SCHOOL OF ECONOMICS Adelaide University SA 5005 AUSTRALIA

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1 Open Economy chumpeerian Growh Raul A. Barreo and Kaori Kobayashi Working Paper -9 CHOOL OF ECONOMIC Adelaide Universiy A 55 AUTRALIA IN

2 Open Economy chumpeerian Growh by Raul A. Barreo ** and Kaori Kobayashi *** epember Absrac This paper examines he Aghhion and Howi [99] creaive desrucion endogenous growh model in an open economy seing. We consider four alernaive rade regimes. The firs wo regimes allow he monopoly producer of he inermediae good o aain worldwide monopoly rens. In he firs of he wo, he counries engage in rade of only he imperfecly produced inermediae good. In he second, he wo counries rade in boh he inermediae good as well as in ideas. The las wo regimes consider wo counries which are idenical before and afer rade opens such ha pro-compeiive gains from rade are achieved. We again consider when only inermediaries may be raded and hereafer when boh inermediaries and ideas may be raded. We find ha he effecs of rade on growh and welfare depend criically on he assumpions one imposes. Keywords: Creaive Desrucion, Obsolescence, Endogenous Growh, Inernaional Trade, Imperfec Compeiion ** Raul A. Barreo, chool of Economics, Adelaide Universiy, Adelaide, A 55, Ausralia. Ph , fax , raul.barreo@adelaide.edu.au *** Kaori Kobayashi, Economics Deparmen, Kansai Universiy, Osaka, , Japan, ph , fax , kaorik@cam.hi-ho.ne.jp

3 . Inroducion The goal of new growh heory is o explain how long run growh in per capia income can occur. When echnological advances are assumed o be exogenous, as hey are in he predecessors o all he work in his growing srand of lieraure, he ulimae conclusion is always he same. Irrespecive of which model one considers as he basis for growh, he Ramsey (98) model, i s more modern Lucas (988) version, or he Diamond (965) model, he underlying resul is he same. Long run growh in per capia income can only resul from increasing produciviy of labor. In oher words, GDP per capia can only grow in he long run as a resul of echnological growh. As a consequence of his heoreical regulariy, several auhors have considered he naure of echnology and i s evoluion. Two influenial papers in New Growh Theory are Romer (99) and Aghion and Howi (99). They are similar in ha hey boh consider echnological change o be he resul of researchers whose incenive i is o garner monopoly profis from heir invenions. Researchers in Romer (99) make innovaions ha are based on pas innovaions. Once a researcher comes up wih an innovaion, he owns a monopoly over i for ever afer. The model herefore describes a paen sysem where he paens never expire. There exiss a marke for every paen however many generaions back from he mos curren innovaion i was inroduced. This is simply because each successive innovaion is dependen upon is predecessor such ha here exiss a coninuum of invenions all absoluely necessary o he incumben monopolis who holds he mos recen paen. Aghion and Howi (99) consider he same idea wih a slighly differen wis. When a new innovaion is inroduced, i makes is predecessor obsolee. Endogenous echnological change is hence he resul of coninuous obsolescence or creaive desrucion. In heir model, he incumben researcher uses he level of echnology, which he proposes o add o, as opposed o he acual las innovaion. Alhough echnological advances occur randomly, hey do so wih a discernable Poisson arrival rae. Thus on average, one may consider he likelihood of a echnological advance wihin a given span of ime. imilar o Romer (99), he incenive o conduc research sems from he monopoly profis available from holding he mos recen paen. Exensions of he above wo seminal papers are numerous and cover many of he sylized facs ha we observe in he world. Of paricular ineres here is he open economy implicaions of echnological change. Rivera-Baiz and Romer (99) consider he open economy version of Romer (99). Therein, hey consider wo economies ha may rade in he imperfecly produced inermediae good as well as rade in ideas. Their incumben innovaor may garner monopoly rens in boh he home and foreign markes. A sligh problem wih ha paper is ha alhough hey assume ha he wo counries are idenical while in auarky, hey cease o be so wih inegraion. As a resul, he wo counries ake urns innovaing. This paricular issue is addressed in Barreo and Kobayashi (). We consider he implicaions of he wo counries remaining idenical even afer inegraion. Our findings parallel he sandard rade lieraure resuls of procompeiive gains from rade beween counries where one or more of he raded goods is imperfecly produced. Thus, we find ha imperfec compeiion is a sufficien deerminan of rade even beween oherwise idenical counries.

4 In he following paper, we consider boh assumpions. ecion reviews he basic Aghion and Howi (99) model in a closed economy seing. ecion 3 considers economic inegraion of wo counries using heir framework. ecions 3. and 3. consider, as in Rivera-Baiz and Romer (99), he availabiliy of worldwide monopoly rens, firs when only inermediaries may be raded and hen when boh inermediaries as well as ideas may be raded. ecions 3.3 and 3.4 consider, as in Barreo and Kobayashi (), he pro-compeiive gains from rade ha resul from a duopoly afer inegraion. Again, we consider firs if only inermediae goods may be raded and second, if inermediae goods as well as ideas may be raded. ecion 4 compares he resuls across he four possible cases. ecion 5 presens some conclusions.. Closed Economy The following is a summary of he chumpeerian approach o endogenous echnological change inroduced by Aghion and Howi (99). Throughou his secion, we assume auarky wihin each counry. The economy consiss of hree secors: a final goods secor, an inermediae goods secor, and a R&D secor, all of which behave o maximize he represenaive agen s uiliy funcion. r U( y) e yd () Only he final good, y, can only be consumed and i is subjec o discoun rae r. I is produced using only he mos recen version of he inermediae goods, x, according o he following producion funcion. y Ax () This is he essence of he echnological change resuling from obsolescence. Firms compee across ime o produce an ever-improving inermediae good. When a firm develops a successful innovaion, i is rewarded wih monopoly profis derived from he sale of is version of x o he final goods producer of y. The aggregae flow of labor supply, L, has wo compeing uses, inermediae goods producion and research. Inermediae firms employ a simple one for one linear producion funcion such ha x is also he amoun of labor used in producing inermediae goods. The developmen of new innovaions is also a resul of a simple linear echnology such ha n is he amoun of labor used in research. Hence he labormarke clearing condiion is L n+ x (3) The level of echnology, A, increases hrough successive innovaions,, ha make is iniial level, A, ever more producive. Each new innovaion raises produciviy of A by a facor of γ such ha A Aγ γ > (4) Innovaions arrive randomly wih a Poisson arrival rae of λ Φ ( n), where ( n) Φ is a consan reurns o scale funcion of research effor, n, and λ > is he produciviy parameer of research echnology. 3

5 ( n) λφ λn (5) The profi funcion associaed wih a new innovaion is RD Π nv wn (6) λ + n where V + is he discouned expeced payoff o he ( + ) h innovaion from research conduced in during period. x + Π+ V+ (7) r + λn+ Therefore, he research firm s firs order condiion may hen be expressed as a funcion of he expeced payoff. x + λπ + wn* λv+ (8) r + λn+ The profi funcion faced by final goods producers and is consequen firs order condiion are defined as follows. y Π y px Ax px (9) x x px Ax () The profi funcion faced by an inermediary and is consequen firs order condiion are defined as follows. x Π px wx Ax wx () x x x wx* Ax () Noe ha he wage paid by he inermediary may also be used o deermine he demand for labor. A x* (3) wx The inverse demand for he inermediae good may be expressed simply as a funcion of he wage. A wx x* A wx p (4) Therefore, he monopoly profis o he inermediary for he mos recen innovaion may be expressed as follows. x Π * wx x * (5) The labor marke is compeiive so ha wx* wn* and he labor marke clearing condiion may hen be expressed as λγ ( L n *) (6) r+ λ n + * Accordingly, he research labor inpu, n, which saisfies equaion (6) may be expressed as 4

6 λγ L r n* (7) λ+ λγ I is imporan o noe ha he ineres rae r, which is defined as he marginal produc of inermediae goods in final goods producion is, in he seady sae equal o he discoun rae. r Ax (8) y Finally, we are only lef o deermine he real ime growh rae in oupu,. In y order o do so, consider firs he flow of final oupu, y, beween wo successive innovaions, and ( + ). The level of oupu, for any given innovaion, is defined simply as y Ax A ( L n ) (9) Technology changes a he fixed rae per innovaion equal o γ. Therefore he relaionship of oupu beween consecuive innovaions is defined as y + γ y () We may hen inerpre he log of equaion () o imply ha he real ime oupu level, lnγ wih each new innovaion. The real ime growh of oupu is y, increases by deermined by he number of innovaions beween period and ( + ). Therefore ln y ( lnγ ) ε ln y where ε equals he number of innovaions beween period and + () + and is disribued randomly wih a Poisson arrival rae of λ n. imple subsiuion yields ha he average growh rae of oupu is defined as follows. y g λn ( ln γ) () y 3. Open Economy In he closed economy, he inermediary solely owns and herefore explois he leading-edge echnology as a monopolis. However, once rade opens, he effecs on he welfare and he growh rae of he economies in quesion depend criically upon he assumpion ha one adops covering he naure of he wo economies and heir subsequen rade. One may eiher assume ha rade allows each innovaing firm o garner worldwide monopoly rens or ha each counry has is own imperfecly compeiive inermediary ha produces a perfec subsiue for i foreign counerpar. Trade under he laer assumpion resuls in cross border duopolisic compeiion and pro-compeiive gains from rade. Trade in which he inermediae firm esablishes a worldwide monopoly over is innovaion is described in Rivera-Baiz and Romer (99). Therein, hey consider 5

7 knowledge driven endogenous echnological change, as is described in Romer (99), where rade in inermediae goods wihou rade in ideas has no growh or welfare effecs whasoever. Their premise is inuiively simple. If he inermediae goods marke is defined by imperfec compeiion, and he uniqueness of innovaions exends worldwide, rade in a wo-counry model exacly doubles he size of he marke faced by incumben innovaors. Bu since he incumben innovaor, wheher home or foreign, faces wice he compeiion from boh home and foreign R&D firms, he larger marke is only available for half he ime. One effec cancels he oher such ha rade in goods wihou rade in ideas has no ne growh or welfare effecs. Once rade in ideas is allowed, in addiion o rade in inermediae goods, boh posiive welfare and growh effecs resul. Alernaively, if one considers wo idenical counries in auarky and hen mainains ha hey are sill idenical even afer economic inegraion, rade in goods wihou rade in ideas resuls in pro-compeiive gains. The resul is inuiively similar o ha which is found in he rade lieraure on imperfec compeiion as a deerminan o rade beween idenical counries. When wo idenical counries rade and he raded good is produced by local monopolies, he resul is a duopoly where he wo imperfec compeiors share he worldwide marke. This alernaive, again using he Romer (99) framework, is explored by Barreo and Kobayashi (). We find herein ha rade in goods wihou rade in ideas has a negaive growh effec bu a posiive welfare effec. Furhermore, once rade in ideas is also allowed, we show ha he growh benefis of rade in ideas ouweigh he negaive growh effecs of he pro-compeiive gains from rade in inermediae goods. There are analyic srenghs as well as weaknesses o eiher lines of reasoning. The main srengh of Rivera-Baiz and Romer (99) relaes o he concep a worldwide monopoly as he incenive o innovae. The main weakness herein is he sepwise naure of rade where each counry is forced o ake urns innovaing. The main srengh of Barreo and Kobayashi () is he pro-compeiive gains resul and is relaion o he rade lieraure. The main weakness in our paper is ha even wihou rade in ideas, each counry comes up wih idenical compeing innovaions. In he following analysis of economic inegraion in a chumpeerian growh model, we consider boh assumpions. ecions 3. and 3. consider rade in boh inermediae goods and ideas under he same assumpions as Rivera-Baiz and Romer (99). ecions 3.3 and 3.4 consider rade in boh inermediae goods and ideas under he same assumpions as Barreo and Kobayashi (). H F 3. Trade in Inermediae goods ( x x ) uppose ha here are wo monopoliss, one per counry, producing x a any given F H innovaion,. Le x be he foreign inermediae goods and x be he home inermediae good. Assume ha he wo counries are idenical only unil he ime of inegraion. H F Once rade commences, he counries become differeniaed such ha x x and each incumben inermediae good producer can garner monopoly rens across he enire world. 3 Each counry produces final goods according o he following producion funcion. 6

8 ( H F y f x or x ) Ax (.) Thus oupu, a any given ime, is a funcion of he mos curren innovaion. Tha innovaion may originae from home or abroad. As before, he ineres rae and in he seady sae he discoun rae, is he marginal produc of inermediae goods used in final producion. r Ax (.) The profi funcion faced by final goods producers and is consequen firs order condiion are he same as before. y Π y px Ax px (.3) x x p Ax (.4) x Noe ha p x is he monopoly price of he laes innovaion, x, as deermined by he incumben inermediae producer who may be foreign or domesic. The monopolis inermediae goods producer, wheher home or foreign, maximizes he following profi funcion and yields he subsequen firs order condiions. x Π p x w x (.5) x x w * Ax (.6) x A * wx x (.7) The monopoly profis can furher be expressed as follows. x Π * wx x * (.8) The profi funcion faced by each R&D firm, wheher home or foreign, is defined as follows. RD Π nv wn (.9) λ + n The effec of he larger marke again eners he sysem analyically hrough he V + erm, which is defined as he discouned expeced payoff o he ( + ) h innovaion from research conduced in during period. x+ r V Π λn V ( + ) + + ( + ) x+ Π (.) + V + r+ λn + Therefore, he research firm s firs order condiion may be expressed as x + λπ+ wn* λv+ (.) r+ λn + The compeiive labor marke where wx* wn*, yields he labor marke clearing condiion. λγ ( L n *) (.) r+ n * λ + 7

9 Accordingly, he labor inpu, n *, for R&D which saisfies his (.) may be expressed as follows. λγ L r n* (.3) λ+ λγ Noice ha equaion (.3) is idenical o equaion (7). The opimal allocaion of work effor oward research is he same under auarky as i is under rade in inermediae goods. Therefore, he consequen growh raes of oupu under he wo regimes mus also be equal. y g λn* ( ln γ) (4) y H F 3. Trade in Inermediae goods and Ideas ( x x ) Once again we assume, ha boh counries are no idenical upon inegraion. Only now, in addiion o rade in inermediae goods, he counries may also rade ideas. This concep is modeled by allowing he wo counries o share in each ohers research effors F H such ha for each counry, n n + n. As before, each counry produces final goods using he mos curren innovaion, irrespecive of wheher ha innovaion originaes a home or abroad. Therefore, he final goods firm s profi funcion is idenical o ha found in secion 3.. Furhermore, he inermediary monopolis s profi funcion is also idenical o ha from he previous secion. For he sake of coninuiy, hose equaions are reproduced here in summary. y Π y px Ax px (.) x x p Ax (.) x x Π p x w x Ax wx (.3) x x x w * Ax (.4) x A * wx x (.5) x Π * wx x * (.6) As menioned earlier, rade in ideas akes he form of counries sharing heir research effor wih one anoher. Alhough each counry s R&D firm benefis from he oher s effors, each need only pay is own employees. The profi funcion faced by R&D firm herefore akes he following form. F Π + (.7) RD λ n n V+ wn n innovaion from research conduced in during period, is deermined slighly differenly han before. V +, again defined as he discouned expeced payoff o he ( + ) h 8

10 x+ F ( + ) Π+ λ ( )( + ) r V n n V x+ Π (.8) + V + r+ 4λn + The research firm s consequen firs order condiion may be expressed as follows. x + λπ+ wn* λv+ (.9) r + λn+ The compeiive labor marke yields he marke clearing condiion, which may be expressed as λγ ( L n *) (.) r+ λ n + * Accordingly, he opimal labor inpu, n *, for R&D which saisfies his (.) may be expressed as follows. λγ L r n* (.) λ+ λγ Inuiively, once rade in ideas is inroduced in addiion o rade in inermediae goods, he period beween innovaions should be shorer. In oher words, one would expec ha hrough cooperaion in research, one counry s R&D firm can cach up and, using he foreign compeior s idea, improve upon he produc in quesion. The analyic soluion for he growh rae of income demonsraes his idea. y g λ n* ( lnγ ) (.) y H F 3.3 Trade in Inermediae goods ( x x ) In his secion and he nex, we consider he case where he wo counries are absoluely idenical in auarky as well as in rade. This mode of analysis parallels he sandard rade lieraure s approach o imperfec compeiion as a deerminan of rade. As in ha line of research, imperfec compeiion in one or more raded goods leads o procompeiive gains from rade beween oherwise idenical counries. uppose again ha here are wo monopoliss, one per counry, producing x a any given innovaion,. ince hey are compleely idenical, each monopolis produces a version of he mos curren innovaion. The wo versions are perfec subsiue for one anoher. Once rade in inermediae goods is allowed, he final goods producer in each counry effecively faces a duopoly. Jus as in he rade lieraure, i is he abiliy of he final goods producer o buy from abroad ha changes he marke srucure of inermediae goods from monopoly o duopoly. Acual rade in inermediae goods does no occur since here is no need. The firm s producion funcion herefore akes he following form. 9

11 F y A x+ x (3.) As a resul of he new marke srucure, he ineres rae, defined as he marginal produc of inermediae goods in final producion, akes he following form. r A x (3.) The final goods producer s profi funcion and is consequen firs order condiion are hen defined as F ( ) ( ) Π y p x+ x A x p x (3.3) y x x ( ) px A x (3.4) imilar o before, he profi funcion faced by duopolis and is consequen firs order condiions are defined as follows. x Π px wx Ax wx (3.5) x x x w A x (3.6) x* A x* (3.7) wx The profis o he duopolis can herefore be expressed as x Π * wx x * (3.8) As in secion 3., he profi funcion faced by R&D secor is defined as follows. RD Π nv wn (3.9) λ + n where + innovaion from research conduced in during period which is deermined from he following. x + rv Π λn V V + is he discouned expeced payoff o he V h x+ Π (3.) + + r + λn + Therefore, he research firm s firs order condiion may be expressed as x + λπ+ wn* λv+ (3.) r + λn+ The compeiive labor marke clearing condiion may be expressed as λγ ( L n *) (3.) r+ λ n + * Accordingly, he labor inpu in research, n *, which saisfies his (3.) may be expressed as follows. λγ L r n* (3.3) λ+ λγ

12 Noice ha he analyic soluion o he opimal research effor, equaion (3.3), is similar in consrucion o ha from auarky, equaion (7). Bu, i is imporan o noe hey are indeed differen because of he ineres rae under duopoly, equaion (3.), is no he same as he ineres rae under auarky, equaion (8). As a resul, alhough analyically similar o auarky, he average growh rae of income also differs wih rade. y g λn* ( ln γ) (3.4) y H F 3.4 Trade in Inermediae goods and Ideas ( x x ) We again assume ha boh counries are absoluely idenical before and afer inegraion. imilar o he changes from secions 3. o 3., here we modify secion 3.3 o allow rade in ideas in addiion o rade in inermediae goods. Again, his concep is modeled by allowing boh counries R&D firms o share in each oher s research effor F H such ha n n + n. The final good producer s profi funcion, he inermediary s producer s profi funcions and consequen firs order condiions are he same as in secion 3.3. We reproduce hem here o mainain he paper s coninuiy. F y A x+ x (4.) r A x (4.) F ( ) ( ) Π y p x+ x A x p x (4.3) y x x ( ) p A x (4.4) x Π px wx Ax wx (4.5) x x x x w A x (4.6) x* A x* (4.7) wx x Π * wx x * (4.8) The R&D firm in each counry now faces a profi funcion ha mus accoun for he benefis of he added research effor. where V + is deermined as follows. F Π + (4.9) RD λ n n V+ wn n F rv Π λ n + n V x V x+ Π (4.) + + r + λn + Therefore, he research firm s firs order condiion may be expressed as

13 x + λπ+ wn* λv+ (4.) r + λn + The compeiive labor marke resuls in he following marke clearing condiion. λγ ( L n *) (4.) r+ λ n + * Accordingly, he analyic soluion for he opimal labor inpu o he R&D firm which saisfies equaion (4.) may be expressed as follows. λγ L r n* (4.3) λ+ λγ And he average growh rae of income is defined as y g λ n* ( lnγ ) (4.4) y Lile can be said from simple inspecion of he analyic soluion for n* or g. Forunaely hough, careful analysis conduced in he nex secion, reveals ha all four cases are comparable such ha firm conclusions may be drawn abou he effecs of rade in goods and in ideas on growh and welfare when endogenous echnological change is defined by creaive desrucion. 4. Comparison The following analysis considers he effecs of free rade on growh raes and welfare. We compare he resuls of secion (3.) hrough (3.4). Table summarizes he resuls from auarky and he four cases. Noe ha case (3.) is exacly he same as he auarky case (). As menioned before, he inuiion behind his resul is simple. The inermediary monopolis in he case (3.) produces wice as much x as he inermediary monopolis in auarky bu for a half he ime. Thus rade in inermediae goods wihou rade in ideas has no growh or welfare effecs whasoever. Henceforh, we will no menion case (3.) bu insead consider only auarky, case (), as he benchmark. To deermine rade s effec on average growh raes of oupu, we need o compare no only he labor effors across cases, bu also all of he various componens ha direcly and indirecly deermine he average growh rae. The following presens mosly inuiive explanaions for he relaionships across he cases. The analyic proofs ha coincide wih all of he resuls herein are conained in appendix. Firs, compare he opimal research levels in each of he four cases. The resuls may be summarized as follows. * * * * n3. > n3.4 > n > n3.3 When rade in ideas allowed, as in cases (3.) and (3.4), he efficiency of research labor effecively doubles in boh counries. Wih higher marginal producs of labor, boh n 3. and n 3.4 are higher han auarky research effor, n. ince he monopolis in he case (3.) produces wice as much x as he duopolis in he case (3.4), he incumben researcher in

14 case (3.) has ha much more o gain from being he nex innovaor, hus n3. > n3.4. The R&D firm in case (3.3) has he leas o gain as he duopolis wihou he benefi of shared research. His research is he leas producive of all and consequenly he has he lowes relaive research effor. econd, consider he relaive employmen by he inermediaries. Recall ha since he labor markes are compeiive, i.e. L n+ x, he following resuls mus mirror hose from he employmen by he research firms. * * * * x < x < x < x * * * * x3. < x3.4 and x < x3.3 are easily jusified as he pro-compeiive gains from rade resuls. As he marke srucure shifs from monopoly o duopoly, oupu of x increases. The fac * * ha x3.4 < x implies ha he posiive wealh effec from rade in ideas is greaer han he negaive subsiuion effec from rade in inermediae goods. Third, compare he inermediae good prices ha are se by he various imperfec compeiors. p3. > p > p3.4 > p3.3 The inernaional monopolis ses his price, p 3., higher han he monopolis under auarky because his workers have a higher marginal cos given he same relaive demand. Recall ha he researchers in case (3.) are more producive han hose in auarky. The compeiive labor marke herefore drives up he marginal cos o he monopolis as well. The pro-compeiive gains from rade resul implies ha he price of inermediae goods is lower in eiher of he wo duopoly cases (3.3) and (3.4) han under auarky, case (). The duopoly price wih rade in ideas is greaer han he duopoly price wihou rade in ideas, i.e. p3.4 > p3.3, because he former has a higher marginal cos given he same relaive demand. The ineres rae, r, is defined as he marginal produc of inermediae goods, x. r3.4 > { r3., r3.3} > r Trade in inermediae goods, a saple in all four cases, leads o an increase in he demand for hose goods, herefore he auarky marginal produc of x and consequenly he ineres rae, r, mus be less han all of he ohers. The addiion of rade in ideas will increase he produciviy and accordingly he marginal produc of inermediae goods, hus r 3.4 > r 3.3. Furhermore, he marginal produc of x is greaer under duopoly han under monopoly, hus r 3.4 > r 3.. However, i is no clear which is higher, r 3. or r 3.3. The las and mos imporan consideraion is he average growh rae of income. The resuls are summarized as follows. * * * * g > g > g > g * * Purely as a resul of pro-compeiive gains from rade, g > g3.3. In oher words, rade in imperfecly produced inermediae goods wihou rade in ideas beween wo oherwise idenical counries resuls in less research effor due o he reduced incenives under duopoly versus under monopoly. Consequenly he growh rae suffers. Whereas, * * * g3. > g3.4 > g because he counries devoe more effor oward research as he R&D secor becomes more compeiive as well as more effecive. Therefore, he greaer are he incenives o he research firm, i.e. monopoly versus duopoly, he more creaive 3

15 desrucion akes place, and he higher is he rae of echnological advance which ulimaely drives he long run growh in per capia income. 5. Conclusions 4

16 Appendix Welfare analysis of laissez-faire versus social opimum levels of research To undersand he implicaions on welfare of rade when obsolescence moivaes echnological change, consider a social planner s problem when she aemps o maximize he expeced presen value of consumpion, y. The social planner s problem under auarky, case () which exacly he same as case (3.), is o maximize he following expeced welfare. where Π (, ) r r U e yd e Π(, ) Ax d (5.) is he probabiliy of innovaions up o ime. The innovaions process is Poisson wih an arrival rae of λ n, herefore (, ) ( λ n ) λ n Π e (5.)! The social planner mus consider boh echnological change and he labor marke equilibrium. A Aγ γ > (5.3) L n+ x (5.4) The uiliy funcion can herefore be rewrien as U n ( ) λn( γ ) A L n (5.5) r The socially opimal level of research, n, which saisfies he firs-order-condiion, ( n ) U, may be expressed as follows. λ γ r λn ( ) ( L n ) ( γ ) Hence, he socially opimal level of research, n, is λ( γ ) L r n λ( γ ) In case (3.), expeced welfare is r r U e y d e Π(, ) Ax d where Π (, ) is modified as follows. (5.6) (5.7) (5.8) (, ) F ( λ( n+ n ) ) F λ( n+ n ) Π e (5.9)! Therefore he uiliy funcion can be rewrien as 5

17 U n ( ) λn( γ ) A L n And he socially opimal level of research, n 3., is (5.) r λ( γ ) L r3. n3. λ( γ ) In case (3.3), expeced welfare funcion is changed o r r (, ) ( F U e y d e Π A x+ x ) d where Π (, ) (5.) (5.) is again defined as i was under auarky. (, ) ( λ n ) λ n Π e (5.3)! The uiliy funcion and is consequen social opimal level of research, n 3.3, can be expressed as follows. U n ( ) n( γ ) A L n (5.4) λ( γ ) L r3.3 n3.3 λ( γ ) Lasly, in he case (3.4), expeced welfare is r r (, ) ( F U e y d e Π A x+ x ) d where Π (, ) r λ (5.5) (5.6) is defined as follows. (, ) F ( λ( n+ n ) ) F λ( n+ n ) Π e (5.7)! and he uiliy funcion and is consequen social opimal level of research, n 3.4, are U n ( ) n( γ ) A L n (5.8) r λ λ( γ ) L r3.4 n3.4 (5.9) λ( γ ) The parallels beween he compeiive opimum levels of work effor and heir corresponding social opimum levels make he comparisons across he four cases sraigh 6

18 forward. imply pu, if he social opimum level of research is greaer han he laissezfaire level in auarky hen he social opimum will necessarily also be less han he laissez-faire level in all hree of he rade cases. This is because he hree effecs appropriabiliy, business sealing and ineremporal spillovers, ha differeniae he social opimum from he privae equilibrium depend solely on he parameers. For example, he business sealing effec is resul of he relaive size of innovaions, γ. The larger he innovaions, he more incenive for firms o research and he greaer will be he laissezfaire growh rae. The appropriabiliy effec depends on, where he closer is o one, he less he monopolis can appropriae he whole oupu flow and resuling less research han is socially opimal. Irrespecive, since he parameers are he same across cases, he resuls are as well. If he social opimum level of research is greaer han he laissez faire-level, hen i will also be so in he open economy seing as well. 7

19 Bibliography Aghion, Phillipe and Peer Howi (99), A model of growh hrough creaive desrucion, Economerica, Vol. 6, No., Barreo, Raul A. and Kaori Kobayashi (), Economic inegraion and endogenous growh revisied: Pro-compeiive gains from rade in goods and he long run benefis o he exchange of ideas, Adelaide Universiy Working Paper eries, No. -. Diamond, Peer A. (965), Naional Deb in a Neoclassical Growh Model, American Economic Review, 55, 6-5. Lucas, Rober E. (988), On he mechanics of economic developmen Journal of Moneary Economics,, p Ramsey, F. P. (98), A mahemaical heory of aving, Economic Journal, 38, December, p Rivera-Baiz, Luis A. and Paul M. Romer (99), Economic Inegraion and Endogenous Growh, The Quarerly Journal of Economics, May, Romer, Paul M. (99), Endogenous Technological Change, Journal of Poliical Economy, 98, 7-. 8

20 Endnoes For example, see Markusen, e.al. (995), chaper or any oher inermediae o graduae level inernaional rade exbook for a complee descripion imperfec compeiion as a deerminan of rade beween idenical counries. ee Barreo and Kobayashi () for a complee discussion of he pros and cons. 3 ee Rivera-Baiz and Romer (99) for a horough discussion of his assumpion. 9