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PAGE 1 1 ESSAYS IN INTERNATIONAL TRADE, GROW TH AND INDUSTRIAL ORGANIZATION By ALI GUNGORAYDINOGLU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 2007 Ali Gungoraydinoglu PAGE 3 3 Dedicated to my parents Emine and Bekir Gungor aydinoglu, for their endless love and support they have given me through the years. PAGE 4 4 ACKNOWLEDGMENTS Many people have contributed to the developmen t of these ideas and methods over the last few years. First and foremost I acknowledge my advisor, Elias Dinopoulos, for his help and guidance in turning a collection of ideas into a practicable thesis. He has been always interested in my work and has always been available to advise me. I am grateful for his patience, motivation, enthusiasm, and immense knowledge in economics. I would like to thank him for his inspiring and invaluable guidan ce throughout my work, without his help, this work would not be possible. I owe many thanks to my graduate committee, David Denslow, James Seale and Douglas Waldo for their support throughout my graduate work, for their assistance during committee meetings, for attending my seminars, and for reading my dissertation. I would like to thank all my colleagues at th e University of Florida. We shared great moments, laughs and scientific discussions toge ther. My personal gratitude goes to Fuat Sener for his great advice during my study. Our disc ussions with him were always fruitful. I would like to thank my mother, my father, my sister Asli Dinc yurek and my brother Murat Gungoraydinoglu for their faith and support. They were always with me and offered a hand during this long journey. I am indebted to my wifes family for their valued support and help. Last but not least, I would like to thank the most importa nt person in my life, my wife Ozde. She has been always with me with her love and unlimited patience, making me laugh and strongly supporting me when I needed it. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF FIGURES................................................................................................................ .........7 ABSTRACT....................................................................................................................... ..............8 CHAPTER 1 OPTIMAL PATENT LENGTH AN D ENDOGENOUS GROWTH.....................................10 Introduction................................................................................................................... ..........10 Model.......................................................................................................................... ............12 Innovation Process...........................................................................................................13 NonPatented Sector........................................................................................................14 Patented Sector................................................................................................................15 Households..................................................................................................................... .17 Production..................................................................................................................... ...18 Stock Market...................................................................................................................19 Labor Market...................................................................................................................22 SteadyState Equilibrium....................................................................................................... .22 Existence of the SteadyState Equilibrium......................................................................23 Main Properties of the SteadyState Equilibrium............................................................26 Growth Maximizing Patent Length.................................................................................27 Conclusion..................................................................................................................... .........30 Algebraic Details.............................................................................................................. ......32 2 GLOBALIZATION, SCHUMPETERIAN GR OWTH AND NONTRADED GOODS......38 Introduction................................................................................................................... ..........38 Model.......................................................................................................................... ............41 Household Behavior........................................................................................................42 Product Market Characteristics.......................................................................................44 R&D Services..................................................................................................................46 R&D Races......................................................................................................................46 ZeroProfit Conditions.....................................................................................................48 Labor Markets.................................................................................................................51 SteadyState Equilibrium....................................................................................................... .51 Comparative Static Results.....................................................................................................55 Conclusion..................................................................................................................... .........59 Algebraic Details.............................................................................................................. ......61 3 INTERNATIONAL TRADE COSTS AND SCHUMPETERIAN GROWTH.....................65 Introduction................................................................................................................... ..........65 PAGE 6 6 Model.......................................................................................................................... ............70 Household Behavior........................................................................................................71 Production, R&D Services a nd Industry Structure..........................................................73 Transport Costs and Sector Structure..............................................................................75 R&D Races......................................................................................................................77 Pricing and Stock Market................................................................................................79 Labor Markets.................................................................................................................82 Trade Balance..................................................................................................................83 SteadyState Equilibrium....................................................................................................... .84 Relative Supply and R&D Conditions............................................................................84 Innovation..................................................................................................................... ...87 Long Run Growth............................................................................................................89 Comparative Statics............................................................................................................ ....90 Effects on Wage Gap and Sector Range..........................................................................91 Effects on Growth............................................................................................................95 Effects of Globalization...................................................................................................99 Conclusion..................................................................................................................... .......102 Algebraic Details.............................................................................................................. ....104 LIST OF REFERENCES.............................................................................................................125 BIOGRAPHICAL SKETCH.......................................................................................................128 PAGE 7 7 LIST OF FIGURES Figure page 11 Steady state equilibrium................................................................................................... ..37 21 Wage gap and the pattern of trade.....................................................................................64 22 Comparative static results................................................................................................. .64 31 Unique equilibrium......................................................................................................... .123 32 Dynamics of the model....................................................................................................123 33 Effect of an increase in home unit labor requirement......................................................124 34 Effects of globalization................................................................................................... .124 PAGE 8 8 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ESSAYS IN INTERNATIONAL TRADE, GROW TH AND INDUSTRIAL ORGANIZATION By Ali Gungoraydinoglu August 2007 Chair: Elias Dinopoulos Major: Economics We build a dynamic general equilibrium mode l without scaleeff ects, incorporating patented and nonpatented sectors. An innovator ha s two options: either a pplying for a patent and secure the monopoly profits for a finite period or engaging in rent protec ting activitie s to deter the challengers from discovering the next highe r quality product. We endogenously split the industries in the economy into pa tented and nonpatented sector s. The longrun Schumpeterian growth rate is bounded and does not exhibit sc aleeffects; it depe nds positively on R&D difficulty constant in patented sector and R&D subsidy in non patented sector; negatively on RPA productivity constant, quality increment, R& D subsidy to patented sector, researcher productivity in R&D services of patented sector unitlabor requirement in R&D services of nonpatented sector. The optimal patent length that maximizes growth is determined, which depends positively on R&D subsidy to patented sector, researcher productivity in R&D services of patented sector, unitlabor requirement in R&D servic es of nonpatented sector, quality increment and constant effectiveness of RPA and negatively on R&D difficulty constant in patented sector. We investigate the effect of globalization by introducing an exogenous nontraded sector in a twocountry dynamic general e quilibrium model. Firms engage in R&D activities and produce PAGE 9 9 final goods using only labor. The quality of a good is improved by R&D races where the winner becomes the industry leader until the next inve ntion. We determine the wageinequality between countries and the marginal industry that determin es the pattern of trade. We remove the scaleeffects property and suggest th at the liberalization of the economy by shri nking the range of nontraded industries closes the wagegap and wide ns the range of goods exported by both countries. We introduce international trade costs are in to a two country, dynamic general equilibrium model with Ricardian trade. C ontinuum of industries differs in technology, and firms produce final goods and engage in R&D activities. R& D races improve the quality of a good, and the winner of R&D race produces the stateoftheart product. Wageinequality, trade pattern, range of traded and nontraded goods sectors, i nnovation and growth rate s are all endogenous. Countries have different long run growth rates due to the nontraded goods sector and heterogeneity of technology across countries. The growth rate is higher, the higher is the inventive step, the lower is the R&D difficulty, the more productive is the labor, and the larger is the other countrys population si ze. Globalization reduces the wa geinequality between Home and Foreign, and leads the country with wider rang e of export sector to in novate and grow faster than its trade partner. PAGE 10 10 CHAPTER 1 OPTIMAL PATENT LENGTH AN D ENDOGENOUS GROWTH Introduction The question of how intellectual property rights affect the technology, development and economic growth has become more important, esp ecially after the implem entation of the TradeRelated Aspects of Intellectual Property Rights (TRIPs) agreement of the Uruguay Round of the GATT. One requirement is that all the signatory c ountries alter their intellectual property systems to be in line with a North American and European type of system. For example, this requires changes in the patent life from 17 to 20 years in the United States. We see potential theoretical contribu tion by analyzing the effects of such a change in the pate nt policy within a dynamic general equilibrium model. The patentdesign literature, st arting with Nordhaus (1969), examined the need for patents for innovation. However, focuses on static pa rtialequilibrium analysis, these studies overemphasize the importance of monopoly distortions created by patents, because they focus on a single industry and ignore the fact that policy changes affect multiple industries. Patents are used widely in many industries and therefore an y policy change will have economywide affect, thus for a complete analysis of patentdesi gn, a generalequilibrium analysis is needed. Judd (1985) was the first to consider a gene ralequilibrium approach yet an exogenous growth model with scaleeffects. He uses a varyi ng patent life and showed that if patent life is infinite, there will be too much or too little innovation, and unde r CES utility function which is symmetric across all goods, an optimal rate of innovation can be sustai ned. His results follow from the fact that under infinite protection, all go ods are equally priced an d there is no distortion due to monopoly power. He also adds that finite patent life generates cycles of innovation and PAGE 11 11 the equilibrium is not stable. Ther efore, whether patent life is infi nite or finite affects innovation and growth in different ways. The endogenousgrowth models of Romer (1990), Segerstrom, Anant and Dinopoulos (1990), Grossman and Helpman (1990), and Aghi on and Howitt (1992) see R&D as the engine of growth, and emphasize the role of patent protection to stimulate innovation. These models assume that patent length is infinite, and the innovator is protected under the patent system forever, unless there is furthe r innovation by challengers. Furthermore, the impact of patent policy on growth has not been studied in gene ral equilibrium models, and we attempt to determine the patent length that maximi zes longrun Schumpeterian growth rate. Recently, ODonoghue and Zweimuller (2004) de veloped a generalequilibrium model and point out the shortcomings of pa rtialequilibrium analysis. Howeve r, they do not introduce trade secrecy and use only patents as protection of intellectual proper ty. More importantly, as it is common in all the studies mentioned above, thei r model has scaleeffect s property, which have been criticized by Jones (1995a). One aspect of this paper that distinguishes from the models above is removing the scaleeffects property. Jones (1995a) points out that the firstgeneration R&Ddriven endogenous growth models have a scalee ffects property, a positive population growth generates infinite percapita longrun growth, which contradicts the po stwar timeseries evidence that shows an exponential increase in R&D resour ces but almost a constant rate of percapita GDP growth in all major advanced countries. To overcome this problem, secondgeneration R&Ddriven endogenous growth models have been developed that remove the scale eff ect property, including Jones (1995b), Kortum (1997), Dinopoulos a nd Thompson (1999), Segerstrom (1998) and PAGE 12 12 Dinopoulos and Syropoulos (2001). In order to remove scal eeffects property, we assumed increasing R&D difficulty in both pate nted and nonpatented sectors. Considering both patents and rentprotecting ac tivities in a dynamic general equilibrium model without scaleeffects yield important insigh ts about how industries split into patented and nonpatented sectors and enables to analyze parameters that affect growth, and suggests a finite optimal patent length that maximizes growth. In this paper, patents protect the innovator of the stateofthe art product from further innovation and innovator is rewarded with monopoly position for a fixed period T>0. On the other han d, instead of applying for a patent, the innovator can choose to engage in rentprotecting activit ies to decrease the risk of being replaced by a challenger. These activities dela y the invention of hi gher quality products by tightening the flow of knowledge spillovers from incumbents to ch allengers, in this way the productivity of R&D investments by challengers is re duced. We assume that firms ma y engage in rentprotecting activities only after they discover the stateoft he art product. This framework determines a cutoff industry, where the innovator is indifferent in terms of flow of profits between applying for a patent and engaging in rentp rotecting activ ities. In this way, the model endogenously characterizes the industry structure by identify ing the industries in patented and nonpatented sectors completely. More importantly, as an impor tant implication in patent policy, the optimal patent length that maximizes growth is suggested including its comparative static properties. Model Our aim is to introduce patents and rentpro tection activities in an endogenous growth model by extending the works of Grossman and Helpman (1991a) and Dinopoulos and Syropoulos (2001). We assume that in there ar e two sectors in the model: patented and nonpatented. In the patented sector the quality leader secures the monopoly profits for a fixed period of time T>0. In the nonpatented sector, we view the discovery of a new product as the outcome PAGE 13 13 of an innovation contest between the incumben t monopolist and the challengers in which the successful innovator earns the discounted stream of profits the stateoftheart quality product is expected to generate. However, the incumbent monopolist does not remain passive, but devotes resources to limit the knowledge spillovers to ch allengers (rent protection activities, or RPA) to prolong the duration of its monopoly. These act ivities reduce the pr oductivity of R&D investments by challengers and delay the invention of higher quality products. Innovation Process There is a continuum of struct urally identical industries 1 0 ranked by increasing productivity of RPA. In other words, RPA are least effective for the industry0 but become more effective as increases and most effective for the industry1 This ranking of industries enables us to specify the cutoff industry 1 00 which splits industries into0, 0 and 1 ,0 as patented and nonpatented secto rs, respectively. The qualityN j of a product in each industry can be improved an unlimited number of times. Each improvement raises the quality of the stateofthea rt product by the quality increment, a constant > 1. The quality improvements occur stochastically as firms engage in R&D activities. At time t = 0, there is only j = 0 quality produc t available in each industry. Only one firm in each industry knows how to produce the stateoftheart quality product, and no other higher quality product is discovered yet, therefore in each industry the firm with the blueprint becomes the leader and earns monopoly profit s. If the stateoftheart qualit y product in an industry is j, the next leader will be the only producer of j+1 quality pr oduct. R&D activities push each product in an industry one step up its qual ity ladders (Grossman and Helpman, 1991a). PAGE 14 14 We analyze the structure of nonpatented and patented sectors sepa rately and since the model lacks transitional dynamics, we will only use the time argument t to denote variables and functions that grow over time. NonPatented Sector First, we consider the nonpatented sector 1 ,0 where there are sequential stochastic R&D contests in each industry. Following Dinopoulos and Syropoulos (2001), firms enter an industry by winning the R&D contests, and exit the industry at anytime without any cost. A challenger j that invests in R&D discovers the next higherquality product with instantaneous probabilitydt Ij where dt is an infinitesimal interval of time and ) ( ) ( t D t R Ij j (11) The term) ( t Rjcaptures firms js R&D expenditures and D( ,t) is the R&D difficulty. The returns to R&D investments are independe ntly distributed across challenge rs, industries and over time; therefore, by adding the levels of R&D across al l challengers, the industr ywide probability of innovation can be obtained from Equation 11 as ) ( ) ( ) ( t D t R I Ii i (12) To remove the scaleeffects property1, we model the difficulty of R&D in an industry D( ,t) by ) ( ) ( ) (t X t D (13) 1 Earlier models of Schumpeterian growth assumed R&D diffi culty D(t) is constant over time and across industries which created scale effects, because th e rates of innovation and longrun grow th increase exponentially as the scale of the population grows exponentially, which is inconsistent with postwar timeseries evidence presented in Jones (1995a). PAGE 15 15 where X(t) is the level of rentprotecting activities devoted by the incumbents at time t and the effectiveness of RPA is defined as ) ( ) (0 (14) The exogenous parameter 00 is defined as the constant effectiveness which is the common level of resources devoted to RPA in any industry and ) ( captures the effectiveness of RPA in each industry 2. Equation 14 differs from Di nopoulos and Syropoulos (2001), because by our construction of the model, as we move right on the range of industries the productivity of RPA gets more effective and hen ce R&D difficulty increases. Therefore quality leaders are more likely to use RPA ra ther than applying for a patent as increases. Equation 13 captures the idea that the next innovation by a challenger is less likely when the productivity or level of RPA increase, and this specification enab les us to remove the s caleeffects property that is observed in the firstgeneration endogenous gr owth models including Grossman and Helpman (1991a). Patented Sector As an alternative, incumbents in the patented sector 0, 0 can apply for a patent of T>0 duration and secure the monopoly profits for the stateofthe art product discovered in this period. There is a research sector that produces patentable innovation ac cording to the following technology ) (t Z dt L dARj j (15) 2 The effectiveness of RPA is assumed to be concave0 ) ( An example for such a function is 1 ) (0, where ) ( as1 PAGE 16 16 where ) ( ) (t kN t Z is the difficulty of R&D in the patent ed sector, k is a constant and N(t) is the level of population at time t. jdAis the number of patented stateoftheart products produced in an infinitesimal period of time dt, RjLis the number of researchers employed by firm j, and the productivity of each researcher is equal to ) (t Z and depends linearly in the stock of patents. Aggregating over all researchers, we get dt t L t Z dt t A t Z dt t L dA t dAR R j j) ( ) ( ) ( ) ( ) ( ) ( Hence, the growth rate of stock of patented products is ) ( ) ( ) ( t kN t L t AR (16) The term) (t LRis the total number of workers employe d in patented products. Equation 16 implies that the unitlabor requirement pe r design is the inverse of the labor productivity ) ( ) ( t kN t Z and the unitcost of research is w t Z) ( where wis the wage of labor. Note that the condition 0 0) (Tds s A holds in the steadystate. This condition captures the idea that the rate of patent creation is such that when a patent expires, a nother is created. Since Ais constant in the steadystate equilibrium, we have T t A0) ( (17) In the steadystate equilibrium, the flow of pate nts increase as the range on patented sector expands, or the duration of th e patent protection shortens. PAGE 17 17 Households There is a continuum of identical dynastic fam ilies that provide labor services, earn wages, and save by holding assets of firms engaged in R&D. Each individual member of a household is endowed with one unit of labor, and the size of each household grows exponentially at an exogenous rate ofNg We assume that1 ) 0 ( N thus the population of workers at time t ist gNe t N ) (. Each household with identical preferences maximizes a disc ounted intertemporal utility function of the form dt t u e Ut gN) ( ln0 ) ( (18) Denoting the common subject ive discount rate as we assume that the effective discount rate gN is positive. The instantaneous u tility at time t is represented by d t j q t uj j 1 0) ( ln ) ( ln. (19) The term q(j, ,t) denotes the consumption of a product that has j quality improvements in industry at time t. The specification in Equation 19 implies that consumers are willing to pay more for higher quality which in turn gives firms an incentive to improve the quality level of the stateoftheart good. Given the prices for goods, each household choose s an optimal time pattern for spending at each point in time to maximize Equation 19. The solution to this optimal control problem is a unit elastic demand function for the product in ea ch industry with the lowest qualityadjusted price p t N t c ) ( ) ( (110) PAGE 18 18 The term c(t) is per capita consumption expenditure, and p is the price of the good considered. In equilibrium it is only the highest av ailable quality that provides the lowest quality adjusted price; the consumer c hooses the single product that offe rs the lowest quality adjusted price, and the demand for all other goods is zero. Substituting the optimal static allocation of sp ending into Equation 19, and the result into Equation 18, the intertemporal maximization of the representative household is equivalent to 0 ) ( ) () ( ln max dt t c et g t cN i, subject to the intertem poral budget constraint) ( ) ( ) ( ) ( ) ( t a g t c w t a t r t aN where a(t) denotes the per capita financial a ssets and r(t) is the instantaneous rate of return at time t. Consumers can borrow or lend freely on the capital market with riskless rate of interest r(t). The solution to this problem yields the differe ntial equation known as KeynesRamsey rule ) ( ) ( ) ( t r t c t c (111) In the steadystate, percapita consumption expenditure is consta nt only when the subjective discount rate equals the instantaneous interest rate r(t). Production There are three production processes in the model: manufacturing of final goods, production of RPA, and R&D services. Firms enga ge in Bertrand price competition and use labor as the only factor of production. In each industry 1 0 there is manufacturing of fina l goods with a cost function ) ( t Y w (112) Y(t) is output of manufacturing and is the constant unitlabor requirement in manufacturing. PAGE 19 19 In the nonpatented sector1 ,0 a challenger firm j produces ) ( t RJservices with constant unitlabor requirement under the cost function ) ( t R wJ (113) An incumbent in the nonpatented sector 1 ,0 produces the rentprotecting services X(t), with the cost function ) ( t X w (114) The constant unitlabor requirement in rentprotecting services is In the patented sector0, 0 a challenger firm j producesjdA units of patentable innovation by employing RjL units of labor. Stock Market Innovation is financed by consumer savings through stock market in which consumers hold stocks issued by the firms. We consider the stock market value of a successful firm and identify the rewards to innovation. Because of the uncertainty about the winner of the R&D contest, there is a risk in holding the stock of a firm th at engages in this c ontest. However, since there is a continuum of industries and the probab ility of success is i ndependently distributed across industries and firms, by holdi ng a diversified portfo lio of stocks, a risk free investment is possible for a typical consumer. At each instant, a typical challenger in the nonpatented sector wins the R&D contest and as a divi dend pays the flow of profits ) ( ) ( ) ( ) ( t X w p t N t c w p tNP (115) The last term in Equation 115 represents the production cost of RPA. Denoting the expected discounted profits of a successful challenger with) ( t VNP with probability 1Idt the PAGE 20 20 firm will stay in the market and therefore the stock will appreciate by dt t VNP) (, and with probability Idt the firm will be replaced by the ne xt successful firm and shareholders will face a capital loss of) ( t VNP Under noarbitrage the returns from holding a stock or riskless bond should be equal: rdt Idt t V t V dt Idt t V t V dt t V tNP NP NP NP NP NP ) ( 0 ) ( ) 1 ( ) ( ) ( ) ( ) ( Taking the limit as 0 dtand using Equation 115 yields the stock market value of monopoly profits in the nonpatented sector ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t V t V t I t r t X w p t N t c w p t V t V t I t r t t VNP NP NP NP NP NP (116) A monopolist maximizes the stock market valu e by choosing the level of rentprotecting services X(t) to protect its monopoly position an d price for its stateofthe art product. The optimal choice of X(t) yiel ds the following condition3 ) ( ) ( ) ( ) ( t I w t D t VNP (117) Bertrand price competition prevails in the ma rket and since the only competitor for a quality leader is the producer of the product that is one step below the quality ladder, the incumbent sets the price of the stateofthe art produc t equal to the unit co st of producing the product one level below in the quality ladder: w p (118) 3 For tractability, we omit the specialization in labor ma rkets. See Dinopoulos and Syropoulos (2001) for a model with specialized and nonspecialized labor and details about R&D contest. PAGE 21 21 We assume that in an industry challengers maximize their expected discounted profits dt t R w s dt t D t R t VJ N j NP) ( 1 ) ( ) ( ) ( by choosing the level of R&D services, where ) ( ) (t D t Rjis the instantaneous probability of next innovation by a firm j, dt Ij and 0 Ns is the exogenous ad valorem R&D subsidy that reduces the R&D cost ) ( t R wJ of the firm j in the nonpatented sector. Freeentry into each R&D contest gi ves another equilibrium condition w s t D t VN NP 1 ) ( ) ( (119) Combining Equation 117 and E quation 119 the equilibrium le vel of rate of innovation can be found as ) 1 )( ( ) (Ns I (120) At any industry in the nonpatented sector the innovation rate depends positively on unitlabor requirement in RPA and R&D subsidy in the nonpatented sectorNs and negatively on effectiveness of RPA ( ), unitlabor requirement in R&D services of nonpatented sector Note that the risk of bei ng replaced by a challenger ) ( Idecreases as increases; therefore an incumbent firm in the nonpatented sect or is in a safer position for higher On the other hand, for a period of T, each firm in the patented sector charges the limit price w p and obtains the flow of profits ) ( ) ( 1 ) ( t N t c tp (121) Note that there is no risk of being replaced by further innovation and therefore, the steadystate value of discounted profits is PAGE 22 22 N T g T s P pg e t N t c ds e s t t VN ) ( 01 ) ( ) ( 1 ) ( ) ( (122) Freeentry into the patented sector drives the return for innovation to its cost ) 1 ( ) ( ) (p ps t Z w t V (123) Using Equation 122 together with Equation 123 determines the equilibrium level of percapita consumption T g N pNe g s kw c) (1 1 ) 1 ( (124) Labor Market Labor is the only factor for all three production processes in the model, and at each instant in time, the labor market should clear where N(t) the supply of labor equals to the demand for labor: ) ( ) ( ) ( ) 1 ( ) ( ) (1 0 0 00t cN d t R t X t L t NR (125) On the righthandside of the equation, the fi rst term is the demand for labor in patented research sector, the second is the demand for labor in RPA, third is the demand for labor in nonpatented research sector and finally the last term is the demand for labor in manufacturing. SteadyState Equilibrium In order to find the steadystate equilibrium where all the endogenous variables grow at a constant rate, we only need to solve a system of two nonlinear equations, namely the Resource condition and R&D condition which will be derived below. PAGE 23 23 Existence of the SteadyState Equilibrium To start with the Resource Condition notice that Equation 12 and Equation 13 yield ) ( ) ( ) ( ) ( t X I t R and substituting the stea dy state innovation rate ) ( I in Equation 120 results in ) ( ) 1 ( ) ( t X s t RN Using this expression for R( t) in labor market clearing condition Equation 125 together with la bor demand for R&D in patented sector ) (t LR in Equation 16, and dividing both side s by the population N(t), we get w t c s t x t x k AN ) ( 1 1 ) ( ) ( ) 1 ( 10 0 (126) Equation 126 captures the resource allocation sche me that has to be satisfied in the steadystate equilibrium. The first term on the righthand side is the fraction of demand for researchers in the patented sector, and the second one is th e fraction of demand for labor needed for RPA in the nonpatented sector, the thir d term is the fraction of de mand for researchers in the nonpatented sector and the last term is the fracti on of total labor demand for manufacturing in the economy. Using the steady state values for consumption percapita c in Equation 124, A in Equation 17, and solving for percap ita RPA x in Equation 126 gives the Resource Condition (RS curve): N N T g N Ps s T k e g s k RS xN 2 1 ) 1 )( 1 ( ) )( 1 ( 1 ) (0 0 ) ( 0 (127) PAGE 24 24 The term in the bracket is the fraction of labor in nonpatented sector used in research and RPA. This determines a negative relationship between the percapita RPA and the range of patented sector4. The RS curve is shown in Figure 11. For the other steadystate condition, notice that Equation 119 implies 1 1 ) ( ) ( w s t D t VN NP for the nonpatented sector and Equation 123 implies 1 ) 1 ( ) ( ) ( P ps w t kN t V for the patented sector. Therefor e the cutoff industry is given by ) 1 )( ( ) ( 1 ) ( ) (P p N NPs t kN t V s t D t V (128) In the industry where Equation 128 is satisfie d, the return for innovation is equivalent whether the innovator ap plies for a patent of length T>0 or engages in RPA. Thus, in the cutoff industry 0 specified by the above equation, firms are indifferent between applying for a patent or not. Substituting the steadystate value of) ( t VNP in Equation 128,) (t VP in Equation 123 and ) ( t D in Equation 13 together with Equati on 14 into Equation 128, we get the R&D condition (RD curve) : ) 1 ( 1 ) ( 1 2 1 ) (0 0 0T g N P N NNe g s k g s RD x (129) 4 Note that the lefthand side of Equation 126 is constant, and in the case where there is no patented sector, we observe the maximum level of rentprotecting services. When there is no nonpatented sector, there cannot be any rentprotecting services, hence the mi nimum level of rentprotecting services is observed. The RS curve is decreasing and concave if RS(0) is bounded from above, see Algebraic Details for details and comparative static results for RS curve. PAGE 25 25 which is convex and decreasing with0 (see Algebraic Details). The RD curve is shown in Figure 11 and can be expressed equivalently as follows M N Nl g s RD x ) ( 1 2 1 ) (0 0 0 where Mlis the fraction of labor demand in manufacturing. An increase in the range of patented sector0 means higher productivity of RPA) (0 and this implies a decrease on the righthand side of Equation 129, which should be compensated with a decrease in percapita rentprotecting services x to ensure equality. The unique intersection of RS and RD cu rve given in Equation 127 a nd Equation 129 respectively, determines the steadystate equilibrium value of the cutoff industry* 0, and percapita RPA*x. This result is summarized in Propos ition 11 and shown in Figure 11. Proposition 11. If ) 0 ( 2 1 x s T s kN N then unique steady state equilibrium exists where the steadystate equilibrium level of cutoff industry* 0and percapita rentprotecting services *xare identified. Proof. See Algebraic Details. To determine the cutoff industry in the st eadystate equilibrium in which a firm is indifferent between patenting or not patenting its invent ion, we implicitly solve in the Algebraic Details for the intersection of two steadystat e conditions in Equati on 127 and Equation 129 for* 0: N M N N N N M N N N Ms l s g s T k s l s g s l 2 1 1 ) ( 2 1 2 1 1 ) ( 2 1 1* 0 0 0 0 0 (130) PAGE 26 26 Hence, the industries in the range 0, 0 are protected under finitely lived (T>0) patents, and industries in the range 1 ,0 engage in RPA. Main Properties of the SteadyState Equilibrium Having defined the steadystate equilibrium we are now in a position to study the characteristics of the model and answer some in teresting questions such as: How the range of patented sector will be affected by R&D subs idies? or How the i nnovation rate could be increased in patented sector and nonpatented sector? First, we analyze the range of patented sect or and the innovation in the next proposition. Proposition 12. More industries use the patent system and the flow of patents increases as (a) patent length T, R&D s ubsidy to patented sector Ps, researcher productivity in R&D services of patented sector unitlabor requirement in R&D services of nonpatented sector quality increment and constant effectiveness of RPA 0 increases, (b) or R&D subsidy to nonpatented sectorNs and R&D difficulty constant in patented sector k decreases. Proof. Results follow from Figure 11 and the fact that T A* 0. See Algebraic Details. The comparative static propertie s can be shown with the help of Figure 11. An increase in the patent length T yields higher return for innovation in the patented sector from Equation 122, therefore the firms are not indi fferent between patenting and no t patenting anymore, and the demand for labor in the patented sector increases from Equation 125 and th e RS curve shifts up. With less demand for labor in the nonpatented se ctor RD curve shifts down, indicating less percapita rentprotecting services. The new equilibrium is where there are more patented industries with less percapita rentprotecting services in the economy. The flow of patents with more industries engaged in research due to widening the range of pa tented sector. Similarly, any PAGE 27 27 parameter change that stimulates incentives fo r innovating in the patent sector favors patented sector, and hence the flow of patents increase with larger range of patented sector. Next, we consider the nonpa tented sector and investigate the behavior of average innovation rate in the steadystate equilibrium. The results are summarized in Proposition 13. Proposition 13. The average innovation rate 0 11 ) (* 0 d I I in the nonpatented sector a) increases as R&D subs idy to patented sectorPs, researcher productivity in R&D services of patented sector patent length T and quality increment increases; and b) decreases as R&D difficulty consta nt in patented sector k increases. Proof. Substitute the expression for ) ( Idetermined by Equation 120 and differentiate the resulting expression with respect to the appr opriate parameter. For de rivations see Algebraic Details. The intuition behind this result is due to two separate effect s. The average innovation rate can increase because there are few nonpatented industries or the ra te of innovation is stimulated in the nonpatented sector. For instance, if there is an increase in the R&D subsidy to patented sector, then there will be fewer industries that are nonpatented, therefore the denominator of average innovation goes down while the numerat or increases, implying a higher average. Growth Maximizing Patent Length Another interesting question whic h needs to be answered is What is the optimal patent length that gives maximum growth? The economys longrun Schumpeterian growth is defined as the rate of growth of subut ility u(t), which is a standard expression for longrun growth in qualityladders growth models. Hence, in order to answer this questi on, we begin by deriving expressions for longrun percap ita real output and for its lo ngrun growth. Following the PAGE 28 28 standard practice of Schumpeterian growth mode ls, we first derive the following expression for subutility by substituting the demand in Equa tion 110 and price given by Equation 118 into Equation 19: t tds d I ds d A w t c t u0 1 00* 0 0ln ) ( ln ) ( ln (131) Next, we use the expressions for Aand I given by Equation 17 and Equation 120 respectively. Taking ln and differentiating the ut ility given in (31), we get the growth as 1 0 0 0 0* 01 1 ln d s T u u gN U. (132) The longrun Schumpeterian growth give n in Equation 132 is bounded and does not exhibit scale effects. The remova l of scaleeffects is based on the assumption of increasing R&D difficulty in the innovation process. As the popul ation grows, more re searchers should be employed in R&D for further i nnovation, because first the most obvious ideas are pulled out from the invention pool. This property of the model is consistent with the postwar timeseries evidence that in several advanced countries, the R&D resources expands exponentially whereas constant percapita growth is observed during the same period (Jones 1995 a). The behavior of longrun growth depends on innovation in both pate nted and nonpatented sectors, and since the split of sectors is endogenous; any parameter cha nge that affects the position of the cutoff industry will alter the growth rate given in E quation 132. The comparative static results are summarized in Proposition 14. Proposition 14. The longrun Schumpeterian growth rateUg is bounded and does not exhibit scaleeffects; it depends positively on R&D difficulty consta nt in patented sector k and R&D subsidy in nonpatented sectorNs ; negatively on RPA pr oductivity constant0 quality PAGE 29 29 increment R&D subsidy to patented sectorPs, researcher productivity in R&D services of patented sector unitlabor requirement in R&D se rvices of nonpatented sector Proof. See Algebraic Details. The intuition behind this result is as follo ws. The monopoly position creates a distortion in the sense that it gives the patent holder secured returns without any cost, which reduces the incentives for further innovation in that industry. Therefore, an increase in the difficulty of patenting, such as an increase R&D difficulty cons tant in patented sector k, a decrease in R&D subsidy to patented sectorPs or a decrease in researcher productivity in R&D services of patented sector implies faster growth. On the other ha nd, any policy stimulating innovation in nonpatented sector, for instance an increas e in R&D subsidy in nonpatented sectorNs or a decrease in unitlabor requirement in R&D services of nonpatented sector stimulates growth. The next step is to determine the optimal patent length that maximizes longrun growth given in (32). After taking the derivative of growth with respect to patent length T and setting to zero, we find the golden rule in Algebraic Details by solving for T as follows5 Ns T 1 10 *, (133) where 0 0 T T is the elasticity of the patent length T with respect to the cutoff industry* 0. Notice that optimal patent length can be expressed in terms of the innovation rate in the cutoff industry is ) ( 1 1* 0 I T The comparative static propertie s of the optimal patent length T are stated in Proposition 15. 5 See Algebraic Details for the derivation of the optimal patent length. PAGE 30 30 Proposition 15. The longrun Schumpeterian growth rateUg is maximized at the optimal patent length Ns T 1 10 *. T* depends positively on R&D subsidy to patented sectorPs, researcher productivity in R&D services of patented sector unitlabor requirement in R&D services of nonpatented sector quality increment and constant effectiveness of RPA 0 and negatively on R&D difficulty constant in patented sector k for constant Proof. See Algebraic Details. If the duration of patent length is zero, then there will be no patented sector, and all the firms have to engage in RPA which are costly, because as decreases productivity of RPA diminishes. Thus, an innovator would not be safe from further innovation where the only protection is via costly RPA and the drop in the return for invention will slow down the innovation process and hence the growth. On the ot her hand, a patent length of infinite length will turn all the nonpatented industries into pa tented even the industries where RPA is easy. This distortion will reduce the innovation rate and the growth rate will decrease. Therefore there is a finite optimal patent le ngth that maximizes growth whic h is given in Equation 133. Conclusion The aim of this paper is to incorporate patent policy and rentprotecting activities into the endogenous growth models without scaleeffects property. The cha nnels of protection is either by applying for a patent and securing the monopo ly position for a finite period of time or engaging in rentprotecti ng activities to deter the discovery of a better product by challengers. The industries are split endogenous ly into these two groups and the model offers important comparative static results. PAGE 31 31 The average innovation rate can increase becau se there are few nonpa tented industries or the rate of innovation is stimulated in the nonpatented sector The flow of patents increase as there are more industries engaged in research due to widening th e range of patented sector. Any parameter change that stimulates incentives for innovating in the patent s ector extends patented sector, and hence the flow of pa tents increase with more firms operating in the patented sector. The longrun Schumpeterian growth is bounded and does not exhibit scale effects. The monopoly position creates a distortion in the sense th at it gives the patent holder secured returns without any cost, which reduces th e incentives for further innovation in that industry. Therefore, an increase in the difficulty of patenting, such as an increase R&D difficulty constant in patented sector k, a decrease in R&D subsidy to patented sectorPs or a decrease in researcher productivity in R&D services of patented sector, implies faster growth. On the other hand, any policy stimulating innovation in nonpate nted sector, for instance an increase in R&D subsidy in nonpatented sectorNs or a decrease in unitlabor requireme nt in R&D services of nonpatented sector stimulates growth. Another interesting question answ ered is What is the optimal patent length that gives maximum growth? Under a short pa tent length, the firms in the patented sector will not be safe from further innovation and as there are less firm s in the sector, slower rate of innovation will result in slower growth rate; on the other hand, a long patent length will encourage more firms to apply for a patent, tightening the labor in the nonpatented sector. This will reduce the incentives for innovation in the nonpatented sector, reducing the growth. Th erefore, the model suggests the optimal patent length that balances between these two effects. PAGE 32 32 Algebraic Details In this section, we include the proofs and algebraic details for Chapter 1.Starting with the RS curve N N T g N Ps s T k e g s k RS xN 2 1 ) 1 )( 1 ( ) )( 1 ( 1 ) (0 0 ) ( 0 given in Equation 127, we calculate the first partial derivatives as follows: 0, , , (.) T k g s s RS RSN P N 0 1 1 1 1 N N Ns s s RS 0 2 1 ) 1 )( 1 ( ) (0 ) ( N N T g N Ps s e g k s RSN 0 T g NNe g RS 0 T g N N NNe g g g RS 0 2 1 ) 1 )( 1 ( ) )( 1 (0 0 ) ( N N T g N Ps s T e g s k RSN 0 2 1 ) 1 )( 1 ( ) )( 1 (0 0 ) ( N N T g N Ps s T k e g s k RSN 0 2 1 ) 1 ( ) )( 1 (0 ) ( N N T g N Ps s e g s k RSN 0 1 1 10 T e g s T T RST g N PN 0 2 1 ) 1 )( 1 ( ) )( 1 ( 10 0 ) ( N N T g N Ps s T k e g s k RSN 00 RS RS PAGE 33 33 Now for the RD curve ) 1 ( 1 ) ( 1 2 1 ) (0 0 0T g N P N NNe g s k g s RD x given in Equation 129, the first pa rtial derivatives are as follows: 0 2 1 10 2 0 2 p N p N Ns g s g k s RD 0 2 10 2 p N N Ps g g k s RD 0 2 1 1 2 T g N N T g T g NN N NTe g I g e e g I RD 0 2 1 1 2 T g N T g N T g N NN N NTe g I e g e g I g RD 0 ) 1 ( 1 ) ( 1 2 10 0 T g N P N NNe g s g s k RD 0 ) 1 ( 1 ) ( 1 2 12 0 0 T g N P N NNe g s k g s RD 0 RD 0 ) 1 ) ( 1 2 10 0 T g N N P N NNe g g s k g s T RD 0 ) 1 ( 1 2 12 T g N PNe g s k RD 0 ) 1 ( 1 ) ( 1 12 0 0 T g N P N NNe g s k g s RD 0 ) 1 ( 1 ) ( 1 10 2 0 0 T g N P N NNe g s k g s RD PAGE 34 34 Proof Proposition 11. We need to show that two curves intersect at a uni que point in the 0, x space. N N T g N Ps s T k e g s k RS xN 2 1 ) 1 )( 1 ( ) )( 1 ( 1 ) (0 0 ) ( 0 T k e g s k T k e g s k RST g N P T g N PN N ) 1 )( 1 ( ) )( 1 ( 1 0 1 ) 1 )( 1 ( ) )( 1 ( 1) ( 2 0 ) ( 0now, using the labor market clearing condition in Equation 126, this condition is equivalent to ) 2 ( ) 1 (N Ns T s k x Hence, if this condition holds, then RS is decreasing. For concavity, observe that 0 1 ) 1 )( 1 ( ) )( 1 ( 1 24 0 ) ( 2 0 2 T k e g s k RST g N PNunder the same assumption. Therefore, if ) 2 ( ) 1 ( ) 0 (N Ns T s k RS then RS is decreasing and concave in0 Note that this assumption is equivalent to T k lM 1. Continuing with the RD curve, ) 1 ( 1 ) ( 1 2 1 ) (0 0 0 T g N P N NNe g s k g s RD x the first derivative yields, 0 ) ( 1 2 ) ( 1 ) 1 ( ) )( 1 (2 0 0 0 0 ) ( 0 N N N N T g N Pg s g s e g s k RDN For the convexity, using 01 ) (N Ns g A for simplicity, we get that PAGE 35 35 0 2 2 2 2 ) 1 )( 1 ( ) 1 )( )( 1 (4 2 2 ) ( 2 0 2 A A A A A e g s k RDT g N PN Therefore RD is decreasing and convex in0 The intersection of these two curves is given by Equation 131, and if we use N N Ns g s H 1 ) ( 2 1* 0 0 and N Ms l J 2 1, then Equation 131 can be expressed as follows: J H T k J H lM 1* 0 This guarantees that 1 0* 0 since it is assumed that T k lM 1. Therefore, there exists a unique steadyst ate equilibrium, where RS and RD curves intersect at a point where1 0* 0 and the equilibrium is shown by Figure 11. Proof of Proposition 12. In this model, comparative static analysis is easier to conduct compared to Grossman and Helpman (1991) in wh ich first partial deriva tives of the endogenous variables are solved using Cramers rule. Here, it is sufficient to shift th e RD and RS curves in Figure 11 in the appropriate dir ection to sign the derivatives for* 0 *,x. The next step is to sign the first partial deriva tives of the remaining variables in the model, namely Ug I A, and* T To begin with T A* 0 the sign of the derivati ves of flow of patentsA is identical to that of* 0except for 02 0 0 T T T T A PAGE 36 36 Proof of Proposition 13. We define the average innovation in the nonpatented sector as 0 1 01 ) (* 0 d I I and calculate its partial derivatives as follows: 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0* 0 d s IN 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0 0* 0 d s s IP P 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0 0* 0 d k k I 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0 0* 0 d I 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0 0* 0 d T T I 0 1 ) ( 1 1 1 1 1* 0 1 0 0 0 0* 0 d I Next, we derive the optimal patent length and study its behavior. The growth is given by Equation 133 as 1 0 0 0 0* 01 1 ln d s T u u gN U. Taking the derivative of growth with respect to T and set ting it equal to zero gives PAGE 37 37 2 0 0 01 1 0T s T T gN U Denote the term on the left hand side as LHS(T) and RHS(T). 0 12 T T LHSand 0 23 0 T T RHS Therefore, the upward sloping function LHS(T) and downward sloping func tion RHS(T) intersect at a unique point, determining the optimal patent length. Observe th at denoting the elasticity of the cutoff industry with respect to the patent length by 0 0. T T T can also be rewritten as Ns T 1 10 *, which is Equation 134 in the main text. Note that the secondorder condition holds for Ns T 1 10 *: 0 2 1 2 1 13 0 0 0 2 0 2 0 0 0 2 0 2 2 2 T s T T s T T T gN N U Figure 11. Steady st ate equilibrium. PAGE 38 38 CHAPTER 2 GLOBALIZATION, SCHUMPETERIAN GROWTH AND NONTRADED GOODS Introduction The tremendous growth of interna tional trade over the past several decades is an effect of globalization and technologica l change. Drastic developments in transportation and communication revolutionized economic exchange not only increasing its volume but also widening its geographical scope The technological change has substantially decreased transportation costs, and led new final and intermediate goods to appear in the world markets. With more countries opening their markets to in ternational trade, the effects of the rapid globalization became an important research area a nd both the theoretical and empirical research on globalization has been intense in recent year s. An important question is the effect of globalization on the incomeinequality, as the cu rrent opposition to global ization claims that globalization hurts the poor and benefits the rich. The empirical literature investigating the pa ttern of incomeinequality has mixed results due to the measurement of income inequality. For instance, Pritchett ( 1997) measured income inequality by GDP per capita across countries and found that during the period 19801994, the mean per annum growth rate of GDP per capita was 1.5% for 17 advanced capitalist countries and only 0.34% for 28 less develope d countries. However, this measure of income inequality does not take the population size in to consideration as Jones (1997) showed that global income inequality has in fact decreased if each countrys aver age income is weight ed by its population. SalaiMartin (2002) considered withincountry in come inequality and su pported the result that PAGE 39 39 global inequality has decreased substantially since 19806. In the light of these findings, our model takes population size of countries into account and investigates its effects. Our model is related to a literature on Ri cardian trade, Qualit y ladders and endogenous growth, including Dornbusch, Samuelson and Fisc her (1977), Grossman and Helpman (1991c), Segerstrom, Anant and Dinopoulos (1 990), and Taylor (1993). One as pect of our model is that distinguishes from the models a bove is removing the scaleeffect s property. Jones (1995a) points out that the firstgeneration R&Ddriven endoge nous growth models have a scaleeffects property; a positive population growth generates infinite percapita longrun growth, which is contradicting the postwar timeseries evidence7. To overcome this problem, secondgeneration R&Ddriven endogenous growth models have been developed that rem ove the scale effect property, including Jones ( 1995b), Kortum (1997), Young (1998), Dinopoulos and Thompson (1998), Segerstrom (1998), Howitt (1999) and Dinopoulos and Syropoulos (2007). Dinopoulos and Segerstrom (2006) studied the steadystate effects of globalization in a NorthSouth trade model and showed that globa lization leads to less wageinequality between Northern and Southern workers. However, Nort hSouth models do not a llow South to innovate and explain especially the incr ease in internat ional trade in the 1980s and 1990s by focusing only on trade between developed and developing countr ies. This paper differs in this aspect by allowing both countries to innova te. Another difference is the way of modeling globalization; 6 SalaiMartin (2002) uses aggregate GDP data and withincountry income shares for the period 19701998 to assign a level of income to each person in the world an d using different popular indexes shows a reduction in global income inequality between 1980 and 1998. He also reports that although withincountry disparities have increased slightly during the sample period they can not offset the su bstantial reduction in acrossc ountry disparities, therefore global disparities can be account ed for by acrosscountry, not withincountry inequalities. 7 During this period, although all major advanced countr ies devoted exponentially growing resources to research, percapita GDP growth remained almost constant. See Dinopoulos and Thompson (1998, 1999) and Young (1998) for a detailed discussion. PAGE 40 40 globalization is defined as lib eralization of economy by reduci ng the range of nontraded goods8. Dinopoulos and Syropoulos ( 2001) focused on effects of a move from autarky to the integrated world equilibrium in a twoc ountry general equilibrium mode l of endogenous growth without scale effects, and found that globaliz ation results in the convergence of factor prices. In contrast to Proposition 22, Grossman and Helpman (1991a ) found that globalization (increasing the size of the South) has no effect on NorthSouth wa ge inequality. Grossman and Helpman (1991b) found that globalization (increasi ng the size of the Sout h) increases the rate s of innovation and imitation and decreases NorthSouth wage inequali ty. They reported the increase in the rate of innovation as permanent whereas it is temporary in our model as in Dinopoulos and Segerstrom (2006). However, Sener (2003) presented a NorthSouth model where scale effects are removed by assuming that successful innovators engage in rent protection activitie s to deter the innovation and imitation efforts of their rivals and reporte d that globalization incr eases wage inequality. This paper extends work of Taylor (1993) wher e he built on the quality ladders model of Grossman and Helpman (1991c) and constructe d a dynamic analog of continuum Ricardian model of Dornbusch et al. (1977) His model has scale effects, no nontraded sector and country size is not taken into consideration. The models in the literature focus exclusively on the tradedsector only, and disregard an im portant part of the economy: the nontraded sector. We analyze the effects of globalization in a model of quality ladders and Ricardian trade by introducing the nontraded goods sector. A twocountry general equilibrium framework without scaleeffects is constructed to determine the equilibrium relative wages and the pattern of trade and inve stigate the effects of 8 In the literature, globalization is defined in several diffe rent forms. For example, it is modeled as a reduction in trade barriers between developed countries as in Dinopoulos and Segerstrom (1999), as the international movement of resources such as labor migration, formation of multinationals, or as developing countries joining the world trading system. In our model globalization is defined as liberalization of the economy by reducing the range of nontraded sector. PAGE 41 41 nontraded sector as well as ot her exogenous variables. There ar e two countries in the model, home and foreign with a common exogenous rate of population grow th. There is a continuum of industries manufacturing final consumption goods or engaging in research using labor as the only input. The quality of each good can be improved by endogenous innovation through R&D races. The winner of the race in each industry ho lds the blueprints for manufacturing the good and becomes the sole producer of the stateoft heart product. R&D becomes more difficult over time as in temporary effects on growth (TEG) m odel of Segerstrom (1998) where the degree of difficulty of R&D is proportional to the si ze of cumulative R&D effort in each industry9. The main result is Proposition 22 which show s that wage inequality between countries depends positively on quality increment, consume rs subjective discount rate, and population growth; and negatively on R&D di fficulty growth parameter, rela tive size of home countrys labor force and the range of nontraded goods. If an industry that was nontraded before is opened to international trade, the range of exports by each country would extend (Proposition 23) and the wage gap between countries would be reduced (Proposition 22). Model We construct a twocountry dynamic general equilibrium model. Two countries, home and foreign, produce final consumption goods and engage in R&D using labor as the only factor in a continuum of industries indexed by 1 0 Nontraded sector consists of all industries which are assumed to be in the range of ] 1 [ where 1 > > 0 is a constant; and within the traded goods 0, home country exports the goods in the range ] ~ 0 [ and foreign country exports the goods in the range ~ The marginal industry ~ which defines the range of exportable goods by 9 See Dinopoulos and Sener (2004) for an outline of altern ative solutions to the scaleeffects property and an assessment of scaleinvariant Schumpeterian growth models. PAGE 42 42 each country will be determined endogenously, whereas is exogenous. Globalization will be measured with a decrease in th e range of nontraded goods (i.e. an increase in the parameter ). The qualityN j of a product in each industry can be improved an unlimited number of times. Each improvement raises th e quality of the stateoftheart product (i.e. th e best existing quality) by a constant level of > 1. The quality improvements occur stochastically as firms engage in R&D activities. At time t = 0, there is only j = 0 quality product available in each industry. Only one firm in each industry knows how to produce the stateoftheart quality product, therefore in each industr y the firm with the blueprint becomes the leader and enjoys monopoly profits. The challengers try to discover the next hi gherquality product to win the R&D race and become the next leader in a partic ular industry by engaging in R&D. If the stateoftheart quality product in an industry is j, th e next leader will be the only producer of j+1 quality product. R&D activities push each product in an industry one step up its quality ladders (Grossman and Helpman, 1991c). To prevent the leader in each industry engaging in further R&D, it is assumed that once the higherquality pr oduct in an industry is di scovered, all the firms in both countries know how to produce th e products that have lower quality. Throughout the rest of paper, superscripts h an d f are used to identify function and variables of home and foreign c ountries respectively. Also, the subscripts T and NT stand for traded and nontrad ed goods, respectively. Household Behavior Country is population at time t is denoted by Ni(t). Each countrys population growth gN is assumed to be a positive constant. In each country there is a continuum of identical dynastic families that provide labor services, earn wages, and save by holding assets of firms engaged in PAGE 43 43 R&D. Each individual member of a household is endowed with one unit of labor. We assume thati iN N0) 0 (, thus the population of workers at time t in country i is t g i iNe N t N0) (. Households in each country maximize a discoun ted, additively separable intertemporal utility function of the form10 ) ( ln0 ) (dt t u e Ut gN (21) where > 0 is the common subj ective discount rate and d t j q t uj j 1 0) ( ln ) ( ln (22) represents instantaneous utility at time t, where q(j, ,t) denotes the consumption of a product that has j quality improvements in industry at time t. The household maximizes utility by choosing an optimal time pa ttern for spending at each point in time. At time t, given the market pri ces for goods, each household a llocates its income to maximize Equation 22. The solution to this op timal control problem is a unit elastic demand function for the product in each industry w ith the lowest qualityadjusted price ) ( ) ( ) ( ) (t j p t N t c t j qi l i i i l for h f i and NT T l (23) where ci(t) is country is per capita consumption expenditure, and ) ( ) ( ) (t j p t j p t j pT h T h T is the price for traded goods and ) (t j pi NTis the price of nontraded good in country i at time t. For h f i the total expenditure in each country is abbreviated as ) ( ) ( ) (t N t c t Ei i i, hence the global expend iture should equal to ) ( ) ( ) (t E t E t Ef h For each good the consumer should choose the single product that 10 See Barro and SalaiMartin (1995 Ch.2) for details of the households behavior within the context of the Ramsey model of growth. PAGE 44 44 offers the lowest quality adju sted price, and the demand fo r all other goods is zero. In equilibrium it is always the highest available qua lity that provides the lo west quality adjusted price. The global demand for the traded goods are found by aggregating the quantity demanded in each country ) ( ) ( ) ( ) ( ) (t j p t E t j q t j q t j qT f T h T Substituting the optimal static allocation of sp ending into Equation 22, and the result into Equation 21, the intertemporal maximization of country is repres entative household is equivalent to 0 ) ( ) () ( ln max dt t c ei t g t cN i, subject to the intert emporal budget constraint ) ( ) ( ) ( ) ( ) ( ) (t a g t c t w t a t r t ai N i i i where ai(t) denotes the per capita financial assets in country i, wi(t) is the wage earned by th e representative household memb er in country i and r(t) is global instantaneous rate of return at time t. Consumers can borrow or lend freely on an international capital market with riskless rate of inte rest r(t). They take this interest rate as given, although its value will be determined in the gene ral equilibrium. The solution to this problem yields the KeynesRamsey rule ) ( ) ( ) (t r t c t ci i implying that percapita consumption expenditure is constant only wh en the subjective discount rate equals the instantaneous interest rate r(t). Product Market Characteristics Labor markets are perfectly competitive in bot h countries and labor is the only factor of production and R&D services. There exists a continuum of products 1 0 indexed by decreasing home relative unitlabor requirement in R&D as ) ( ) ( ) ( h R f Ra a A and0 ) ( A. To PAGE 45 45 produce a good, firms have to invent it first; th us the sole manufacturer of a stateoftheart quality good is its innovato r earning monopoly profits us ing the production function ) ( ) (t L t Qi i (24) i.e. one unit of labor is requi red to manufacture one unit of th e good. We also assume that each good must be manufactured in the country th at it has discovered, i.e. no international licensing and multinational corporations are allowed11. ) (t Li is the amount of labor used in manufacturing final goods, and ) (t Qiis the output of the final c onsumption good in country i. The quality leader does not fu rther engage in further R&D12 and holds an infinitely lived patent for the stateoft heart good. However, produ cers in the same industry compete as Bertrand oligopolists. Consider a firm that inve nted the next higherqua lity product, which is time better than the nearest competitor. After th e invention of the stateoftheart good, the blueprints for the lower quality good become av ailable for all the firms in both countries; therefore the leader can at mo st charge a price that is times the minimum cost of production of that nearest competitor. Hence, the predecesso rs cannot compete without realizing negative profits. The incumbent in a traded sector is threatened by challengers in both countries, whereas the quality leader in a nontrad ed industry faces domestic competition only; hence this difference between the traded and nontraded sector lead the incumbents in each industry to follow the optimal limitpricing schemes as follows. For the traded goods, f h Tw w p, min ) ( since the unitlabor requirement is assumed to be 1. We also take the wage of foreign labor as a 11 Taylor (1993) introduced multinational corporations in to a model of endogenous growth and trade. The technologies with minimum costs given the prevailing wages and when innovation and implementation occur at different countries, the resulting transactions ar e considered as imports and exports of R&D. 12 The gain from improving further own product to an incumbent is strictly less than the gain of a onestepquality advantage to a challenger. In Dinopoulos and Syropoulos (2001, 2007) the innovation process is modeled as a contest between the global quality leader and the challenger s. The quality leader can in crease the expected duration of its global monopoly by engaging in rentprotection activities that reduce probability of further innovation. PAGE 46 46 numeraire1fw, then wage of home labor becomes the relative wage, 1 hw. A sufficient condition that guarantees the relativ e wage of home to be strictly greater than one is given in Proposition 22. In the steadystat e equilibrium the relative wage of home is constant over time. Hence, the prices for the traded a nd nontraded goods are respectively ) (Tp, ) (h NTp and ) (f NTp. (25) R&D Services Firms targeting each industry engage in R&D using the la bor as the only factor of production of R&D services. Denoting ) (t Li Rand ) (t Ri as the amount of labor employed and the level of R&D services in industry in country i respectively, production function of R&D is given by i R i R ia t L t R, ) ( where ) (i Radenotes country is unitlabor requirement in R&D services. Following Taylor (1993), the unitl abor requirements are assumed to be different across countries and industries as well. This spec ification allows us to determine the pattern of R&D services and also the pattern in the trade of manufacturing goods since a firm is allowed to manufacture the final good if and only if it has discovered it by engaging in research. R&D Races Firms in each industry engage in R&D to b ecome the next leader, hence in time, the winner of the sequential and stochastic R&D race replaces the old producer in each industry. A challenger firm located targeti ng a quality leader in country h f i enters the R&D race in industry with an instantaneous probability dt t Ii k) (to win which is defined as ) ( ) ( ) ( t X t R t Ii k i k (26) PAGE 47 47 where ) (t Ri kis firm ks R&D outlays and X( ,t) measures the difficulty of R&D in industry at time t which is introduced to remove the scale effects. The effective R&D ) (t Ii which is the industrywide proba bility of innovation, can be obt ained by adding up the level of R&D across all the challe ngers in that country ) ( ) ( ) ( ) ( t X t R t I t Ii k i k i where ) (t Riis country is total R&D services in industry The global rate of innovation, which is the arrival of innovations in each industry, follows a memoryless Poisson process with intensity i it X t R t I) ( ) ( ) ( Temporary effects of growth (TEG) specifica tion is used following Segerstrom (1998). R&D becomes more difficult over time because t he most obvious ideas are discovered first. The longrun growth rate is pr oportional to the popul ation growth and is not affected by any policy instruments. At time t = 0, R&D starts being equally difficu lt in all industries X( ,0) = 1, and the level of R&D difficulty grows according to ) ( ) ( ) ( ) ( ) ( t I t I t I t X t Xf h (27) where R&D difficulty growth parameter > 0 is a constant. Consumer savings are channeled to firms engaging in R&D through the stock market, therefore a portfolio allocation problem has to be solved for the representative household member. Although claims on a particular firms bear s risk, the risk attach ed to each equities is idiosyncratic, therefore an investor can earn a sure rate of return by holding a diversified portfolio of shares. The stream of profits to a stateofthea rt good producer continues until the time that another firm succeeds in improving the same product, and the value of the shares of the displaced monopolist then fa lls to zero. Denoting Vi(t) as the expected discounted profits of a PAGE 48 48 successful firm at time t in country i, a shareholder faces a capital loss of Vi(t) if further innovation occurs. In a time interval dt the probability of a discovery is Idt. The expected return to any equity can be calculated as follows. Th e shareholder of an incumbents stock receives a dividend dt, and the value of the incumbent appreciates by dt t V dt t t V t dVi i i) ( ) ( ) ( There is a continuum of industries and the returns to engaging in R&D races are independently distributed across firms and industries, so each in vestor can completely diversify away the risk by holding a diversified portfolio of stocks. Expected rate of re turn from holding a stock of successful innovator should be equal to r rdt dt t I t V t V dt t V t dt dt t I t V t Vi i i i i i ) ( ) ( 0 ) ( ) ( ) ( ) ( 1 ) ( ) ( taking limits as 0 dtyields ) ( ) ( ) ( ) ( ) ( ) ( t V t V t I t r t t Vi i i l i (28) ZeroProfit Conditions A challenger in country i can attain stock market value Vi( ,t) with probability dt t Ii k) ( by undertaking research at intensity ) (t Ii kfor a time interval of length dt. ) ( ) (t X t Ii k is the level of R&D services, so the cost of research is ) ( ) ( ) (t X t I a wi k i R i Free entry to R&D race drives the expected discounted pr ofits of a challenger to zero 0 ) ( ) ( ) ( ) ( ) ( dt t I t X a w dt t I t Vi k i R i i k i or equivalently the R&D condition ) ( ) ( ) (t X a w t Vi R i i (29) The stream of profits of firms in country h f i in sector NT T l is ) ( ) (t q w p tl i l i l (210) PAGE 49 49 Substituting demand in Equation 23 and price in Equation 25 into Equation 210, and the result into Equation 29 yields ) ( ) ( ) ) ( ( ) ( h R Na t X g t I t E for ~ 0 (211a) ) ( ) ( ) ) ( ( ) ( 1 h R N ha t X g t I t E for 1 (211b) ) ( ) ( ) ) ( ( ) ( 1 f R Na t X g t I t E for ~ (212a) ) ( ) ( ) ) ( ( ) ( 1 f R N fa t X g t I t E for 1 (212b) The lefthand side of equations above is the expect ed discounted profits or simply rewards to innovation and the righthand si de is the cost of innovating in the corresponding country and sector. The rewards to innovation increases as the number of c onsumers in either or both countries increases (an increase in Nh and/or Nf), the quality increment increases ( increases), a consumers expenditure c increases, fu ture profits are discounted less ( decreases), the likelihood of replacing the quality le ader decreases (innovation rate I( ,t) decreases) and population growth slows down (gN decreases). The cost of innovating increases as R&D becomes more difficult (X( ,t) increases) and unitlabor requirement increases. The pattern of R&D services, and hence the production is determined by the zeroprofit conditions for traded goods (Equation 211a) and (Equation 212a) at the marginal industry ~ where firms in both countries are indiffere nt in engaging in R&D. This gives the mutual R&D condition, relating the relative wage at home with a competitive margin ~ 0 by PAGE 50 50 1 ) ~ ( ) ~ ( ) ~ ( A A RD, (213) where 0 ) ~ ( that is the larger th e range of goods that home engages in R&D, the lower the relative wage. The following lemma ch aracterizes the pattern of trade for any equilibrium level of home relative wage and the marginal industry. Lemma 21. If there exists an industry ~ 0defined by Equation 213 where (i) ) ~ ( RD curve is downward sloping, i.e. 0 ) ~ ( D R, (ii) at the marginal industry ~ firms in foreign or home ar e indifferent be tween conducting R&D, (iii) only home engages in R&D for ] ~ 0 [ and only foreign engages in R&D for ) ~ ( Proof. See Algebraic Details. The intuition behind Lemma 21 is based on the zeroprofit conditi ons and the law of comparative advantage in R&D services. The larg er the range that home exports, the lower the homes comparative advantage in R&D and hence the higher the relative cost of R&D. Therefore as ~ increases, the relative wage at home has to be lower in order to keep home firms to engage in R&D in the extended range of industries wh ere home has lower comparative advantage. The decreasing mutual R&D conditi on suggests that home firms ha ve higher expected discount profits than foreign firms for the goods in the range ~ 0 Hence, in the range ~ 0 home firms equities would be preferred over foreign. Foreign challengers woul d not be able to finance their R&D costs in the industries ~ 0, and choose not to engage in R&D since this would yield negative profits (see Equation 12a) otherwise. Si milarly, home challengers would not undertake R&D in the industries ~ where foreign challengers operate. PAGE 51 51 Labor Markets All labor is employed in e ither production of traded and nontraded goods, or R&D services in traded and nontrad ed goods. It is assumed that workers are perfectly mobile across industries and activities in each country to sustai n full employment of labor at each instant in time while wages adjust instantaneously to clear the market. We focus on the home labor market first. It follows from Equation 24 that at home the total labor in production of traded goods and nontraded goods is d t qT) ( ~ 0 and d t qNT) (1 respectively. The total employment in R&D services is d a t Rh R h T) ( ) ( ~ 0for traded goods, and d a t Rh R h NT) ( ) (1for nontraded goods. Hence, homes full employment of labor condition at time t is ) (t Nh= d t qT) ( ~ 0+ d t qh NT) (1+ d a t Rh R h T) ( ) ( ~ 0+ d a t Rh R h NT) ( ) (1 (214) Similarly at foreign, full employment of labor condition at time t is ) (t Nf= d t qT) (~+ d t qf NT) (1+ d a t Rf R f T) ( ) (~+ d a t Rf R f NT) ( ) (1 (215) The model is closed with Equation 214 and Equation 215. SteadyState Equilibrium In the steadystate equilibrium all percapita variables are constant (not necessarily the same), therefore the level of R&D difficulty should grow at th e rate of population Ng t N t N t X t X ) ( ) ( ) ( ) ( .This result with the TEG specification yields PAGE 52 52 N Ng t I g t I t X t X ) ( ) ( ) ( ) (. (216) Thus, the steadystate innovati on rate depends only on the population growth rate gN and the R&D difficulty growth parameter In steadystate equilibrium, productivity of researchers is declining; hence the number of researchers should increase over time. This is only possible with population growth; therefor e for a longrun technological ch ange, population growth is needed. In the steadystate, Equation 29 implies that N i ig t X t X t V t V ) ( ) ( ) ( ) ( Substituting Equation 216 into zeroprofit conditions (Equations 211a, 211b, 212a, and 212b), integrating over the co rresponding range of industrie s and substituting out for Eh(t) and Ef(t), labor markets clearing c ondition (Equation 220 a nd Equation 221) coul d be expressed in terms of ~ and E(t) as N N h R h R N i R h R hg g d a d a g d a d a t E t N 1 ~ 0 1 ~ 0) ( ) ( 1 ) ( ) ( ) ( 1 ~ ) ( ) ( (217) ) ( ) ( ) ( 1 ) ( ) ( 1 1 ) ~ )( ( ) (1 ~ 1 ~ N N f R f R N f R f R fg g d a d a g d a d a t E t N (218) Solving Equation 217 for E(t) and substituting in Equation 218 yields mutual resource condition ) ~ ( ) ) ~ ( ( ) ( ) ( ) ~ ( ) ~ ( ) 1 ~ ( ) ~ (1 1 1 1 h f f h f hB D C B t N t N B B D MR (219) PAGE 53 53 where S B B g B Cf f N f ) ) ~ ( ( 12 1 2 S B B g B Dh h N h ) ) ~ ( ( 12 1 2 ) (N Ng g S ~ 0 1) ( ) ~ (d a Bh R h, ~ 1) ( ) ~ ( d a Bf R f and 1 2, ) ( d a Bi R i for h f i The mutual resource schedule is an increasing function of ~ i.e. 0 ) ~ ( R M. The larger the range of goods that home engages in R&D, the higher the relative wage. The reason behind an increasing is the la bor markets; as the home expands the range of goods exported, its demand for labor increases; on the other hand foreign countrys range of exported goods shrinks resulting in a lower demand for labor, in result these effects pull the relative wage of labor at home up. The increasing) ~ (MR(defined in Equation 223) t ogether with the decreasing mutual R&D condition) ~ (RD(given in Equation 221) are illustrate d in Figure 21. These curves are proved to intersect at a unique point and thus the steadyst ate values of relative wage and the marginal industry ~ are determined accordingly. This result is summarized in Proposition 21. Proposition 21. If ) ( ) ( h R f Ra a then there exists a unique equilibrium such that (i) the equilibrium relative wage of home is strictly greater than 1, 1*, (ii) home has a sustained compara tive advantage in the range of goods ~ 0 Home engages in R&D, produces and exports the stateof the art product for each industry ~ 0 (iii) foreign has a sust ained comparative advant age in the range of goods ~* Foreign engages in R&D, produces and exports the stateof the ar t product for each industry ~ Proof. See Algebraic Details. Figure 21 specifies the unique steadystate equilibrium level of home relative wage and the marginal industry by the mutual R&D and resource conditions. At this equilibrium, the PAGE 54 54 economy is at full employment with all markets cl earing and the pattern of trade is specified, because no multinational firms and trade in R&D sector are allowed13. In each industry, only the leader has the blueprint required to manufactur e the stateoftheart good. Home and foreign firms engage in R&D, discover, manufacture and export the next superior good in the range of industries ~ 0 and ~ respectively. By construction, for each industry1 both countries engage in R&D, produce and consum e the stateof theart product domestically. These results are similar of those found in Dornbusch et al. (1977) where their static continuum Ricardian model determ ines the pattern of trade by comparative advantage. In our model, this similar result is not only based on co mparative advantage in R&D services, but also other factors such as the level qual ity increment, and population growth. To see that the consumers utility grows at a constant rate in the steadystate equilibrium, we substitute the demand for quality leader products Equation 23 into utility Equation 22: d t j t E t E d t E d t Ei i t j t j 1 1 ) ( 0 ) () ( ln ) ( ln ) 1 ( ) ( ln ) ( ln ) ( ln where the last term is the e xpected number of R&D successes in a typical industry before time t, which is equal to d It0) (. The derivative of individual ut ility lnu(t) with respect to time gives the endogenous longr un Schumpeterian growth rate ln ln ). (N ug t I u u g The individual growth rate depe nds on the quality increment and also the rate at which better products are discovered. The older models gene rate a positive link between trade and growth which is based on the existence of scale effect s. Under the TEG specification no scaleeffects 13 Taylor (1993) developed a model where there is heterogene ity in research technologies and allowed for trade in R&D services as well. PAGE 55 55 property is observed, the longrun growth rate is proportional to the population growth rate and it is not affected by standard policy instru ments but remains endogenous as suggested by Segerstrom (1998). Comparative Static Results Having a model of quality ladders and Ricardian trade with n ontraded sector, comparative statics results are rich and have novel expl anations. Among many interesting questions, the steadystate effects of globaliza tion especially on the wageg ap across countries could be answered. For the comparative steadystate analysis, the two equilibrium c onditions (Equation 213 and Equation 219) are revised in the following form for convenience ) ~ ( RD (220) where 0 02 1 RD RD ) , ~ ( N h fg N N MR (221) where 0 0 0 0 0 0 0 08 7 6 5 4 3 2 1 MR MR MR MR MR MR MR MR Totally differentiating the equilibrium conditions in Equation 220 and Equation 221, the comparative static properties of the steadystat e equilibrium are examined. If home country has absolute advantage in all industries with a sufficien tly large relative labor force, then we have the following results Proposition 22. If ) ( ) ( h R f Ra a for all ) 0 [ and 1 ~ h fN N then in the steadystate, homes relative wage depends positively on f NN g and negatively onhN, Proof. See Algebraic Details PAGE 56 56 Proposition 23. If ) ( ) ( h R f Ra a for all ) 0 [ and 1 ~ h fN N then in the steadystate, the marginal industry ~ that splits the range of expor ted goods among countries depends positively on hN, and negatively onf NN g ,. Proof. See Algebraic Details. The results presented in Propos ition 22 and Proposition 23 can be derived graphically using Figure 22. We examine the steadystate equilibrium effect s of globalization first. An increase in the parameter has no effect on mutual RD curve, sin ce the zero profit condition (Equation 211a) and (Equation 212a) are not affected. Market clearing condition at hom e (Equation 214) and foreign (Equation 215) indicates that at home wo rkers are released from the industry that was nontraded before the liberalizati on. Relatively, more workers b ecome available for employment in the R&D sector and at the given marginal industry* ~ the relative wage of home has to fall as a consequence to maintain full employment of labor in both countries, which makes it more attractive for home firms to expand their R&D activ ities. This is illustrated in Figure 22 by a downshift in the MR curve. The fact that the industries are indexed in decreasing home comparative advantage implies that home firms would star t operating on industries beyond ~ where they have comparative advantage over fo reign firms. Starting from the steadystate equilibrium given by point A, an increase in leads to a new steadyst ate equilibrium given by point B, where the relative wage at home is declined and the range of home exports have expanded to maintain the equilibrium. With th e reduction of nontraded sector allocation of researchers is more efficient, in the sense th at globalization enabled the law of comparative advantage to work and determine the specializ ation in industries. The foreign firms conduct PAGE 57 57 research on the same industry that was nontrad ed before but this time selling to world consumers rather than domestic, stimulating inn ovation. On the other ha nd home allocates labors released from the nontraded sector at the ne w industry where their productivity is higher. Having more workers available for employment in the R&D sector lowers home relative wage and makes it more attractive for Northern firms to expand their R&D activities. Therefore, in the shortrun, globalization causes th e industrylevel innovation rate I to jump up but the industrylevel innovation rate gradually falls back to the original steadystate level Ng I because as innovation rate increases, R&D difficulty ) ( ) ( ) ( I t X t X becomes relatively more difficult. An increase in the supply of home labor (or a decrease in th e supply of foreign labor) does not affect the mutual RD condition, however sinc e the relative supply of labor at home is lower the labor markets are cleared at a lower wage than at the initial equilibrium at A. The mutual resource condition, which determines the relative wage at home to clear the labor markets, shifts down and lower costs give home firms a relativ e advantage over foreign beyond the marginal industry ~ enabling home to extend th e range of exports up to the marginal industry ~ at a lower equilibrium relative wage of *determined by the intersection of the original RD curve and the new MR curve at point B as illustrated in Figure 22. An increase in the growth rate of population (or a decline in the growth of R&D difficulty parameter) raises the innovation rate, leaving the mutual R&D condition (Equation 213) intact since the change in the zeroprofit conditions of home (Equation 211a) and foreign (Equation 212a) would be cancelled out. On th e other hand, higher innovation ra te stimulates research and demand of labor at home (Equation 214) to forei gn (Equation 215) increas es due to increased demand for researchers. To sust ain full employment in both c ountries, relative wage at home PAGE 58 58 should increase causing the mutual res ource condition curv e to shift up to) ~ (MR. As it is seen in Figure 22, the steadystate equilibrium move s from point A to point B where the relative wage at home is higher and the ra nge of home exports has shrunk. The result of an increase in the quality increment on the marginal industry is ambiguous, although a higher relative wage at home is implied since an increase in shifts both RD curve and MR up. The reason that RD curve shifts up could be explained by th e relative zeroprofit of home (expressed by dividing Equation 211a to Equation 212a) at the marginal industry* ~ which is ) ~ ( ) ~ ( 1* f R h Ra a Note that the lefthand side of this expression increases while the righthand side remains the same. Given the relative wage*, home firms relatively have higher profit from manufacturing the pr oduct at the marginal industry ~ than before while the relative cost is intact. The rela tive wage should increase to offset the increase in the lefthand side, which shifts the RD curve up. On the other hand, at the marginal industry* ~ labor markets condition is altered, suggesting a high er relative wage than the initia l equilibrium which is sustained by shifting the MR curve up. In contrast to results of Grossman and Help man (1991c), in our model relative wage at home depends on other factors such as relative country size and growth of population and factor price equalization is not a pr operty of the steadystate equi librium. The properties of the equilibrium depicted in Figure 21 shares many common features with the work of Taylor (1993), however some comparativestatic results ch ange, for example the eff ect of an increase in quality increment creates a deficit in balance of payments for home country since the loyalty payments that home has to pay for the frontlin e technology increases. The reason is that in his model a successful innovator either implements its improvement or it can go multinational and PAGE 59 59 carry the innovation ab road in return for a loyalty. This leads home to extend the range of goods produced, and also reduce the re liance on imported R&D by conducti ng more research at home. Relative wage at home did not ch ange however the marginal indus try has moved right on the unit interval of industries. Results presented in Proposition 22 and Propos ition 23 are similar that of Dinopoulos and Segerstrom (2006). They report th at globalization leads to a dec line in the wage gap between North and South. On the other ha nd, using rent protection activiti es rather than increasing R&D difficulty, Sener (2003) finds that globalization in fact increases the wagegap. In another NorthSouth trade model based on expa nsion in the variety of pr oducts, Grossman and Helpman (1991b) find that increasing the size of the South increases the rates of innovation and imitation and decreases NorthSouth wage inequality with a permanent increase in the rate of innovation. The recent empirical literature a bout incomeinequality obtains sim ilar results in the direction of Proposition 22. For example, the finding of declining global income inequality reported in Jones (1997) and SalaiMartin (2002) provides empirical evidence in support for Proposition 22. Conclusion We construct a twocountry general equilib rium framework without scaleeffects to determine the equilibrium relative wages and the pattern of trade between the two countries, and investigate the effects of globalizatio n on the wagegap across countries. Our model contributes to the literature by extending the model that embodies quality ladders and Ricardian trade by in troducing nontraded sector. The model with nontraded sector in the economy mostly supports th e results in the literature, al though for example, Factor Price Equalization does not hold in the steadystate equilibrium in contrast to Grossman and Helpman (1991c); also an increase in th e quality increment increases th e wagegap with an ambiguous effect on the marginal industry wh ereas Taylor (1993) reports that marginal industry moves right PAGE 60 60 without effecting the relative wa ge. Unlike the models mentione d above, the model presented here does not exhibit unpleasan t scaleeffectsproperty, whic h is removed by employing TEG (temporary effects on growth) specification follo wing Segerstrom (1998). The main results find some theoretical support from the work of Di nopoulos and Segerstrom (2006), in which they find that globalization reduces NorthSouth wage inequality. Jones (1997) and SalaiMartin (2002) empirically show a declining tr end in global income inequality. Homes relative wage depends positively on quality increment, consumers subjective discount rate, relative size of foreign countrys labor force and population growth; and negatively on the range of R&D difficulty growth parame ter and the range of nontraded goods. As the range of nontraded goods shrinks, the range of homes exportable goods widens, and the relative wage of home decreases. Globalization widens th e range of exportable g oods for both countries and reduces the wagegap across countries and yiel ds a faster technological change in the short run. While the long run innovation ra te in each industry is unaltered, in the shortrun a temporary increase in the innovation rate is observed along the transition path from the old to the new steadystate equilibrium. A model without nontraded goods may underor overestimate the effects of some variables on the endogenous variables, for instance as1 all nontraded goods become traded and a mutual resource curv e which lies below the actual curve would be used, leading to a lower relative home wage and a la rger range of home e xports than the actual. A model of nontraded goods is not only more realistic, but also allows us to answer some questions about liberaliz ation of nontraded goods, for exampl e opening of financial services to international trade in a country The wage gap between countries reduces as more nontraded goods become tradable. PAGE 61 61 The dynamic formulation of the model presente d here provides a richer framework for further study. The most obvious extension is introduction of nontrad ed goods endogenously, whether a good is going to be traded or nontrad ed is determined by the model using transport costs. Home and/or foreign tariffs, labor migratio n could be taken into account and their effects on technological progress and wage inequality can be examined. Algebraic Details Proof of Lemma 21. 0 ) 1 ) ~ ( ( ) ~ ( ) 1 ( ) ~ ( ~2 A A D R d d, Consider the traded sector in both countrie s at the steadystate equilibrium. For any equilibrium value of1 there exists a unique ) 0 [ ~ such that ) ~ ( RD holds, found by dividing the profit and cost of R&D of the countries at the marginal industry in Equation 211a and (Equation 212a) ) ~ ( ) ~ ( 1 f R h Ra a The left and right hand side are the relative profit from manufacturing and relative labor cost of R&D at home respectively. At the marginal industry ~ the relative wage given by ) ~ ( RD leaves none of the firms in both c ountries with a relative advantage, so firms in both countries are in different in enga ging R&D at the marginal industry ~ Assume that firms are indiffe rent in engaging R&D at the marginal industry ~ at a relative wage other than) ~ ( RD For any relative wage at home ) ~ ( RD the left hand side of (Equation 222) is lower while the right hand side is higher, i. e. the relative profit of home decreases as its relative cost of R&D increases. Therefore at the marginal industry ~ foreign firms will have higher return to R&D, an advantage over home firms which will result in higher PAGE 62 62 expected discounted profits for foreign firms. Hence, home firms would not be able to issue equities to finance their R&D costs, a nd decide not to engage in R&D at the marginal industry ~ a contradiction. A similar arguments holds fo r the case where the relative wage at home is lower than ) ~ ( RD In this case the home firms will have higher return leaving foreign firms out of the market at the marginal industry ~ again a contradiction. Therefore the relative wage given by ) ~ ( RD leaves both firms indifferen t in engaging R&D at the marginal industry ~ Without loss of generality, we assume that the firms in the home country engages in R&D at the marginal industry ~ Assume that in the steadystate, the equilibrium levels of relative wage at home and the marginal industry are *and ~ respectively. For any ] ~ 0 [* ) ~ ( ) (* A A since 0 ) ( A. Hence, dividing by ] ~ 0 [* leaves the left hand side of the equation intact, where the right hand side is smaller at any industry ] ~ 0 [* at *. Therefore for the industries ] ~ 0 [* home firms equities will be preferred to foreign firms since home firms have higher returns to R&D. Therefore, for ] ~ 0 [* foreign firms do not to engage in R&D and home firms will engage in R&D, discover and produce the product, and export it. Proof of Proposition 21. If ) ( ) ( h R f Ra a holds for 0 then 1 ) ( 1 ) ( ) ( 1 ) ( ) 1 ( 1 ) ( ) ( ) ( RD A A A a a Ah R f R. Intersection of ) ~ (*MRand ) ~ (*RDspecifies*. From Lemma 21, at these equilibrium levels, home and foreign has sustained comparative a dvantage in R&D in the industries ] ~ 0 [*and ) ~ (* respectively. There are no multinational firms, so patentholder of each invention produces the PAGE 63 63 good. Hence, home and foreign engages in R& D produces and exports the stateof the art product for each industry ~ 0 and ~ respectively. Proof of Proposition 23 and Proposition 24. The two equilibrium conditions (Equation 219) and (Equation 223) do not have an expl icit solution for the two endogenous variables and ~ Totally differentiating the equilibrium c onditions (Equation 220) and (Equation 221) results in a system of two equations in the differentials of the tw o endogenous variables as d RD d RD d2 1~ d MR dg MR d MR d MR d MR dN MR dN MR d MR dN h f 8 7 6 5 4 3 2 1 ~ We construct the reduced form as follows d dg d d d dN dN MR MR MR MR MR MR MR RD d d MR RDN h f 8 7 6 5 4 3 2 2 1 10 0 0 0 0 0 ~ 1 1 The determinant of the coefficient matrix is 0 1 11 1 1 1 RD MR MR RD Cramers rule for the endogenous variable yields 01 2 RD MR d N df, 01 3 RD MR d N dh, 01 4 RD MR d d 01 5 2 1 RD MR RD MR d d 01 6 RD MR d d 01 7 RD MR dg dN, 01 8 RD MR d d For the endogenous variable ~ PAGE 64 64 0 ~ 2 MR d N df, 0 ~ 3 MR d N dh, 0 ~ 4 MR d d ? 0 ~ 2 5 RD MR d d 0 ~ 6 MR d d 0 ~ 7 MR dg dN, 0 ~ 2 MR d d Figure 21. Wagegap and the pattern of trade. Figure 22. Comparativ e static results. PAGE 65 65 CHAPTER 3 INTERNATIONAL TRADE COSTS AND SCHUMPETERIAN GROWTH Introduction Globalization and technological progress have contributed to the acceleration of global growth and the volume of international tr ade. Developments in transportation and communication revolutionized economic exchange not only increasing its volume but also expanding its geographical scope. Wacziarg and Welch (2002) found that the percentage of the countries in the world that ha ve open trade policies increased from %15.6 in 1960 to 47% in 200014. The recent policies removing tr ade barriers and attempting to integrate the markets in Europe and North America have attracted the interest of many economists. As more countries opened their markets to international trade, the effects of the globalization became an important research area, and both the theoretical and empi rical research on globali zation has been intense in recent years. The main difference between this research a nd the endogenous growth literature is an endogenous nontraded goods sector determined via international trade costs, and a continuum of industries that differ in producti on and technological capabilities. Intern ational trade costs account for all costs except production and R&D costs, and Anderson and Wincoop (2004) stated that transportation, tariff and nontariff cost more than production. For industrialized countries, tariff equivalent of trad e costs is estimated to be 170% of which 21% is transportation costs, 44% is border related trade barriers, and 55% is re tail and wholesale margins. Trade costs started to play a significant role in recent models such as Melitz (2003), Ghironi and Melitz (2005) where firms with different productivitie s decide whether to export or 14 In the sense of Sachs and Warner (1995), a country is cla ssified as closed if it displays one of the following five characteristics: average tariff rates 40% or more; nontariff barriers covering 40% or more of trade; a black market exchange rate that is depreciated by 20% or more relative to the official ex change rate; a state monopoly on major exports; a socialist economic system. According to this widely used classification, India and China remain as closed economies even in 2000. PAGE 66 66 not. This literature is able to explain intraindustry trade and sheds light on microfoundations of trade, but it does not focus on the link betw een globalization, wage, innovation intensity and growth differences between countries. Eaton an d Kortum (2002) developed a Ricardian trade model with geographic features and employ a probabilistic fo rmulation of technological heterogeneity at the firm level to examine intraindustry trade, where more than one country may export the same good. Consistent wi th our results, their estimates s how that as inte rnational trade costs increases, a move to autar ky increases the relative wage of the country that has a larger export sector. The significance of the nontraded goods is st udied in the empirical literature. Kehoe and Ruhl (2002) examined countries after trade liberalizations, a nd reported that the increased volume in trade is mostly attributed to pr eviously nontraded goods. They found that export shares of the least traded goods account for 99% of exports from Canada to Mexico after NAFTA, and more than 100% of exports from Sweden and Italy after the EU. Disregarding the nontraded goods sector grea tly simplifies the algebra; however this limits the scope of the model and makes it impossibl e to study some interesting issues such as the effects of liberalization of the nontraded goods sector on th e economy. For example, without nontraded goods, all countries would have iden tical growth rates even if we allow for technological differences across i ndustries and countries The reason is that in a world where all the goods are traded, consumers can enjoy all the goods available in the rest of the world, and countries have a common growth rate. However, not all goods are traded due to international trade costs, and hence innovation and growth rates differ between countries. To account for within and crosscountry effects, we add an ex tra dimension to the endogenous growth theory by PAGE 67 67 introducing endogenously determin ed nontraded goods and allow for heterogeneous technology across industries. To our knowledge, Dinopoulos and Syropoulos (1997) is the only other work in the relevant literature that allo ws for a good to be nontraded a nd suggest a longrun growth gap between countries. In their model with one nontr aded and three traded goods, they find that globalization raises long run growth of all countries provided grow th intensity is larger in the nontraded goods sector than the traded goods sector15. A decrease in tariffs shift expenditure form the only nontraded good to the traded goods and therefore increase the profitability of R&D of the traded goods more than the nontrad ed good. Hence, any difference in nontraded goods creates a growth gap between countries. We generalize their approa ch in an endogenous growth model where there is a c ontinuum of industries, and the tr ade pattern and relative wage are endogenous. Another important question that we attempt to give an answer is whether the wagegap has been rising across nations due to globalization, as antiglobalization activists argue that globalization benefits the rich at the cost of poor16. Dinopoulos and Segerstrom (2006) examine three types of trade liberalization17: decrease in trade costs, an increase in the size of South and 15 Xu (2002) extended Ricardian trade model to twofactor model, where the nontraded sector is endogenously determined via iceberg transport costs, however there is no endogenous innovation in his model. He found that trade liberalization in the South reduces the range of nontraded g oods; and it reduces wage ineq uality if trade barriers are high to start with and incr eases it if they are low. 16 The empirical literature investigating the pattern of wage gap has different results due to different specifications in the measurement of incomeinequality. For instance, Pritchett (1997) measured incomeinequality by GDP per capita across countries and finds that during the period 19801994, the mean per annum growth rate of GDP per capita was 1.5% for 17 advanced capitalist countries and only 0.35% for 29 less developed countries. However, this measure does not take the population size into consideration and assumes that all the countries have same size. Jones (1997) showed that global incomeinequality has in fact d ecreased if each countrys average income is weighted by its population. SalaiMartin (2002) considered withincountry incomeinequality and supported the result that global inequality has decreased substantially since 1980. In the light of these findings, we consider population size and population growth of countries. 17 In the literature, globalization is defined in several different forms. For example, Dinopoulos and Segerstrom (1999) modeled it as a reduction in trade barriers between developed countries, as the international movement of resources such as labor migration and/or the formation of multinationals, or as developing countries joining the PAGE 68 68 stronger intellectual property right s in a NorthSouth trade model. They show that a decrease in trade costs lead firms in the No rthern market produ ce less for domestic market, and export more because the Northern market is larger and more competitive and South market is more profitable. Thus, wage inequality reduces. This finding is clos e to the result in our model in the sense that lower trade costs decrease the re lative wage of the c ountry that has a larg er range of export sector. This paper uses building blocks from Do rnbusch, Fischer and Samuelson (1977) (DFS from now on) and Grossman and Helpman (1991c). Following the seminal work of DFS (1977), we consider a continuum of industries that differ in productivities. We account for the endogenous technological change by borrowing the notion of creativ e destruction via repeated innovations of Segerstrom, Anant and Dinopoul os (1990), Aghion and Howitt (1992) and Grossman and Helpman (1991c). These studies develop a dynamic general equilibrium setting that results in longrun growth based on endogenous technical change18. Taylor (1993, 1994) also extends the Ricard ian model of DFS (1977) following Gr ossman and Helpman (1991c). He incorporates heterogeneity in productivities ac ross industries in research and production. Our model differs in several ways, and in the questions we ask. His m odel treats all goods as tradable and does not allow for international trade costs and nontraded goods. It also has scaleeffects problem; and innovation intensity at industry and sector levels or the growth gap are not studied. He also assumes that R&D resu lts are exportable which allow le ss developed countries to export R&D results from developed countries and reap all the benefits of innovation. In our model, R&D activities are stimulated by rewards to innovation, and the innovator who holds the world trading system. In this paper, globalization is defi ned as a decrease in trade cost s and therefore liberalization of the economy by reducing the range of nontraded sector. 18 Barro and SalaiMartin (1995) provides excellent source for the evolution of growth models. PAGE 69 69 blueprints is protected by pate nts. Consequently, we assume that firms in both countries conduct research, and trade pattern is determined based on comparative advantage. Another aspect that sets this paper apart from the models mentioned earlier is the removal of the scaleeffects property. Jones (1995a) pointed out that the firstgeneration endogenous growth models have a scaleeffects property. That is, a positive populat ion growth generates infinite percapita longrun growth, which is cont radicting the postwar timeseries evidence that shows an exponential increase in R&D resources but almost a constant rate of percapita GDP growth in all advanced countries19. To fix this problem, secondgeneration endogenous growth models have been developed to remove the scale effect property20. This paper removes the scaleeffects property by implementing PEG specification, which captures the idea that it is harder to improve the quality of a product in large ma rkets, following Dinopoulos and Thompson (1998). This paper is the first to include nontrade d goods sector in a scalefree dynamic general equilibrium model, producing nove l results about innovation intensi ties, growth rate, growth gap and globalization, and generalizing the main re sults of Ricardian trade and endogenous growth. We consider longrun Schumpeterian growth which is based on the process of creative destruction. The essential feat ure is the incorporation of t echnological progress which is generated by endogenously introduced product or process innovations. Through time, new products emerge in the market s and replace the old products. There are two countries in the model, ho me and foreign. The population grows at a common exogenous rate. There is a continuum of industries in which fi rms are manufacturing 19 During this period, although all major advanced countries devoted exponentially growing resources to research, percapita GDP growth remained almost constant. See Dinopoulos and Thompson (1998) and Young (1998) for a detailed discussion. 20 See Jones (1999), Young (1998), Dinopoulos and Thom pson (1998), Segerstrom (1998), Howitt (1999), Dinopoulos and Syropoulos (2007), and Dinopoulos and Sener (2004) for an outline of alternative solutions to the scaleeffects property and an assessment of s caleinvariant Schumpeterian growth models. PAGE 70 70 final consumption goods and engaging in research activities using only la bor. The quality of each good can be improved by endogenous innovation thr ough R&D races. The winner of the race in each industry holds the blueprints for manufact uring the good, and becomes the sole producer of the stateoftheart product. Some of the main results ar e: wage inequality between home and foreign depends positively on the range of ho me sectors, productiv ity of home labor, international trade cost, foreign population size, subjective discount rate and R&D difficulty; and negatively on inventive step, home populatio n size, population growth and productivity of foreign labor (Proposition 32 and 33). If an industry that was nontraded before is liberalized, the range of goods exported to other country ex tends, and innovation in tensity increases at industry and sector levels (Propos ition 37). Home sectors innovate faster than foreign and the increase in innovation intensity at home traded sector is more th an its nontraded sector, whereas the increase in foreign nontraded goods sector is more than its traded goods sector (Proposition 35 and 36). Growth rates of both countries in crease, but growth rate gap between home and foreign widens, since home growth rate is faster than that of foreign. Model In this paper, a dynamic general equilibrium mo del with two countries is considered: home and foreign. Firms in both countries engage in R&D and produce final consumption goods using labor as the only f actor in industry 1 0 Following DFS (1977), the continuum of industries is indexed by decreasing home comparative advantage. International trade costs generate two endoge nously determined sectors in each country, namely the traded and nontraded goods sectors. The traded and nontraded goods sectors in home consist of industr ies in the range of 1, 0 and 2 1, respectively, and the marginal industries 1 and 2 are endogenous. Similarly, the traded and nontr aded goods sectors in PAGE 71 71 foreign are defined to be in the range of 2 1, and 1 ,2 respectively where1 0 ,2 1 Globalization will be measured with a decr ease in the international trade costs1 which lowers the cost of exporting and hence decr eases the range of nontraded goods sector. For the ease of notation, throughout the rest of the chapter superscr ipts h and f are used to identify function and variables of home and foreign countries respectively. The subscripts T and NT stand for traded and no ntraded goods, respectiv ely. In addition, time arguments are omitted when no confusion is caused by doing so. Household Behavior Country is population at time t is denoted by) ( t Ni, and each countrys common population growth 0 ) ( ) ( t N t N gi i N is assumed to be constant. In each country, there is a continuum of identical dynastic families that provide labor services, earn wages, and save by holding assets of firms in R&D race. Each individual member of a household is endowed with one unit of labor. We assume that i iN N ) 0 (, thus the population of workers at time t in country i is t g i iNe N t N ) (. Households in each country maximize a discoun ted, additively separable intertemporal utility function of the form21 dt t u e Ut gN) ( ln0 ) ( (31) where 0 is the common subjective discount rate, and it is as sumed that the effective discount rate Ng is positive. 21 See Barro and SalaiMartin (1995 Ch.2) for details of the households behavior within the context of the Ramsey model of growth. PAGE 72 72 d t j q t uj t j 1 0 ) () ( ln ) ( ln (32) represents instantaneous utility at time t, where is the inventive step, t j q denotes the consumption of a product that has t j quality improvements in industry at time t. The specification in Equation 32 indicat es that consumers derive more utility from consumption of higherquality goods and are so willing to pay more for quality, which in turn gives firms an incentive to improve the quality le vel of the stateoftheart good. The household maximizes utility by choosing an optimal time pattern of spending at each point in time. At any time t, given the mark et prices for goods, each household allocates its income to maximize utility given in Equation 32. The wellknown solution to this optimal control problem is a unit elastic demand functio n for the good with the lo west qualityadjusted price ) ( ) ( ) ( t j p t E t j qi l i i l for country h f i and sector NT T l (33) where ) ( t Ei is the total expenditure and the global expenditure ) ( t Eis the sum of total expenditure in two countries,) ( ) ( ) ( t E t E t Ef h Price of a good in sector NT T l of country i is denoted by) ( t j pi l. The consumer chooses the single product that offers the lowest quality adjusted price, and the demand for all other goods is zero. Therefore, in equilibrium it is only the highest available quality that provides the lowest qualityadjusted price. The global demand for traded goods is found by aggreg ating the demands in each country, ) ( ) ( ) ( ) ( ) ( t j p t E t j q t j q t j qT f T h T T (34) PAGE 73 73 Substituting the optimal static allocation of sp ending into Equation 32, and the result into Equation 31, the intertemporal maximization of representative house hold in country i is equivalent to 0 ) ( ) () ( ln max dt t E ei t g t EN i, (35) subject to the intertem poral budget constraint ) ( ) ( ) ( ) ( ) ( ) ( ) ( t s g t E t N t w t s t r t si N i i i i i where ) ( t sidenotes the per capita financial assets, ) ( t wiis the wage earned by the representative household member in country i and r(t) is global in stantaneous rate of return at time t. Consumers can borrow or lend freely on an international capital market with riskless rate of interest r(t). They take this interest rate as given, although its value will be determined in the general equilibrium. The representative house hold member allocates her income between consumption expenditure and savings and the solu tion to this problem yields the differential Equation known as KeynesRamsey rule ) ( ) ( ) ( t r t E t Ei i (36) Percapita consumption expenditure is consta nt only when the subjective discount rate equals the instantaneous interest rate r. Th e homothetic preferences assumption implies that Equation 36 applies not only to each representa tive household member, but also to the aggregate economy. Production, R&D Services and Industry Structure A continuum of products1 0 is available in different quality levels. In order to produce a good, firms have to invent it first. Th us, the sole manufacturer of a stateoftheart PAGE 74 74 quality good is its innovator. La bor is the only factor of produ ction and R&D services. A firm targeting an industry 1 0 engages in R&D activities to di scover the next higherquality product using the cons tantreturnstoscale production function ) ( ) ( ) ( i R i R ia t L t R (37) where ) (i Ra denotes country is unitlabor requirement in R&D services and differs across industries and countries. Level of labor employment in research and R&D services produced in country i in industry is denoted by ) ( t Li R and (,),i R trespectively. Manufacturing is similar to R&D services. A suc cessful firm in a typical industry produces the final consumption goods by the constantreturnstoscale production function ) ( ) ( ) ( i Q i Q ia t L Q (38) where ) (i Qais the unitlabor requirement for ma nufacturing in country i for the good ) ( t Li Qis the level of labor employe d in manufacturing final good in country i, and) (iQ is the output level of the final consumption good in country i. One important feature of our model is that unitlabor requirements in R&D services and manufacturing differ across countri es and industries as well. This specification allows us to determine the pattern of R&D services and in turn the trade pattern of manufacturing goods. Specifically, following DFS (1977), the continuum of products 1 0 is indexed by diminishing home country comparative advantag e in goods production, with relative unit labor requirement of home with respect to foreign defined as ) ( ) ( ) ( h Q f Qa a A where0 ) ( A (39) PAGE 75 75 This structure of diminishing comparative a dvantage of home country in goods production applies also to R&D services. It is suggested by Taylor (1994) that ther e is a relation between production and R&D activities in th e sense that, there are common factors such as education, labor standards, and geographical structure wh ich affect both producti on and R&D technologies in the same direction, but not necessarily at the same strength22. Hence, we assume that in any industry, the country with an absolute advantag e in production has also an advantage in R&D. Specifically, the relationship between the innova tion and production process is captured by an additional term0 ) ( where) ( ) ( ) ( i Q i Ra a in each industry. Therefore, the ranking of continuum of industries by diminishing home country comparative advantage in goods production is preserved in R& D services as well. The ) ( Aschedule in Equation 39 also represents the relativ e unit labor requirements of th e two countries in R&D services23. Transport Costs and Sector Structure We introduce trade barriers in the form of unit transport costs for each unit traded, regardless of the direction of trade. Following Samuelson (1954), the tr ansport costs are of iceberg type in the sense that only a portion of the good transporte d reaches its destination. An exporter must ship 1 1 units of a good to guarantee th e delivery of exactly one unit24. 22 Taylor (1993) assumed that th ere are no other costs for trade and all the goods are traded wit hout any barrier; and in his model nontraded goods sector does not exist. He also treated R&D services as final goods and firms always export their R&D activities. 23 If home country has absolute advantage in goods production in an industry then ) ( ) ( f Q h Qa a should hold. This implies that) ( ) ( ) ( ) ( ) ( ) ( f R f Q h Q h Ra a a a that is home country has absolute advantage in R&D services also. Similarly, the ranking of industries with respect to diminishing home country comparative advantage in goods production is preserved in R&D services, since ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( h R f R h R f R h Q f Qa a a a a a A 24 The iceberg transport cost causes only a portion of the good to arrive its destination, i.e. in order to supply the market abroad with exactly one unit, the exporter should ship 1 1 units. PAGE 76 76 An exporting firm in home incurs a unit cost of ) ( ) 1 ( h Qa to produce and transport one unit to foreign market. A foreign firm can produce the same good at a unit cost of ) (f Qawithout paying for transportation costs. Hence, a home firm can export if and only if its cost is lower than a foreign firm or) ( ) ( ) 1 ( f Q h Qa a holds. Using) ( A schedule given in Equation 39, and denoting home relative wage as f hw w this condition is equivalent to 1 ) ( A (310) At the marginal industry1 Equation 310 holds with equality where home exporters and foreign producers have the same unit cost. For the ease of notation, without loss of generality we assume that home will be the exporter in the industry1 ; hence home export sector is defined to be the range of industries1, 0 Similarly, a foreign firm e xports a good if and only if ) ( ) 1 ( ) ( f Q h Qa a holds, or equivalently Equation 311holds ) ( ) 1 ( A (311) At the marginal industry2 Equation 310 holds with equality. Again, for notation purposes, we assume that foreign will be the exporter in the industry2 hence foreign export sector is defined to be th e range of industries 1 ,2 The remaining industries in the range 2 1, are nontraded, since cost of an exporter firm at abroad would be higher than that of the domestic firm. Specifica lly, nontraded sector consists of industries where Equation 312 holds: 1 ) 1 ( A A (312) PAGE 77 77 R&D Races The quality N j of a product in each industry can be improved an unlimited number of times. Each improvement raises the quality of the stateoftheart product (i.e. the best existing quality) by a constant level of > 1. The quality improvements occur stochastically as firms engage in R&D activities. At time t = 0, there is only j = 0 quality product available in each industry. Only one firm in each industry knows how to produce the stateoftheart quality product, and no other higher quality product is discovered yet; hen ce the firm with the blueprint becomes the leader. If the stateoftheart quality product in an industry is j, the next leader will be the only producer of j+1 quality product. R& D races push each product in an industry one step up its quality ladders in the sense of Grossman and Helpman, (1991c). Once the higherquality product in an industry is discovere d, the blueprint of lower quality good becomes available to all the firms. As a result, any firm can produce th e lower quality good and therefore leader does not engage in further R&D. A challenger firm targeting a quality leader in country h f i enters the R&D race in industry 1 0 with an instantaneous probability dt t Ii z) (to win where ) ( ) ( ) ( t X t R t Ii i z i z (313) ) ( t Ri zis R&D outlays of firm z and ) ( t Ximeasures the difficulty of R&D in industry at time t. A challenger increases its own chance to win the next race by increasing the level of R&D outlays which is costly.) ( t Ii, the industrywide probability of innovation, follows a memoryless Poisson process and is obtained by adding up the level of R&D across all the challengers in that country as follows PAGE 78 78 ) ( ) ( ) ( ) ( t X t R t I t Ii i z i z i (314) where ) ( t Riis country is total R&D services in industry This paper implements permanent effects of growth (PEG) specification of Dinopoulos and Thompson (1998)25. R&D difficulty increases in each country separately according to ) ( ) ( t kN t Xi i, (315) where R&D difficulty growth parameter k > 0 is a constant. This specification captures the notion that it is more difficult to improve the quality of a product in a larger market. The effect of independent variables on the l ongrun growth rate is not te mporary, and therefore this specification is called the permanent effects of growth model. Consumer savings are channeled to firms engaging in R&D through the stock market, therefore a portfolio allocation pr oblem has to be solved, i.e. simply a choice among shares in a variety of profitmaking firms has to be done. Al though a particular firm bears risk, the risk attached to any equity is idiosyncratic; therefor e an investor can earn a sure rate of return by holding a well diversified portfolio of shares. In the equilibrium, all assets must earn the same rate of return. Denoting ) ( t Vias the expected discounted profits of a successful firm in industry at time t in country i, a shareholder faces a loss of ) ( t Viif a higher quality product is innovated. The probability of such an innovation is dt t Ii) (, whereas the probability of no innovation in the time interval dt is dt t Ii) ( 1 The shareholder of an incumbents stock receives a dividend dti, and therefore the value of th e successful innovator appreciates 25 See Segerstrom (1998) for temporary effects of growth (TEG) model, where R&D becomes more difficult over time because the most obvious ideas are discovered first. The innovation rate is same for all industries and does not vary over time. The longrun growth rate is proportional to the exogenous rate of population growth and it is not affected by any policy; thus any effects on growth would not be permanent. PAGE 79 79 by dt t V dt t t V t dVi i i) ( ) ( ) ( An investor can completely diversify away the risk by holding a diversified portfolio of stocks. Therefore, expected rate of return from holding a stock of successful innovator must be equal to the riskless rate of return r, rdt t V t V dt t V t dt dt t I t V t Vi i i i i i i ) ( 0 ) ( ) ( ) ( ) ( 1 ) ( ) ( and taking limit 0 dtyields the expected discounted profits of a successful innovator in industry at time t in country i as ) ( ) ( ) ( ) ( ) ( ) ( t V t V t I t r t t Vi i i i l i (316) Pricing and Stock Market The quality leader does not enga ge in further R&D and holds an infinitely lived patent for the stateoftheart good26. However, producers in the same industry 1 0 compete as Bertrand oligopolists. Consider a firm that invented th e next higherquality pr oduct with quality being times better than the nearest competitor. After th e invention of the stat eoftheart good, the blueprints for the lower quality good become availa ble to all the firms. Th us, the quality leader charges a price that is times the minimum cost of produc tion of that nearest competitor. The incumbent in the traded goods sector is threatened by challeng ers in both countries, whereas the quality leader in a nontraded goods sector faces only domestic competition. This difference between sectors leads the incumbents in each industry to use the optimal limitpricing schemes as follows. The leader in home can at most charge a price times higher than the nearest competitors cost, which is) (h Q ha wif it is located in home and ) ( ) 1 ( f Q fa w if it is in 26 The gain from improving own product further is strictly less than the gain of a onestepquality advantage to a challenger. See Dinopoulos and Syropoulos (2007), the in novation process is modeled as a contest between the quality leader and the challengers. The incumbent can increase the expected duration of its monopoly by engaging in rentprotection activities that reduce probability of further innovation. PAGE 80 80 foreign, since a foreign firm has to pay the intern ational trade costs. Spec ifically, the leader in home charges the price f Q f h Q h h Ta w a w p ) 1 ( min ) ( Taking the wage of foreign labor as numeraire 1 fw, the wage of home labor becomes the relative wagehw. Using ) 1 ( ) ( A in Equation 310, the price charged by the winner in home is h Q h Ta p ) (27. (317) Similarly, in the home nontraded goods sector, the incumbent faces only domestic competition and hence can charge times higher than the nearest competitors cost, h Qa. In any industry 2 1, in the home nontraded goods sector, ) ( ) 1 ( 1 ) ( A A holds from Equation 312, therefore incumbent charges a price h Q h NTa p ) (. (318) Price scheme in foreign nontrad ed goods sector is determined in a similar way. In any industry 2 1, in the foreign nontraded goods sector, the leader is threatened by domestic challengers having a cost of ) (f Qa, hence the price charged by foreign leader is f Q f NTa p ) (. (319) Quality leader in foreign traded sector is th reatened by challengers from both countries and can at most charge a price times the nearest competitors marginal cost) ( ) 1 ( h Qa if it is 27 ) (h Tpis times the minimum of production costs in both countries, or A ah Q, min .. For any industry 1, 0 in home export sector, 1 Aby Equation 310. Therefore, h Q h Q h Ta A a p min ) (, since A A 1. PAGE 81 81 located in home and ) (f Qaif it is in foreign. Hence the pricing condition f Q h Q f Ta a p ) 1 ( min ) ( of a winner in the foreign export sector yields f Q f Ta p ) (. (320) These results are summarized in Lemma 31. Lemma 31. For any there exists two marginal industries1 and 2 such that home firms engage in R&D, produce and export the stat eof the art product for industries in the home export sector 1, 0 ; foreign firms engage in R&D, pr oduce and export the stateof the art product for industries in the foreign export sector 1 ,2 ; firms in both countries engage in R&D and produce the stateof the art product fo r industries in the nontraded goods sector, 2 1, Proof. See Algebraic Details. The stream of profits of a quality leader in country h f i at sector NT T l is ) ( ) ( ) ( i l i i l i lq w p (321) where ) (i lq is the demand for a good in industry Among all the challengers that engage in costly R&D activities, only one will be the sole winner of the R&D race. A challenger z in country i can attain stock market value) ( t Viwith probability dt t Ii z) ( by undertaking research at intensity ) ( t Ii zfor a time interval of length dt. The only cost of such research activity is the labor cost ()(,)()iiii RzwaItXtwhere (,)(,)()iii zz R tItXt is the level of R&D services and ()(,)()iii RzaItXtis the level of labor employed in research. Free entry to R&D race drives the expected discounted profits of a challenger to zero (,)(,)()()(,)0iiiiii zRzVtItdtwaXtItdt which specifies the R&D condition PAGE 82 82 (,)()()iiii RVtwaXt (322) Substituting Equation 316 into Equation 322 yiel ds the zero profit condition of a firm in sector NT T l (,) ()() (,) ()(,) (,)i iii l R i i it waXt Vt rtIt Vt (323) The lefthand side of the above Equation is the expected discounted profits or simply rewards to innovation, and the righthand side refers to the cost of innovating in the corresponding country and industry. Take for in stance the zeroprofit co ndition for a challenger firm in home in the export sector. Substituting home firms profit ) ( th T into Equation 323 gives (1) () ()() (,) ()(,) (,)hhh R h h hEt waXt Vt rtIt Vt and the rewards to innovation increases as the inventive step increases ( increases), expenditure ) ( t E increases, future profits are discounted less () ( t r decreases) and the likelihood of replacing the quality lead er decreases (innovation rate ) ( t I decreases). The cost of innovating increases as R& D becomes more difficult (()i X t increases) and unitlabor requi rement or wage increases. Labor Markets All labor is employed in either production of final goods or R&D services. Labor is perfectly mobile across industries and activ ities in each country, and wages adjust instantaneously to clear the market to sustain full employment of labor at each instant in time. Focusing on the home labor market first, it fo llows from Equation 38 that the total labor demand in production of traded goods and nontraded goods is d a qh Q h T) (10 PAGE 83 83 and d a qh Q h NT) (2 1 respectively. The total employment in R&D services is d a Rh R h T) ( ) (10for traded goods, and d a Rh R h NT) ( ) (2 1for nontraded goods. Hence, home full employment of labor condition is hN = d a qh Q T) (10+ d a qh Q h NT) (2 1+10()()hh TRRad +2 1()()hh NTR R ad (324) The left hand side of Equation 324 is the s upply of home labor and the right hand side is the demand for home labor. Similarly, foreign fu ll employment of labor condition at time t is: fN =21()f TQqad + d a qf Q f NT) (2 1+21()()ff TR R ad +2 1()()ff NTR R ad (325) Trade Balance We close the model by imposing the trade bala nce. Overall, trade in goods between the two countries must be balanced, since we do not allow for international capital flows. Under balanced trade, the payments for traded goods fl owing into home from foreign must equal the payments flowing out of home to foreign. Buyers in home spends ) ( ) ( f T f Tq p for each imported good 1 ,2 from foreign and in total, homes payments to foreign are d q pf T f T) ( ) (12. On the other hand buyers in foreign spends ) ( ) ( h T h Tq p for an imported good1, 0 from home and total payments to home is d q ph T h T) ( ) (10. The value of exports should be equal to imports in or der to have the trade balanced, PAGE 84 84 or d q p d q pf T f T h T h T) ( ) ( ) ( ) (1 02 1 Using ) ( ) ( h T f h Tp E q and ) ( ) ( f T h f Tp E q from Equation 33 and then evaluating th e integrals yields the balanced trade condition : ) 1 )( ( ) (2 1 t E t Eh f (326) SteadyState Equilibrium In this section we solve for the unique steadystate equilibrium and determine home relative wage, innovation intensities at indus try and sector levels, and growth rates. Grossman and Helpman (1991c) have four nonlinear equations in the steadystate equilibrium and the sign of the first order deriva tives contain complicated determinants, and their model does not yield any result ab out the effect of trade liberali zation on relative wage since the model is not tractable. In contra st, in our model, there are three steady state conditions to be met and all the comparative statics re sults can be obtained graphically. In the steadystate equilibrium all variables grow at a constant rate, as Equation 316 implies that N i i i i i ig t N t N t X t X t V t V ) ( ) ( ) ( ) ( ) ( ) ( Also, Equation 36 yields that the instantaneous interest rate r should be equa l to the subjective discount rate Relative Supply and R&D Conditions. There are three conditions to be met in the steady state equilibrium, the relative supply (RS) and two R&D (hRD andfRD ) conditions. Focusing on the la bor markets cl earing condition together with Equation 322, we get the RS curve (see Algebraic Details): 2 10 1 1 2 2 1 2 1) ( 1 ) ( 1 1 1 1 1 ) ( d a g k d a g k N N RSh Q N f Q N h f (327) PAGE 85 85 The RS curve in Equation 327 features the labor market dynamics on home relative wage. RS curve is increasing in 1 and 2 since home relative wage increases if home expands its export sector 1 or the range of home sectors2 It determines home relative wage needed to clear labor markets when home and forei gn firms undertake R&D and produce goods in the range of industries 2, 0 and 1 ,1 respectively. Nontraded goods elaborate the analysis and yi elds novel results. For example, an increase in the unit labor requirement of home has no effect on labo r markets in DFS (1977), and it increases the relative wage in Taylor (1993). On the other hand, in our model, home firms need less labor to maintain same manufacturing and R&D output levels, whereas there is no change in foreign. Therefore, has to decrease to clear the home labor market. R&D curves for home and foreign are 1 ) ( ) ( A RDhand ) ( 1 ) ( A RDf (328) Similar to DFS (1977), given home relative wage in Equation 327, the marginal industries1 and2 are specified by 1(,)hRD and 2(,)fRD respectively. The unique steadystate equilibrium is shown in Figure 31. The R&D curves in Equation 328 are downwardsloping in ,space, indicating decreasing home country comparative a dvantage as in DFS (1977). Following the schedule h Q f Qa a A ) (, the continuum of industries is indexe d in a way that home has the highest advantage in the industry 0 and foreign has the highest comparative advantage in the industry1 The intersection of RS curve with ) ( hRD at point A and ) ( fRD at point B determine the marginal industries. This result is presented in Proposition 31. PAGE 86 86 Proposition 31. There exists a unique steadystate equilibrium such that RS curve in Equation 327, together with ) ( hRD and ) ( fRD in Equation 328 determine home relative wage and the marginal industries 1 0 ,2 1 and (i) home and foreign firms engage in R&D, pr oduce and export the stateof the art product in industries 1, 0 and1 ,2 ,respectively, (ii) firms in both countries engage in R& D and produce the stateof the art product for domestic markets in the nontraded goods sector, 2 1, Proof. See Algebraic Details. Proposition 31 presents the unique steadystat e equilibrium level of home relative wage and the marginal industries1 and2 determined by the RS and R&D curves At the steadystate equilibrium, the pattern of trade is spec ified and the world economy is at full employment with all markets clearing. The intuition behi nd Proposition 31 is based on the zeroprofit conditions and the law of comparative advantage. The larger the range of home sectors, the higher is the demand for labor and hen ce the higher is home relative wage. The dynamic model in our model generalizes some results of DFS (1977) where their static continuum Ricardian model determines the patte rn of trade by comparative advantage. For instance, in our model the pattern of trade is no t only based on comparative advantage, but also on other factors such as the quality level incr ement, R&D difficulty, population growth and the range of nontraded sector which is a novel result In contrast to DFS (1977), in our model unit labor requirements affect the labor market equilibrium. The decreasing hRD curve suggests that home firms have lower R&D costs than foreign firms for the goods in the range1, 0 Hence, in the range 1, 0 home firms equities would be preferred over foreign and forei gn challengers would not be able to finance their R&D costs in industries1, 0 Thus, they choose not to conduct R&D sin ce this would yield to negative profits PAGE 87 87 (see Equation 321). A simila r argument using decreasing fRD curve implies that home challengers would not undert ake R&D in the industries 1 ,2 In the analysis of the model, Taylor (1994) assumes that f ha a since innovators can undertake research in any country and expor t the results, hence the RD schedule reduces to 1 a a RD Therefore at the equilibrium, the country that has the lowest cost engages in R&D activities and none of the firms in the other country conducts R&D. However, in our model patents protect the quality leader and in each indus try, it is only the quality leader that has the right to manufacture the stateoftheart product. Consequently law of comparative advantage applies and even the country with absolute disadvantage engages in R&D activities. Innovation The nontraded goods sector and heterogeneity of research technologies across industries and countries enable us to analyze innovation ra tes in depth. Innovation rates at industry and sector levels can be examined within and acr oss countries (see Algebr aic Details). The steadystate innovation rate at indus try level depends on paramete rs such as inventive step R&D difficulty in the countryi X productivity of researchers in industry) (i Ra and wage rate. In the steadystate equilibrium, we analyze innovation in tensities separately at industry and sector levels. From the zeroprofit conditions in Equation 323, the innovation intensity for traded goods at the industry level in country f h i can be determined as N i i R i i Tg X a w E I ) ( 1 ) ( (329) and for nontraded goods as PAGE 88 88 N i i R i i i NTg X a w E I ) ( 1 ) (. (330) In an industry if cost of R&D) (i R ia w decreases, R&D becomes less difficult (a decrease in i X ), inventive step is larger, and the effective discount rate Ng is higher or expenditure E increases. Then, incentives to challenge the quali ty leader in that industry increase, which in turn increases the innovation intensity at that industry. A nontraded a nd traded industry will differ in research produc tivities and expenditure levels. Hen ce, innovation rate s are higher in a traded industry where rewards to inn ovation are higher due to global demand, i E E For innovation intensities at the sector level, we aggregate the i ndustry level innovation intensity over the sector. The aggregate innovation in tensity in home traded goods sector is 1 0 01 1) ( 1 1 ) ( N h R h h T h Tg d a X E d I I (331) in foreign traded goods sector, 2 1 11 ) ( 1 1 ) (2 2 N f R f f f T f Tg d a X w E d I I (332) and in nontraded goods sector in country f h i 1 22 1 2 1) ( 1 1 ) ( N i R i i i i NT i NTg d a X w E d I I (333) The expressions in Equation 331, Equation 332 and Equation 333 allow us to analyze the total innovation activities in a given sector. Si milar to industry level analysis, the sector level innovation intensities depend negatively on cost of R&D) (i R ia w R&D difficultyi X inventive step and positively on expenditure level and effective discount rateNg However, unlike the industry level, the sector level innovation rates depend on th e range of the sector that a PAGE 89 89 country is operating; the larger the sector, the higher is the i nnovation intensity in that sector. Comparison of sectors within and across countries and a detailed comparative statics analysis are presented in the Algebraic Details. Long Run Growth In this section we focus on the longrun Schumpeterian grow th. Schumpeterian growth is based on the process of creative destruction. The essential feature is the incorporation of technological progress which is generated by endogenously introduced product or process innovations. Through time, new products emerge in the markets and replace the old products. A novel result that sheds light on the effects of nontraded goods sector is that, in the equilibrium the consumers utility grows at a cons tant rate, but unlike the relevant literature, it differs with respect to location of the consum er. Substituting the demand for stateoftheart products Equation 33 into utility Equation 32 yields the utility of a consumer located in country f h i as d t E d t E d t E t ui t j t j t j i 2 1 2 1) ( ln ) ( ln ) ( ln ) ( ln) ( 1 ) ( 0 ) (, (334) where t j is the number of quality improvements in industry at time t. The integrands on the right hand side are the quality level of the stateofthe art good in industry at time t ) ( t j, times the consumption level of the good. A c onsumer enjoys higher qua lity level or if she consumes more. The utility of a consumer is summed up for all the domestic and imported goods. The derivative of ) ( ln t uiwith respect to time gives the longrun Schumpeterian growth rate f T h NT h T hI I I g ln and h T f NT f T fI I I g ln (335) PAGE 90 90 in home and foreign respectively, si nce along a balanced growth path ) ( t E and ) ( t Ei are constants as 0 E E As a product climbs up its quality ladder with each innovation, the instantaneous utility jumps by the constant factor ln. The expected frequency of an innovation in sector NT T l of country i is captured by i lI which is the sum of intensities in that sector. Adding up intensities in the expor t, nontraded goods and import sectors yields the aggregate innovation intensity in that count ry which is captured by the thr ee terms in brackets of Equation 335. There is no scaleeffects property and a ny effect on the growth rate is permanent. The existence of international trade costs generates novel insights. If there were no international trade costs0, there would be no nontraded goods sector, and0 h NT h NTI I Countries would share the same growth rate ln ln I I I g gf T h T f h which is standard in Schumpeterian growth models. Endogenous ly determined nontraded goods and the heterogeneity in technologies lead to differe nt growth rates across countries and enables comparison of countries. Comparative Statics Having a model of quality ladders and Ricardi an trade with a nontraded goods sector, comparative steadystate equilibrium exercises are rich and provide novel insights. Among many interesting questions, the steadystate effects of globa lization on innovation in tensities, growth rates of countries and wagegap across countries are some that could be analyzed. The growthgap between countries, created by th e nontraded goods sector, is also examined in this section. One feature of the model is that comparative statics analysis can be carried out by using RS and RD curves plotted in Figure 31, instead of to tally differentiating the equilibrium conditions Equation 327 and Equation 328, and solving the system of equations for the unknowns. PAGE 91 91 Effects on Wage Gap and Sector Range To study the effects of a parameter change, we focus on RS,hRDandfRD curves separately and determine the dire ction of shift using first order derivatives given in Algebraic Details. Any increase in variablesNg and hN or a decrease in variablesk or fN, have no affect on hRDandfRD curves, but shifts the RS curve down. The new steady state equilibrium for home is reached (a movement from point A to A ) at a lower home relative wage with a wider export sector 1, 0and at the new steadystate equilibrium of foreign (a movement from point B to B), traded sectors range shrinks to 1 ,2 which is demonstrated in Figure 32. An increase in the supply of home labor hN (or a decrease in the supply of foreign labor fN ) does not affect any of the R&D conditions in Equation 328. The first direct effect is the increase in relative supply of labor in home, requiring a lower home relative wage to clear labor markets. On the other hand, R&D becomes relatively difficult in home ash X increases, which lowers the innovation rate in home and decreasing demand for researchers. Lower wage give home firms a relative advantage ove r foreign beyond the marginal industry1 enabling home to extend the range of expor ts up to the marginal industry 1 at a lower equilibrium relative wage of as shown in Figure 32. Due to the increas e in its relative wage, foreign firms cant compete with exporting home firms in industries 1 1, and home firms take over these industries that are formerly nontraded. Furthermore, foreign firm s can no more afford to export goods in the industries2 2, hence these industries become nontraded, and foreign traded goods sector shrinks to 1 ,2. Contrary to this result, Di nopoulos and Segerstrom (2006) find that an increase in the population size of Sout h reduces the North relative wage because more PAGE 92 92 jobs move from North to South due to lower wa ges in South, since they allow for imitation in their model. A decline in the growth of R&D difficulty k raises the innovation rate in any industry given in Equation 329 and Equation 330, and in turn the sector i nnovation intensities in Equation 332 and Equation 333, while leaving R&D conditions in Equation 328 intact. Higher innovation intensities stimulate research activ ities and increases demand for foreign labor Equation 321 more than that of home Equation 320 if and only if 2 1 10) ( ) ( d a d ah Q f Qholds. The left and right hand side of this assumption is the total unit labor requirement in foreign and home, respectivel y. In other words, the country with relatively higher total unit labor requirement (or relatively less total productivity of labor) needs relatively more labor which increases the relative wage of th at country. In this case, home relative wage decreases due to a decrease in research difficu lty. Full employment condition is sustained in both countries at point B where home has a lower relative wage An increase in inventive step does not affect the R&D c onditions but yields higher returns to innovation, E 1 and therefore) ( ) ( i R i i la w I the demand for researchers in country i and sector NT T l rises. Quality leaders charge higher prices i Q ia w and in return manufacturing output levels decrease. If both countries ha ve the same measure of traded goods, then effects on labor ma rkets cancel out, leaving RS curve intact. The countries have the same nontraded goods sector; hence only the ra nge of the traded goods sector creates a difference in the labor markets. Specifically, re lative supply condition in Equation 327 implies that the country that has a larger traded goods sect or has lower relative wa ge due to an increase in If 2 11 holds, home traded goods sector is rela tively larger, and home relative wage PAGE 93 93 decreases to This case is shown in Figure 32 where home traded goods sector range expands to1 while range of foreign tr aded goods sector shrinks to21 A decrease in subjective discount rate (or an increase in population growthNg ) has no effect on R&D conditions. In the steadystate equilibrium, where ) ( t r and N i ig t V t V ) ( ) ( the expected profits are discounted le ss as the subjectiv e discount rate Ng in zeroprofit conditions in Equation 323 goes down. If both countries have the same total unit labor requirements, then the effects on labor markets ca ncel off. However, foreign innovation activities relatively increase more and demand for foreign la bor increases Equation 321 more than that of home Equation 320 if and only if 2 1 10) ( ) ( d a d ah Q f Qholds. In this case, the new equilibrium for home and fore ign is sustained at points A andB in Figure 32, respectively. A uniform increase in home unitlabor requirement h Qa(or a decrease inf Qa) has a direct effect on comparative advantage via) ( A. Homes comparative advantage declines as hRD curve in Figure 33 shifts down, and foreign firms gain comparative advantage while fRD curve shifts down. The range of traded goods sector shrinks in home and expands in foreign. Moreover, there is an indirect effect through labor markets. Ho me firms are active in fewer industries due to lower productivity and need less labor which pushes home relative wage down. As shown in Figure 33, this indirect effect moves steady stat e equilibrium from point A to A for home, where its tradedgoods sector shrinks to1 For foreign, the new equilibrium at point B implies a larger range of tradedgoods sector21 These comparative steadystate exercises are presented in Proposition 32 and Proposition 33. PAGE 94 94 Proposition 32. In the steadystate, home relative wage depends (i) positively on the range of home traded sector1 foreign population size fN, home unit labor requirement ) (h Qa; and R&D difficulty parameter k and subjective discount rate (if and only if 2 1 10) ( ) ( d a d ah Q f Q), (ii) negatively on foreign unit labor requirement ) (f Qa, home population size hN ; population growth Ng (if and only if 2 1 10) ( ) ( d a d ah Q f Q); and inventive step (if and only if home export sector is larger). Proof. See Algebraic Details. Proposition 33. In the steadystate, the marginal industries1 and2 that define the range of traded and nontraded goods s ector in each country depend (i) positively on foreign unit labor requirement ) (f Qa, home population size hN;and population growth Ng (if and only if 2 1 10) ( ) ( d a d ah Q f Q); and inventive step (if and only if home export sector is larger), (ii) negatively on home unit labor requirement ) (h Qa, foreign population size fN ; and R&D difficulty parameter k and subjective discount rate (if and only if 2 1 10) ( ) ( d a d ah Q f Q). Proof. See Algebraic Details. The intuition behind Proposition 32 and Propos ition 33 relies on comparative advantage and resource effects. Any parameter change that affects relative res ource condition alters the relative wage and in turn the competitiveness of firms. Hence, the tradability or location of production of a good can change. If a nontraded good becomes traded, the enlarged market size due to global markets yields higher returns fo r innovation and stimulates R&D, speeding up the innovation process. PAGE 95 95 Among the characteristics of the steadystate equilibrium, an increase in the labor supply of home results in a decrease in home relative wa ge, similar to the static Ricardian trade model of DFS. In contrast to resu lts of Grossman and Helpman ( 1991c), in our model home relative wage depends on other factors such as range of nontraded goods sector, in ternational trade cost, country size, population growth rate The reason is that they assu me homogeneous industries and that there is no nontraded goods s ector, an industry expands at the cost of other independent of whether it is an export or nontr aded sector. However, our model has not only different effects across countries, but also analyzes differences between sectors within a country. The properties of the equilibrium depicted in Figure 31 shares many common features with the work of Taylor (1993). Factor price equalization is not a ge neric property of the equilibrium and some comparative static results are similar such as an increase in home R&D costs reduces home relative wage and reduces the range of traded goods sector. Proposition 32 has theoretical support from the work of Dinopoulos and Segerstrom (2006), where they report that gl obalization reduces NorthSouth wa ge inequality. On the other hand, Sener (2004) finds that gl obalization increases the NorthS outh wage inequality in a scalefree model based on closed economy model of Dinopoulos and Syropoulos (2007) with rent protection activities. The main re sults receive some empirical s upport from the work of Jones (1997) and SalaiMartin (2002) who show a declining trend in global income inequality. Effects on Growth To simplify the analysis, the endogenous grow th literature assumes identical industries and assumes no nontraded goods and as a result fi nds identical growth ra tes for all countries. However, this paper shows that if there are nontraded goods and hetero geneity in technology across industries, countries do not necessarily have the same technological progress and countries do not share the same gr owth rate, which is a novel result. PAGE 96 96 The parameters have permanent effect on the long run Schumpeterian growth in Equation 335 through aggregate innovation in tensities in export, nontraded and import sectors given in Equation 331, Equation 332 and Equation 333 re spectively. Therefore, growth rate of a country increases by any parameter that stimul ates innovation in nontr aded goods sector and traded goods sectors of both countries. Moreover, since the current model has a nontraded goods sector due to international trade costs and hetero geneity in productivity of labor in R&D services and manufacturing across industrie s and countries, contrary to the endogenous growth models, countries do not necessarily have common growth rates. The consumers in both countries can buy goods that have the same quality level for the traded goods sectors 1, 0 and1 ,2 since they are available everywhere in the world. Howeve r, due to international trade costs, not all the goods are traded in the economy and any difference in quality of the goods across countries in the nontraded sector will lead to di fferent growth rate s across countries. To account for these changes and study how count ries are affected differently in their growth rates, we focus on the gr owth differential between countries f NT h NT f hI I g g ln, which is using Equation 331, Equation 332 and Equation 333, equivalent to d a d a g gf R h R f h2 1 2 11 1 (336) where 1 2 1 11) ( 1 1 1 1 ln d a g k kf Q Nis a positive common term. The integrand in Equation 336 is the difference in R&D costs between foreign and home nontraded goods industries adjusted for productivities of bot h countries. Hence, home country will grow faster than foreign if unit cost of R&D in ho me decreases compared to that of foreign. PAGE 97 97 To analyze the effects on growth gap across coun tries, we use the results on relative innovation intensity in nontraded goods sect or and determine the change in growth gap between home and foreign. For example, an increase in the invent ive step has a direct effect on growth. From Proposition 32 and 3, home relative wage decreas es and traded sector expands if and only if home has a wider range of traded goods sector. Trade balance in Equation 326 2 11 f hE Erises to 2 11 Hence, home firms receive relatively highe r benefits for innovati on and therefore home sectors innovate faster than foreign. Furthermor e, the expenditure in n ontraded goods sector h E increases relatively to that of in traded sectorf h E E E In home, innovation activities in nontraded goods sector increases mo re than traded sector. In this case, nontraded goods sectors in both of the countries will innovate more. Howe ver, if one country innovates relatively faster than the other, then a growth gap will occur. Focusing on the relative innovation rate in the non traded sectors between home and foreign, we see that compared to foreign, home innovates relatively more in the nontraded goods sector due to the decrease in its relative wage and as a result the growth gap expands. Similarly, any parameter that stimulates innovation in the nontraded goods sector in home more than forei gn widens the growth ga p. These effects are presented in Proposition 34. Proposition 34. (growth and growth gap). In the steadystate, (i) ig the growth rate of country i, is scalefree and home growth rate depends positively on inventive step (if and only if home export sector la rger), productivity of its researchers ) ( 1h Qa; and negatively on R&D difficulty parameter k (if and only if 2 1 10) ( ) ( d a d ah Q f Q); PAGE 98 98 (ii) the growth rate gap between countries f hg g depends positively on home productivity in nontraded goods sector, foreign population size fN, and inventive step (if and only if home export sector larger); negatively on R&D difficulty parameter k (if and only if 2 1 10) ( ) ( d a d ah Q f Q), foreign productivity in nontraded goods sector, and home population size hN. Proof. See Algebraic Details. Some of the results fo r growth rate is shared by Gr ossman and Helpman (1991c), where the growth rate gets faster, th e larger the inventive step is and the less productive are the researchers in that country. However, novel result s are predicted from the current model, none of which would be anticipated if there were no in ternational traded cost s and heterogeneity in technology across industries and between countries. Internationa l trade costs together with heterogeneous technology across industries and c ountries create a growth gap between countries, and the gap between home and foreign widens as foreign population, ho me productivity in nontraded sector, inventive step and R&D difficulty increases, or home population size and foreign productivity in nontraded sector decreases. Proposition 34 complements the growth gap analysis of Dinopoulos and Syr opoulos (1997). They use a threecountry framework with a nontraded good and three traded goods instead of a continuum, and thei r model generates differences in long run growth. Their main re sults such as countries with hi gher innovation inte nsities in the nontraded sector experience hi gher growth and growth gap de pends on R&D productivities and country size, are supported by this paper where a continuum of industries exists. Moreover, in our model, sectors are endogenously determined scale effects are removed and growthgap depends on other factors such as inventive step international trade costs and R&D difficulty. If there are no international trade costs0 then the model implies only one R&D condition since ) ( 1 ) ( A A RDh and) ( ) 1 )( ( A A RDf ; therefore th e nontraded PAGE 99 99 goods sector disappears 01 2 and the growth gap across countries vanishes0 f hg g as it is observed in the lite rature without nontraded goods. Effects of Globalization Globalization is interpreted as a decrease in international trad e cost which is governed by a decrease in the parameter0 Lower international trade costs lifts up trade barriers and let once nontraded goods available in global markets. The pattern of trade is governed by marginal industries1 and2 where in the marginal industry 1 a home firm is indifferent between whether to export a good or not, si nce the cost of exported good is equal to the cost of a foreign producers,) ( ) 1 )( (1 1 f Q h Qa a A decrease in international trade cost from to indicates an advantage for home exporter firms since ) ( ) 1 )( (1 1 f Q h Qa a Hence, home firms become exporters in the i ndustries to the right of 1 until 1 ) ( A is satisfied. Similarly, foreign firms export in industries to the left of 2 until 1 ) ( Aholds. In Figure 34, 1 ) ( A RDh shifts down and) 1 )( ( A RDfshifts up indicating an increase in the range of tradedgoods in the world. Globaliza tion can also have an indirect e ffect on the pattern of trade. If the measure of traded goods sectors is the same (i.e.2 11 ), then the cost effect on labor markets cancels out. If the measure of traded sect ors is not equal, say home exports more than foreign, then home firms require relatively less workers and home relative wage decreases from Equation 326. In Figure 34, starting from pointA, a decrease in shiftshRDdown, fRD up, and RS curve down to a new steadystate equilibrium at point A Lower relative wage gives home firms advantage over foreign, thus home traded goods sector expands from 1 to1 In foreign, the new equilibrium moves from point B toB expanding traded sector to21 The PAGE 100 100 range of nontraded goods sector shrinks to1 2 in both countries. Trade balance is sustained as 2 11 f hE Erises to 2 11 Thus, home firms receive relativ ely higher benefits for innovation and innovate faster than foreign. The expenditure in nontraded goods sector h E increases relatively to that of in traded sectorf h E E E At home, innovation acti vities in nontraded goods sector increases more than traded sect or. Home nontraded goods sector innovates more than foreign, widening the growth gapf hg g The intuition behind this result is, each non traded good is specific to its domestic markets. Country having a higher innovation rate has a higher quality for the same product that exists in the other country. Ho wever, since the good is nontraded, only domestic consumers can enjoy th e higher quality product, creating a difference in utility between consumers in different countr ies. The effects of globalization are summarized in Proposition 35. Proposition 35 (Globalization). In the steadystate, globalization (a decrease in the international trade cost0 ) (i) decreases home relative wage (ii) widens the range of traded goods sector s, and reduces the range of nontraded goods. (iii) implies faster innovation for traded industries and sector than nontraded, (iv) leads home nontraded and trad edgoods sectors to innovate rela tively faster than foreign, (v) yields faster gr owth rate for home, (vi) widens the growth gap across countries, f hg g if and only if the range of home traded sector is larger. Proof. See Algebraic Details. Globalization has a direct effect on trade pa ttern through comparative advantage. Some nontraded goods become tradable due to lower international trade costs, and cause the range of PAGE 101 101 traded goods sectors in both countries to expa nd while the range on nontraded goods sector shrinks. Innovation rate in a country increase s as more goods become traded since global markets are larger than domestic markets and th e returns to innovation are higher. In the case of identical traded goods sectors, the effect of globalization on the labor markets cancels out. However, if one country (for example home) has la rger range of export sect or than foreign, then the foreign labor markets become relatively tight er and therefore home relative wage decreases. International trade cost enriches the model, and the results given in Proposition 35 would vanish without it. To illustrate this, let us set0 which implies only one R&D condition since) ( A RD RDf h and therefore 2 1. The continuum of industries is split into home and foreign tr aded goods sector 0 and 1 ,, respectively with no nontraded goods sector. Consumers in the world share the comm on set of consumption goods and therefore the growth rates of count ries are identical, ln ln ) ( I I I g gf h f h which is a standard result in Schumpeterian growth models. Results presented in Proposition 35 are s upported by Dinopoulos and Segerstrom (2006). They report that globalization leads to a decline in the wagegap between North and South. In this paper, globalization has di fferent effects across traded an d nontraded goods sectors within and across countries. For example, if home has a larger range of exports than foreign, then a decrease in results in i NT i TI I, from Proposition 37. The decrease in gives cost advantage to exporting firms only and home, having the larger range of expor t sector, benefits more. Hence from Proposition 36, innovation intensities in the tr aded goods sector of both countries increases more than the nontraded h NT h TI Iand f NT f TI I. There are more exporting industries in home, resulting in an increase in innova tion intensity in home sectors more than foreign. Globalization PAGE 102 102 stimulates innovation in traded goods industries an d sector more than th e nontraded. Moreover, the country with a wider range of traded sector innovates faster than its trade partner. Eaton and Kortum (2002) also show that higher internationa l trade costs increases the relative wage of the country that has a larger expor t sector. The finding of declin ing global income inequality reported in Jones (1997) and SalaiMartin (2002) provide s some empirical evidence. If all the goods are assumed to be traded in th e absence of internationa l trade costs as in the relevant literature, crosscountry differences in innovation and growth rates cannot be accounted for. Nontraded goods sector complements the gr owing body of research that aims to determine whether globalization has diffe rent effects on countries a nd relates trade to growth Conclusion In this paper, a dynamic twocountry s calefree general equilibrium model with endogenously determined nontraded goods sector is constructed to study the pattern of trade, equilibrium relative wages, innovatio n, growth, and the effects of globalization. We add an extra dimension to the endogenous growth theory with an endogenously determined nontraded goods sector, and hope to contribute to the literature by devel oping an analytically tractable model that embodies quality ladders and R icardian trade frameworks. We define globalization as the extent of nontraded goods sector determined by international trade costs. This distinction is not observed in the relevant liter ature and the effects of a nontraded goods sector remained unexplored. The model does not exhibit unpleasant scaleeffects property, which is removed by employing permanent effects on growth (P EG) specification following Dinopoulos and Thompson (1998). Our analysis with nontraded goods enables us to look at the model through a magnifying glass and examine the differences at industry and sector levels within and across countries. For example, globalization (a decrease in the interna tional trade costs) decreases the relative wage of PAGE 103 103 the country that is exporting more, reduces the ra nge of nontraded sector, and widens the range of traded sectors in both countries (Propositi on 33). The decrease in in ternational trade costs gives cost advantage to only expor ting firms. Hence, innovation rate in the traded goods sector in both countries increases more than the nontraded sector. However, the country that has a larger range of export sector compared to its trade part ner benefits more as it s traded sector expands and hence has a higher innovation rate in traded and nontraded sectors th an its trade partner. Compared to a nontraded good industry, innovati on intensity is higher in a traded goods industry, since global market is larger than domestic markets. Hence, when a nontraded goods industry becomes tradable, higher returns to inno vation gives firms more incentive to engage in R&D activities and increases the innovation rate. Ther efore, policies that affect the tradability of a good change innovation intensities, and hence the long run growth rate. In Section IV, we examined the growth rates of countries: for inst ance we show that an increase in the inventive step will stimulate innovation and raise the growth rate in both countries. Moreover, the heterogeneity in technology among industries and countries together with the nontraded goods sector create unequal growth rate s between countries. The country with a lower unit cost of R&D in the nontraded sector grows fa ster. Globalization implies faster growth for both countries, but it increases the growth ra te of the country that is exporting le ss, thus decreasing the growth gap. We show that if there are no in ternational trade costs and all goods are tradable then innovation rates are identical in all sectors and countries The growth gap between countries in turn vanishes, which is a standard re sult in the endogenous gr owth literature. In this paper trade and growth are determined simultaneously by th e dynamics of the mode l and are positively correlated. PAGE 104 104 Nontraded goods elaborate the comparative stat ics results and yields novel results. For example, an increase in the inventive step in creases the relative wage of the country exporting more. On the contrary, Taylor (1993) reports that marginal industr y moves right without affecting the relative wage. An increase in the unit labor requirement has no effect on labor markets in DFS (1977), and it incr eases the relative wage in Tayl or (1993). However, in the proposed model, home traded goods sector shrink s whereas foreign export sector expands at lower home relative wage. Innovation rates decrease in home and increase in foreign, and further within country effects differ due to nontraded goods. Home loses its comparative advantage due to lower productivity, and innovation rate diminishes in the traded goods sector more than the nontraded goods sector. On the other hand, foreig n expands its traded sect or and the increase in innovation rate is higher in nontraded goods sect or. Another interesting result is that home relative wage depends positively on range of its export sector, consumers subjective discount rate and population growth, and negatively on fo reign export sector. If a nontraded good is liberalized, then the range of tr aded goods expands and the wage gap between countries reduces. The purpose of this paper is to illustrate a ri cher variety of questions that may open up in the endogenous growth theory literature if we consider endogenously determined nontraded goods. We also hope that our results may be gene ralized if R&D subsidies, labor migration, imitation, technology transfer and intellectual prop erty rights are incorpor ated into the existing model. Algebraic Details We focus on home and foreign full employment of labor cond ition at time t in Equation 324 and Equation 325. For the first two integran ds, substitute manufacturing output levels ) ( ) ( ) (t j p t E t j qi l i i l from Equation 33 for country h f i and sector NT T l and global PAGE 105 105 demand ) ( ) ( T f h Tp E E q from Equation 34. For the last two integrands, R&D output levels ) ( ) ( ) ( i R i R ia t L t R from Equation 37 and ) ( ) ( ) ( i i i lX R I gives) ( ) ( ) ( ) ( i i R i l i RX a I L substituting this expression into E quation 324 and Equation 325, we get d a X I d a X I d E d E E Nh R h h NT h R h h T h f h h) ( ) ( ) ( ) ( ) 1 (2 1 1 2 1 10 0 d a X I d a X I d E d E E Nf R f f NT f R f f T f h f f) ( ) ( ) ( ) ( ) 1 (2 1 2 2 1 21 1 In the next step we use the zeroprofit conditions ) ( ) ( ) ( ) ( ) ( ) ( ) (t X a w t V t V t I t r ti R i i i i l from Equation 323. Using N i ig t V t V ) ( ) ( profits f h i TE E t 1 ) ( and i i NTE t 1 ) ( yields ) ( 1 ) ( ) (N f h i i R i i Tg E E w a X I ) ( 1 ) ( ) (N i i i R i i NTg E w a X I Then, using Equation 327 with Equation 324 and Equation 325 and then evaluating the integrals yields 20 2 1 1 2) ( 1 ) 1 ( 1 d a X g E E E E E Nh Q h N h h f f h h 1 2 1 1 21) ( ) 1 ( 1 1 ) 1 ( ) 1 ( ) 1 ( 1 d a X g E E E E Nf Q f N h f f h f Rearranging the terms usingi ikN X and 1 21 h fE E from the trade balance in Equation 326 yields PAGE 106 106 1 ) ( 11 2 02f h h Q N hE E d a g k N and 1 ) 1 ( ) 1 ( ) ( 12 1 11h f f Q N fE E d a g k N Solving for h E and substituting the result into Equation 324 yields relative supply condition Equation 327 in the main text. Proof of Lemma 31. By construction) ( hRDand) ( hRDare decreasing in Hence, for any given home firms export the goods in industries where ) 1 ( ) ( A in Equation 310 holds, and the marginal industry 1 01 is uniquely determined by ) 1 ( ) (1 A. Similarly, foreign firms export goods in industries where ) ( ) 1 ( A holds and the marginal industry1 02 is uniquely determined by) 1 )( (2 A. Hence, at any industry 2 1, in the nontraded goods sector, no firms in any country can afford to export the good, since ) ( ) 1 ( 1 ) ( A A holds. Therefore, the two marginal industries1 and 2 defines home export sector1, 0 foreign export sector 1 ,2 and nontraded goods sector2 1, Proof of Proposition 31. By construction) ( hRDand) ( hRD in Figure 32 are decreasing in and the RS curve is upward sloping in 1 and2 Therefore, given the equilibrium level of home relative wage Lemma 31 implies that the unique intersection of RS with) ( hRDand) ( hRD define the unique steadystate equilibrium levels of marginal industries 1 and2 and hence the home export sector 1, 0 foreign export sector 1 ,2 and nontraded goods sector2 1, PAGE 107 107 Proofs of Propositions 32 and 33. The tw o equilibrium conditions Equation 321 and Equation 323 are revised in the following form for convenience as 1 ) ( ) (A RDhwhere 0 ) ( A, hence 0 ) ( hRDand 0 ) ( hRD. Similarly, 1 ) ( ) (2A RDf, hence 0 ) ( fRDand 0 ) ( fRD. ) , , ; (2 1 f h N f ha a g k N N RS where the sign of the firstorder partial derivatives0 0 0 0 0 0 0 0 0 0 011 10 9 8 7 6 5 4 3 2 1 RS RS RS RS RS RS RS RS RS RS RS are calculated using the RS curve and taking the derivatives after disregarding constants: 0 1 11 1 1 1 11 d a g k a g k sign RS signh Q N h Q N since 1 11 h Q h Qa d a and 1 11 1 1 2 2 2 1 1 21 11 1 1 1 1 d a g k d a g k a sign RS signh Q N h Q N h Q 0 1 1 1 11 2 2 11 d a g k a signh Q N h Q, since1 11 h Q h Qa d a. 0 1 12 h h h hN N N sign N RS sign, 0 f f fN N sign N RS sign. PAGE 108 108 2 1 2 1 2 1 1 21 0 1 1 1 1 1 1 1 1 1 RS sign sign sign RS sign 2 1 2 1 2 10 1 0 1 0 1) ( ) ( 0 ) ( ) ( ) ( 1 ) ( 1 d a d a k RS d a d a sign d a g k d a g k k sign k RS signh Q f Q h Q f Q h Q N f Q N 2 1 2 1 2 10 1 0 1 0 1) ( ) ( 0 ) ( ) ( ) ( 1 ) ( 1 d a d a RS d a d a sign d a g k d a g k sign RS signh Q f Q h Q f Q h Q N f Q N 2 1 2 1 2 10 1 0 1 0 1) ( ) ( 0 ) ( ) ( ) ( 1 ) ( 1 d a d a g RS d a d a sign d a g k d a g k g sign g RS signh Q f Q N h Q f Q h Q N f Q N N N 2 1 1 21 1 1 1 sign sign RS sign 2 11 0 RS 0 ) ( 1 1 ) (20 d a g k sign a RS signh Q N h Q, 0 ) ( 1 ) (11 d a g k sign a RS signf Q N f Q PAGE 109 109 Using these partial derivatives, comparativ e statics exercises of the steadystate equilibrium are easily examined by shifting the re levant curves in Figure 32. The equilibrium conditions in Equation 337, Equation 338 and E quation 338 do not have an explicit solution for the endogenous variables 1 and2 Using the implicit solution given by these three conditions, a comparative statics analysis is held to examine the behavior at steadystate using the first partial derivatives of RS curve. Effects on Innovation. The innovation levels for country f h i at the industry level ) (i TI and ) (i NTIin Equation 329 and Equation 330, respec tively play an important role in the dynamics of the model and yield rich and novel re sults. The change in relative innovation rate is examined at industry and sector levels. First we study the relative innovation in tensities at industr y level within the countryf h i, Using Equation 329 and Equation 330, we focus on the relative innovation intensity across nontraded and traded industries: 1 21 1 ) ( ) ( ) ( ) ( i T i R i NT i R N i NT N i Ta a g I g IHence, analyzing ) ( ) (h NT h TI I is equivalent to study the expression 1 21 1 ) ( ) ( h T h R h NT h Ra a. The intuition is that in a country if the productivity of researcher ) (i NT i Radecreases in a nontrade d industry, then R&D costs rise resulting in lower i nnovation intensity in the nontraded industry than traded. Other comparative statics results are obtained with th e help of Proposition 32 and Proposition 33. For example if population size increases in home hN then the effect of R&D difficulty h hkN X cancels out since we are comparing two i ndustries in the same country. However, Proposition 32 implies that due to supply incr ease relative wage decreases and this gives comparative advantage to home beyond its tr aded and nontraded goods sectors, hence PAGE 110 110 21and 1 ) ( ) (i NT i TI I This results in relatively lowe r innovation intensity in traded goods industry than nontraded goods industry. To compare innovation intensity in nontrad ed industries between countries, we use Equation 330 and focus on the relative innovation intensity 1 2() () ()()1h fff NTN RNT fhhh NTNRNTIg aN IgaN substituting from Equation 327, we get that for ) ( ) (f NT h NTI I it is sufficient to analyze the effects on 1 2() 1 ()1ff f RNT hhh RNTa N aN .Again, using Proposition 32 a nd proposition 33, comparative statics results are obtained. Fo r example, if inventive step increases, innovation intensities rise as returns to R&D increases. If 2 11 then home relative wagegiving comparative advantage to home and hence 21and 1 ) ( ) (f NT h NTI I Trade balance in Equation 326 is sustained as 2 11 f hE Erises to 2 11 Hence, home firms receive relatively higher benefits for innovation intensity and yields re latively higher innovation intensit y in home than foreign in a nontraded goods industry. For the comparis on of innovation intensities between traded industries across countries, we use 2 11 1 ) ( ) ( ) ( ) ( h T h R f T f R N f T N h Ta a g I g I, therefore for ) ( ) (f T h TI I it is sufficient to analyze the effects on 2 11 1 ) ( ) ( h T h R f T f Ra a. Using the parameter effects on 21 and1 effects on ) ( ) (f T h TI I can be analyzed. For instance, it follows that if R&D difficulty PAGE 111 111 kincreases, home innovates less if 2 1 10) ( ) ( d a d ah Q f Qholds, since 21and 1giving comparative advantage to foreign since trade balance 2 11 f hE Ein Equation 326 decreases to 2 11 ; hence ) ( ) (f T h TI I Proposition 35. In the steadystate within a country i, an industry in tradedgoods sector innovates faster than an industr y in the nontraded goods sector and the relative innovation intensity i NT i TI I across traded and nontraded industries depends positively on international trade cost subjective discount rate productivity of researchers in traded goods sector, foreign population size f N and R&D difficulty para meter k (if and only if 2 1 10) ( ) ( d a d ah Q f Q); and negatively on home population size hN, inventive step (if and only if 2 11 ), population growthNg and productivity of research ers in nontraded goods sect or; comparing industries in traded goods sectors across countries, the country with lower total R&D cost and R&D difficulty have higher innovation intensity; the relative innovation intensity across countries in traded goods industries f T h TI I depends positively on productivity of researchers in home, foreign population size f N, and inventive step (if and only if2 11 ); and on population growthNg(if and only if 2 1 10) ( ) ( d a d ah Q f Q) ; and negatively on home population size hN, productivity of researchers in foreign, and R&D difficulty k and s ubjective discount rate (if PAGE 112 112 and only if 2 1 10) ( ) ( d a d ah Q f Q); international trade cost (if and only if2 11 ), comparing industries in nontraded goods sectors across countries, the country with lower total R&D cost and R&D difficulty ha ve higher innovation intensity; the relative innovation intensity across countries in nontraded goods industries f NT h NTI I depends positively on productivity of researchers in home, foreign population size f N, population growthNg(if and only if 2 1 10) ( ) ( d a d ah Q f Q) and inventive step (if and only if2 11 ); and negatively on home population size hN, productivity of researchers in forei gn, and R&D difficulty k and subjective discount rate (if and only if 2 1 10) ( ) ( d a d ah Q f Q); international trade cost (if and only if2 11 Proof. See Equations 341, 342 and 343 toge ther with Propositions 32 and 33. Similarly, to analyze the s ectoral innovation in each c ountry, we focus on the innovation intensity ratios at the sectoral level in each country. To study the relative innovation intensities across home sectors, we sum up i ndustrial innovation inte nsity in numerator and denominator of expression in Equation 341 over the traded goods and nontraded goods sectors get the expression for the ratio of sectoral innovati on intensity. Hence, analyzing effects on h NT h TI I is equivalent to study 2 1 1) ( 1 ) ( 1 1 10 1 2 d a d ah R h R where the integrands in expression are the marginal product of a researcher in the corresponding indu stry and country, and hence the integrals are PAGE 113 113 total labor productivity. With the help of Propos itions 32 and 33, the comparative steadystate statics can be easily calculated, for instance for h NT h TI I, we get: 12,,,(),,,h ff T R h NTI Nka I, 12,,(),,h hh T NR h NTI Nga I, and h NT h TI I2 1, To compare innovation intensity in nontr aded sectors across countries, we sum up industrial innovation intensity in numerator and denominator of expression Equation 342 over range of nontraded goods sectors, 2 1, to get the expression for the ratio of sectoral innovation intensity. Therefore, for the effects on f NT h NTI I, we study 2 1 2 11 21 () 1 1 1 ()hh f RNT h ff RNTd a N N d a to get 12,,(),,,h ff NT RN f NTI Nag I, 12,,,(),,h hh NT R f NTI Nka I and f NT h NTI I2 1, Similarly, analyzing the effects on f T h TI I is equivalent to study 1 211 () 1 1 ()hh f RT o h ff RTd a N N d a 12,,(),,,h ff T RN f T I Nag I 12,,,(),,h hh T R f T I Nka I and f T h TI I2 1, These results for are summa rized in Proposition 36. PAGE 114 114 Proposition 36. (relative sectoral innovation) In the steadystat e, within a country total innovation intensity in traded goods sector is higher than non traded goods sector if total productivity of traded goods sector is higher; comparing traded goods sect or across countries, the country with lower R&D difficulty and total R& D cost have higher innov ation intensity. The relative innovation intensity across nontraded and traded sectors at home h NT h TI I depends positively on productivity of researchers in the traded goods sector in home, R&D difficulty k and subjective discount rate (if and only if 2 1 10) ( ) ( d a d ah Q f Q); foreign population size f N, population growthNg(if and only if 2 1 10) ( ) ( d a d ah Q f Q); and negatively on home population size hN, productivity of researchers in foreign international trade cost and inventive step (if and only if2 11 ) and on population growthNg(if and only if 2 1 10) ( ) ( d a d ah Q f Q). Comparing nontraded goods sector across countries, the country with lower R&D difficulty and total R&D cost ha ve higher innovation intensity; the relative innovation intensity in nontraded goods sector across countries f NT h NTI I (and relative innovation intensity in traded goods sector across countries f T h TI I) depends positively on inventive step (if and only if2 11 ); productivity of researchers in home, foreign population size f N; and on population growthNg(if and only if 2 1 10) ( ) ( d a d ah Q f Q); and negatively on home population size hN, productivity of researchers in forei gn, and R&D difficulty k and subjective PAGE 115 115 discount rate (if and only if 2 1 10) ( ) ( d a d ah Q f Q); international trade cost (if and only if2 11 ). Proof. See Equations 344, 345 and 346. Comparative statics results of innovation intensity in nontraded and traded goods industries) (i NTIand) (i TIand sectorsNTIandTI, respectively are presented in Proposition 37 under the condition that total unitlabor requirement in any sector is suffi ciently higher than any industrys. Proposition 37. (industry and sector innovation) In the steadystate, foreign innovation intensities in nontraded and traded industries f NTIand f TI(and nontraded and traded sectorf NTI andf TI) depend positively on productivity of re searchers at forei gn, home population size hN, and inventive step (if and only if2 11 ); and negatively on foreign population size f N, R&D difficulty k (if and only if 2 1 10) ( ) ( d a d ah Q f Q), international trade cost (if and only if2 11 ). Home innovation intensities in nontraded and traded industries h NTI and h TI (and in nontraded and traded sectorsh NTI andh TI) depend positively on productivity of researchers in home, foreign population size f N, and inventive step (if and only if2 11 ); and negatively on home population size hN, R&D difficulty k (if and only if 2 1 10) ( ) ( d a d ah Q f Q), international trade cost (if and only if2 11 ). Proof. 1 11) ( 1 1 1 ) ( d a g k sign I signf Q N f NT PAGE 116 116 1 1 1 1 1 1 11 11 1 ) ( 1 1 ) ( 1 ) ( 1 1 1 1 d a a d a g k signf Q f Q f Q N 0 1 1 ) ( 1 1 ) ( 1 ) ( 1 1 11 1 1 1 1 1 1 11 1 d a a d a g k signf Q f Q f Q Nif 0 1 1 ) ( 1 1 ) ( 1 ) (1 1 1 1 1 11 1 d a a d af Q f Q f Q. Now, since 1 11 this condition is satisfied if 1 1 1 1 11 11 1 ) ( ) ( 1 ) ( d a a d af Q f Q f Qor ) ( 1 1 ) (1 11 f Q f Qa d a which is satisfied if total unitlabor requirement in any se ctor is sufficiently highe r than any industrys: i i Q i i Qa d a 1 ) ( 1 1 ) ( where 1 1i. For instance if the function ) ( ) ( ) ( h R f Ra a A is linear of the form 1 ) ( A the condition for elas ticity is satisfied. Specifically, any function ) ( ) ( ) ( h R f Ra a A of the form 0 ) ( Aand0 ) ( A (a function that is convex to the origin) is sufficient. 1 ) ( 1 ) (1 11d a g k sign k I signf Q N f NT PAGE 117 117 0 ) ( ) ( 11 1 1 1 11 f Q f Q Na d a g k k sign if0 ) ( ) (1 1 11 f Q f Qa d aor 1 1 11) ( ) ( f Q f Qa d a. 1 ) ( 1 ) (1 11d a g k sign I signf Q N f NT 2 1 1 1 1 1 11 1 ) ( 1 1 ) (1 d a g k a g k signf Q N f Q N 0 0 ) ( ) ( h Q f NTa I sign, 0 ) ( ) ( f Q f NTa I sign. For tradedsector, we analyze 1 1 2 1 12 1) ( 1 1 1 1 ) ( 1 1 d a d a g k k If Q f Q N f Tin two separate terms. The derivative of 2 1 11 1 ) ( 11 d a g kf Q Nwith respect to a parameter is 2 2 1 1 2 1 2 1 11 ) ( 1 1 1 ) (1 d a g k a g kf Q N f Q Nwhich is positive if 01 or negative if01 The second term 1 ) ( 11 12d af Qs derivative have the sign equal to expression 1 1 1 2 22) ( 1 1 1 ) ( 1 d a af Q f Q, which is positive if 0 ,2 1 or PAGE 118 118 negative if0 ,2 1 Therefore, if 12,,0ff TNkI and 12,,,0hf TNI Similarly, f NTIhas the same results as industry level ) (f NTI. In home, ) (i NTIand ) (i TIhave same comparative statics results. 20 21() () 1 1h NQ h NT hhkgad I signsign NN 0 1 ) ( ) (2 2 0 22 h Q h Q Na d a g k sign. 20 21() () 1 1h NQ h NT ffkgad I signsign NN 0 1 ) ( ) (2 2 0 22 T T a d a T g k T signh Q h Q N. 0 ) ( h NTI signsince 0 ) ( ) ( f NT h NTI Iand 0 ) ( f NTI. 0 ) ( k I signh NTsince 0 ) ( ) ( k I If NT h NT and 0 ) ( k If NT. ) (h NTI sign0 from 0 ) ( ) ( f NT h NTI Iand A1. 0 ) ( ) ( h Q h NTa I sign, 0 ) ( ) ( f Q h NTa I sign. PAGE 119 119 For results at tradedsector level, using 1 1 ) ( 1 1 1 ) ( 1 ) (2 0 1 2 0 01 2 1d a d a g k d I Ih Q h Q N h T h T, we get that if ) ( f Raor h T h T h RI I a k) ( ), ( ,1 If hNthen 1 1 ) ( 11 2 02 d a g kh Q Nsince the sign of its derivative is equal to the sign of 0 ) ( 1 ) ( ) (1 0 2 21 d a g k a a g kh Q N h Q h Q N. 1 1 ) ( 12 01d ah Qsince the sign of its first partial derivative is equal to 0 1 ) ( 1 1 1 ) ( 12 0 2 1 11 d a ah Q h Q. Therefore, 1 1 ) ( 1 1 1 ) ( 1 12 0 1 2 01 2d a d a g k k Ih Q h Q N h T, and similarly if hNthen h TI. For results at nontraded goods sector level, using2 1) ( d I Ih NT h NTgives that h NTIhas the same comparative statics results as ) (h NTI. An increase in the home unit labor re quirement in the nontraded sector haresults in f NT f T h NT h TI I I I, ,from Proposition 36 and cause less home firms and more foreign firms to export. Within country effects differ due to the change in range of traded versus nontraded PAGE 120 120 goods sectors. Traded goods sector of home shrinks and foreign export sector expands, implying f h E E. Home relative expenditure be tween traded and nontraded goods increases h f h f h E E E E E1, and from Proposition 36, i nnovation intensity in the traded goods sector increases more than the nontraded h NT h TI I. In foreign, nontraded goods sector innovates more due to decreased rewards, and th e increase in the traded goods sector is more than the nontraded goods sector f NT f TI I, and in home the decrease in innovation intensity in the traded sector is more. Globalization affects sectors in both countries differently. If home has a larger range of exports than foreign, then results in i NT i TI I, from Proposition 36. Home and foreign traded goods sectors expand. gives cost advantage to expor ting firms only, and home having the larger range of export sector benefits more than foreign. Hence from Proposition 36, both countries innovation intensities in the traded goods sector incr eases more than the nontraded as h NT h TI Iand f NT f TI I. Sectoral Innovation intensity increa ses in home more than foreign. Focusing on Propositions 5, 6 and 7 again, we get that if home exports more, then kor f NT f T h NT h T f NT h NT i lI I I I I I I, ,. 1 expands and 21 shrinks, implying f hE E. Home relative expenditure between trad ed and nontraded goods decreases h f h f h E E E E E1, stimulating innovation in the nontraded goods sector more. In foreign, traded goods sector innovates more, due to increased relative rewards to innovation in the traded goods sector. We PAGE 121 121 can compare sectoral innovati on intensity across countries f T h TI Iand f NT h NTI Iusing Propositions 35, 36 and 37. Home, having a wider range of e xports is affected more by any change in ork, and hence if kor f NT h NT f T h T i lI I I I I, ,suggesting a higher innovation rate for home sectors than foreign. An increase in the population size affect s the traded sector more in both countries. Proof of Proposition 34. The growth rate of country i is given in Equation 335 as 22 1111i hf RRgdd aa where 1 2 1 11) ( 1 1 1 1 ln d a g k kf Q N. All the parameters have permanent effect on Schumpeterian growth rate and growth rate expres sion does not include any of the population sizeshNorfN, and hence is scale free. For comparative statics analysis of growth ra te, we use results pres ented in Proposition 37 and get: i NT i T i T i h NT h T f T f TI I I g I I I I ln ,, and i NT i T i T i h NT h T f T f TI I I g I I I I kln ,. For the analysis of growth gap between home and foreign, we focus on the difference of growth rates f NT h NT f hI I g g ln. Having the comparative steady state results on relative innovation intensity in nontraded sectors across countries, we sign the growth gap. f h f NT h NT f NT h NTg g I I I I, ,, ,,h hhf NT NTNThf f NTI NIIgg I ,,h fhf NT NTNThf f NTI NIIgg I f h f NT h NT f NT h NTg g I I I I k ,, and PAGE 122 122 f h f NT h NT f NT h NTg g I I I I ,, f h f NT h NT f NT h NT hg g I I I I a f h f NT h NT f NT h NT fg g I I I I a ,. Proof of Proposition 35. A decrease in international trade cost shifts RS curve down if and only if 2 11 since 2 11 sign RS sign 2 11 0 RS. 0 1 ) ( ) (2 A RDh and 0 ) ( ) ( A RDf, thereforehRDcurve shifts down and fRDcurve shifts up, widening the range of traded goods sectors, and reducing the range of nontraded goods if and only if 2 11 (see Figure 34). From Proposition 36, and expression in Equation 340, 1 21 1 ) ( ) ( ) ( ) ( i T i R i NT i R N i NT N i Ta a g I g Iand 1 1 11 2 implies) ( ) (i NT i TI I From Proposition 36, f NT h NTI I increases as decreases, and hence home tradedgoods sector to innovate relatively more than foreign if and only if 2 11 As f h f NT h NT f NT h NTg g I I I I since h T h T h NT hI I I g ln, and f T f T f NT fI I I g ln. Therefore hgincreases more thanfgif and only if2 11 A decrease in 2 1, andand f NT h NTI I, therefore globalization wide ns the growth gap across countries, f hg g if and only if2 11 PAGE 123 123 Figure 31. The uni que equilibrium. Figure 32. Dynamics of the model (an increase in N hg N, or a decrease in k, or fN). PAGE 124 124 Figure 33. Effect of an increa se in home (or a decrease in foreign) unit labor requirement. Figure 34. Effects of globalization. PAGE 125 125 LIST OF REFERENCES Aghion, P. and Howitt P., 1992. A model of grow th through creative destruction. 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He received his Master of Science degree in economics in July 1999. In August 1999, he began doctoral st udies in finance at Bogazici University. However, before completing his studi es there, he transferred to Gainesville, Florida, USA, in August 2001. Here he continued his doctoral studies in economics. He sp ecialized i n internatio nal trade, industrial organization, growth, and technologic al change. For his dissertation, he investigated the effects of globalization and also determined the optimum patent length to maximize the longrun growth rate. In August 2007, he will join the faculty of the Economics Department and Croft Institute of International Studies, at the Universi ty of Mississippi, in Oxfo rd, Mississippi. 