Economic growth and convergence with international differences in technology

Journal of Macroeconomics 29 (2007) 145–168

www.elsevier.com/locate/jmacro

Economic growth and convergencewith international differences in technology

Youngwan Goo a, Hyun Park b,*

a Department of Economics, Korea National Defense University, Seoul, Republic of Koreab Department of Economics, Kyung Hee University, #1 Hoegi-Dong, Dongdaemoon-Ku,

Seoul 130-701, Republic of Korea

Received 4 June 2002; accepted 26 April 2005Available online 13 December 2006

Abstract

In the two-country world economy, this paper considers that factor markets are not perfectlycompetitive and technology changes endogenously. We analyze how differences in technology affectdynamic comparative advantages and thereby economic growth. The factor price equalization andthe relative degree of input substitutions determine dynamics of comparative advantages and therebyresource competition in the factor markets. Both with and without the factor price equalization forinput markets, critical values of a CES-index for the long-run R&D and consumption growth arederived. We show that competitiveness in the final good market stimulates economics growth, butexcessive resource competition in the input and R&D markets can have a detrimental effect on eco-nomic growth. In particular, when the latter dominates the former, the trade liberalization does notnecessarily stimulate economic growth. We also show the different convergence property for theR&D and consumption sectors: convergence of R&D and divergence of consumption.� 2006 Elsevier Inc. All rights reserved.

JEL classification: F21; L1; O41

Keywords: Imperfect competition; Dynamic comparative advantages; Endogenous growth

0164-0704/$ - see front matter � 2006 Elsevier Inc. All rights reserved.

doi:10.1016/j.jmacro.2005.04.007

* Corresponding author. Tel.: +82 2 961 9375; fax: +82 2 966 7426.E-mail address: [email protected] (H. Park).

mailto:[email protected]

146 Y. Goo, H. Park / Journal of Macroeconomics 29 (2007) 145–168

1. Introduction

Dynamic general equilibrium models with imperfect competition and endogenous tech-nological changes can enrich our understanding the relation between dynamics of inter-national trade and economic performance in the world economy. Imputed monopolyrents in monopolistically competitive endogenous growth models can stimulate researchand development (R&D), in turn determines dynamic comparative advantages, andthereby has an effect on economic growth. In this paper we explore economic perfor-mances in an imperfectly competitive world economy. In particular, this paper introducesa simple general equilibrium model to capture the effects of an imperfect competition andthe differences in technologies.1 Our main focus is to reexamine the relationship betweentrade openness and economic growth in an endogenous growth model with technologicaldifferences. We investigate long-run growth effects of the factor market competition andthe convergence property of both R&D and consumption in a two-country worldeconomy.

The trade literature offers mixed results on growth and competition in internationaltrade. Many works predict the positive relation between trade openness and economicgrowth based on a variety of economic factors: expanding market sizes provides new tradeopportunities (Grossman and Helpman, 1991, Ch. 6; Rivera-Batiz and Romer, 1991);felicitating transmission of technical relationships allows learning-by-trading (Goh andOlivier, 2002; Grossman and Helpman, 1990; Young, 1991), the existing arrangementallows the possibility of knowledge spillovers (Grossman and Helpman, 1991, Ch. 7),and imitation and diffusion (Segerstrom et al., 1990). Some empirical evidences includingDinopoulos and Thompson (2000) and Nickell (1996) also find a beneficial effect ongrowth and welfare.

However, a variety of criticisms and controversies still remain in the literature, a discus-sion of which can be found in, for example, Little et al. (1970), Edwards (1998), and Fran-kel et al. (1996). Notably, Edwards (1992) and Rodrik (1997) suggested that tradedampens the incentive for research and whereby long-run growth. It is also possible thattrade creates no sufficient common pool of knowledge (Grossman and Helpman, 1991, Ch.6); it leads to comparative advantage in the sector with the lesser long-run growth pros-pects (Matsuyama, 1991; Grossman and Helpman, 1990); and it induces excess resourcecompetition between manufacturing and R&D sectors (Feenstra, 1996).

We build on growth models with endogenous technological changes (e.g., Romer, 1990;Lucas, 1988; Grossman and Helpman, 1991; Aghion and Howitt, 1992; Baldwin and For-slid, 2000), and trade models with both monopolistic competition (e.g., Lancaster, 1975;Spence, 1976; Dixit and Stiglitz, 1977; Krugman, 1979; Ethier, 1982) and differences intechnology (e.g., Markusen and Svensson, 1985; Venables, 1990). It is a dynamic generalequilibrium model with endogenous technological changes in a two-country world econ-omy, in which individual countries interact with each other in an imperfectly competitiveenvironment. This model introduces the technological difference in the final good produc-tion function between the two countries. The difference of elasticity of intermediate inputs

1 Differences in technology have been considered a determinant of the direction of trade in the literature. Inparticular, Markusen and Svensson (1985, pp. 175) pointed out that the importance determinants of trade are‘‘differences in production technology, increasing returns to scale, imperfect competition, and domesticdistortion’’.

Y. Goo, H. Park / Journal of Macroeconomics 29 (2007) 145–168 147

is a way to capture differences in technology between two countries.2 In particular, substi-tutability among intermediate inputs plays an important role of technological differencesin imperfectly competitive factor markets. More specifically, each final good productionhas its own elasticity of substitution, that is, a CES-index of input factors is not necessarilyequal in both countries (see, e.g., Spilimbergo and Vamvakidis, 2003).3 Thus, it impliesthat inputs can be substituted at a different rate; the market for inputs itself be imperfectlycompetitive; and thus a monopolist can earn monopoly rents. In fact, as in endogenousgrowth models with monopolistic competition, this imputed monopoly rent induces theincentive for a new blueprint.4

Adding to the difference in final good product technologies, the difference in the initialstate-of-the-art technology (or, knowledge) takes on rich possibilities for a pattern of inter-national trade. To maintain the difference in the initial levels of technologies and to avoidthe immediate integration of all economies, no diffusion of knowledge is postulated in theinternational market (also see Aghion and Howitt, 1998, Ch. 7; Feenstra, 1996). Moreimportantly, an innovator in a technologically advanced economy acquires tacit knowl-edge that cannot be duplicated by a rival in a technologically lagging economy withoutengaging its own R&D to catch up in the international R&D markets (Aghion et al.,2001). It enforces that every economy develops a new blueprint for itself. Consequently,a country lagging behind technologically must, in a sense, reinvent the wheel (for detailimplications, see, Aghion and Howitt, 1998, Section 7.4).5 It also implies that, if a firmcontrols the blueprint without any competition, it will remain a monopolist over the worldmarkets. On the other hand, when firms share the same blueprint, they face competitorsand act accordingly. We then focus on the Cournout-quantity competition between thosecompetitors.

The main contribution in this paper is to relate the technological differences with thegrowth and convergence property for R&D and consumption. First, we show that the rel-ative competitiveness (in terms of CES-indices) in output technologies and the factor priceequalization are the two main elements for economic performance in the two-country

2 There are many ways to introduce technological differences. For example, Markusen (1983) studied a non-factor proportions model of technological differences; Markusen and Svensson (1985) analyzed Hicks-neutraltechnological differences; and Findley and Grubert (1959) examined Ricardian technological differences. Feenstra(1996) considered the different final good productions in a world economy, in which each country produces itsown final (consumption) good and imports other’s final goods.

3 Also, empirical studies have shown a different elasticity of differential products in manufacturing sectors, e.g.,Blonigen and Wilson (1999) for an estimate of the difference in elasticities between US domestic and foreigngoods and Berry et al. (1995) for an estimate of demand parameters in the oligopolistically differentiated USautomobile market. Similarly, our model is based on the difference in available manufacturing inputs in amonopolistic competitive model with international trade.

4 Also see Romer (1990), Grossman and Helpman (1990), Rivera-Batiz and Romer (1991) and many others. Tofocus on our analysis, this model abstracts from differences in the nature of knowledge spillovers (Boldrin andSheinkman, 1988); diffusion and imitation of R&D (Young, 1991; Stokey, 1991); and a capital market condition(Rodrik, 1997).

5 See more discussion of this postulate in Feenstra (1996) and Grossman and Helpman (1991, pp. 179).Furthermore, we shall not consider patent licensing in the world markets by an R&D firm. In contrast to thismodel, Krugman (1979) assumed that countries always invent new goods that have not yet been invented in theother country. In his setting, it is obvious that a lagging country never invests for a new good since its productivityis always lower than an advanced country in our context. Unlike our result in this paper, no convergence occurs inR&D.


world economy. The former determines comparative advantage in the final and interme-diate good markets, whereas the latter affects total profits of intermediate input marketsand thereby the price of a new blueprint. We show that competitiveness in the manufac-turing sectors stimulates economic growth, but excessive resource competition in the inputand R&D markets can have a detrimental effect on economic growth. This result differsfrom previous literature that link dynamic comparative advantages directly to initial fac-tor endowments – either the size of labor and human capital or physical capital (e.g.,Dinopoulos and Thompson, 2000; Grossman and Helpman, 1990, 1991). This paper alsodiffers from the analyses of long-run growth in integrated economies (e.g., Rivera-Batizand Romer, 1991).

Second, we also show that these economies with a different initial technological levelcan achieve convergence of R&D. In contrast to Feenstra (1996) and Ventura (1997), thisconvergence property occurs in the competitive R&D markets; does not rely on any ofthose direct technology transfers or knowledge diffusion.6 Intuitively, this convergenceproperty for R&D is obtained by equalizing the prices of new blueprints and the monop-oly rents in Cournout–Nash competitive factor markets. Thus, the incentive for inventinga new blueprint is equalized in two economies and it leads to the convergence of R&D inthe world economy. This implies that a country lagging behind technologically is likely tospeed up through its international trade, while a technologically advanced country will notnecessarily stimulate its growth in R&D with international trade.

Third, we extend to examine the convergence property for consumption growth ininternational trade. More specifically, under the CES-index difference in the manufactur-ing sectors, a wage equalization mechanism does not ensure consumption convergence inthe imperfectly competitive world economy.7 This divergence property for consumption isobtained by the following steps. First, we establish the difference in the growth ratesbetween consumption and R&D in individual countries. That is, the convergence ofR&D does not lead to the convergence of consumption. Second, the same wage rate itselfdoes not equalize the factor market share and thus maintains the difference in their totalprofits in input markets. In fact, we show that the equalization in wage rates intensifies theresource competition in intermediate inputs. Third, together with specialization for thefinal good production, the difference of the sum of total profits eventually contributesthe difference in consumption growth between individual economies. This implies thattrade openness is not necessarily to improve income distribution in the world economy.

Finally, we provide a critical degree of CES-indices, which mainly determines whetheropenness is either beneficial or detrimental to R&D and consumption growth. Openness isbeneficial to any economy when its relative competitiveness in the manufacturing allows itsmarkets to expand in the world economy. As mentioned before, it is because this relativecompetitiveness determines the comparative advantage of the final good production andthe size of the potential total profits for the input production under the condition for fac-tor price equalization. Hence, although manufacturing does not play a direct role for an

6 In addition, the current literature ascribes these convergence properties to economic integration, leaning-by-trading, imitation and diffusion, patent licensing, and other cross-border transaction (e.g., Grossman andHelpman, 1991; Barro and Sala-i-Martin, 2004).

7 See Barro and Sala-i-Martin (2004, Ch. 3) and Slaughter (1997) for the further discussion. In particular,Slaughter pointed out other factors – capital accumulation, knowledge spillovers, or trade-mediated technologytransfer – through which convergence takes place.


engine for growth, the ability for the final good production affects welfare improvement aswell as economic growth. This is consistent with the result in Aghion et al. (2001).

The layout of this paper is as follows. Section 2 introduces the benchmark autarkyeconomy and illustrates the relationship between a CES-index and long-run growth. Sec-tion 3 extends the autarky economy to a world economy, describes the nature of tradecompetition, and characterizes an equilibrium path with trade. The patterns of dynamiccomparative advantages and the balanced equilibrium growth both on R&D and con-sumption are examined in Section 4. This section also examines the convergence propertyof R&D and the divergence property of consumption. In addition, the effects of tradeopenness on R&D and consumption growth are reported. The concluding remarks arein Section 5.

2. Economic growth in an autarky economy

Before examining a world economy, we setup a competitive autarky economy withendogenous technological changes. The present model is a straightforward adaptationof the endogenous growth models developed by Romer (1990) and Grossman and Help-man (1990). Yet the main difference is of a specification of product technology in terms ofa CES-index, which will play an important role for international differences in technology.We will also establish different growth rates between R&D and consumption in the longrun.

2.1. Description of the model

There is a consumable final good, inelastically supplied labor, and a continuum of inter-mediate inputs and blueprints. The final and R&D sectors are perfectly competitive andthe intermediate input sectors are monopolistically competitive. The final good is pro-duced only by intermediate inputs and all intermediate inputs and new blueprints onlyby labor. Each intermediate input producer is differentiated from the others in the sensethat it can solely access its own blueprint and thus can maintain its monopoly power overtime. In essence, the production technology of the final good exhibits imperfect substitu-tion among intermediate inputs. A new intermediate input producer emerges wheneverthere is a potential monopoly rent for the new product. There is no physical and humancapital, and there is no population growth. Time is continuous.

The immortal representative consumer maximizes its lifetime utility over time t,t 2 [0,1),

U ¼Z 1

0

uðCtÞe�qtdt; ð1Þ

which is the discounted sum of the felicity,8 uðCtÞ � C1�rt =ð1� rÞ, r > 0, at the rate of time

preference q > 0 by allocating its income to either consumption Ct or investment _at. In-come comes from wages wtLt where wt and Lt denote the wage rate and labor supply attime t, respectively, and the returns on assets at occur at the market rate of returns rt.For simplicity, we assume that Lt ¼ 1 at each time t.

8 This felicity function is monotonically increasing and concave, and satisfies the Inada conditions.


The consumer’s budget constraints are, given the initial stock of assets, a0, P Ct Ct þ _at 6

wt þ rtat, where P Ct is the price of consumption good at time t.9 Therefore, the necessaryconditions for the consumer’s optimization problem are:

_Ct

Ct¼ 1

rrt � q�

_P Ct

P Ct

� �; ð2Þ

P Ct Ct þ _at 6 wt þ rtat: ð3Þ

In addition, the transversality condition is limt!0e�qtu0ðCtÞat ¼ 0, where u 0(Ct) is the mar-ginal utility of Ct.

The final good Y is produced by intermediate inputs Xi, i 2 [0, At], where At denotes thetotal number of blueprints at time t, which is considered as the measure of a technological

level for the economy.10 To be specific, Y ¼R A

0X l

i dih i1

l, where l 2 (0,1). (From now on,

unless it cause confusion, we will omit time subscripts.) As mentioned above, the param-eter value l determines the elasticity of inputs, the degree of substitution among inputs,thus the intensity of competition in the intermediate inputs markets.

Profit of the final good producer is defined as P Y Y �R A

0P X i X idi, given the price PY of

the final good and the prices P X i of inputs. Then, the inverse demand for the ith input is:

P X i ¼ P Y X�½1�l�i

Z A

0

X lj dj

� �1�ll

: ð4Þ

Given the demand for the ith input, the monopoly producer for the ith input seeks its max-imum profit, PX i ¼ P X i X i � wLX i . The ith production function is specified as X i ¼ bLX i .Then the necessary condition for optimal Xi becomes:

P X i 1� 1

1� l

� ��1" #

¼ wb: ð5Þ

The monopoly price is inversely related with the elasticity of the demand, n � [1 � l]�1.That is, the degree of competitiveness reflects the elasticity of substitution in the CES-in-dex for intermediate inputs.

Suppose all firms in the intermediate input sector have the same production function,the final good production function and (5) lead to symmetric optimal inputs and thus,for each i

X i ¼ A�1lY : ð6Þ

Eq. (6) implies that the final good production function, Y ¼ A1lX i, is essentially an ‘‘AK’’-

function. Such an AK-model exhibits the property that an equilibrium path immediately

9 Contrary to Grossman and Helpman (1991) and Young (1991), the consumer’s income is not normalized.And, for our purpose, the price of consumption is explicitly introduced and will determine comparativeadvantages.10 There are also models of endogenous technological change by introducing vertical product differentiation

(e.g., Flam and Helpman, 1987; Segerstrom et al., 1990; Aghion and Howitt, 1992). Implications with bothhorizontal and vertical product differentiation are quite similar in autarky, but can have very differentimplications in trade models, e.g., Grossman and Helpman (1991, Ch. 12).


converges to a stationary equilibrium (in detail, Grossman and Helpman, 1991, pp. 61).This property justifies long-run analysis.

Moreover, the zero profit condition in the perfectly competitive market implies that thefinal good price becomes:

P Y ¼ A�1�ll

wlb: ð7Þ

Now we explicitly compute the profit for each intermediate input producer, and we exam-ine how the elasticity n, determines the size of each firm’s profit. By using (5) and (6), thefirm’s profit becomes:

PX i ¼1� llb

wA�1lY : ð8Þ

Hence, the profit for each intermediate input producer is positive.11 The positive profit,then, provides market incentive for an intermediate input producer to demand a new blue-print or technological changes.

Now, let us endogenize A. The R&D technology is defined as:

_At ¼ uAtLAt ; ð9Þ

where u > 0 is a constant coefficient. The R&D firm competitively maximizes its profit,PA ¼ P A

_A� wLA, at the price of a blueprint PA. The necessary condition for profit max-imization is

P AuA ¼ w: ð10Þ

Finally, the price of the blueprint is the sum of the expected future profits of production ofan intermediate input discounted by market interest rates, i.e., P At ¼

R1t e�RsPX iðsÞds,

where Rs ¼R s

t rhdh. Hence, the asset the household owns is equal to the total value ofthe firms in the economy: at ¼ AtP At . Moreover, the non-arbitrage condition for R&Dinvestment at equilibrium can be derived by differentiating PA respect to time:

PX tðtÞ þ _P At ¼ rtP At : ð11Þ

Therefore, the set of all necessary conditions, the market clearing conditions, and thetransversality condition can complete an equilibrium in the autarky economy: For everyt, there exist P Ct ; P Y t , and P At such that (i) each agent solves its optimal problem; (ii)Ct = Yt, (iii) 1 ¼ LX t þ LAt , where LX t �

R At

0LX i;t di12; (iv) at ¼ P At At, with given the initial

number of blueprints A0 and the initial assets, a0 ¼ P A0A0.

2.2. Balanced growth equilibrium

We now focus on the long-run equilibrium, in which ðLx; LAÞ remain a constant; andC and A grow at a constant rate. Hence, PA and r do not change. Similarly to Barroand Sala-i-Martin (2004) and Grossman and Helpman (1991), Appendix I derives the

11 The Inada conditions of the felicity and final good function ensure non-zero final good production.12 Hereafter, the upper bar over variables denotes an aggregate amount of each variable.


balanced growth rate of consumption and blueprints. From (AI.4) and (AI.5) inAppendix I,

cA ¼1

1þ ru� ql

1� l

� �; ð12aÞ

cC ¼1� l

lð1þ rÞ u� ql1� l

� �; ð12bÞ

where c denotes a balanced growth rate with a subscript indicating the variable. It is easyto see that the economy enjoys positive persistent growth in consumption and R&D if andonly if u > lq

1�l, together with the transversality condition, q > 1�r2

1�ll u.13 Hence,

Lemma 1. The elasticity of the demand in the production technology and the growth rates of

consumption and R&D are negatively related. Furthermore, the growth rate of final gooddeviates from the growth rate of R&D. That is, when n P 2, cA 6 cC; while when

n < 2,cA > cC.

Proof. Recall the rate of growth cA, cC in (12a) and (12b). The first half of the Lemma isimmediate since ql

1�l increases as n � [1 � l]�1 increases. Furthermore, n P 2 (resp. n < 2)implies that 1�l

lð1þrÞ P1

1þr (resp. 1�llð1þrÞ >

11þrÞ. Therefore, from (12a) and (12b) (and also see

(AI.3)), the second half holds. h

It is worthwhile to note that Lemma 1 reports the critical value of elasticity, n = 2, todetermine the growth differences between the consumption and the R&D sector, i.e.,cC ¼ 1�l

l cA in (12a) and (12b) or in (AI.3). We will see in the following sections that thedifference in technology in a term of a CES-index continuously plays an important rolefor determining growth rates of R&D and a final and consumption good in the worldeconomy.

3. Two open economies with imperfectly competitive markets

In the previous section we established that a CES-index causes dispersion between con-sumption and R&D growth in a closed economy. Now we explain how each country’s per-formance relates to this difference in technology in a two-country world economy.14 Ourstrategy is to show that a CES-index affects the prices of final and intermediate goods, andthus the wage rates determine the dynamic comparative advantages. Then, we show thatthese comparative advantages, thereby, shape the pattern of international trade; and henceinfluence growth rates of new blueprints and consumption.

13 This condition is implied by the condition that lifetime utility has a finite value, i.e., q > (1 � r)cC.14 Technologies in two countries do not necessarily exhibit the same degree of input substitutability in a

monopolistic competition model. Spilimbergo and Vamvakidis (2003) have shown that the elasticity ofsubstitution for products from OECD countries is not the same as for products from non-OECD countries. Theyalso found that OECD exports are more price sensitive than non-OECD exports. In our context, this suggeststhat the degree of intermediate input substitutability in a technologically advanced economy (with moreblueprints) is higher than in a technologically lagging economy (with less blueprints), since the former can employmore alterable domestic inputs than the latter.


3.1. Trade environment in the world economy

The world economy consists of two economies, one in the East and one in the West. Weassume that the consumer’s preference is identical in the two economies. We also assumethat production functions for the intermediate sectors and the R&D sector are identical inboth economies. Furthermore, the endowments of immobile labor in both countries are aconstant, say 1 unit. However, these economies differ in two aspects. First, the West istechnologically more advanced than the East, i.e., AE

0 6 AW0 .15 In our setting the technolog-

ically advanced West has every blueprint, i, i 2 [0,AE], which is also available in the East;and additionally available blueprints, j, j 2 [AE,AW]. Hence, it implies that, for eachi 2 [0, AE], there are two ith intermediate input producers; and, for each j 2 [AE,AW], thereis a monopolist in the world market. Also, a new blueprint is demanded by a firm only inthe same country; thereby intermediate input production is country specific and cannot beintegrated in the world market.

Second, but most importantly, each the final good production function is different interms of its own degree of input–substitution, i.e., the CES-index, ln, n = E, W. The elas-ticity of substitution among intermediate inputs is reflected in the degree of intermediateinput differentiation: the greater the difference of intermediate inputs, the lower is the elas-ticity of substitution between intermediate inputs in technologies. The literature also foundthat the degree of input differentiation does not depend on physical characteristics amonginputs alone (see details in Blonigen and Wilson, 1999). More empirical studies justify oursetting by showing equally mixed results for either home-biased (Swenson, 1997) or forforeign-biased elasticity (Trefler, 1995). This paper will consider every case in which thetechnological advanced or the technologically lagging country can have a high degree ofsubstitutability for intermediate inputs in the world market.

We also suppose that the two economies can trade both the final and intermediateinputs, but cannot trade labor and blueprints. The inability to trade blueprints requiresmanufacturing facilities to locate in the same country as its R&D lab. As mentioned inthe Introduction, this condition forces every economy to develop its own new ideas or tacitknowledge. This assumption is also consistent with the argument that R&D knowledgedoes not close boards without any costs. Then, we define the country-specific R&D pro-duction functions as _An ¼ uAnLn

A, for n = E, W. That is, each country’s productivity ofR&D technology is uAn, n = E, W, which represents country-specific and historically-accumulated tacit knowledge. Moreover, given the initial conditions, AE

0 6 AW0 , the

R&D production functions represent that the (lagging) East exhibits lower productivitythan does the (advanced) West. We will show that our R&D convergence result (Propo-sition 2) requires a general equilibrium framework with monopolistically competitiveinternational input markets, where the value of knowledge is endogenously determinedby a country-specific wage and interest rate.

Finally, if a firm owns solely its blueprint, it will remain a monopolist, whereas if manyfirms share the same blueprint, they compete for the world market. We then focus on theCournout-quantity competition between those competitors.16 Alternatively, it can be

15 The superscript ‘E’ and ‘W’ denote economies in the East and in the West, respectively.16 For tractability of analysis, we abstract away from any other strategic behaviors among the competitors. With

somewhat different settings and purposes, Venables (1990) considered different types of strategic games ininternational trade. Later in the paper, we will discuss different types of competition.


assumed that knowledge transfer occurs without any cost, and thus _An ¼ u½AE þ AW�LnA,

n = E, W, (e.g., Rivera-Batiz and Romer (1991) for an integrated world economy). Thereality of technology transfers in the world economy lies somewhere between the two.Later in this paper, we will discuss implications of alternative assumptions for knowledgetransfers, and will basically argue that their convergence properties of consumption as wellas R&D are rather trivial.

3.2. Dynamics of endogenous comparative advantages

In this subsection we endogenize the pattern of comparative advantages. The utilitymaximization problem for consumers and the profit maximization problem for final goodproducers are the same as in the autarky economy, except that they can access the finalgood and inputs supplied by both a domestic and a foreign country. Let X n

k be the kthinput used in Country n, where k 2 [0,A] and n = E, W. That is, the production functionis

Y n ¼Z AE

i¼0

½X ni �

ln

diþZ AW

j¼AE

½X nj �

ln

dj

" # 1ln

:17 ð13Þ

Similarly, the input cost for the final good production isZ A

k¼0

P nX k

X nkdk �

Z AE

i¼0

P nX i

X ni diþ

Z AW

j¼AE

P nX j

X nj dj: ð14Þ

Notice that we write this problem by separating employed intermediate inputs into twosets: (i) the ith input, i 2 [0,AE], that both countries supply, and (ii) the jth input,j 2 [AE,AW] that the (technologically advanced) West supplies. The final good producerin Country n solves the problem: max Pn

Y ¼ P nY Y n �

R Ak¼0 P n

X kX n

kdk. The necessary conditionfor optimal demand for X n

k , k 2 [0, AE] [ [AE,AW], is

P nX k¼ P n

Y

Y n

X nk

� �1�ln

: ð15Þ

Note that elasticity nn � [1 � ln]�1 affects the Country n’s input demand.Now let us examine optimality conditions in the intermediate input markets. Since the

West’s stocks of knowledge are larger than those in the East, some of monopolists in theWest remain as a monopolist in the world economy since they can produce their interme-diate inputs over and above the East’s capacity. Suppose that X n

k;m is the quantity of inputk supplied to Country n by the firm located in Country m. The necessary condition for theoptimality of X n

j;W is

P nX j

1� 1

1� ln

� ��1" #

¼ wW

b; ð16Þ

17 It is clear that these functions have a different marginal productivity for the same input. But all inputs for eachproduction function have the identical marginal productivity. Hence, the technological differences in this modelare qualitatively similar to the ones in a non-factor proportions model of technological differences (e.g.,Markusen, 1983).


given the price P nX j

of Xj in Country n. It is similar to (5) in the autarky economy. Also,since the jth firm is the sole supplier of Xj in the world market, its total supply shouldbe equal to the sum of demand for each economy, i.e., X n

j;W ¼ X nj , n = E, W. Hence, from

(15) and (16), we can derive the optimal allocations for intermediate inputs in both coun-ties: For j 2 [AE,AW],

X nj ¼ Y n P n

Y

P nX j

" # 11�ln

¼ Y n wW

blnP nY

� �� 11�ln

; ð17Þ

where n = E, W. It is clear that the optimal allocations depend only on the wage rate in theWest, because labor is not mobile and these intermediate inputs are produced in the West.

On the other hand, for i 2 [0,AE], the ith firm in the East and the other ith firm in theWest access the same ith blueprint, and so both are capable of producing the same ithinput. They then supply the ith inputs competitively in the world markets. In Cournout-quantity competition,18 the necessary condition for ith firm’s optimal X n

i;E in the East is

P nX i

1�½1� ln�X n

i;E

X ni;E þ X n

i;W

" #¼ wE

b; ð18aÞ

where X ni;W is given for n = E, W. Similarly, the necessary condition for ith firm’s optimum

X ni;W in the West is

P nX i

1�½1� ln�X n

i;W

X ni;E þ X n

i;W

" #¼ wW

b; ð18bÞ

where X ni;E is given for n = E, W. Then, (18a) and (18b) imply that

X Ei;W ¼

wE � lEwW

wW � lEwEX E

i;E; X Wi;E ¼

wW � lWwE

wE � lWwWX W

i;W: ð19Þ

Again, combining (18a) and (18b) with (19) yields

P nX i¼ wE þ wW

b½1þ ln� : ð20Þ

Thus, unlike the case of the monopolists in the world markets (see (16)), the price of theintermediate input in an oligopoly market depends not only on its own, but also its coun-terpart’s wage.19 As long as the two country’s elasticities are not the same, they will notcharge the same price for the same intermediate input.

Notice that these ex ante prices are different because the demand for an intermediateinput is not the same in the two countries and the supply of each intermediate inputrequires its own knowledge or blueprints. This price difference determines which producer,with the same blueprint, has a comparative advantage for its production. It is clear that

18 Alternative competition can be employed among the firms that hold identical blueprints. For instance, theycan engage in Bertrand-price competition. Since no firm in this type of competition can make a positive profit, atechnologically lagging country has no incentive to develop a new blueprint, thereby has no economic growth.19 It is worthwhile to note that monopolists in the West after opening to world markets can take advantage of

monopolistic power to curtail production of oligopolists. It then involves a game among international firms overtime. It will involve complex analysis.


any firm supplying at the lowest price becomes a monopolist; the lowest price becomes theequilibrium price, ex post in each country. Therefore, in addition to the condition on com-plete specialization in the final goods market, an intermediate input equilibrium price isunique in the world market. Moreover, the price of the intermediate input supplied bythe monopolist is unique in the West, i.e., (16). Therefore, the equilibrium price for eachintermediate input is uniquely determined in the world market.

Once again, from (15) and (20), we can find equilibrium quantities of an intermediateinput in the duopolistic market in the world economy:

X ni ¼ Y n wE þ wW

b½1þ ln�P nY

� �� 11�ln

: ð21Þ

From the optimality condition for differentiated goods, we can derive the equilibriumprices for the final good P n

Y , n = E, W. The zero-profit condition for the final good andthe symmetric demand for intermediate inputs, together with (17) and (21), imply that

P nY ¼

1

bAE wE þ wW

1þ ln

� �� ln

1�ln

þ AW � AE� � wW

ln

� �� ln

1�ln

24

35�1�ln

ln

: ð22Þ

It is important to note that the price of the final good for each economy depends on thewage rates of both countries and exclusively on its own CES-index. It is because that eachcountry uses available worldwide inputs in its own final good production. Therefore, theprice of the final good has the following property:

Lemma 2. When the intermediate input markets in the East (resp. the West) is more

competitive than ones in the West (resp. the East), i.e., nE > nW (resp. nE < nW), the final

good price in the East (the West) is lower than one in the West (resp. East), i.e., P EY < P W

Y(resp. P E

Y > P WY ) provided that AE > 1 and AW � AE > 1.20

Proof. It is immediate from the price of the final good in (22). h

Hence, the economy with relatively more competitive manufacturing markets is likelyto have the comparative advantage on the final good. It is because that the more compet-itive market has the lower cost of producing the final good. In fact, the perfectly compet-itive final good market induces that the country with more competitive intermediate inputsmarket will have a completely specialized final good production.21 Therefore, the finalgood and intermediate input allocations are:

20 These conditions are rather technical but innocuous. Also, the second one is consistent with our results below,i.e., we will show that a convergence property is for growth rates, not growth levels, of R&D, and thus the leveldifference of R&D can remain in the long-run.21 When both countries have the same final good production function, i.e., lE = lW, we have P E

Y ¼ P WY . In this

case, the final good markets are not completely specialized and thus the intermediate goods markets are also nolonger specialized. Then, we can show that the labor market clearing condition will not be satisfied in anequilibrium when both countries have the same wage rate. Moreover, when a wage rate in the East is lower thanin the West (see below), we cannot pin down equilibrium prices of any intermediate goods and an equilibriumallocation unless we introduce an additional assumption. We are indebted to the referee for this point.


Proposition 1. Under the conditions in Lemma 2, when the East (resp, the West) is more

competitive than the West (resp. the East) in the manufacturing markets, the West (resp. the

East) produces no final good, i.e., YW = 0, (resp. YE = 0), and whereby the West (resp. the

East) demands no intermediate inputs, i.e., X Wi;E ¼ 0; X W

i;W ¼ 0, and X Wj;W ¼ 0 (resp.

X Ei;E ¼ 0; X E

i;W ¼ 0, and X Ej;W ¼ 0Þ, " i 2 [0,AE], " j 2 [AE,AW].

Proof. From Lemma 2, the price of the final good is lower when manufacturing market ismore elastic. Hence, the perfect competition in the final good market implies theproposition. h

3.3. Monopolistic competition in input markets

Now we are ready to determine the market share of duopolists for the world input mar-ket. The symmetry of (18a, 18b) suggests that an intermediate producer in a low wage rateeconomy has a cost advantage to producers in an economy with higher wages. Conse-quently, this advantage enables the producer to supply positive quantities in both markets.On the other hand, if two economies have the same wage rate, the same type of duopolistscan compete at the same market. Therefore, we will show that the wage rates determine themarket share of intermediate inputs; thereby profits for intermediate inputs; and incentivesfor a new blueprint.

Formally, by (18a), (18b) and (19), the optimal quantities of the ith intermediate firmfor i 2 [0, AE] in the East:

X ni;E ¼

1

1� ln

wW � lnwE

wE þ wWX n

i : ð23aÞ

Similarly, the optimal quantities of the ith intermediate firm for i 2 [0,AE] in the West, wehave:

X ni;W ¼

1

1� ln

wE � lnwW

wE þ wWX n

i : ð23bÞ

Therefore, when wE = wW, the optimality conditions in (23a,b) together with Proposition1, satisfy the intermediate input market clearing conditions that X n

i ¼ X ni;E þ X n

i;W. It is easyto check that the labor market clearing conditions are also satisfied in both economies,therefore, a factor price equalization (FPE, hereafter) equilibrium exists.22

On the other hand, when wE < wW with nE > nW, Proposition 1 and (23a,b) imply thatwE = lEwW. Similarly, when wE < wW with nE < nW, wE = lWwW. Hence, both cases sat-isfy the labor market clearing condition and thus an equilibrium is analytical. However,when wE > wW, either the case of nE > nW or nE < nW violates the labor market clearingcondition. Hence, there exists a non-FPE equilibrium only when the wage rate of the tech-nologically advanced country is higher than that of the technologically lagging country.23

22 Since it is clear that the prices of intermediate input factors are not necessarily equalized in this model, we cansomewhat abuse the term of ‘factor price equalization’, which means that the wage rates are equalized in theworld markets.23 It is also easy to show that there is no equilibrium allocation when wE > wW. Since the West has a cost-

advantage in producing intermediate inputs, X Ei;W ¼ X E

i and X Ei;E ¼ 0. So, LE

X ¼ 0. Furthermore, PEX i¼ 0, and

thereby P EA ¼ 0 and there is no incentive to invest on a new blueprint and hence LE

A ¼ 0. Therefore, theequilibrium condition of the labor market is violated.


Recall Proposition 1 that YW = 0 when the East is more competitive than the West. Wealso know that Inada conditions ensure that the final good production in the world econ-omy should be strictly positive over time, and thus YE > 0. We then have two possibleequilibria: Case E.I for a FPE equilibrium (i.e., wE = wW); and Case E.II for an equilib-rium without FPE (i.e., wE < wW).

On the other hand, when the West is more competitive than the East, by using the sameargument above, we have YW > 0. Again, we have two possible equilibria: Case W.I for anequilibrium with FPE (i.e., wE = wW); and Case W.II without FPE (i.e., wE < wW). Unfor-tunately, we are unable to explicitly pin down an equilibrium wage rate in this modelunless we introduce further restrictions in the model. Following Helpman (1993),24 wethen decide to consider all four possible equilibrium wage rates.

In sum, we consider the following wage structure: Firstly, there is no equilibrium whenthe wage rate in the East is higher than in the West (see footnote 23). Secondly, there existthe critical wage rates wE and wW determining the comparative advantage for ith interme-diate input production, i 2 [0,AE], in the world market. In fact, this critical wage rate in the

West wW is in wE; wE

ln

h i, n = E, W. Thirdly, for invoking an analytic solution in equilibrium,

we further specify (1) Cases E.I and W.I. for the same wage rates wE = wW in the two coun-tries; (2) Cases E.II and W.II that the wage rates in the West are higher than in the East,wE < wW, more specifically, wE = lnwW, n = E, W. This specification of wage rates capturesall possible dynamic comparative advantages for equilibrium allocations in the intermedi-ate input markets under technological differences in the final good production.

Then, by using the same method as in (8), (23a,b) yield profits for intermediate produc-ers in the world economy. Appendix II reports equilibrium profits for the Case E.I. andE.II. Also, by using the same arguments as in (9) and (10), and (15) for the autarkyeconomy, we determine the price of new blueprints as the sum of the lifetime profitsand thus the growth rates of consumption and R&D in each economy. Appendix IIIreports these results for Case E.I and those for the other cases can be found by usingthe same method.

4. Balance growth path in the world economy

In the previous section we established the pattern of dynamic comparative advantagesfor the final and intermediate goods. We also establish the growth rate of R&D and con-sumption for all four cases. In this section we analyze the impact of international trade in acomparison of these growth rates with and without FPE. We also discuss implications ofdifferences in growth rates before and after international trade. Furthermore, we examineconvergence properties for R&D and consumption in the world economy. We, however,limit ourselves to focus on the long-run equilibrium.

4.1. R&D growth and convergence

Although the improvement of welfare eventually becomes a core objective of free trade,technological advance through international trade can have its own merit of long-run

24 See also Helpman (1993, pp. 1260) for further details. This is a rather common feature in dynamicmonopolistic competition models.


performance in a world economy. Let us analyze R&D growth in all four cases, and thencompare results as a group, starting with FPE Case E.I and W.I.

Lemma 3 (FPE R&D). The rate of R&D growth in the East and the West is declining after

the international trade when the factor prices are equalized in E.I and W.I.

Proof. Recall that the autarky R&D growth rate: cnA ¼ 1

1þr u� lnq1�ln

h i, n = E, W in (AI.4),

Appendix I. We also have that, for Case E.1,

cnA ¼

1� lE

1� lE þ rð1þ lEÞ u� qð1þ lEÞ1� lE

� �; ð24aÞ

n = E, W, as in (AIII.4), Appendix III. Similarly, we can derive, n = E, W,

cnA ¼

1� lW

1� lW þ rð1þ lWÞ u� qð1þ lWÞ1� lW

� �; ð24bÞ

for Case W.1. Clearly, comparing those growth rates, (24a) and (24b) with (12a) in autarkyyields the result. h

This result is quite intuitive. The similarity of wage rates eliminates the possibility offorming comparative advantages that free trade would have created among sectors.Instead, manufacturing sectors increase competition, which drives down monopolisticprofits that would discourage new blueprints in international trade. This possibility ofslowdown of worldwide growth was also recognized in Grossman and Helpman (1990).However, in contrast to our result, their argument is based on the comparative advantagewith respect to distribution of initial resource endowments.

We next move to the non-FPE cases in which the two economies have different wagerates in a long-run equilibrium with international trade. In non-FPE Cases E.II andW.II,25 we then find

Lemma 4 (Non-FPE R&D). Suppose nE > 2 with nE > nW; or nW > 2 with nE < nW, then

the long-run non-FPE equilibrium rate of R&D growth for each economy slows down after

international trade. On the other hand, suppose nE < 2 with nE > nW, then the long-run non-FPE equilibrium rate of R&D growth in the East is improved after openness, whereas,

suppose nW < 2 with nE < nW, then so is the long-run non-FPE equilibrium rate of R&D

growth in the West.

Proof. By using the same method in Appendix III, it is easy to drive the growth rates atstationary non-FPE equilibrium. They are:

cnA ¼

1� lE

1� lEð1� rÞ u� lEq1� lE

� �; ð24cÞ

25 Notice that Cases E.I and E.II are not symmetric to Cases W.I and W.II, respectively. That is, in Cases E.Iand E.II, the East will be behind the West in the long run if the East remains in an autarky economy. However,while in Cases W.I and W.II, the East will catch-up and eventually overtake the West if there is no openness toworld markets. This implies that each country has a different expectation for trade openness.


n = E, W, for Case E.II. Similarly,

cnA ¼

1� lW

1� lWð1� rÞ u� lWq1� lW

� �; ð24dÞ

n = E, W, for Case W.II. By Proposition 1, nE > nW determines that the East perfectly spe-cializes the final good production. Furthermore, nE, nW > 2 implies that 1

1þr >1�lE

1�lEð1�rÞ and1

1þr >1�lW

1�lWð1�rÞ, respectively. Comparing with the autarky growth rates in (12a), thesegrowth rates imply the first part of Lemma.

Clearly, by the same arguments, the second part of Lemma holds when nE, nW < 2. h

Two aspects of this Lemma are interesting. First, as in autarky (see Lemma 1), the crit-ical value 2 of nE, nW plays a role of determining the growth rate differences between thefinal good and R&D. It is because labor markets are segregated, the final good productionis completely specialized, and intermediate input markets are essentially segmented. Sec-ond, the international trade can dampen R&D growth by competing labor allocationexcessively in Nash competition. This shows the same spirit as excess resource competitionargument for international trade as in Feenstra (1996) and Rodrik (1997).

So far, we have compared rates of growth in R&D between the autarky economy andthe world economy. The next proposition establishes the convergence property for R&Dgrowth rates in the world economy.

Proposition 2. In the world economy both with and without factor price equalization, the

East and the West improve the levels of technology at the same rate in the long run.

Proof. It is immediate from the R&D growth rates, i.e., (24a)–(24d), reported in Proofs ofLemmas 3 and 4. That is, in each case, the R&D growth rates are identical for the twocountries. h

In the general equilibrium model, given the profits of the duopolists and the monopo-lists (referring to Appendix II), the equilibrium price of a new blueprint for each country isequalized by the change in interest rates, which reflect the future expectation of earningsfrom a new blueprint to each economy. This R&D price equalization then generates thesame incentive for developing a new blueprint and therefore its convergence. Thus, theR&D convergence property in this Proposition is rather intuitive.

We further discuss special cases and compare them with our R&D convergence result.If the lagging East is allowed to invent a new (non-existing) blueprint which can be sold toa potential producer at the integrated intermediate input market (Rivera-Batiz andRomer, 1991), the advanced and highly productive West will have comparative advantageand be specialized completely to invent all new blueprints, ceteris paribus, and thus theEast is able to produce only its existing intermediate inputs. Hence, there is no R&D con-vergence in the two economies. This is not the case in Proposition 2 in our model with sep-arated intermediate input markets.

In our framework except that the lagging and advanced economies expect to invent atotally new blueprint in separated intermediate input markets, both successful inventorswill expect to compete for its intermediate input producer in each economy. That is, anew intermediate input market is to be oligopolistically ex ante competitive. Hence, thisalternative setting implies qualitatively the same ex ante convergence result as in a model


with integrated R&D because there is no ex ante monopolist, i.e. the ex ante value forR&D activities in the lagging East will be the same as the one for a totally new blueprintin the West.

Our convergence result for R&D growth rates is also in contrast with a divergenceresult in a monopolistic competitive model of no R&D spillover and integrated interme-diate input markets, as in, e.g., Grossman and Helpman (1991, Ch. 9), where a newlyinvented blueprint can be sold to (potential) intermediate input producers at both the Eastand the West, thereby both countries will invent a new idea and their different rates ofR&D growth will depend on different initial labor endowments.

Finally, it is worthwhile to note that this convergence property provides a sharp con-trast to those in the literature that they need to introduce a technological transfer or dif-fusion among countries (e.g., Feenstra, 1996; Ventura, 1997). Grossman and Helpman(1991, pp. 240) also argued that free trade could eliminate investment redundancies onnew knowledge such that the world market for R&D is more efficient. Obviously, in thisscenario, all countries benefit and economies grow more quickly than prior to open trade.Also, the convergence of R&D is trivial since every country can access the same blueprints.On the other hand, Helpman (1993) examined that the lagging country can only imitatesthe technologies of a technologically advanced country, while the advanced country devel-ops new ideas alone. Similarly, an autarky version of innovation and imitation can befound in Segerstrom (1991). Their model is a special case of ours because reinvention inour model is qualitatively equivalent to the imitation in their model. Moreover, the coststructure of our innovation (or their imitation) is general in our model. That is, the cost(wage in the East) of reinvention can either be smaller than or equal to the cost (wagein the West) of innovation.

4.2. Consumption growth and convergence

We now observe how differences in technology and factor price equalization affect long-run growth rates of consumption and final good. Let us begin with summarizing the prop-erty of FPE equilibria in Case E.I and Case W.I:

Lemma 5 (FPE consumption). When nE > nW with nE < 21�r , the long-run FPE consump-

tion in the East grows slowly after international trade. On the other hand, when nE < nW with

nW < 21�r, so does the long-run FPE consumption in the West. Moreover, when nE > nW with

21�r > nE > 2, the long-run FPE consumption in the West grows slowly after international

trade. On the other hand, when nE < nW with 21�r > nW > 2, so does the long-run consumption

in the East.

Proof. Recall the consumption growth rate in the autarky economy for East and West:

For n ¼ E;W; cnC ¼

1�ln

lnð1þrÞ u� lnq1�ln

h iin (12b). Furthermore, in (AIII.5) and (AIII.6) of

Appendix III,

cEC ¼

1� ln

1� ln þ rð1þ lnÞ u� qð1þ lnÞ1� ln

� �; ð25aÞ

cWC ¼

1

Y n � CEcE

C

ln

1� lnY n � CE

� �; ð25bÞ


where n = E for Case E.I and n = W for Case W.I. Since nn < 21�r with Proposition 1 im-

plies that 1�ln

lnð1þrÞ >1�ln

1�lnþrð1þlnÞ, cnC in the autarky economy is larger than cn

C in the FPE equi-librium, n = E, W.

Moreover, it is easy to show that, when 21�r > nn > 2, n = E, W, the above growth rates

for Cases E.I and W.I imply the other half of the Lemma. h

Notice that the critical values of nE and nW continuously plays a role of determinescomparative advantages for the final good sectors and FPE mechanism determines the sizeof profits for the intermediate inputs and thus incentive for a new blueprint. While thisLemma suggests that opening trade can cause slow growth in consumption for each econ-omy, the conditions outlined in the lemma are merely sufficient for slow growth of both

economies. Of course, it has not been ruled out that a country without comparative advan-tage at the final good could grow at a faster rate.

Consider now a non-FPE equilibrium in Cases E.II and W.II, i.e., the wage rate of theWest is higher than that of the East.

Lemma 6 (Non-FPE consumption). When nE > nW with nE > 2, consumption in the East

grows faster at the long-run non-FPE equilibrium with international trade than the long-run

equilibrium with autarky. Moreover, when nE < nW with nW > 2, so does consumption in the

West. On the other hand, when nE > nW with nE < 2, or nE < nW with nW < 2, consumption inboth economies grows less rapidly at the long-run non-FPE equilibrium with international

trade than a long-run equilibrium with autarky.

Proof. Again recall, from (12b), cnC ¼ 1�ln

lnð1þrÞ u� lnq1�ln

h ifor the autarky growth rate for

Country n = E, W. Now, from (AIII.5) in Appendix III, we have

cEC ¼

1� ln

1� lnð1� rÞ u� lnq1� ln

� �; ð25cÞ

where n = E for Case E.II, and n = W for Case W.II. Since nE > nW with nE > 2 is equiv-alent to 1�ln

lnð1þrÞ <1�ln

1�lnð1�rÞ, cEC in autarky is larger than cE

C both in Cases E.II and W.II.Furthermore, we can also compute the consumption growth rate for the West

cWC ¼

1

Y n � CEcE

C

ln

1� lnY n � CE

� �; ð25dÞ

where n = E for Case E.II and n = W for Case W.II. Using the same argument as above,nE < nW and nW > 2 imply that cW

C in autarky is larger than cWC both in Cases E.II and

W.II.Conversely, in both cases for nE > nW with nE < 2, and nE < nW with nW < 2, we can use

the same arguments for the proof of the rest of the Lemma. h

This lemma shows that properties of the non-FPE equilibrium are different from thosewith the FPE equilibrium. Unlike Lemma 5, the sufficient conditions outlined in thisLemma suggest that either economy can enjoy the long-run consumption growth afteropenness as long as it maintains its competitiveness in the final good world markets.Therefore, similar to Aghion et al. (2001), the combination of competitiveness in the finalgood with non-FPE in the factor markets stimulates long-run growth. This result suggests


that the economic performance for each economy depends of the tradeoff between compet-itiveness in the final good markets and one in the intermediate factor markets in monop-olistic competitive endogenous models.

So far, we have examined how the rate of consumption growth changes after openingup international trade. Given the above information on the growth rates of consumptionin Lemmas 5 and 6, the rates of consumption growth between two open economies can becompared. The next proposition summarizes such comparison:

Proposition 3. When nE > nW with nE < 2 (resp. nE > 2) the consumption in the East grows

more (resp. less) rapidly than the consumption in the West both at the long-run FPE and the

long-run non-FPE equilibrium. On the other hand, when nE < nW with nW < 2 (resp. nW > 2)

the consumption in the East grows more (resp. less) rapidly than the consumption in the West

both at the long-run FPE or the long-run non-FPE equilibrium.

Proof. It follows immediately from all consumption growth rates in (25a)–(25d) reportedin the proofs of Lemmas 5 and 6. That is, for every case, the consumption growth rates areidentical for the two countries. h

This confirms that the economy that has the comparative advantage for the final gooddetermines the growth rates in the world markets. Also, this suggests that as long as acountry can maintain monopolists in the world market, this country gets more of the fruitsof international trade than its counterpart does. Thus, the technologically leading econ-omy desires expansion to the international market. This lack of consumption convergencesharpens the conflicts in trade openness between a technologically advanced economy anda technologically lagging economy.

5. Concluding remarks

In this paper we have studied the relationship between imperfect competition and eco-nomic growth, with particular emphasis on differences in technology in the two-countryworld economy. The nature of international competition in manufacturing sectors – notdirectly in R&D sectors – affects long-run economic growth through generating dynamiccomparative advantages and incentives for investing new blueprints. We showed thatprofit-seeking competition plays a crucial role for technological change, so that interna-tional trade in the monopolistically competitive world economy may not always improvelong-run economic growth when resource competition is too excessive. It leads to thedivergence of consumption growth in the long run.

One of the interesting extensions of the present model is to introduce transaction costsin international trade at either final or intermediate input markets. We may observe non-trade equilibrium with a sufficiently high transaction cost. An effect of transaction cost ondynamics of a pattern of trade and its implications of welfare and growth rates with inter-national trade can then be explained. Hence, this model is also capable studying an opti-mal tariff when each economy exhibits its own technological level and intensity ofcompetition.

This paper also leads to further avenues for future research on the relationship betweena market structure and economic performance. For example, we consider technologicaltransfer, learning-by-doing, diffusion and imitation. Likewise, international cooperation


through patent license and trade secret protection may influence the results here. Omittedfrom this analysis were alternative views on the nature of competition in manufacturingmarkets and R&D sectors.

Acknowledgements

We wish to thank Winston Chang, Issac Ehrlich, Sajal Lahiri, Apostolis Philippopoulusand the participants at seminars in University of Essex, Kyoto University and State Uni-versity of New York at Buffalo for helpful comments and suggestions. We also are in-debted to the anonymous referee for constructive comments and suggestions. Of course,errors and omissions are our sole responsibility.

Appendix I. A balanced growth rate for the consumption and R&D in autarky

Recall that LX , LA is constant; and C, Y, A grow at a constant rate at a balanced growthpath. In addition, the value of the blueprint does not change.

First, we will establish that cr = 0 at the balanced growth path. Eqs. (11) and (8), and_P A ¼ 0 imply

P A ¼PX i

r¼ 1� l

blrwA�

1lY : ðAI:1Þ

Then, substituting (AI.1) into (10) and using (6), we get

X i ¼bl

u½1� l�rA: ðAI:2Þ

Hence, cX = cr � cA. On the other hand, since LX i ¼ LX j by (5), the production function:X i ¼ bLX i implies that LX ¼ A X i

b . Thus, cA = �cX. Therefore, cr = 0.Second, we will find the stationary interest rate r. By combining (AI.2) and (6), we have

Y ¼ blru½1�l�A

1�ll . Thus, cY ¼ cr þ 1�l

l cA. Since cr = 0, we have the following:

cY ¼1� l

lcA: ðAI:3Þ

Without loss of generality, we can set PY = PC = 1. The labor market clearing condition isLX þ LA ¼ A X i

b þ u _AA ¼

blru½1�l� þ ucA ¼ 1. The first equality is from the final good production

function and the R&D function, and the second equality is from (AI.2). Now, the Euler’s

Eq. (2) for a consumer, cC ¼ 1r ðr � qÞ, and (AI.3) yield r ¼ r

rþ11�ll uþ q

rl

1�l

h i.

Finally, together with (AI.3) and the above r, (2) implies that

cA ¼1

1þ ru� ql

1� l

� �; ðAI:4Þ

cC ¼ cY ¼1� l

lð1þ rÞ u� ql1� l

� �: ðAI:5Þ

Appendix II. Economic profits with international trade

We will compute profits for a FPE Equilibrium in Case E.1 and a non-FPE equilibriumin Case E.II.


In Case E.I ðwE ¼ wW; nE > nWÞ X Ei;E;X

Ei;W; i 2 ½0;AE�, and X E

j;W > 0; j 2 ½AE;AW�, byProposition 1. Thus, we already know that X E

i;E ¼ X Ei;W ¼ 1

2X E

i . By applying (23a,b) tothe profit equations with w � wE = wW, it is easy to have

PEX i¼ PW

X i¼ 1� lE

4

2wb½1þ lE�

� �� lE

1�lE

Y E; PWX j¼ ½1� lE� w

blE

� �� lE

1�lE

Y E: ðAII:1Þ

Similarly, we use (23a,b) for Case E.II (wE < wW; nE > nW). Recall that, in this case, wE =lEwW in Section 3. Thus X E

i;Eð¼ X Ei Þ; X E

j;W > 0; i 2 ½0;AE�; j 2 ½AE;AW�. Thus, we have

PEX i¼ ½1� lE� wE

blE

� �� lE

1�lE

Y E; PWX j¼ ½1� lE� wE

b½lE�2

" #� lE

1�lE

Y E: ðAII:2Þ

Profits for Cases W.I and W.II can be found by using the same method.

Appendix III. A balanced growth rate for consumption and R&D in international trade

We will examine Case E.I as a showcase. We then report the other results for the othercases in Lemmas 3–6.

Recall that the necessary conditions for the R&D sector in the East (refer to (10) and(11)) are

P EAuAE ¼ wE; ðAIII:1Þ

PEX tðtÞ ¼ rE

t P EAt: ðAIII:2Þ

From (AII.1) and (AIII.2), P EA ¼

ð1�lEÞY E

4rE2w

bð1þlEÞ

h i� lE

1�lE

. On the other hand, (23a,b) and

(AIII.2) also yield that P EA ¼

ð1�lEÞw2bð1þlEÞrE X E

i . Hence, (AIII.1) yields

X Ei ¼

2bð1þ lEÞrE

uð1� lEÞAE: ðAIII:3Þ

We will use (AIII.3) to establish the growth relation between A, w, r, Y. First, without theloss of generality, we assume that P E

Y ¼ 1. Also, (23a,b) imply that Y E ¼ 2bð1þlEÞrE

uð1�lEÞAE

2wbð1þlEÞ

h i 11�lE

. Since cEA ¼ cE

w from (AIII.1), this expression implies that cEY ¼ cE

r þ lE

1�lE cEA .

Second, using (AIII.3) again with LEX þ LE

A ¼ 1, these two growth relations imply cEr ¼ 0.

Again, (AIII.3) shows that cEA ¼ u� 1þlE

1�lE rE, and cEX ¼ �uþ 1þlE

1�lE rE. Finally, Combing

(AIII.3) and cEY implies cE

Y ¼lE

1�lE u� lEð1þlEÞð1�lEÞ2 rE.

Now we will go for the stationary interest rate. Notice that, from the trade balance oftrade condition – the value of the total amounts of the intermediate input imported fromthe West is equal to the total value of the export of the final goods to the West, a station-ary equilibrium implies

CE ¼ Y E � CW ¼ AEP EX i

X Ei

2

� �; CW ¼ AEP E

X i

X Ei

2

� �þ ½AW � AE�P E

X jX E

j;W:


Moreover, the final good production function plus (20) and (AII.1) simplifies the level ofconsumption in the East:

CE ¼ 1� lE

ð1� lEÞ þ rð1þ lEÞ2wu

uþ qr

h i:

Hence, cEC ¼ cE

W. Therefore, by combining the necessary condition for CE (see (2)), with theexpression CE above and cE

A , we find the stationary interest rate in the East:

rE ¼ rð1� lEÞð1� lEÞ þ rð1þ lEÞ uþ q

r

h i:

Hence we will find the growth rate of AE, CE, YE by using the above stationary interest rE.First, the rate of R&D growth becomes:

cEA ¼

1� lE

ð1� lEÞ þ rð1þ lEÞ u� qð1þ lEÞ1� lE

� �: ðAIII:4Þ

Furthermore, with cEY ¼

lE

1�lE cEA , we can find the balanced growth rate of the final good and

consumption

cEY ¼ cE

C ¼lE

1� lE þ rð1þ lEÞ u� qð1þ lEÞ1� lE

� �: ðAIII:5Þ

So far, we derived the balanced growth rates for the East. We can derive the growth ratesof R&D and consumption in the West by using the wage relation between both countriesin the case wE = wW. Since the growth rate of technology is equal to the changes in thewage rates, i.e., (AIII.1), the growth rates of technology in two countries are identical. No-tice that this is also true even when the wages are not equalized (in non-FPE cases). Now,given the profits of the duopolists and monopolists (Appendix II), the price of a new blue-print for each country is equalized by the equilibrium interest rates in the general equilib-rium model, which reflect the future expectation on earnings of a new blueprint.Furthermore, we know that the stationary growth rate of R&D in the West is equal tothe stationary growth rate of R&D in the East, i.e., cW

A ¼ cEA . Then, the trade balance trade

condition implies

cWC ¼

1

Y E � CE½cE

Y Y E � cECCE�: ðAIII:6Þ

For the other cases, the same arguments are employed to derive growth rates of variables(refer to the Appendix for reader’s request).

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Economic growth and convergence with international differences in technology