi% %en%e, (roduction %(eciali+ation induced L! free trade can Le 8ieKed a% a (articular ca%e of choice of techniOue#

according to the (rofit &a/i&i%ing criterion -ainKaring, 19@3.

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@. COMPARATI(E AD(ANTAGE? ALANCE OF TRADE? AND GRO7TH

To con%ider the relation LetKeen econo&ic %(eciali+ation, Lalance of trade and econo&ic groKth,

a%%u&e that the ortugue%e econo&! i% groKing at it% &a/i&u& rate. nder a free trade regi&e, it% i&(ort%,

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To e/tend the &odel de8elo(ed in the (re8iou% %ection% to the Korld econo&! the fir%t %te( i% to

con%ider that ortugalN% i&(ort% re(re%ent the re%t of the KorldN% e/(ortN% and ortugalN% e/(ort% are the re%t

of the KorldN% i&(ort%#

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r-X 1'&a/{A-Y d-3'-[ 1 @.2

and, acce(ting the icardian notion of co&&odit!B&one!, the (rice le8el i% %till deter&ined L! 2.@.15

$t thi% %tage of anal!%i%, it %ee&% clear that the icardian theor! of co&(arati8e ad8antagein8olucrate% a contradiction# a%%u&ing that the Korld econo&! can Le di8ided in tKo different (art%

ortugalN% econo&! and the re%t of the Korld econo&! it i% not difficult to %ee that, although trade

liLeration increa%e% ortugalN% (rofit rate, it &a! cau%e the re%t of the KorldN% (rofit rate to fall.

The Oue%tion i% that, unle%% the ortugue%e econo&! ha% aL%olute ad8antage% in %o&e %ector%, it%

&erge Kith the re%t of the KorldN% econo&! cau%e% a lo%% of efficienc! and (roduce% a loKer rate of (rofit

for the re%t of the KorldN% econo&!. To (ro8e thi% (ro(o%ition it i% %ufficient to a%%u&e that ortugal ha% no

aL%olute ad8antage in an! %ector and ne8erthele%% (artici(ate% in the Korld econo&!. "n thi% ca%e, the

%(ectral radiu% of &atri/ [AYd3'W Kill Le loKer than the %(ectral radiu% of &atri/ [A-Yd-3'-W. $% a

re%ult, Loth the KorldN% afterBtrade %ur(lu% rate and (rofit rate Kould Le loKer than the re%t of the KorldN%autarchic %ur(lu% rate and (rofit rate#

RX rR\ MX rM @.3

$nother Ka! to looM at the %a&e Oue%tion i% through ?Mi%hioN% Theore&, Khich en%ure% that a gi8en

technolog! Kill Le u%ed onl! if, at the (re8ailing (rice%, the co%t% of (roduction re%ulting fro& the u%e of

thi% technolog! i% loKer or eOual than the co%t% of (roduction a%%ociated Kith the (re8ailing technolog!. "n

other Kord%, if ortugal u%e% a gi8en techniOue to (roduce co&&odit! j, it Kill continue (roducing it after

ado(ting free trade if and onl! if

2-A.jY d3'j 2-A.jY d3'j @.4

Con8er%el!, a%%u&ing a Korld econo&! co&(o%ed L! ortugal and the re%t of the Korld and

%u((o%ing that ortugal ha% no aL%olute ad8antage in (roducing an! co&&odit!, the re%t of the KorldN%

entre(reneur Kould u%e their technolog! to e/(el ortugue%e (roducer% fro& the Korld &arMet.

"n %u&, in an econo&! Khere gold i% the %tandard of 8alue, there can not Le an! (rinci(le of

co&(arati8e ad8antage%# aL%olute ad8antage% in the Korld econo&! and a countr! that doe% not (roduce

an! co&&odit! at co%t% eOual or loKer than the other countrie% i% %i&(l! e/cluded fro& the Korld econo&ic%!%te&.

15)! a%%u&(tion, &one! gold i% (roduced in onl! one countr!.

1D

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. COMPARATI(E AD(ANTAGES AND THE EXCHANGE RATE

$lthough the aLo8e rea%oning i% 8alid for an econo&! Kith co&&odit!B&one!, it doe% not %ee& to

Le e/tendaLle to an econo&! Kith fiat &one! Lecau%e in thi% econo&! the laK of one (rice doe% not hold

and international (rice% are related to do&e%tic (rice% through the e/change rate e %uch that (rice %!%te&

of countr! Leco&e%#

2X 1 Y rTP V2AY e 2AY 2d3'Y e 2d3'W D.1

The introduction of the e/change rate &aMe% roo& for a KeaM 8er%ion of the co&(arati8e ad8antage

theor!. )ecau%e a countr! liMe ortugal Kill continue u%ing an a8ailaLle techniOue to (roduce co&&odit!

j after ado(ting free trade if and onl! if

2A.jYd3'j Y e2 A.jYd3'j e2A.jYd3'j Y 2A.jYd3'j

it folloK% that it can &aMe thi% techniOue co&(etiti8e in the international &arMet deter&ining the e/change

rate greater than the Ouotient LetKeen the difference LetKeen the do&e%tic co&(onent of the co%t of

(roduction in countr! and the i&(orted co&(onent of co%t of (roduction in the re%t of the Korld and the

difference LetKeen the do&e%tic co&(onent of the co%t of (roduction in the re%t of the Korld and the

i&(orted co&(onent of co%t of (roduction in countr! #

2A.jYd3'j 2A.jYd3'j

e BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB D.2

2 A.jYd3'j

A.jYd3'j

The co%t of %uch a (olic! for countr! , hoKe8er, can Le high in ter&% of inflation, Lecau%e, a%

identit! D.3 %hoK%, in an econo&! Kith fiat &one! the e/change rate KorM% a% the anchor for the (rice

le8el16

2X 1 Y rT e 2AY d3'V 1 Y rTAY d3'WB1 D.3

For the Korld econo&! the co%t of u%ing the e/change rate a% a co&(etiti8e 8ariaLle i% al%o high in

ter&% of lo%% of efficienc!. "ndeed, introducing the e/change rate in the KorldN% (rice %!%te& gi8e%

2-]"\ X 1 Y r- 2-]"\ A-Y d-3'-

16 The role of the e/change rate a% an anchor for the (rice le8el in o((o%ition of the intere%t rate and &onetar! control ha%

Leen de&on%trated L! the effect of e/change rate a((reciation on the do&e%tic (rice le8el, and L! the &an! %taLili+atione/(erience% of currencie% %uLject to high inflation' h!(erinflation in thi% centur!. ;ee, for in%tance, Hini, 1993.

19

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Khere ]"\ %tand% for the diagonal &atri/ of e/change rate%. )ecau%e it i% nonB%ingular, the international

(rice %!%te& &a! Le e/(re%%ed a%#

2-X 1 Y r- 2-]"\ A-Y d-3'- ]"\B1 D.4

Khich &ean% that the international (rofit rate i% %till deter&ined L! identit! @.2 %ince

&a/{]"\ A-Yd-3'- ]"\B1[ X &a/{]"\[ &a/ZA-Yd-3'-[1'&a/{]"\[

X &a/ZA-Yd-3'-[

)ut %ince &atri/ A-Yd-3'- include% %o&e ortugue%e indu%trie% that ha8e higher co%t% than

the re%t of the Korld corre%(onding %ector%, it can Le concluded that the Korld econo&! that co&e%

aLout fro& ortugalN% u%e of the e/change rate to &aMe roo& for the%e indu%trie% i% le%% efficient then

the %!%te& that Kould re%ult fro& ortugal e/clu%ion fro& the Korld econo&!.

. A NUMERICAL EXAMPLE

To ha8e a clearer under%tanding of the i%%ue% in8ol8ed in thi% di%cu%%ion, %u((o%e tKo

econo&ie% characteri+ed in the folloKing Ka!#

ortugal

AX 0.3 0,D 3'X 0.2 0.10.3 0,2

DX 0.40.4

e%t of the Korld#

AX 0.4 0.5 3'X 0.2 0.10.1 0.3

dX 0.40.4

%ing 2.1 it can Le %een that ortugalN% Lefore trade (rofit rate, r, i% 13.@3^, Khile the re%t of

the KorldN% Lefore trade (rofit rate, r, i% 3@.0@^ and that, if co&&odit! 2 i% taMen a% the numeraireof

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the (rice %!%te& (2X(2X_ 1, then the (rice of co&&odit! 1 i% _ 0.@610@ in ortugal and _ 0.@2135 in

the re%t of the Korld. The no&inal Kage i% _ 0.@0443 in ortugal and _ 0.6DD54 in the re%t of the Korld.

"f the (rinci(le of co&(arati8e ad8antage KorMed, the ado(tion of free trade Kould force

ortugal to %(eciali+e in the (roduction of co&&odit! 2 and i&(ort co&&odit! 1 fro& the re%t of the

Korld. $%%u&ing that ortugal i% a P%&all econo&!Q in the %en%e that the (rice of co&&odit! 1 Kould

not change if ortugal joined the international econo&!, the co%t of (roduction of co&&odit! 2 Kould

fall to _ 0.D6D96, Khich i% loKer than it% Lefore trade co%t of (roduction _ 0.D@930. The (rofit rate

Kould increa%e to 15,09^, Khile the co%t of the Kage La%Met Kould fall fro& _ 0.@0443 to _ 0.69926. "n

other Korld, the (rofitBrate cur8e Kould %hift %uch that at the current real Kage there Kould Le an

increa%e in ortugalN% (rofit rate Figure 2.

Figure 2: Shifting of the Wage-Profit Curve

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.00 1.00 2.00 3.00 4.00

Real wage (

)

r

before trade

after trade

*oKe8er, the (rinci(le of co&(arati8e ad8antage a%%u&e% that the re%t of the Korld Kould

%(eciali+e in the (roduction of co&&odit! 1. $% a re%ult, the KorldN% econo&ic %!%te& Kould Le

characteri+ed L! the folloKing &atri/e%#

A-X 0.4 0.D 3'-X 0.2 0.1

0.1 0.2

d-X 0.40.4

Con%idering that in thi% econo&ic %!%te& the (rofit rate 30.39^ Kould Le loKer than the re%t

of the KorldN% Lefore trade (rofit rate and that the co%t of (roduction of co&&odit! 2 _ 0.@6694 Kould

Le higher, it i% clear that the re%t of the Korld Kould lo%e trading Kith ortugal. For the re%t of the Korld

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it Kould Le &ore (rofitaLle to (roduce co&&odit! 2 in%tead of Lu!ing it fro& ortugal. $% a

con%eOuence, ortugal Kould Le e/cluded fro& the international econo&!.

)ut in a Korld Khere the e/change can Le deter&ined L! the go8ern&ent, ortugal &a! change

it in order to &aMe it% (roduction of an! co&&odit! co&(etiti8e in the international &arMet. Figure 3

%hoK% the relation%hi( LetKeen ortugalN% e/change rate and the co%t of (roduction of co&&odit! 2 L!Loth ortugal and the re%t of econo&!. "f ortugalN% e/change rate Kere greater than _ 1.D52@, it% co%t of

(roduction in international currenc! Kould Le loKer than in the re%t of the Korld. $%%u&ing that the

(re8ailing e/change rate i% _ 1.0000 and that the ortugue%e econo&! (roduce% 1,6D2,363 unit% of

co&&odit! 1 and 1,000,000 unit% of co&&odit! 2,1@an e/change rate of _ 1.D52@ Kould &aMe the (rice

le8el increa%e 346.@^ %ince the do&e%tic (rice of co&&odit! 1 Kould Le _ 1.1649 and the (rice of

co&&odit! 2 Kould Le _ 5.9454. Therefore, the Korld econo&!N% (rofit rate Kould Le loKer than the

re%t of the Korld Lefore trade (rofit rate, Khich %hoK% that a% a re%ult of ortugalN% entr! into the

international econo&! there Kould Le a lo%% of efficienc! of the Korld econo&ic %!%te&.

Figure 3: Exchange Rate and the Cot of Production of

Co!!odit" 2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Exchange Rate

Cot

PortugalWorld

17The%e nu&Ler% oLe! the (ro(ortion% gi8en L! 3.4, Khich are co&(atiLle Kith the &a/i&u& rate of econo&ic groKth.

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1'. CONCLUSIONS

Fro& the aLo8e it can Le concluded that the icardian theor! of co&(arati8e ad8antage re%t% on

%and! ground% and a countr! that ha% no aL%olute ad8antage in the (roduction of %o&e co&&oditie% i%

e/cluded fro& the international &arMet unle%% it u%e% the e/change rate a% a co&(etiti8e in%tru&ent.

*oKe8er, the Korld econo&ic %!%te& co&(o%ed L! countrie% that u%e thi% Mind of Larrier i% le%% efficient

than an econo&ic %!%te& Khere the countrie% Kithout aL%olute ad8antage% are e/cluded.

#PPE$%&': (#)*R +#(,E #$% &$-ER$#-&*$#( C*.PE-&-&+E$ESS

"n hi% Ricardoss Economics (. 131B133, -ori%hi&a a%%ert% that Khen (rice% are not

(ro(ortional to their laLor 8alue%, the laLor theor! of 8alue ha% nothing to do Kith deter&ining the

co&(arati8e ad8antage LetKeen tKo countrie%. Thi% i% true in %o far a% it refer% to the fact that Khat

&atter% in international trade are eOuiliLriu& (rice% and not laLor 8alue%. *oKe8er, laLor 8alue% are

inti&atel! related the degree of co&(etiti8ene%% of a countr!.

"ndeed, it i% ea%! to 8erif! that the %ur(lu% rate , Khich &ea%ure% a countr!N% degree of

co&(etiti8ene%% i% eOual to the rate of %ur(lu% 8alue, , defined a% the ratio LetKeen %ur(lu% laLor 3'

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