ENDOGENOUS WEALTH AND KNOWLEDGE IN HECKSCHER-OHLIN THEORY

Transcription

1 Inernaional Journal of Developmen and Conflic () 9 ENDOGENOUS WEALTH AND KNOWLEDGE IN HECKSCHER-OHLIN THEORY PROF. WEI-BIN ZHANG* Risumeikan Asia Pacific Universiy, Japan This sudy inroduces endogenous knowledge in he wo-counry free-rade model wih endogenous capial recenly proposed by Zhang (). We examine he role of knowledge uilizaion efficiencies, learning by doing efficiencies, oal facor produciviies, and preferences in influencing dynamics of capial socks, knowledge, and paern of rade on he basis of he generalized Heckscher-Ohlin (H-O) heory of inernaional rade. The paper consrucs a free rade model wih wealh and knowledge accumulaion as growh deerminans. Labor and capial disribuions beween counries and beween secors are deermined in perfecly compeiive markes. The model is an inegraion of he Oniki-Uzawa rade model, he H-O model, he Solow-Uzawa neoclassical growh model, Arrow s learning-by-doing model, and Zhang s reamen of knowledge as inernaional public sock. The model is simulaed. The exisence of equilibrium poin is confirmed. The moion of he dynamic sysem is ploed. We carry ou comparaive dynamic analysis wih regard o he knowledge uilizaion efficiencies, populaion expansion, he propensiy o consume capial good, he propensiy o consume counries specified goods, and he propensiy o hold wealh. Keywords: O-H model; learning by doing; knowledge uilizaion efficiency; global economic growh; knowledge accumulaion. Inroducion This sudy inegraes endogenous knowledge wih he generalized Heckscher-Ohlin (H-O) model recenly proposed by Zhang (). As one of he core models in modern inernaional rade heory, he H-O model is originally consruced for wo counries (Heckscher, 99; Ohlin, 9; and Heckscher and Ohlin, 99). The original model is basically saic. The global economy produces wo goods by employing wo fixed inpu facors (labor and capial). Markes in naional economies and rade beween counries are perfecly compeiive wih consan reurns o scale. The wo sric assumpions in he model are ha counries share he same echnology and inpu facors of producion are immobile beween counries. Moreover, i is assumed ha producion facors are exogenously fixed. We relax hese assumpions by inroducing endogenous capial, * wbz@apu.ac.jp Copyrigh Wei-Bin Zhang Licensed under he Creaive Commons Aribuion-NonCommercial License.

2 Wei-Bin Zhang endogenous knowledge and free rade. The imporance of examining differences in saving and knowledge uilizaion is illusraed by wha Chen (99: 9-) describes when reviewing he lieraure of O-H heory and inernaional rade: I appears o be he general consensus in his body of lieraure ha he main deerminan of long-run comparaive advanage is he counries savings raes. The quesion of wha has caused he difference in savings raes among counries, however, is rarely explicily discussed in he lieraure. The models ha do endogenize savings raes (e.g., Sigliz 9) aribue he difference in savings raes and hence long-run comparaive advanage o a difference in preferences; in paricular, a difference in agens ime discoun facors among counries. Ye explaining rade in erms of differences in preferences is no longer in he spiri of he Heckscher-Ohlin model in which rade arises because of differences in relaive facor proporions. Many sudies are conduced in generalizing and exending he H-O heory. For insance, Chen (99) examines open economies in he H-O modelling framework. Chen inroduces endogenous labor supply and savings. Baxer (99) applies a model srucurally similar o Chen s model and includes differen ax raes across counries. Venura (99) examines rade issues wihin an Ramsey growh modelling framework. A dynamic H-O model is proposed by Bajona and Kehoe (). The model inegraes a saic sandard H-O rade model wih a wo-secor growh model of infiniely lived consumers wih borrowing and lending. A recen exension of he H-O model o a dynamic neoclassical framework is given by Zhang (). The model by Zhang deals wih rade paerns wih differen propensiies o save and o consume by applying he approach o describing household behavior proposed by Zhang (99). This sudy generalizes Zhang s sudy by inroducing endogenous knowledge hrough Arrow s idea of learning by doing. This sudy deals wih a dynamic inerdependence beween global economic growh, economic srucural change, wealh accumulaion, knowledge accumulaion, and inernaional rade. Produciviy differences and echnological changes are imporan deerminans of variaions in incomes across counries (Manasse and Turrini, ; Agénor, ; Aghion e al. 9; Gersbach e al. ). The model is buil on he basis of neoclassical growh heory wih endogenous capial and neoclassical growh heory wih endogenous knowledge. I is a synhesis of he H-O heory, he Solow growh model (Solow, 9), he Uzawa wo-secor model (Uzawa, 9, 9), and he Oniki-Uzawa rade model (Oniki and Uzawa, 9). We model echnological change on he basis of lieraure of endogenous economic growh (Arrow, 9, Uzawa, 9, Romer, 9; Lucas, 9; Grossman and Helpman, 99; Aghion and Howi, 99). There are differen ways of inroducing endogenous knowledge ino rade heory (e.g., Chari and Hopenhayn, 99; Marin and Oaviano, ; Brecher e al. ; Nocco, ; Hinloopen, ). In his sudy knowledge is assumed o be an inernaional public good. All counries have free access o knowledge and knowledge uilizaion by any counry does no influence ha by ohers (Zhang, 99). I should be noed ha he model in his sudy is Ricardian. I assumes differences beween counries in echnology and labor produciviy. IThe radiional Ricardian heory does no explains endogenous deerminans of he differences. I should be noed ha excep endogenous knowledge (Zhang, 99), mos of our model

3 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory based on Zhang (). The res of he paper is developed in he following way. The basic model is cinsruced in Secion. The dynamic analysis and simulaion of he global economy are carried ou in Secion. Comparaive dynamic analysis is conduced in Secion. In Secion we conclude he sudy. The main resuls in Secion are checked in he Appendix.. The Model This sudy synhesizes he models developed by Zhang (99, ). The rade model by Zhang () is influenced by he H-O model and neoclassical rade growh heory. The global economy is composed of wo naional economies. They are indexed by j =, No ariff on any good exiss in he global economy. A naional economy supplies hree goods. The wo counries produce a homogeneous capial good. Capial good is used as capial and consumer goods. The secor which supplies capial good is called he capial goods secor. The capial goods secor has almos he same feaures as he producion secor in radiional neoclassical rade heory wih a homogeneous good and endogenous capial (e.g., Ikeda and Ono, 99). There is inernaionally free mobiliy of capial goods. Each counry provides service. Services is only consumed by domesic consumers. Each naional economy also supplies a counry specified-good. I is produced only by he counry and is inernaionally radable. Specified goods are pure consumpion goods. Hence, each counry has he capial goods secor, specified goods secor, and service secor, indexed by i, j, s. Each secor uses wo inpu facors, capial and labor. All markes are perfecly compeiive. Inpu facors are fully employed a every momen in ime. There is no inernaional mobiliy in labor markes. Labor is freely mobile wihin each naional economy. Capial is freely domesically and inernaionally mobile. Saving is made only by households. All earnings of firms are paid o inpu facors of producion. There is no possibiliy of hoarding oupu in he form of nonproducive invenories. Le all he prices be measured in erms of capial good. We use p j () o represen he price of counry j s service. The price of counry j s specified good is p j (). No inernaional migraion implies difference in wage raes w j () beween counries. Free movemen of capial implies equalizaion of rae of ineres r(). Capial depreciaion raes, δ jk, are fixed. Le N jq () and K jq () represen labor force and capial socks employed by secor q in counry j We use F jq () o represen oupu level of secor q in counry j Producion funcions Following Zhang (99), we assume ha knowledge is an inernaional public good. Knowledge can be applied by any secor wihou affecing ohers. Knowledge is a public good which can be freely used by differen producers. The producion funcions are neoclassical and homogeneous of degree one wih he inpus. We ake he producion funcion of secion q in counry j on he following form m jq α jq βjq,, α, β, α β, F = A Z K N A > + = () jq jq jq jq jq jq jq jq jq

4 Wei-Bin Zhang in which Z() (> ) is he knowledge sock a ime, and A jq, α jq, and β jq are posiive parameers. Here, m jq is called (j, q) s knowledge uilizaion efficiency parameer. If m jq / β jq Z N j is inerpreed as (j, q) s qualified labor force, we see ha he producion funcion is a neoclassical one and homogeneous of degree one wih he inpus. I should be noed ha he Richardian rade heory is buil wih echnological differences beween counries, while he H-O heory is buil for differences in capial and labor endowmens bu idenical echnology beween counries. This paper akes accoun of no only differences in capial and labor endowmens bu also differences in echnologies beween counries. The marginal condiions for he capial goods secors All prices are deermined by freely compeiive markes. Each individual firm has rae of ineres, wage rae, and prices as given. The capial goods secor selecs K ji () and N ji () The marginal condiions for maximizing profi are α ji Fji βji Fji r + δ jk =, wj =, j=,. K N () The marginal condiions for counry j s specified goods secors The marginal condiions imply ji ji α jj pj Fjj βjj pj Fjj r + δ jk =, wj =, j=,. () K N The marginal condiions for service secors The marginal condiions for service secors imply jj jj α js pjs Fjs βjs pjs Fjs r + δ jk =, wj =, j=,. () K N The curren income and disposable income js This sudy applies an alernaive approach o household behavior developed by (Zhang, 99). Consumers choose consumpion levels of goods and saving. We use kj ( ) o represen he value of wealh of household in counry j. Per household's curren income from he ineres paymen rk j ( ) and he wage paymen w j () is = +. y rk w j j j I is assumed ha selling and buying wealh can be conduced insananeously wihou any ransacion cos. The per capia disposable income is he sum of he curren income and he value of he wealh js yˆ = y + k = + r k + w. () j j j j j The disposable income is disribued beween saving and consumpion.

5 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory The budges and uiliy funcions We use c jq () o represen consumpion level of consumer good q in counry j Le s j () sand for he represenaive household s saving. Consumer j s budge consrain implies cji + p cj + p cj + pjs cjs + sj = yˆ j. () Consumers uiliy is dependen on he consumpion levels of goods and services, and he saving as follows ξji ξj ξj γ js λj U = c c c c s > () j ji j j js j, ξji, ξj, ξj, ξjs, λj, where ξ ji is he propensiy o consume capial good, ξ jj he propensiy o consume counry j s specified good, and λ j he propensiy o save. Maximizing () subjec o () yields where = ξ ˆ = ξ ˆ = ξ ˆ = ξ ˆ, = λ ˆ, c y, p c y, p c y, ji ji j j j j j j j p c y s y js js js j j j j ξ ρ ξ, ξ ρ ξ, ξ ρ ξ, ξ ρ ξ, λ ρ λ, ji j ji j j j j j j js j js j j j ρ j ξ + ξ + ξ + ξ + λ ji j j js j. Wealh accumulaion The change in wealh is he saving minus he dissaving. The definiions of s j () implies he following equaion for he wealh change of he represenaive household k = s k (9). j j j Facors being fully employed The capial socks employed by counry j is denoed by K j () The full employmen of naional capial sock implies,,. K + K + K = K j = () ji jj js j Fully employmen of naional labor force implies,,. N + N + N = N j = () ji jj js j Marke clearing for wo radable goods We have,,. c N = F j = () js j js Marke clearing in each specified good markes We have cq N + cq N = Fqq, q =,. () ()

6 Wei-Bin Zhang Marke clearing in capial markes The global ne savings equals he global capial producion ( sj N j kj N j + δkjk j ) = Fji j= j=. () Wealh balance All he households wealh equals he oal global wealh k N + k N = K + K = K, j =,. () Knowledge creaion Following Arrow s idea of learning-by-doing (Arrow, 9), we have he following equaion o model knowledge growh (Zhang, 99) τ ji Fji τ jj Fjj τ js Fjs Z = + + δ z Z, ε j ji εjj ε () = js Z Z Z where δ z ( ) is he fixed rae of knowledge depreciaion, and ε jq and τ jq are parameers. ε jq The parameers τ jq are non-negaive. The erm τ jqf / Z is he conribuion of counry j s capial goods secor o knowledge growh hrough learning by doing. We hus buil he dynamic model wih endogenous wealh accumulaion.. Dynamic Analysis The sysem we buil o describe moion of global economy are nonlinear differenial equaions. I is usually no possible o solve such nonlinear equaions. We simulae he model. Before we provide a compuaional procedure o follow he movemen of he global economy, we inroduce he following variable z r + δ w The following lemma is checked in he Appendix. Lemma We describe movemen of variables z (), differenial equaions k. k and Z() by he following hree, (,, ), (,, ), =Λ z z k Z k =Φ z, k, Z, Z z k Z =Λ ()

7 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory where Λ, and Φ, and Λ are funcions of Z (),, Appendix. The values of he oher variables are given as funcions of Z (), k and Z() defined in he k, and Z() a any poin in ime as follows: r() by (A) w j () by (A) p j () by (A) p js () by (A) k ( ) by (A) K() by (A) N jj () by (A) N ji () by (A) N js by (A) K ji (), K jj (), K js () by (A) F jq () by () yˆ j ( ) by (A) K j () by () c j (), c j () and s j () by (). This lemma enables us o follow he moion of he sysem. For simulaion, we specify values of he parameers as follows N =, N =, =., A =., A =., A =., A =., A =, A =, jk i i s s m =., m =., m =., m =., m =., m =., δ =., τ =., i i s s z i ε =., τ =., ε =., τ =., ε =., τ =., ε =., α =., i i i i α =., α =., α =., α =.9, α =., ξ =., ξ =., ξ =., i s s i ξ =., λ =., ξ =., ξ =., s s i ξ =., ξ =., λ =.. s s Counry s populaion is smaller han counry 's populaion. Depreciaion raes of physical capial are equal beween he wo counries and beween he secors. The oal facor produciviies vary beween he wo counries. Counry s knowledge uilizaion efficiencies are higher han counry s. Counry is more efficien in learning by doing han counry. The oal facor produciviy of counry s indusrial secor is lower han counry s. The propensiy o save of counry s represenaive household is higher han ha of counry s. The iniial condiions are z =., k =, Z =. We plo he moion of he sysem in Figure in which he naional incomes and he global income are defined as follows: Y F + p F + p F, Y Y + Y. j ji js js j jj Before he global economy becomes saionary, he global income, naional incomes, and wealh rise in associaion wih falling in knowledge. In he iniial sage counry is in rade defici and in he long erm counry is in rade surplus. Economic srucural changes ake place in he wo naional economies. The oupu of counry s capial secor rises and he oupu of counry s capial secor alls. The oupu levels of he wo counries domesic goods secors are increased. The oupu of counry s service secor rises and he oupu of counry s service secor falls. The rae of ineres falls and he wage raes rise slighly. The represenaive household of counry has more wealh and consumes more goods and service. The wealh and consumpion levels of he goods and service of he naive household of counry are slighly changed.

8 Wei-Bin Zhang. K Y. Z F K s K 9 k K K F K s F. i i N K. F K s N s. 9.9 N F s N s K. r. 9 w c. c c. c s i 9.. c.. c s k c i.. c Figure. The Moion of he Global Economy F i w Y Figure shows ha he sysem ends o be saionary as ime passes. The procedure in he lemma enables us calculae he equilibrium values of he variables as follows Y =., Z =.9, K =., Y =., Y =.9, K =., K =., N p N i p K i K i Y p s p s K =., K =., r =., w =., w =., p =.9, p =., p =., p =., c =.9, c =., c =., c =., c =., c s s i i =., c =., cs =.99, k =., k =., s F i F i. F. F 9. N i =., N i =., N =., N =., Ki 9 Ki. K 9 K. Fs. Fs 9. N =., N =... s s Ks. Ks We calculae he hree eigenvalues {.,.,. }. All he eigenvalues are negaive. This implies ha he world economy is sable. The sabiliy guaranees comparaive dynamic analysis.

9 Comparaive Dynamic Analysis Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory The previous secion simulaed he moion of he dynamic sysem. We now conduc comparaive dynamic analysis. Basing on he resuls in he previous secion, we can examine ransiory and long-erm effecs of changes in any parameer. A variable x inroduced o represen he change rae of he variable x() in percenage due o changes in he parameer value. A rise in he knowledge uilizaion efficiency of counry s capial goods secor Firs, we sudy he impac on he movemen of he global economy when he knowledge uilizaion efficiency of counry s capial goods secor is enhanced as follows: m i :... The simulaion resuls are ploed in Figure. Secor (, i) s oupu is augmened. The wage rae in counry rises. The rae of ineres falls. Secor (, i) increases labor and capial inpus. Secor (, ) reduces labor inpu. Secor (, s) iniially reduces labor inpu and raise labor inpu in he long erm. Secors (, ) and (, s) iniially produce less and in he long erm produce more. Secors (, ) and (, s) employ more capial. In counry he wage rae is reduced. Secor (, i) reduces is oupu and employs less labor and capial. Secor (, ) augmens is oupu and employs more labor. The capial sock employed by secor (, ) is slighly changed. The prices of counry s specified good and service in counry are lowered and he prices of counry s specified good and service in counry are enhanced. The household in counry owns iniially less wealh and in he long erm more wealh; iniially consumes less he capial good, counry s specified good and service and in he long erm re; consumes more counry s specified good. The household in counry owns less wealh, consumes less he capial good, counry s specified good, and consumes more service and counry s specified good. K 9 K K Z K 9 K.. Y 9 F i F i N i 9 N i Y.. 9 K i 9 K i Y F 9 N N 9 F K K 9. F s F s 9. N s N s 9 K s K s 9 k k 9. r. 9 c i 9 c i 9 w c w c 9. p 9 p c 9 c. p s 9 p s c s c s 9 Figure. A Rise in he Knowledge Uilizaion Efficiency of Counry s Capial Goods Secor

10 Wei-Bin Zhang An improvemen in he oal facor produciviy of counry s specified goods secor We now deal wih he effecs of an improvemen in he oal facor produciviy of counry 's specified goods secor. The oal facor produciviy is shifed as follows A :... We plo he simulaion resuls in Figure. Counry 's specified goods secor expands. The secor increases oupu, raises capial inpu, and reduce labor inpu. Counry s service secor produces more, raises capial inpu and reduces labor inpu. Counry s capial goods secor raises oupu and raises labor and capial inpu facors. Counry s capial and service secors raise oupu and employ more capial. In he long erm he wo secors employ less labor. Counry s specified goods secor produces more and employs more he wo inpu facors. The global wealh and oal produc are augmened. Knowledge is increased. The wo counries naional producs are enhanced. The rae of ineres rises iniially and does no change in he long erm. The wage raes are augmened. The prices of he services in he wo counries are increased. The price of counry s specified good falls and he price of counry s specified good rises. All he households in he global economy own more wealh, consume more goods and services... 9 F F 9.. K. K K 9 K s K s 9 k k K K N. 9 9 Z r c i N c i Y F i w p N s N s c. 9. N i F i K i 9 N i K K Figure. A Rise in he Toal Facor Produciviy of Counry s Specified Goods secor w c p Y F s F s c c Y K i p s p s c s c s Counry s populaion rises We now deal wih he impac on he moion of he global economy when counry s populaion rises as follows: N :. We have he simulaion resuls in Figure. There is lile impac on he knowledge sock. There are increases in he global produc and wealh. Counry s oal oupu level falls and counry s oal oupu level rises. From he figure we also see he economic srucural changes in he wo economies. In he long erm he per households wealh and consumpion levels are slighly affeced. We see ha

11 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory 9 in he long erm he change in counry s populaion has lile impac on he households wealh and consumpion levels... Z... K Y K. K F F. 9.. k. K K 9 N. 9. K s r. K s 9 9 k N 9 K i 9 i K. 9.. F i N F i N K i i K 9 N 9.. p 9. p p s p s. w w 9 9 c c c i c s c. c. c c s i.... Figure. Counry s Populaion Rises F s Y Y N s F s s Counry s populaion rises We show ha a change in counry s populaion has lile impac on he households wealh and consumpion levels. We now examine he impac on he moion of he global economy when counry s populaion rises as follows: N:. We have he simulaion resuls in Figure. Comparing es and, we observe difference in he effecs of changes in he wo counries populaion. A rise in counry s populaion benefis all he households in he global economy. The difference comes from ha counry uses knowledge more effecively and is more efficien in learning by doing han counry. Combining Figures and, we see ha if some of counry s populaion is migraed o counry and he immigrans can adap o counry s social and economic condiions, he global economy benefis.

12 Wei-Bin Zhang K F K K F K s K s 9 k 9 K K 9... Z 9 9 F i 9 9 Y F i c 9 N i 9 9 N i c 9 K i 9. K F s N. N s N K F s. N s r w 9 c i c i c s k c. c Figure. Counry s Populaion Rises w Y p p Y p s K i c s p s Counry raises he propensiy o consume is specified good We now deal wih he effec of a rise in in counry s propensiy o consume he counry s specified good: ξ :... We have he resuls in Figure. Counry s household raises he consumpion of he counry s specified good. The household s wealh and consumpion levels of he oher goods and services fall. Counry s household has less he wealh level and consumes less he s and service. We see ha excep ha he household in counry consumes more counry s specified good, all he micro variables for all he households are reduced. Excep ha counry produces more counry s specified good, he oupu levels of all he oher secors are reduced. The global wealh, knowledge and global produc are reduced. The wo counries oal producs fall.

13 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory K Z Y. 9 K 9 9. K F N K s F K s. 9 K K N 9 r N i F i K i F s 9 K 9 K F s. F i 9 w.. p 9... N s 9 9 p s c k s c c i 9 c k c c i c c 9 s w N i Y Y s p N p s K i Figure. Counry Raises he Propensiy o Consume Is Specified Good Counry augmening he propensiy o consume counry s specified good We now examine he impac of a rise in counry s propensiy o consume he oher counry s specified good: ξ :... We have he simulaion resuls in Figure. Counry s household consumes more counry s specified good. The household s wealh and consumpion levels of he oher goods and service fall. Counry s household slighly changes he wealh and he consumpion levels of goods and service. The global wealh, global produc, and he wo counries oal producs are reduced. The knowledge sock rises. The rae of ineres and he wage raes rise. Counry s rade balance is deerioraed and counry s rade balance is improved. Secor (, i) produces more and employs more he wo inpu facors and secor (, i) produce less and employs less he wo inpu facors. Secor (, s) supplies less and employs less he wo inpu facors. The oupu level of secor (, s) is slighly affeced. Secor (, ) supplies less and employs less he wo inpu facors. Secor (, ) supplies more and employs more he wo inpu facors.

14 Wei-Bin Zhang.. K K s K k K F F K s k K 9 N 9 9. K r c i Z N c i Y F i 9 K 9 9 w w c c N i 9 F s 9 c K i 9 F N i i K i K c Y Y F s s p p 9 N s 9 N p s 9 p s c s 9 c s Figure. Counry Augmening he Propensiy o Consume Counry s Specified Good Counry raises he propensiy o save We now examine he impac of a rise in counry s propensiy o save: :... λ We have he simulaion resuls in Figure. The global oal income, global wealh, and he wo counries oal incomes are increased. The knowledge sock rises. Counry s household increase he wealh over ime. The consumpion levels of he wo goods and service of counry s household fall iniially and rise in he long erm. The wealh and he consumpion levels of he wo goods and service in counry rise. The wage raes rise. The rae of ineres falls. The prices of he wo counries specified goods and services are increased. Counry s rade balance is improved and counry s rade balance is deerioraed.

15 K K K F F 9 K s K s 9 k k 9.. Z 9 r Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory K.. K F i i F i N i K i.. N K i K N F s Ns N K 9. F.. s N 9 s c i c c c s c i c c c s Y w Figure. Counry Raises he Propensiy o Save w Y p p Y p s p s. Concluding Remarks This sudy inroduced endogenous knowledge in he wo-counry free-rade model wih endogenous capial recenly proposed by Zhang (). We examined he role of knowledge uilizaion efficiencies, learning by doing efficiencies, oal facor produciviies, and preferences in influencing dynamics of capial socks, knowledge, and paern of rade on he basis of he generalized H-O heory of inernaional rade. The paper consrucs a free rade model wih wealh and knowledge accumulaion as growh deerminans. Labor and capial disribuions beween counries and beween secors are deermined in perfecly compeiive markes. The model is an inegraion of he Oniki-Uzawa rade model, he H-O model, he Solow-Uzawa neoclassical growh model, Arrow s learningby-doing model, and Zhang s reamen of knowledge as inernaional public sock. The model was simulaed. The exisence of equilibrium poin was confirmed. The moion of he dynamic sysem was ploed. Comparaive dynamic analysis wih regard o he knowledge uilizaion efficiencies, populaion expansion, he propensiy o consume capial good, he propensiy o consume counries specified goods, and he propensiy o hold wealh was conduced. We may exend he model in differen direcions. We may, for insance, furher simulae he model wih differen ypes of uiliy and producion funcions. We may also conduc more comparaive dynamic analysis wih regard o oher parameers. As he model is buil on a few core models in he lieraure of economics and here is a vas lieraure on generalizing and exending each model, we may generalize he model on he basis of he rich lieraure.

16 Wei-Bin Zhang Appendix: Proving he Lemma The appendix checks he lemma. Equaions ()-() imply z j r + δ α N α N α N = = = w K K K jk ji ji jj jj js js j ji jj js, (A) where α α / β. From (A), (), and (), we ge jq jq jq m ji β ji α ji Aji Z zj r + δ jk r( zj, Z) = δ jk, wj ( zj, Z) =. β ji α z j ji (A) From (A) we have From (A), (), and (), we have Equaions (), () and (A) imply From (A) and () we ge Equaions () and () imply / βi r + δ k ( ) = mi αi αi Ai Z z z, Z. α jj (A) wj zj pj ( z, Z) =. m jj α jj (A) β A Z α jj jj jj α js wj zj pjs ( z, Z) =. m js α (A) js β A Z α js js js α N + α N + α N = z K. (A) ji ji jj jj js js j j N = n k + β ξ N, (A) js j j js js j where Subsiue (A) ino () + r n j ( z, Z) βjs ξjs N j. wj where n ( β ξ ) N ji = nj n j kj N jj, j =,, (A) N. Subsiue (A) and (A) ino (A) j js js j N jj = zj K j α js βjs ξjs N j α ji nj α js α ji n j k j. (A9) ( α jj α ji )

17 Endogenous Wealh and Knowledge in Heckscher-Ohlin Theory Subsiue () ino () ξ yn ˆ + ξ yˆ N = pf, j=,. j j j jj (A) Subsiue () ino (A) N Subsiue () ino (A) jj βjj ξj yn ˆ βjjξj yˆ N = +, j =,. (A) w w j j w j k + w j k + w j = N jj, j =,. (A) where ( + ) ( + ) r β ξ N r β ξ N w β ξ N w β ξ N w, w, w. jj j jj j jj j jj j j j j + wj wj wj wj Equaling (A) and (A9) yields k w ( α α ) ( α α ) ( α α ) i w s i n i k z z α α w + α β ξ N + α n z i s s s i ( α α ) ( α α ) ( α α ) w k i k i w s i n z z α α w + α β ξ N + α n z Add he wo equaions in (A) i s s s i = K, = K. (A) where ak + ak + a = K, (A) ( α α ) ( α α ) ( α α ) i + s i + i z z a w n w a ( α α ) + ( α α ) w + ( α α ) n a i i s i z z α α w + α β ξ N + α n α α w + α β ξ N + α n + z z i s s s i i s s s i w,,. From () and (A) we solve N a a k =Φ z, k, Z k. a N a N (A)

18 Wei-Bin Zhang Hence, we show ha all he variables are represened as funcions of z, k and Z as follows: r by (A) w j by (A) z by (A) p j by (A) p js by (A) k by (A) K by (A) N jj by (A) N ji by (A) N js by (A) F jq by () y ˆ j by () c j, c j and s j by () K ji, K jj, K js by (A) K j by (). From his procedure and (), we have k =Φ( z, k, Z) s ϕ, (A) k =Φ z, k, Z s k, ji Fji jj Fjj js Fjs Z τ τ τ =Λ( z, k, Z) + + δ z Z. ε j ji εjj ε = js Z Z Z We aking derivaives of (A) in k z Z k In which (A) is used. Subsiue (A) ino (A) (A) = Φ z +Λ Λ +Φ Φ, (A) (,, Λ Φ Φ z =Λ z k Z) Φ Λ Φ Z k z. (A9) The procedure in he lemma resuls he dynamics of he economic sysem. The lemma is checked. References Agénor, P.R.. Does Globalizaion Hur he Poor? Inernaional Economics and Economic Policy : -. Aghion, P., Blundell, R., Griffih, R., Howi, P., and Pranl, S. 9. The Effecs of Enry on Incumben Innovaion and Produciviy. The Review of Economics and Saisics 9:. Aghion, P. and Howi, P. 99. A Model of Growh hrough Creaive Desrucion. Economerica :. Arrow, K.J. 9. The Economic Implicaions of Learning by Doing. Review of Economic Sudies 9:-. Barro, R.J. and X. Sala-i-Marin. 99. Economic Growh. New York: McGraw-Hill, Inc. Baxer, M. 99. Fiscal Policy, Specializaion, and Trade in he Two-Secor Model: The Reurn of Ricardo? Journal of Poliical Economy :. Bajona, C. and Kehoe, T.J.. Trade, Growh, and Convergence in a Dynamic Heckscher- Ohlin Model. Review of Economic Dynamics :-. Brecher, R.A., Chen, Z.Q. and Choudhri, E.U.. Absolue and Comparaive Advanage, Reconsidered: The Paern of Inernaional Trade wih Opimal Saving. Review of Inernaional Economics :-. Bresnahan, T.F. and Trajenberg, M. 99. General Purpose Technologies: Engines of Growh? Journal of Economerics : -. Chari, V.V. and Hopenhayn, H. 99. Vinage Human Capial, Growh, and he Diffusion of New Technology. The Journal of Poliical Economy 99:-.

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