ABSTRACT. ARABSHAHI, MARYAM. Essays on International Trade and Endogenous Growth. (Under the direction of Dr. John Seater.)

Transcription

1 STRCT RSI, MRYM. Essays on Inernaonal Trade and Endogenous Growh. Under he drecon of Dr. John Seaer. In hs research we have suded he effec of rade on economc growh hrough comarave advanage whou ncludng any of he usual channels ha rade could affec growh, such as he scale effec, research and develomen, echnology ransfer or even foregn nvesmen. Frs, we consder a secor endogenous growh model n whch wo goods are beng roduced usng yes of reroducble facors of roducon wh Cobb- Douglas ye roducon funcons. In hs model here are wo counres ha could rade n goods bu here s no nernaonal lendng or borrowng. In resen of free nernaonal rade, our model mled ha counres would comleely secalze n roducng one good on he alanced Growh Pah GP and boh counres enjoy hgher growh raes wh rade. Nex we used a more general form of roducon funcons. In hs secon we showed ha he roducon aerns on he GP wll be of yes, deendng on he relave rce of he counres under auary o he rce afer rade. We showed he exsence and unqueness of a rce a whch boh goods are beng roduced on he GP. Ths rce would be he rce of he counry under auary. owever f he rce of he counry under auary s dfferen from he rce afer rade, he counry wll shu down he roducon of one secor. On he ranson o he seady sae also comlee secalzaon could haen. Fnally n he las secon we consdered esng he mlcaon of a smler model where goods beng roduced, one good beng urely consumon and one beng nvesmen, usng only one ye of caal. In hs model

2 counres wll also comleely secalze on he GP. The counry ha secalzes n consumon goods and mors caal could enjoy hgher growh rae wh rade. The oher counry secalzes n roducng caal goods and so mors consumon good and s growh rae wll reman unchanged wh rade. We esed hs mlcaon usng a large anel of 9 counres over he erod of We used an nsrumenal varable aroach when usng yearly anel daa. We also reor he GMM esmaes of he model usng non-overlang fve year averages. We used an esmaon mehod suggesed by rellano and ond 99 o ge he conssen esmaes. Our resuls mly ha secalzng n consumon goods affecs he growh raes sgnfcanly osve. owever we dd no fnd any sgnfcan effec for secalzng n caal goods.

3 Essays on Inernaonal Trade and Endogenous Growh by MRYM RSI dsseraon submed o he Graduae Faculy of Norh Carolna Sae Unversy n aral fulfllmen of he requremens for he Degree of Docor of Phlosohy ECONOMICS Ralegh, Norh Carolna 7 PPROVED Y: Prof. John Seaer Char of dvsory Commee Prof. arry Goodwn Prof. lasar all Prof. sl Leblebcoglu

4 DEDICTION To my arens, Nader and Shdoh, my husband, Omd, and my broher, ras.

5 IOGRPY Maryam rabshah has born n December, 4 of 973 o a lovng arens n Tehran, Iran. She receved her achelor degree n economcs n summer of 996 from Shahd ehesh Unversy n Tehran, Iran. She hen came o he Uned Sae of merca o ursue her hgher educaon. She sared her Maser rogram n economcs a Illnos Sae Unversy n ugus 997 and receved her degree n December 999. She wored as R n Economcs as well as Women Sudes rogram whle she was aendng a Illnos Sae Unversy. In wner of she came o Ralegh, Norh Carolna o sar her Ph.D rogram n Economcs a Norh Carolna Sae Unversy. Durng her rogram she wored as T and lecurer for varous courses n economcs. She also wored as an nern n Research Trangle Insue, ealh Economcs dvson for abou a year. She s now marred and lvng n Ralegh.

6 CNOWLEDGEMENTS I han God and all whom whou her love and suor I would no be able ge where I am now. To my dear faher and moher, I han you for your endless love and suor hroughou my lfe. I am and wll always be graeful for all your sacrfces and hard wor o rovde me he greaes oorunes n lfe and hel me acheve my goal. I also han my broher whose suor always warms my hear. I would le o exress my deees love and hans o my husband, Omd. I han you for beng nex o me durng he srugglng years. Whou your aence and suor I would no be able o fnsh hs rojec. Secal hans exended o my commee char Dr. John Seaer, for hs hel and gudance n comleon of my dsseraon. I also han my commee members, Dr. arry Goodwn, Dr. lasar all and Dr. sl Leblebcoglu. I would also le o han Dr. Dens Pelleer and Dr. reendom Chanda. To all my frends n economcs dearmen, I han you all for your hel and commens over he years worng ogeher. Secal han o my dear frend, Dr. Clfford Mensah for always suorng and encouragng me. v

7 TLE OF CONTENTS Page LIST OF TLES... v LIST OF FIGURES... x INTRODUCTION.... TRDE, GROWT ND COMPRTIVE DVNTGE...6. Inroducon...6. Revew of Some Leraure Model The model n he bsence of Trade Inroducng Trade, he Smle Model Trade and Growh, he General Model Oher Cases Concluson...44 endces o Chaer Dervng he PPF for he Case where Dervng he Sloe of PPF for he Case where...47.c Dervng / Rao for Each Secor a Seady Sae...5.D Growh Raes on he alanced Growh Pah...54.E Dervng he uary Growh Raes as a Funcon of Prce Level...56.F Equlbrum Prce and Growh Raes wh Trade, Oher Cases...58.G Growh Raes wh Comlee Secalzaon...6. Smlfyng he Prce Level TRDE ND GROWT WIT ENDOGENOUS CPITL CCUMULTION Inroducon The Model uary Condon alanced Growh Pah wh Trade Exsence of a Unque alance Growh Pah Exsence and Unqueness of Inernaonal Prce Transonal Dynamcs Summary and Concluson... v

8 endces o Chaer.... Smlfyng he Prce Level.... Dervng he Equlbrum Condon for he Prce Level Closed Economy Oen Economy INTERNTIONL SPECILIZTION ND ECONOMIC GROWT Inroducon Revew of Some Leraure The Model Inernaonal Secalzaon and Growh Economerc Model Daa Source and Measure of Inernaonal Secalzaon Resuls Cross-Counry Resuls Resuls of Yearly Panel Daa Resuls of Fve-Year verages Panel Daa Invesmen and Trade Conclusons...69 endces o Chaer Man Grou of Commodes SITC The EC road Economc Caegores C Three man roduc grou rovded by Lewer and erg D Tables of Resuls E Ls of Counres F Fgures of LFI ndex for each counry n he samle SUMMRY ND RECOMMENDTION FOR FUTURE RESERC LIST OF REFERRENCES...8 v

9 LIST OF TLES Page Table : Table : Table 3: Table 4: Table 5: Table 6: Table 7: Table 8: Table 9: Leas Square esmaes of equaon usng cross counry daa and mor share...74 Leas Square esmaes of equaon usng cross counry daa and exor share...75 Leas Square esmaes of equaon usng cross counry daa and LFI ndex...76 Yearly anel esmaes of equaon 4 and 7 usng share of mor of caal m...77 Yearly anel esmaes of equaon 4 and 7 usng share of mor of consumon Cm...78 Yearly anel esmaes of equaon 4 and 7 usng share of mor of caal Im...79 Yearly anel esmaes of equaon 4 and 7 usng share of exor caal ex...8 Yearly anel esmaes of equaon 4 and 7 usng share of exor of consumon Cex...8 Yearly anel esmaes of equaon 4 and 7 usng share of exor of nermedaes Iex...8 Table : Yearly anel esmaes of equaon 4 and 7 usng LFI ndex for caal lf...83 Table : Yearly anel esmaes of equaon 4 and 7 usng LFI ndex for consumon Clf...84 Table : Yearly anel esmaes of equaon 4 and 7 usng LFI ndex for nermedaes Ilf...85 Table 3: Fve-year average anel daa, usng mor share of caal m...86 Table 4: Fve-year average anel daa, usng mor share of consumon Cm...87 Table 5: Fve-year average anel daa, usng mor share of nermedaes Im...88 v

10 Table 6: Fve-year average anel daa, usng exor share of caal ex...89 Table 7: Fve-year average anel daa, usng exor share of consumon Cex...9 Table 8: Fve-year average anel daa, usng exor share of nermedaes Iex...9 Table 9: Fve-year average anel daa, usng LFI ndex for caal lf...9 Table : Fve-year average anel daa, usng LFI ndex for consumon Clf...93 Table : Fve-year average anel daa, usng LFI ndex for nermedaes Ilf...94 Table : Fxed-Effecs Regressons of Growh on INV...95 Table 3: Fxed-Effecs Regressons of INV and growh on Imor Share Caal...95 Table 4: Fxed-Effecs Regressons of INV and growh on Imor Share Consumon...96 Table 5: Fxed-Effecs Regressons of INV and growh on Imor Share Inermedaes...96 Table 6: Fxed-Effecs Regressons of INV and growh on LFI Caal...97 Table 7: Fxed-Effecs Regressons of INV and growh on LFI Consumon...97 Table 8: Fxed-Effecs Regressons of INV on LFI Inermedaes...98 v

11 LIST OF FIGURES Page Fgure -: Producon ossbly froners for he case where...8 Fgure -: Producon ossbly froners for he case where...9 Fgure -: Facor rces sasfyng neremoral arbrage and zero rofs...79 Fgure -: The bang-bang condon...9 Fgure -3: Fgure -4: Prce froners...95 Prce froner conssen wh he roducon aern on he ranson ah...96 Fgure -5: Phase dagram when here s comlee secalzaon n Y and b >.5 Fgure -6: Phase dagram when here s comlee secalzaon n Y and b >.6 Fgure -: Fgure -: Ineremoral arbrage condon for dfferen facor nenses n auary...9 Ineremoral rbrage condon a counry s auary relave o ha a rade equlbrum when >...4 Z Y Fgure -3: Fgure F-: Ineremoral rbrage condon a counry s auary relave o rade equlbrum when <...3 z Y Fgures of LFI ndex for each counry n he samle... x

12 INTRODUCTION Snce he emergence of endogenous growh models here have been a flow of aers on endogenous growh n he leraure. Many of hese wors have conrbued n sudyng he relaonsh beween endogenous growh and nernaonal rade. In hese leraures here are many ways ha relaes rade o economc growh. For nsance rade can affec growh hrough ncreases n he global soc of nowledge whch ncreases he effcency of research and develomen n counres ha engage n rade. lso rade can be he channel hrough whch counres can learn abou new and advanced echnologes develoed n her radng arner counres. Trade also can ncrease he rae of economc growh hrough ncreases n sze of mares or hrough demograhc changes n counres. These are all moran channels however we could as wheher rade could affec growh hrough he mechansm of comarave advanage n a dynamc model smlar o he way ha rases ncome level n sac models. lhough n some of he sudes, such as Grossman and elman 99, ch7 and cemuglu and Venura he role of comarave advanage has been consdered n deermnng he aern of secalzaon bu rade affecs growh hrough he channels oher han comarave advanage. Seaer 7 however exlores hs maer by consderng a model n whch here s no research and develomen, echnology ransfer, scale effec or even nernaonal nvesmen, n order o focus on he effec of rade hrough he mechansm of comarave advanage only. e exends he wo secor endogenous growh model descrbed n arro and Sala--Marn 995, ch5. In hs model he consders wo counres each roducng wo yes of goods usng wo reroducble facors of roducon. When engage n rade, here wll be a sable seady sae n whch each counry wll comleely

13 secalze n roducon of one secor accordng o her comarave advanage aern. The growh raes wll be hgher wh rade relave o ha under auary for each counry. owever he exsence of he balanced growh ah and he effec of rade on growh deend on he absolue advanage of he counres engage n rade. When each counry has absolue advanage n roducng of one of he goods hen balance growh ah exss and nernaonal rade rases he growh raes on he balanced growh ah and counres grow a he same rae. In addon, he shows ha he resulng growh raes n hs case are hose ha would resul from echnology ransfer, even hough no echnology ransfer occurs. In hs model, Seaer 7 assumes ha echnologes are dfferen across secors and beween counres. owever hese dfferences of echnologes are refleced hrough he facor roducvy arameers alone snce he consders equaly beween facor shares across secors and beween counres n he roducon funcons of Cobb-Douglas ye. The frs objecve of hs research s o relax hs smlfed assumon and consder he more general form of roducon funcons n whch facor shares across secors of roducon as well as beween counres are dfferen. Then usng hese general forms of roducon funcon, we also show ha a balanced growh ah n whch all varables ha are growng grow a he same rae, exss and s sable. lso he roducon aerns are smlar o wha Seaer 7 has obaned. On he balanced growh ah each counry comleely secalzes n roducon of one secor and he growh raes rse wh rade and counres grow a he same rae. owever hese resuls deend on he value of he equlbrum world rce. If he value of he world rce says beween he auary rces hen he balanced growh ah exss and he growh raes of he counres are hgher wh rade and are of hose ha would resul from echnology ransfers. When usng he general form of roducon funcons, hese resuls do

14 no reflec he requremens of absolue advanage. In he oher world he condon of absolue advanage ha guaranees he exsence of balanced growh ah as obaned n Seaer 7, does no hold when we consder he general model. We could furher show ha he absolue advanage requremen s he resul of consderng he smle verson of roducon funcons as Seaer 7 dd. The second objecve of hs research s o generalze he form of roducon funcons even more. y dong so we could sudy he neracon beween nernaonal rade and he caal accumulaon rocess. Followng ond and Tras 997, we ulzed a dynamc general equlbrum model n whch here are wo raded goods roduced n wo dfferen secors and usng wo yes of reroducble facors of roducon. Ouu s smlarly assumed o be roduced under condons of consan reurns o scale and erfec comeon. Therefore he model exhbs endogenous growh because has consan reurns o scale n he reroducble facors. The model ha we consdered n hs secon, whch s smlar o wha we consdered n he revous secor, s relaed o he wo by wo ecscher- Ohln model of nernaonal rade heory, snce has wo rmary facors and wo raded goods. owever noce ha n hs model boh facors are reroducble. Therefore s dfferen from dynamc ecscher-ohln models snce n he laer yes of models one facor hyscal caal s deermned endogenously whle he oher facor labor force s exogenously gven. We show ha when boh facors are roducon of reroducble, he model roduces he Rcardan ye of resuls. We frs esablsh he exsence of a balance growh ah and show he relaonsh beween he world rce and he aern of roducon on he balanced growh ah. When he world rce s he same as he rce under auary hen he counry s ncomleely secalzed. For any rce oher han hs rce he counry 3

15 wll secalze n roducon of one secor. We hen show ha here wll be a unque facor rao on he balanced growh ah for he equlbra wh secalzaon n one of he raded goods and we esablsh he saddle ah sably of hese equlbra. In he fnal secon we consdered a wo secor model n whch wo goods, a ure consumon and a ure nvesmen good s beng roduced usng one ye of caal. Smlarly when he equlbrum world rce s beween he auary rces, on he balanced growh ah each counry secalzes n roducon of one secor. owever he effec of rade on growh raes deend on he ye of good a couny s morng. When a counry secalzes n roducng consumon good and an mor caal good, s growh rae rses wh rade. owever for he counry ha secalzed n caal good and mor consumon good, he growh rae reman unchanged. Mos of he sudes ha examne he relaonsh beween growh rae and nernaonal rade usually do no consder he ye of radng good and nsead hey focus on he effec of rade n general. The urose of hs secon s o es wheher he secalzaon maers when comes o he effec of rade on growh raes. We exend an secfcaon develoed by ond, Leblebcoglu and Schanarell 6 o allow he long run growh rae n each counry deend on he varable ha our model redc o affec he long run growh rae. We esmae hs secfcaon usng a anel of 9 counres over he erod of To caure he effec of he naure of radng goods we use hree measures, mor share, exor share boh as a ercenage of GDP and an secalzaon ndex nown as Laffay ndex. We also reor he effec of rade secalzaon on growh usng boh yearly anel and non-overlang fve-year averages. When consderng yearly anel we esmae he model usng nsrumenal varable aroach usng he dfferen lagged values of endogenous varables as well a few addonal nsrumens. 4

16 lso reor he esmaes of he model for he fve-year average daa usng an aroach develoed by rellano and ond 99 o oban he conssen esmaes. Our resuls show ha secalzng n consumon goods ncrease he long-run growh rae sascally sgnfcan whle we could no fnd any evdence of secalzng n caal goods. 5

17 CPTER TRDE, GROWT ND COMPRTIVE DVNTGE. INTRODUCTION There are varees of models whch ry o ln he cross-counry dfferences n longrun rae of growh o nernaonal rade hrough dfferen channels. For nsance, sudes such as remer 993, arro and Sala--Marn 997 and Connolly consder he case where oenng o rade ncreases he sze of mares for roducers leadng o more secalzaon and hgher growh. In he models where research and develomen s he source of growh, rade n secalzed nus rases he level and he rae of growh of real ouu. Grossman and elman s 99 wors are examles of hs ye. Trade can also affec long-run growh rae hrough exchange of echnology and nowledge. For nsance, Rvera-az and Romer 99 consder wo models wh dfferen secfcaons of he research and develomen secor. In her model rade oens counres o each oher s nowledge and herefore negraon could ncrease he worldwde long-run rae of growh hrough he growh n soc of nowledge n each counry. lhough all hese sudes consder moran channels hrough whch rade could affec growh bu mos of hem do no rovde a srong ln beween comarave advanage and he aerns of rade beween counres. Seaer 7 however, sudes hs morance by rovdng a mechansm where rade could rase he rae of growh hrough comarave advanage. e consders he wo secor model nroduced n arro and Sala--Marn 995, ch5, where wo goods are beng roduced usng wo yes of reroducble facors of roducon and Cobb-Douglas roducon funcons. One secor roduces a unfed good ha 6

18 could be used as consumon or nvesmen good and he oher secor roduces anoher ye of caal good and boh goods are radable. e exends hs closed economy model o examne he effec of free rade on he growh erformances of counres engaged n rade. e assumes ha he echnology for roducng each ye of good s dfferen whn secors of roducon n each counry as well as across counres. e also assumes ha he dfferences n echnologes arse only from he dfferences n oal facor roducvy arameers. s model herefore s a smle wo counry wo good model, whch has been smlfed o focus on he growh effecs of rade hrough comarave advanage whou recourse o scale effecs, echnology ransfer, research and develomen, or even nernaonal nvesmen. s resuls show ha f each counry has an absolue advanage n he roducon of one of he raded goods hen rade could rase he growh rae of boh counres and balance growh ah exss for ndvdual counres as well as he world. In addon alhough here s no echnology ransfer however by radng n goods ha are facors of roducon he growh raes mly he resuls ha would emerge f counres exchanged echnology, Comarave advanage however deermnes he aern of rade whn he counres. The urose of hs secon s o exend Seaer s 7 wor o consder he more general case where he source of echnology dfferences whn he secors and across he counres s no jus refleced n oal facor arameers. We could show ha even n he general model smlar o he smle model ha Seaer 7 consdered, free rade could rase he growh raed of counres hrough he channel of comarave advanage. In wha fallows, we frs revew some of he exsng models ha sudy he relaonsh beween rade and growh. Then we exlan he model Seaer s 7 have suded and resen some of hs 7

19 resuls. Then descrbe he model wh more general form of he roducon funcon and examne he effec of free rade on he growh erformances.. REVIEW OF SOME LITERTURES lhough mos of he early researches on he rade and growh have adoed dfferen versons of he neoclasscal model o examne wde range of ssues n he feld of nernaonal rade, snce Romer 986 suggesed a model ha endogenzes he growh rae of economes, varey of hs dea has been examned o sudy he effecs of nernaonal rade on growh rae of ouu and ncome. For examles Grossman and elman 99, chaer 7, 8 and 9, Rvera-az and Romer 99 and cemoglu and Venura have exended endogenous growh models of echnologcal rogress o analyze he effec of nernaonal rade on growh. Smlarly learnng by dong models or he models wh human caal accumulaon has been used o sudy hs relaonsh. Lucas 988, 993, Young 99, Soey 99, ond and Tras 997 and Seaer 7 are examles of such sudes. acus, ehoe, and ehoe 99, remer 993 relae growh and nernaonal rade hrough channels of scale effec. arro and Sala-I-Marn 997 and Connolly nvesgae he neracon beween rade and growh hrough nnovaon and maon of roducs. In wha follows we brefly summarze some of hese researches. In a model where research and develomen s he engne of growh, Grossman and elman 99, ch7 nvesgae he deermnans of endogenous comarave advanage when nnovaors develo new varees of horzonally dfferenaed roducs. Ther resuls mly ha counres n whch human caal s relavely abundan wll secalze n research on he seady sae. Therefore hs couny acqures he now-how o roduce a relavely 8

20 wder range of nnovaon goods. In addon n he world wh free rade each counry have access o he wder range of nnovave roducs whch maes he growh raes o be hgher wh rade han ha under auary for boh counres. Grossman and elman 99, ch9 also rovded an analyss lnng long-run rae of growh o rade and nernaonal condon n an endogenous growh model n whch nowledge s he engne of growh due o he resence of scale economes. They consder a model wh wo counres and 3 roducon acves; roducon of fnal good, roducon of a connuum of varees of dfferenaed mddle roducs and R&D secor ha roduces desgns for new roducs usng rmary resources and revously accumulaed nowledge. They consder wo counres ha have smlar roducon funcons bu have dfferen endowmens. They showed free rade n goods and nus brng nernaonal sllovers of nowledge, hen rade leads o an ncrease n he growh raes of boh counres. Rvera-az and Romer 99 consder wo yes of rade beween wo economes ha are smlar n her endowmens and echnologes and are nally searaed and are a her balanced growh ah. They consder wo dfferen ways of rade beween he economes: free rade n goods bu no deas, and free rade n deas bu no goods. Followng Romer 99 her model as well ncludes wo yes of manufacurng acves; roducon of consumon goods and roducon of he hyscal uns of yes of caal ha have already been nvened. Research and develomen s he hrd acvy, whch creaes desgns for new yes of caal goods. They consder wo secfcaons of he echnology for R&D. One secfcaon assumes ha human caal and nowledge are he only nus ha nfluence he ouu of desgns nowledge drven secfcaon, whle anoher assumes ha echnology for R&D uses he same nus, n he same roorons as he manufacurng 9

21 echnology lab equmen model. These secfcaons erm a shar dsncon beween flows of goods and flows of deas. To sudy he effec of rade, frs hey allow for he full negraon so ha economes are comleely negraed no a sngle economy. fer full negraon aes lace, regardless of he secfcaon of he echnology for R&D he rae of growh wll ncrease. In he nex se hey only allow for rade n goods bu resrc he flow of deas, under hs assumon hey show ha rade n goods has no effec on he long-run rae of growh under he nowledge drven secfcaon for R&D echnology. owever when hey consder he effecs of rade n goods under he lab equmen secfcaon oenng rade n goods alone causes he same ermanen ncrease n he rae of growh as comlee negraon. Then hey nclude he effec of oenng communcaons newors along wh rade n goods n he nowledge drven secfcaon for R&D, under hs assumon her resuls show ha allowng for flow of deas creaes a ermanenly hgher growh raes. cemoglu and Venura also show ha nernaonal rade based on secalzaon- could lead o a sable world ncome dsrbuon even f here s no dmnshng reurn n roducon and echnologcal sllovers. They model he world as a collecon of economes a la Rebelo 99 wh growh resulng from accumulaon of caal. Two fnal good consumon and nvesmen and a sream of nermedae goods are beng roduced. Caal and nermedaes are beng used n roducon of boh goods whle he echnology of roducng nermedaes requres one un of caal o roduce one un of nermedae. The ably of roducng hgher number of nermedaes mly how advanced he echnology of a counry s. In hs world, counres could rade n nermedae goods. On he seady sae counres secalze n a se of nermedae goods. Counres wh greaer

22 roducon for each varey of nermedaes exerence a declne n her erms of rade whch ranslaes o slower caal accumulaon and reverse haens for he oher counres. s he resul, on he seady sae counres wll grow a he same rae and s sable. Models of dffuson of echnology are anoher ye of models ha have been consdered n sudyng he relaonsh beween rade and growh. arro and Sala-I-Marn 997 ry o consruc a model lnng he long-run growh mlcaons of he endogenous growh heores wh he convergence mlcaons of he neoclasscal growh model. They consder wo counres ha are engaged n roducng fnal consumable good and roducon of nermedaes and R&D roducon ha amed a learnng abou new varees of nermedaes. n agen can learn by nvenng a new ye of good or by mang a roduc ha s nown o each counry. They assumed ha one counry s he echnologcal leader and he oher s he follower. Therefore he number of yes of nermedaes s larger n he echnologcal leader han ha n he follower counry. Imaon s ycally cheaer han nvenon and herefore follower refer o mae he nermedae goods nown n he leader counry raher han nvenng hem. The lower cos of maon mles ha he follower would grow fas and ends o cach u o he leader. In he long run, all economes would grow a he rae of dscovery n he leadng counry. Therefore n hs ye of model rade exands mares for nermedae goods and he roducon of hose goods and as he resul he growh raes are hgher. Connolly sudes he ransonal dynamcs for a develoed and less develoed counry when Norh-Souh rade leads o echnologcal dffuson hrough reverse engneerng of nermedae goods n a qualy ladder model of endogenous growh. Domesc echnologcal rogress occurs va nnovaon or maon, whle growh s drven by echnologcal advances n he qualy of domescally avalable

23 nus, regardless of counry of orgn. For reasonable arameer values, he raes of nnovaon and maon are boh fallng n ranson o seady-sae and ye reman above ha under auary. Increased neracon beween he Norh and he Souh, hrough ncreased oenness o mors of Norhern nermedae goods, leads o hgher world growh. remer 993 n he oher hand consrucs a model n whch oulaon growh could affec he long-run rae of growh. e frs shows ha he growh rae of oulaon s rooronal o he level of oulaon. In hs model, each erson s chance o be smar enough o nven somehng s ndeenden of oulaon. owever even f each erson s roducvy s ndeenden of oulaon, oal research ouu wll ncrease wh oulaon and so he argues ha rade would ncrease he oulaon sze and herefore could rase he rae of echnology mrovemens. Smlarly acus, ehoe, and ehoe 99 suded he scale effecs of rade on growh by dervng he heorecal relaons beween scale and growh n 3 dfferen models where growh s drven from learnng by dong, nvesmen n human caal and from develomen of secalzed nus o roducon. They furher examne he scale effecs redced by hose heores of rade and growh. Ther evdence however showed mxed suor for scale effecs of rade on growh. Lucas 988 exends hs one-secor model of accdenal learnng by dong o a wogood model and examnes he roles of human caal accumulaon n nernaonal rade. e consders wo secors roducng wo consumons good usng only labor as nu. owever worers can accumulae exerence or human caal by worng n a frm. The echnologes are of Rcardan ye n whch he ouu of a good s equal o he effcency uns of labor nu. e consders one secor o be he hgh-echnology secor n whch a > a, where a

24 > s a measure of he effcency of learnng. If consumon goods are oor subsues hen he seady sae ends o be sable wh dversfcaon n roducon of wo goods, when economy s closed. Lucas 993 hen exends hs model o rade, assumng a connuum of small counres facng exogenously gven world rces under free rade. The comarave advanage of a counry deends on he counry s auarc rce rao and he world s rce rao. Counres end o be comleely secalzed, bu each counry wll accumulae only he ye of human caal ha s secfc o he good roduced. Therefore when dfferen counres roduce dfferen goods under free rade and so hey wll have dfferen growh raes. Oher models of rade wh learnng by dong also have been suggesed. Young 99 consders accdenal learnng and allows for sllovers across goods. e however shows ha when Less Develoed Counres LDCs oen o rade, hese counres wll secalze n radonal goods where learnng has been exhaused. Therefore hey exerence lower growh raes under free rade relave o he auary. ll hese models rovde moran nsghs n relaon beween rade and rae of economc growh however n mos of hese sudes comarave advanage lays no role. Comarave advanage mgh defne he aern of rade n some of hese sudes such as Grossman and elman 99 or cemoglu and Venura, however he effec of rade on growh comes from channels oher han he effec of comarave advanage mechansm smlar o he one we consder o rases he ncome level n sac models whou growh. Seaer 7 however rooses an aroach n whch rade, n and of self, rases growh hrough he comarave advanage by consderng a model n whch here s no scale effecs, no research and develomen or no echnology ransfer and no nernaonal nvesmen. e consders a wo secor endogenous growh model n whch wo goods are beng roduced 3

25 usng wo ye of reroducble nu. s resuls mly ha comarave advanage guaranees rade, however he effec of rade on growh deends on he absolue advanages of he radng counres. When each counry has an absolue advanage n roducng somehng, rade could rase boh counres growh raes and relcaes he resul ha would emerge f counres exchanged echnologes, even hough no echnology ransfer acually aes lace. In he followng secon we descrbe hs model and resuls wh more deal..3 TE MODEL.3. TE MODEL IN TE SENCE OF TRDE In hs secon whou geng no he deals, we frs summarze he model for he closed economy, whch has been suded by arro and Sala-I-Marn 995-ch5. We hen connue by revewng Seaer s 7 n whch he has modfed he model o sudy he effecs of rade on growh. Consder an economy ha roduces wo goods, good Y ha can be used as consumon good or as gross nvesmen n hyscal caal, and he good Z. Good Z could be used as only a ye of caal, for nsance human caal. These wo goods are assumed o be roduced n dfferen secors and by dfferen echnologes. lso boh reroducble facors are essenal o roducon of boh goods. Each secor s echnology s assumed o be Cobb-Douglas. Therefore he roducon echnologes could be wren as, Y C I v u, I does no need necessarly be human caal. I could be any oher yes of caal whch s no. I could also be hough of any caal ha could augmen labor bu s no human caal. Examle of such caal could be comuers or comuer sofware. 4

26 5 ν δ ] [ ] [ u Z &, where, > are echnologcal arameers, and are he shares of -ye caal n he ouus of each secor, v and u are he fracons of -ye and -ye caal, resecvely, used n he roducon of good Y. oh ye of caal are assume o derecae a he same rae, δ. The gross domesc roduc for he economy, Q, can be defned as Y Q δ &, 3 where s he rce of n erms of Y. The uly funcon s assumed o be CRR, herefore d e C U ρ θ θ, 4 s he lfeme uly. The reresenave agen maxmzes 4 subjec o and. Ths roblem s a sandard model of household omzaon and herefore we can wre he amlonan as, [ ] C u e C V δ ν φ θ ρ θ [ ] u δ ν ψ ] [ ] [. 5 Usng he frs-order condons, he growh rae of consumon could be obaned as 3 ρ δ ν θ γ u C. 6 Noe ha here s assumed ha labor s a consan normalzed o be one. 3 Snce he deals for dervng he soluon has been rovded n Seaer 7 we only resen he fnal soluons.

27 6 On he balanced growh ah he growh raes of,, Y and Q wll all be equal o he growh rae of C see Seaer 7 for deals, and he common growh rae can be calculaed as ρ δ θ γ, 7 where he value of s. 8 s menoned hs s he model where he couny s assumed o be closed. Nex we dscuss how Seaer 7 exends hs model o nclude rade..3. INTRODUCING TRDE, TE SIMPLE MODEL To nroduce foregn rade no he model Seaer 7 begns wh a smle case. e consders a Rcardan ye model of rade wh wo counres havng dfferen echnologes and no fxed facors. In addon he assumes ha he facor share for o be he same whn wo secors of roducon as well as beween he wo counres. In he oher word he assumes, Ths resrcon mles ha he cross-counry and cross-ndusry echnology dfferences wll be caured only by he oal facor roducvy arameers and. In he general case where, could be shown ha he followng relaon beween v, u,, and holds,

28 ν ν u u 9 Therefore assumng mles v u. Ths ndeed smlfes he roducon funcons for Y and as, Y v, ν Z & δ, where ndcaes he counry. Now he omzaon roblem s o maxmze he lfeme uly funcon descrbed n equaon 4 subjec o hese modfed roducon funcons. Smlarly by usng he frs order and necessary condons of such omzaon roblem he auarc growh rae for each counry 4 wll be oban as, γ θ, T δ ρ To sudy he effec of rade, Seaer 7 consders wo relavely large counres such ha her oulaon s fxed and of equal sze and each counry consss of a large number of comeve frms wh dencal roducon funcons. When counres are oen hey could rade n boh goods freely. There are however no nernaonal lendng and borrowng. Consder X o be he exors of good Y and f sll reresens he relave rce of n erms of Y, hen he consrans for counry would be modfed as follow, Y C & δ X v, 4 For deals lease refer o Seaer 7. 7

29 8 X Z ν δ &. Now each couny should choose X along wh everyhng else. Noce ha neher of counres s small and hey are relaed o each oher hrough rade, herefore we need o deermne he growh rae for counres smulaneously. To do hs, Seaer 7 solves he roblem n wo ses. Frs he solves each counry s roblem ang as gven and hen moses he rade balance condon X X o fnd he equlbrum value for. In each counry he reresenave agen maxmzes 4 subjec o and, and herefore he amlonan s, [ ] X C e C V δ ν φ θ ρ θ X δ ν ψ. 3 Frs order and necessary condons could be obaned as he usual forms. owever here s one condon ha needs a lle more aenon. Consder he frs order condon wh resec o X, X V ψ φ. 4 s can be seen hs equaon does no deend on any conrol varable. Ths s he sandard case of bang-bang conrol for X, whch n urn mles ha equaon 4 mgh no be always sasfed. Noce ha when counres are engage n rade wh each oher reresens he nernaonal rce of n erms of Y. Now we now ha he cosae varables ϕ and ψ are, resecvely, counry s margnal value of Y-good and -good Z from nernal

30 roducon. Therefore her rao s he margnal value of n erms of Y whch s he counry s nernal rce of n erms of Y. Therefore n general hese wo mgh no be equal o each oher. Consequenly we can consder 3 cases as follow, V ψ. φ ψ > > X φ. V X ψ φ ψ φ. V X ψ φ ψ < < φ The frs case where ψ φ > mles ha he margnal value of X s osve regardless of he value of X herefore counry would choose X as hgh as ossble. In oher words wll choose o roduce only Y and exor o oban. owever f ψ φ <, hen he reverse wll haen, n hs case he margnal value of X wll always be negave and herefore counry wll choose o se X as low as ossble and herefore roduce only and ψ rade o oban Y. Fnally f φ he margnal value of X wll always be zero. Therefore he counry would be ndfferen o he value of X. When, could be shown ha ψ 5 φ. Consderng hs equaly he bang-bang condon could be rewren as, 5 I could be easly obaned by ung n equaon 4. In addon Seaer 7 has obaned hs equaly by usng he frs order and necessary condons of he omzaon roblem for hs case. 9

31 counry secalzes n roducng Y when >, when hen he counry connue o oerae n boh secons and 3 wll secalze n roducng when <. In order for counres o be neresed n rade wh each oher, he equlbrum world rce should fall beween and, nernal rces of counry and counry resecvely. Whou loss of generaly, could be assumed ha > 6 and so he necessary condon for rade s,. ccordng o wha we exlaned above, he laer condon mles ha counry one secalzes n roducng good Y and counry secalzes n roducng good. Now havng hs nformaon he omzaon roblem for each counry can be rewren and solved for each counry. ere we only resen he resuls of such roblems 7. Counry secalzes n roducng Y and rade hs o oban, whch mles counry ses vu. The amlonan for hs counry can be wren as V θ C e θ ρ φ [ C δ X ] ψ δ X 5 and counry does he oose herefore ses vu. The amlonan for hs counry s hen, 6 The reverse could be assumed and he only dfference would be ha our resuls wll be reverse for he counres. 7 More deal could be found n Seaer 7.

32 [ ] X X C e C V δ ψ δ φ θ ρ θ 6 When counres are oen o rade wh each oher, hey should do so a he world rce. Therefore for each counry now φ ψ s equal o. Now, usng he necessary and frs-order condons he growh rae for each counry wll be obaned as, ρ δ θ γ, T 7 [ ] ρ δ θ γ P T, 8 For any,, could be seen ha hese growh raes are greaer han he growh raes under auary. Consder counry for whch <, hen, [ ] u T,, γ ρ δ θ ρ δ θ γ >, For counry, we have >, herefore, [ ] u T,, γ ρ δ θ ρ δ θ γ > These resuls mly ha rade could rase he growh raes of boh counres for any,. owever noce ha he growh raes are no equal for any arbrary.

33 To ge equal growh raes s necessary and suffcen for o be equal o. If hs condon holds hen he common growh rae would be, [ δ ρ] γ γ, T γ, T 9 θ Now from he consrans for counry and counry we have, & C X & δ C X δ. & C X & C X δ δ. In addon, he rade balance mles X X. balanced growh ah for each ndvdual counry requres ha he level of consumon and he soc of and caal grow a he same rae,.e. γ γ γ. Therefore, all he erms on he rgh sdes of C equaons 9 and should be consan, whch n urn requres ha,, X, C and Y all grow a he same rae n each counry. owever noce ha X X, herefore for each counry o have balanced growh ndvdually, s necessary ha he wo counres have he same growh rae on he balanced growh ah. s dscussed earler he equaly of growh raes could be acheved only when. I s moran o noe ha hs argumen holds only when falls n he nerval of,,. owever, here s no guaranee ha fall beween and, and f

34 falls ousde hs nerval, hen can no be equal o, and balance growh ah for he world as well as for ndvdual counes could no exs. To oban he condon ha guaranees he exsence of a balance growh ah, consder he case where falls nsde he nerval,.e. < <. Ths nequaly mles ha > and >. s argued before he source of dfference beween echnologes across counres or whn he secons of roducon are from he dfferences beween her oal facor roducves and. > and > hen means ha counry has absolue advanage n roducng Y and counry has absolue advanage n roducng. Therefore he requremen for he exsence of balance growh ah for each counry or for he world as a whole s ha each counry o have absolue advanage n roducng somehng. In he model consdered here, hs condon mles ha counry o have absolue advanage n roducng good Y and counry have absolue advanage n roducng good. If hs condon mee hen growh rae of each counry wll be hgher wh free rade, balanced growh s ossble and s asymocally sable 8 and he common growh rae would he one descrbed n 9. s can be seen hs common growh rae deends on he facor roducvy arameer of effcen echnology n each counry,.e. roducon of good Y n counry and roducon of good n counry. Ths n urn mles ha each counry abandon s nferor echnology and subsue by s rade arner s effcen echnology. 8 See Seaer 7 for deals. 3

35 Now consder where falls ousde he nerval, hen can no be equal o bu wll be equal o he value of he boundares whchever s closer o. For nsance f < < hen wll be equal o. In hs case he growh rae of one counry wll say he same as was under auary whle he growh rae of he oher counry wll rse, and growh raes of counres wll no be equal. For nsance, suose >. In hs case can no be equal o, and so. Now he growh raes for each counry afer rade would be obaned as γ and, γ θ [ δ ρ] δ ρ γ, u, T θ θ [ δ ρ] > δ ρ γ, u, T θ,. Noce ha we have assumed >, herefore γ, T > γ, T. Now > > mles >, and >. Ths means ha counry has an absolue advanage n boh goods whle counry has only a comarave advanage n roducng. In hs case counry connues o roduce boh goods and s growh rae deends only on s own echnology and wll say he same as was under auary. owever counry 4

36 secalzes n, hus roducng only and exors o oban Y and so s growh rae rses bu says below ha for counry. Case of Small Counry: So far has been assumed ha counres are no small relave o each oher. owever Seaer 7 also sudes he case where one of he counres s small relave o he res of he world. s we now n he case of small counry he world rce would be exogenous o he small counry and herefore unaffeced by s choce. If he s small counry s TFP rao s greaer han, he counry roduces only Y and f s s smaller han wll roduce only and he res of he world wll be unaffeced by rade. In hs case f small counry has absolue advanage n roducng one good and he world has absolue advanage n he oher good hen rade wll rase small counry s growh rae o he world s growh rae. owever f small counry does no have absolue advanage n any of he goods s growh rae wll ncrease by rade bu remans below he world s growh rae. Fnally f he small counry has an absolue advanage n boh goods hen s growh rae wll be hgher han ha for he world and wll be unaffeced by rade..3.3 TRDE ND GROWT, TE GENERL MODEL In he revous secon we revewed a smle case of wo good wo counry model ha Seaer 7 has consdered n sudyng he effec of rade on growh. s we descrbed earler, n hs model Seaer 7 has assumed equaly of facor shares of caals beween wo secons of roducon as well as across counres. In hs secon, we wll relax hs assumon and examne he relaonsh beween rade and economc erformance n a more 5

37 6 general case where he facor shares are no only dfferen beween wo roducon secons bu also across counres 9. When counres are no oen o rade wh each oher, he omzaon roblem for each counry would be exacly he same as he one descrbed n secon.. ssumng dfferen facor shares beween counres and roducon secons, he equaons,, 7 and 8 reresen he roducon funcon for each secor, growh rae and he rce level on he balanced growh ah n auary. gan hese equaons are, I C Y u v 3 u ν δ ] [ ] [ & 4 ρ δ θ γ 5 6 Noce here f we mose, we ge he case ha Seaer 7 has consdered. s dscussed n secon 3.. afer counres oen o free rade hey secalze comleely n he secor ha has comarave advanage n and by dong so each counry s growh rae wll rse and wll become equal on he balanced growh ah. These resuls however are he neror soluon ha wll be guaraneed f each counry has an absolue advanage n roducng somehng. The corner soluon would be somewha dfferen. For a counry a he 9 Oher case where he facor share s only dfferen beween secors or only across he counres has also been suded. Some of he resuls are beng resened n aendx F.

38 corner, ha s he counry whose auarc rce wll be he same as he world rce, rade would no rase s growh rae and wll connue o oerae n boh secons of roducon. The growh rae of he oher counry also wll rse bu wll say below ha of s radng arner f he counry does no have absolue advanage n any roducon secor. In hs secon hen we are ryng o examne f we could oban hese resuls afer relaxng he assumon of equaly of facor shares. s dscussed earler, n he case of neror soluon boh counres are gong o comleely secalze meanng ha hey shu down roducon of one of he secors. Each counry roduces only one facor of roducon domescally and mors he oher facor. Ths resul s wha we oban n he classcal Rcardan nernaonal rade model where here s only one facor of roducon and he roducvy of labor n roducon of goods s he source of echnology dfferences and herefore comarave advanage. In aendx. we have shown ha when he roducon ossbly froner for each counry become lnear wh a sloe of. Recall ha and are he oal facor roducvy arameers n roducon of Y and Z resecvely. I has be shown Seaer 7 ha n hs case he rao of oal facor roducvy arameers reresens he domesc rce of good Z n uns of good Y. When, he roducon ossbly froner for each counry has been llusraed n fgure - a and b by lne for counry and and counry. When here s no rade, counry roduces and consumes a on C and counry roduces and consumes a on D. Noce ha he sloe of he roducon ossbly froner s he domesc relave rce when counres are closed,.e.. 7

39 fer counres oen o rade wh each oher, he rce level a whch hey rade wll be dfferen from ha under auary. For counry he world rce s lower han he auarc rce < whle wll be hgher han he auarc rce for counry >. Counry hen wll se X s exor of Y good as hgh as ossble and roduces a on. hs on roduces only Y and exors o oban Z. lso s consumon on wll move o on C T as he resul of rade. Insead counry wll shu down he roducon of good Y and roduces only good Z snce wll se X as low as ossble. The roducon on for hs counry moves o on and s consumon on moves o D T. Therefore resuls ha have been obaned here are smlar o wha Rcardan model s redced n a sac seng. Y Y C T C D T D Z Z a: Counry b: Counry < φ ψ < > φ ψ < Fgure -: Producon ossbly froners for he case where 8

40 Now consder he case where. I could be shown ha for hs case he roducon ossbly froners are no longer lnear. Fgure - a and b llusrae he roducon ossbles froners for each counry when. Whou loss of generaly, we agan assume ha > where and are he auarc rces for counry and counry resecvely. From he rncles of sac nernaonal rade when counres are no oen o rade wh each oher, hen each counry wll roduce and consume where he sloe of roducon ossbly froner s equal o s domesc rce of he counry under auary. Ths s shown by on for counry and by on C for counry. When counres engage n nernaonal rade hen he world rce would be, such ha < <. Y Y T T C T C P P D P P Z Z a: Counry b: Counry Fgure -: Producon ossbly froners for he case where See endx. for more deal. 9

41 fer rade hen he rce level s gong o change for each counry. Each counry s roducon on wll now move o he on a whch he rce lne s angen o he roducon ossbly froner. Counry s roducon on wll move o on fgure - aand counry s roducon on wll move o on Dfgure - b. In he oher words counry wll roduce more of good Y and exor n order o mor good ncomlee secalzaon n good Y. Counry wll do he oose, roduce more of good and exor o oban good Y ncomlee secalzaon n good. y solvng he dynamc omzaon roblem for he case where he roducon aern on he balanced growh ah was smlar o wha sac Rcardan model of nernaonal rade redcs. Nex we examne how hese resuls mgh change when we relax he assumon of equaly of facor shares. lhough we wll no longer assume he equaly of facor shares beween he secors and counres bu we connue o assume ha counres are no small relave o each oher, hey have fxed oulaon of equal sze and each counry consss of a large number of comeve frms wh dencal roducon funcons. Smlarly le X denoes exors of Y n each counry. The accumulaon consrans hen are, Y C & δ X, v u, 7 Z & δ [ ν ] [ u ] X. 8 3

42 3 In each counry he reresenave agen wll maxmze s lfeme uly funcon as descrbed n 4 subjec o 7 and 8. Smlarly each counry mus choose X along wh everyhng else and he equlbrum value of wll deend on he decson of boh counres. To solve hs dynamc roblem we wll follow Seaer 7 and wll fnd he world equlbrum n wo ses. Frs, we ry o solve each counry s omzaon roblem assumng s gven. Then n he second se we wll mose he rade balance condon X - X o fnd he value for equlbrum. The amlonan and he necessary and frs order condons are as follow, [ ] X C u v e C V δ φ θ ρ θ X u v δ ψ, 9. X C u v V δ φ &, 9. X u v V δ ψ &, 9.3 [ ] [ v u v v V ψ δ φ φ & ] u v, 9.4 [ ] [ u u v u V ψ φ ψ & ] δ u v, 9.5 e C C V φ ρ θ, 9.6

43 3 v V [ ] u v φ [ ] u v ψ, 9.7 u V [ ] u v φ [ ] u v ψ, 9.8 X V ψ φ. 9.9 Noce ha equaon 9.9 does no deend on any conrol varable, ndcang bangbang conrol for X. gan he cosae φ s he margnal value of good Y and ψ s he margnal value of good from nernal roducon. Therefore φ ψ reresens he margnal value of good Z n erms of good Y ha s he nernal rce of good Z n uns of good Y. avng he bang-bang conrol for X, we can consder 3 cases X V φ ψ ψ φ < > >, where counry wll ry o se X as hgh as ossble and f X V φ ψ ψ φ > < <, counry wll ry o se X as low as ossble, and fnally f X V φ ψ ψ φ counry s ndfferen wh resec o he value of X. Smlarly we assume > and snce we are neresed n he case where rade occurs, hen < <. Under hs assumon hen counry wll ry o roduce more of good Y and exor o oban Z and counry wll ry o roduce more of good Z and exor

44 33 o oban Y Fgure -a and b. Noe agan ha afer counres oen o rade hey do so a he world rces, herefore wh rade φ ψ. From equaon 9.6 we have: ρ φ φ θ γ φ ρ θ C C e C C V & &. 3 Usng equaon 9.4 and 9.7 we can show ha, δ ν φ φ u &, 3 Subsung for φ φ & from 3 no equaon 3 he growh rae of consumon for counry could be wren as, ρ δ θ γ u v C. 3 I also can be shown ha he growh raes of,, Y and Q all are equal o he growh rae of C. s descrbed above wh nernaonal rade, φ ψ, herefore ψ γ φ γ γ. Noe ha rade balance requres [ ], assumng >, where he auarc rce level for each counry s,. See aendx.c-i for deals. See aendx.d.

45 Therefore he equlbrum world level of rces mus fall n a consan nerval. lso a balanced growh ah requres everyhng ha grows should do so a a consan rae. Therefore as well mus grow a a consan rae along he balanced growh ah. These wo condons ogeher mly ha he only rae ha could grow a and say n a consan nerval s zero. Now f γ henγ γ φ γ. ψ Usng 9.4, 9.5, 9.7 and 9.8 and zero growh rae of rce level on he balanced growh ah, he growh raes of cosae varables can be oban as 3, and, & φ φ ν u δ, 33 ψ& ψ v u δ. 34 s exlaned hese growh raes are equal on he balanced growh ah. Therefore by equang hem for counry we can oban, ν u, 35 Subsung for he caal raos from equaon 35 no 3, we ge he growh rae for counry n he resence of rade as, or, γ θ δ ρ, T, 3 Deals are resened n aendx.c. 34

46 35 [ ] ρ δ θ γ,. T. 36 Smlarly, n endx.c we have shown he growh raes of φ and ψ could also be obaned as, δ ν φ φ u &, 37 and, δ ψ ψ u v &. 38 Equang equaons 37 and 38 we ge, u v. 39 The growh rae for consumon as shown n 3 s, ρ φ φ θ γ C C & &. 4 Then subsue 39 no 37 for counry we ge, δ φ φ &, 4 and hen subsung 4 no 4 he growh rae of counry wll become, ρ δ θ γ C, 4 or alernavely, [ ] ρ δ θ γ,. T. 43

47 36 The growh raes for boh counres are greaer han he growh raes under auary for any n he nerval,. To see hs, remember he growh rae and he rce level under auary are, ρ δ θ γ,. endx.e.i and.e.ii show ha we can smlfy he auarc growh rae for each counry as, [ ] ρ δ θ γ, u, [ ] ρ δ θ γ, u. Now <, hen [ ] ρ δ θ γ,. T, ρ δ θ., > ρ δ θ. u γ,. also, <, hen [ ] ρ δ θ γ,. T,

48 37 [ ] ρ δ θ >. u γ,. These nequales mly ha rade wll rase he growh raes of boh counres for any,. owever we should noce ha he growh raes n 36 and 43 are no equal for any arbrary. The rce level a whch he growh raes n wo counres wll be equal can be obaned by equang he growh raes n 36 and 43, and ha rce level wll hen be,,, * γ γ T T. 44 y subsung hs value no equaons 36 and 43 we can ge he equlbrum growh rae as, ρ δ θ γ γ γ,, T T. 45 Now consder he growh raes for and, X C u v X C u v δ δ & &, 46 X C u v X C u v δ δ & &. 47 If we mose he rade balance condon,.e. X X, hen we can rewre he equaon 47 as, X C u v δ &. 48