International R&D subsidy competition, industrial agglomeration and growth

Journal of International Economics 89 (2013) 233–251

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Journal of International Economics

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International R&D subsidy competition, industrial agglomeration and growth☆

Hiroki Kondo ⁎Department of Economics, Sophia University, 7-1 Kioicho Chiyoda-ku, Tokyo 102-8554, Japan

☆ The author would like to thank the editor and an antremely helpful comments and suggestions. The authorments of Tomoya Mori, Se-il Mun and seminar participremaining errors are the responsibility of the author.⁎ Tel./fax: +81 3 3238 3219.

E-mail address: [email protected].

0022-1996/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.jinteco.2012.04.004

a b s t r a c t
a r t i c l e i n f o
Article history:Received 17 January 2008Received in revised form 9 April 2012Accepted 9 April 2012Available online 18 April 2012

JEL classification:F12O25O31R11

Keywords:Spatial agglomerationEndogenous growthR&D subsidyGlobalizationTrade costs

I construct a model with endogenous growth and new economic geography. Using this framework, I considerthe outcomes of R&D subsidy competition among countries under different trade costs. When trade costs arehigher, less industrialized countries are more eager to attract industries with vertical linkages. To prevent theindustries from relocating, more industrialized countries choose much higher R&D subsidies. As a result, theindustries never relocate and the growth rate is very high. When trade costs decrease, countries are less will-ing to host industries with vertical linkages. R&D subsidy competition becomes less intense, and the growthrate decreases.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

As globalization proceeds, industries with scale effects tend to con-centrate in a limited number of regions. This, in turn, makes the differ-ences in the industrial structures among countries more prominentand persistent. In such circumstances, less industrialized countriesmust implement much bolder industrial policies to attract industrieswith scale effects. Does globalization thus causemuch fiercer industri-al policy competition among countries? Alternatively, are countrieswilling to impose industries with scale effects on other countries? Bydoing so, they can free themselves of the burden of hosting such in-dustries while enjoying cheaper imports of their products.

This paper analyzes the effects of R&D subsidy competition amongcountries on growth and international pattern of specialization. Theanalyses employ the frameworks of endogenous growth and neweconomic geography models. When international trade costs arehigher, less industrialized countries are more eager to attractindustries with scale effects and, thus, are more willing to chooseintense R&D subsidies. Facing such a strategy on the part of the less

onymous referee for their ex-also benefited from the com-ants at Kyoto University. Any

rights reserved.

industrialized countries, the more industrialized countries choosemuch higher R&D subsidies. Thus, the industries never relocate andthe growth rate remains very high. When international trade costsare at a medium level, only the more industrialized countries subsi-dize R&D. When international trade costs become much lower, coun-tries are less willing to host industries with scale effects. Rather thanhosting these industries and incurring the costs of the R&D subsidies,they choose to impose the industries with scale effects on other coun-tries and import their products. In equilibrium, the more industrial-ized countries subsidize R&D while the less industrialized countriestax R&D. The growth rate is lower than when international tradecosts are higher. To sum up, as globalization proceeds, the R&D subsi-dy competition becomes less intense, and the economic growth ratedecreases. That is, globalization reduces economic growth throughthe endogenously determined industrial policy interactions.

In the frameworks of endogenous growth and new economicgeography models, scale effects lead to industrial concentration andhigher growth in the process of globalization. At the same time, how-ever, globalization causes an income gap among countries. The scaleeffects and income gaps will induce industrial policy interventions.However, little research has explicitly focused on the industrialpolicy interactions in endogenous spatial agglomeration and growthmodels.

Krugman (1979) and Rivera-Batiz and Romer (1991) introducedscale effects in production and in investment processes, respectively,and showed that globalization increases output levels and growth

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234 H. Kondo / Journal of International Economics 89 (2013) 233–251

rates. Employing an endogenous growthmodel in which dynamic tech-nological externalities bring about sustainable growth, Grossman andHelpman (1991) showed that dynamic technological externalities thatwork locally in scopemake high technology industries concentrate per-sistently in one country. A less industrialized country can attract hightechnology industries and leapfrog over the more industrialized coun-try by offering larger R&D subsidies. However, this study did not consid-er competition in subsidizing R&D. For example, this study did notanalyze how themore industrialized country reacts to the less industri-alized country's R&D subsidies.

Walz (1996), Baldwin et al. (2001), Martin and Ottaviano (2001),and Gao (2005) studied the effects of globalization on internationalspecialization patterns and economic growth by combining a neweconomic geography model and an endogenous growth model. InBaldwin et al. (2001), when high trade costs divide the domestic mar-kets of countries, high technology industries disperse among coun-tries. However, when trade costs fall, technological externalities thatare local in scope become more crucial for location patterns. As inGrossman and Helpman (1991), high technology industries tend toconcentrate in one country. This enhances agglomeration and growthby making R&D in that country more efficient. However, the incomegap becomes persistent. Martin and Ottaviano (2001) and Gao(2005) introduced pecuniary external effects as well as technologicalexternal effects by explicitly considering industries with vertical link-ages, as did Krugman and Venables (1995) and Venables (1996). Inthese studies, globalization contributed to economic growth. Gao(2005) introduced foreign direct investment (FDI) in these frame-works. When trade costs decrease, the firms in more industrializedcountries will shift manufacturing production processes to less indus-trialized countries through FDI. In the more industrialized countries,more resources shift to R&D process and thus the growth rate rises.However, industrial policies were not analyzed, although external ef-fects and income gaps will induce industrial policy interventions.

Impullitti (2010) conducted one of the few analyses on how glob-alization affects economic growth through R&D subsidy competitionamong governments. Impullitti (2010) employs a quality laddertype of endogenous growth model in which firms in each industryor variety engage in R&D competition to improve their productivityor the quality of their products. Globalization leads to internationalR&D competition among firms from different countries in more in-dustries or in wider range of varieties. In such circumstances, govern-ments are more willing to subsidize R&D to protect or expand themonopolistic competition rents of domestic firms (internationalbusiness-stealing motive). Consequently, globalization leads to fierc-er competition between firms and governments and thus enhancesgrowth.1

In contrast, I construct a framework combining a new economicgeography model of vertical linkages with an endogenous growthmodel of a variety expansion type. Then, there is no internationalR&D competition among firms to improve their products within eachindustry or variety. Thus, there is no international R&D subsidy com-petition among governments with international business-stealingmotives. In this model, R&D introduces new varieties of products. Pro-ductivity and R&D efficiency both rise in a country with greater varie-ty, attractingmore R&D in the country. This, in turn, leads to industrialagglomeration. A country hosting an industrial agglomeration canenjoy higher productivity and cheaper varieties of products. In thismodel, this motivates governments to subsidize R&D. As globalizationproceeds, however, the agglomeration rent becomes less prominentand governments become less eager to subsidize R&D.

Baldwin and Krugman (2004), Ludema and Wooton (2000), andKind et al. (2000) analyzed tax (subsidy) competition on internationally

1 Haaland and Kind (2008) analyzed R&D subsidy competition and coordinationusing a strategic trade policy model. The outcome is asymmetric in that only one coun-try subsidizes R&D.

mobile factors, such as capital, in the framework of a new economicgeography model. In traditional studies of tax competition, suchas those by Zodrow and Mieszkowski (1986), Wilson (1986), andWildasin (1988), the rate for the source tax on mobile capital is belowthe optimal rate. In contrast, recent studies based on a new economicgeography model showed that agglomeration rents in the more indus-trialized countriesmake tax competition lessfierce. That is, themore in-dustrialized countries can choose higher tax rates on capital withoutlosing it. Baldwin and Krugman (2004) showed that agglomerationrents are highest under moderate trade costs, and so themore industri-alized countries can enjoy the highest tax rates.2

In contrast, this paper shows that when trade costs are high ormoderate, the more advanced countries are at a disadvantage. Insuch cases, a less industrialized country is more eager to attract in-dustries with scale effects to within its borders. Thus, to prevent theindustries from relocating, the more industrialized country mustchoose a higher investment subsidy rate (an R&D subsidy in thispaper). Furthermore, this paper shows that when the trade costs arevery low, countries are less willing to host industries with scale ef-fects. They are more willing to free-ride on the other country's R&Dsubsidy policies.

This paper is organized as follows. Section 2 constructs a frame-work of endogenous growth and new economic geography in whichindustries with vertical linkages play a crucial role. Section 3 analyzesgrowth and agglomeration patterns of the industries on equilibrium.Section 4 discusses the outcomes of R&D subsidy competition.Section 5 discusses a cooperative R&D subsidy policy, including trans-fer payments from one country to the other. Concluding remarks aregiven in Section 6.

2. A model with final and intermediate differentiated goods

I consider an economy which has two countries, A and B, and twosectors, manufacturing and agriculture. Each country is endowedwith unit measure of households which are immobile between coun-tries. Households have the following identical intertemporal utilityfunction:

X∞t¼0

11þ ρ

� �t

α lnCiXt þ 1−αð Þ lnCi

Yt

h i;

CiXt ¼ ∫κ∈IAt ∪IBt Ci

t κð Þ� �γ

dκh i1

γ ; i ¼ A;B:

ð1Þ

In Eq. (1), CXti is the consumption of a constant elasticity of substi-tution (CES) composite of differentiated manufacturing goods, CYti isthe consumption of homogenous agricultural goods in country i inperiod t, ρ is the subjective discount rate, 0bαb1 and 0bγb1. Cti(κ)is the consumption of each differentiated manufacturing goods, andIti is the set of differentiated goods produced in country i in period t.In each country, a household maximizes Eq. (1) subject to the follow-ing intertemporal budget constraint:

Wit ¼ 1þ rtð ÞWi

t−1 þwit−Ti

t−Eit ; i ¼ A;B: ð2Þ

In Eq. (2), Wti is per capita financial assets in country i in period t,

and rt is the rate of return on the financial assets when they are car-ried over from period t−1; wt

i is the wage, Tti is the lump sum tax lev-ied by the government, and Et

i is the consumption expenditure:Eti≡Pt

iCXti +pYt

i CYti . I assume that financial assets are traded in an effi-

cient international financial market. Therefore, households in bothcountries face the same rates of return on the assets. I also assume

2 Martin (1999) analyzed the effects of a coordinated R&D subsidy policy on inequal-ities and growth by combining an endogenous growth model and a new economic ge-ography model.

3 Gao (2005) assumed that the past stock of local R&D reduced the costs of R&D. Inthis paper I assume that the more recent stock of R&D reduces the costs of R&D moresignificantly.

235H. Kondo / Journal of International Economics 89 (2013) 233–251

that initially there is no gap in the quantity of financial assets be-tween countries. In Et

i, pYti is the price of agricultural goods, and Pti is

the minimum cost of purchasing a unit of the CES composite CXti in

country i in period t:

Pit ¼ ∫κ∈IAt ∪IBt pDit κ ′ð Þ

� �1−�dκ ′

� � 11−�

; i ¼ A;B; ð3Þ

where ptDi(κ) is the consumer price (c.i.f. price or delivered price) of

goods κ in country i in period t, and �=1/(1−γ)≥1. Optimizationyields:

Ci κð Þ ¼pDi κð Þ� �−�

Pi� 1−�

αEi; i ¼ A;B; ð4Þ

CiY ¼ 1−αð Þ Ei

piY

!; i ¼ A;B; ð5Þ

and

1Eit

¼ 1þ rt1þ ρ

� �1

Eitþ1

!; i ¼ A;B: ð6Þ

One unit of homogenous agricultural goods is produced using oneunit of labor as an input and supplied in a perfectly competitive mar-ket. If the preference for homogenous agricultural goods is sufficient-ly large, the agricultural sector operates in both countries, and thewages are equalized between two countries. I set the wages as thenumeraire. Then:

pAYt ¼ pBYt ¼ wA ¼ wB ¼ 1: ð7Þ

If the preference for homogenous agricultural goods is extremelysmall, the agricultural sector operates only in one country, and thewages are unequal between the two countries. In this case, the anal-ysis becomes complicated. I eliminate this extreme case and concen-trate on the equal wage case. To do so, I must check that theemployment in the agricultural goods sector is larger than the laborendowment in one country after I solve the model with Eq. (7).

Each differentiated manufacturing good is monopolistically sup-plied by the firm that invented that good. In addition to labor, eachgood is produced by using manufacturing differentiated goods them-selves as intermediate inputs. Specifically, the production of each dif-ferentiated good is a Cobb–Douglas function of labor and CEScomposite of manufacturing differentiated goods, with CES compositeshare a (0bab1). I assume that in the production function the CEScomposite has the same CES rate as CXi . Then, the unit cost to producea differentiated good in country i is (Pi)a (wi)1−a=(Pi)a. The choicefor the mill price (f.o.b. price) pi by a firm in country i so as to maxi-mize monopolistic competition profits is a constant markup (γ) overthe unit cost (Pi)a.

Trading manufactured goods is costly. As is common in new eco-nomic geography models, I assume an iceberg form of trade costssuch that one unit of differentiated good melts down to 1/τ (τ≥1)units when it crosses the border. If good κ is produced in country i,the consumption price (c.i.f. price) pDi(κ) is equal to pi. In contrast,if good κ is produced in the other country, it is equal to τp j.

The monopolistic competition profits motivate R&D investmentsto enter into the manufacturing sector. The number of manufacturinggoods produced in period t+1 depends proportionally on theamount of labor engaged in R&D in the preceding period t, lR&Dt

i :

nitþ1 ¼ ni

t þ λnjt

� � liR&Dt

b

!; i; j ¼ A;B; i≠j; ð8Þ

where nti denotes the measure of Iti, the set of differentiated goods

produced in country i in period t. For tractability, I assume that R&Dinvestments in the last period bring the know-how to producemanufacturing goods, but that the know-how will be totally dissipat-ed in the next period. That is, I assume that knowledge capital depre-ciates at a 100% rate after one period of use, as does physical capital inmany basic economic growth and real business cycle models. Eachmanufacturing good is produced only in the country where it hasbeen invented. Moreover, I assume dynamic technological externaleffects such that the more R&D that has been accumulated, the moreefficient the present R&D.3 Yet such external effects are limited ingeographical scope. I let λ∈ [0,1] denote the geographical scope. Alarger λ indicates that more globally dynamic technological externaleffects work. Note that b in Eq. (8) is the same for the two countries.That is, if past R&D accumulation is equal, there is no difference inR&D efficiency between the two countries.

A financial market matches the needs of households and potentialentrants into the manufacturing sector. On the one hand, given theprevailing market interest rate rt, households will save to smoothout their consumption path as in Eq. (6). On the other hand, potentialentrants will borrow to invest in R&D and exploit a new manufactur-ing good. Given the interest rate, the present value of the profit permanufacturing good created by current R&D is:

vit ¼πitþ1

1þ rt

!; i ¼ A;B; ð9Þ

where πt+1i is the profit permanufacturing good firm in country i in pe-

riod t+1. When a potential entrant issues an equity in order to raisefund for its R&D investment, this is the fundamental value of this equity.From Eq. (8), the R&D cost per manufacturing good is b/(ni+λnj).When the government subsidizes the R&D investments in that countrywith the subsidy rate of si, it becomes b(1−si)/(ni+λnj). For finitelabor to engage in R&D, the present value of the profit must be equalto or less than the cost of R&D in both countries:

MAX vA,

b 1−sA� �nA þ λnB

0@

1A; vB

,b 1−sB� �λnA þ nB

0@

1A

24

35≤1: ð10Þ

For R&D to be active in country i, Eq. (10) must be binding for thatcountry. This condition is called a ‘free entry condition.’

Our model is dynamic in the sense that households and potentialentrants in the manufacturing sector respectively maximize theirintertemporal benefits and as a result the model dynamically evolves.Knowledge capital is means of saving, traded and accumulated in thefinancial market. I have assumed that the knowledge lasted just oneperiod yet introduced dynamic technological external effects. There-fore, the current level of knowledge enhances R&D efficiency and in-creases it in the next period, generating economic growth.

3. Dynamic equilibrium path

The international specialization pattern, as well as consumption,savings, investment, growth, and interest rates, are endogenouslydetermined. Trade costs τ and the scope of dynamic technologicalexternal effects λ are exogenous. The factors of where R&D cost islower and where expected profit is larger are important in determin-ing where R&D investments take place. In this section, I analyze howthe scope of dynamic technological external effects λ and trade costs τdetermine the international specialization pattern affecting thesetwo, respectively. In this section, I assume that the two countries A

1.5 2 2.5 3 3.5

-0.6

-0.4

-0.2

0.2

0.4

0.6

τ*τ

]),,0,0,(ln[ τλCh

]),,0,0,(ln[ τλPh

Fig. 1. α=0.16, a=0.54, ε=3.8, γ=0.74, ρ=1 and λ=0.85.1 1.5 2 2.5 3

0.5

0.6

0.7

0.8

0.9

1λ

Area AB

Area A

τ

Fig. 2. Area A shows the area of τ and λ under which the agglomeration of themanufacturing sector takes place. Area AB shows the area of τ and λ under whichthere are two agglomeration equilibria.


and B are expected to offer R&D subsidies at fixed rates of sA and sB

permanently. I will consider how the governments choose them inthe next section.

First, I consider the equilibrium that the manufacturing sector hasbeen agglomerating in country A. Henceforth, the country in whichthe manufacturing sector concentrates is called ‘the core’ while theother is called ‘the periphery’. When country A has been the core,Eq. (10) must be binding only in country A. I derive the variables inthe equilibrium by solving dynamic equilibrium conditions includingthis one, and check the condition under which Eq. (10) is bindingonly in country A. Among the endogenous variables, the (gross)growth rate in the number of manufacturing goods g≡n=n is:

g sA� �

¼ 2 1−γð Þαb 1−γð Þα þ 1−aγ−α þ αγð Þ 1þ ρð Þ 1−sAð Þf g : ð11Þ

And the conditionunderwhichEq. (10) is bindingonly in countryA is:

h C; sA; sB;λ; τ� �

¼π C; sA; sB; τ� �π P; sB; sA; τ�

0@

1A 1

λ

� �1−sB

1−sA

!≥1; ð12Þ

where π(C,sA,sB,τ) is the profit per differentiated good firm in the corecountry A, and C represents country A's core status. Also, π(P,sB,sA,τ) isthe profit that afirmwould earn if it located in country B alone, and P rep-resents country B's peripheral status. See Appendix A.1 for the detailsabout the derivations of Eqs. (11) and (12), and the derivations and ex-pressions of the other endogenous variables.4 If Eq. (12) holds, underthe expectation that all R&D activities will be concentrated in country A,the expected future profits of R&D, vi, can be equal to the cost of theR&D only in country A. No onewill shift its R&D to country B. Thus, an ex-pectation becomes self-fulfilling.

Next, I consider the case where there are two equilibria. Themanufacturing sector can agglomerate in either of the two countriesif both Eq. (12) and the following hold:

h P; sB; sA;λ; τ� �

¼π C; sB; sA; τ� �π P; sA; sB; τ�

0@

1Aλ

1−sA

1−sB

!≥1: ð13Þ

The manufacturing sector will agglomerate where it is expected toagglomerate. Under the expectation that all R&D activities will takeplace in country B, the expected future profits of R&D, vi, can be equalto the cost of the R&D only in country B. Consequently, country B attracts

4 In Eq. (11), we can see that the effect of R&D subsidies sA on growth rate g is pos-itive only if (1−aγ−α+αγ)>0. Appendix A.1 shows that it holds in the derivationsof these equations. Appendix A.1 also shows that there is no gap in the amount offinancial assets between the two countries. Lastly, I must check that employment inthe agricultural goods sector is larger than the labor endowment in one country so thatEq. (7) holds. See Appendix A.1 for the derivation of this condition.

the whole of the manufacturing sector that country A has been hostingup to the present. Thus, an expectation can become self-fulfilling.

If Eq. (13) holds but Eq. (12) does not hold, the manufacturingsector shifts to country B. It never returns to country A.

Fig. 1 shows h(C,sA,sB,λ,τ) and h(P,sA,sB,λ,τ) as a function oftrade costs. The former is higher than the latter, reflecting the gapin the terms 1/λ in Eq. (12) and λ in Eq. (13), stemming from thedynamic technological external effects, which are local in scope. InFig. 2, Area AB shows (τ,λ) under which both Eqs. (12) and (13)hold, and there are two agglomeration equilibria. Area A shows(τ,λ) under which only Eq. (12) holds, and agglomeration takesplace only in country A. Note that in Figs. 1 and 2, in order to observehow (τ,λ) affects international patterns of specialization, it is as-sumed that there is no gap in the R&D subsidy rate si. If there is agap, the area where agglomeration takes place varies. Also, the areain which the manufacturing sector agglomerates only in country B(Eq. (13) holds while Eq. (12) does not) appears.5

The observations of Fig. 2 and the analyses of Eqs. (12) and (13) inAppendix B.1 yield the following Proposition:

Proposition 1.

(i) The less global in scope the dynamic technological external effectsare (the lower λ is), the more likely it is that the manufacturingsector will agglomerate in one country. Once it agglomerates, itcontinues to agglomerate in that country.

(ii) The lower the trade costs (the lower τ is), the more likely it is thatthe manufacturing sector will agglomerate in one country.

(iii) When the trade costs become much lower and when the dynamictechnological external effects work globally in scope, there are twoequilibria. The manufacturing sector can agglomerate in either ofthe two countries.

Proof. See Appendix B.1.

The dynamic technological external effects that are local in scopemake the R&D in the country where a larger number of differentiatedmanufacturing goods firms locates more advantageous. Consequent-ly, the manufacturing sector agglomerates and persistently continuesto do so in that country.

When trade costs are very high, the profit that a firm can earnwhen it locates in the core is smaller than the profit that a firm can

5 The parameter values in this paper are set to reflect the scale and characteristics ofthe industries which correspond to the manufacturing sector in this model by observ-ing the input–output table released by OECD. See Appendix C for the details about theprocess of setting parameters.


earn when it locates in the periphery alone, as we will see later. There-fore, the manufacturing sector disperses. However, when the dynamictechnological external effects are very local in scope, the R&D cost inthe core is much lower than that in the periphery. Therefore, R&D andmanufacturing production keep agglomerating in one country.

When trade costs become lower, the profit that a firm earns in thecountry with a larger number of firms exceeds the profit that a firmwould earn if it located in the other country, as I will discuss intuitive-ly shortly. In this case, the manufacturing sector agglomerates in thecountry where it is expected to agglomerate. It does not necessarilyagglomerate in the country where it has been agglomerated. Supposethat the manufacturing sector has been agglomerating in country A,but it is expected to agglomerate in B. The profit that a firm willearn in country B is much larger than the profit that a firm will earnin country A. This large gap in the profit expected in the next periodexceeds the current disadvantage in R&D in country B. Therefore,R&D is conducted in country B in a self-fulfilling manner.

Here I intuitively consider how trade costs affect the manufactur-ing sector's location through the gap in the profit per firm betweenthe two countries. Three forces determine the stability of agglomera-tion affecting the gap in the profit: the forward linkage effect, backwardlinkage effect, and local market competition effect. Among them,forward and backward linkage effects work in favor of agglomeration.Firms are eager to locate in a country with a larger number of sup-pliers ready to sell their inputs. This positive effect of a larger numberof suppliers on a firm's location choice is called the forward linkageeffect. Firms also prefer to locate themselves in a country with a largernumber of customers to purchase their output. This positive effect ofa relatively large market on a firm's location choice is called the back-ward linkage effect. In this model, differentiated goods firms tradetheir products with one another. Hence, a country with a larger num-ber of differentiated goods firms attracts more firms through both theforward and backward linkage effects.

On the other hand, the local market competition effect tends to de-stabilize agglomeration. International trade costs shelter domestic

6 Note that when trade costs fall, for a firm shifting its location from country A to countryThis is because access to the large foreign market is improved. This benefit motivates a firm tis halfway. On the one hand, it is too low to protect the domestic market and ensure sufficienis too high to ensure sufficiently large profits from the foreign market for a firm in country B.lower, a firm in country B can earn almost the same profits as those that a firm in country A ein country A remains stable.

7 It is more reasonable that households also form a rational expectation on the sequencesplicated. However, in some circumstances, subsidy rate, savings, and consumption will havmation hypothesis on household side we can, to some extent, examine how subsidies tend

markets, and thus make competition less fierce in the domestic mar-ket, where a smaller number of firms locate. When choosing their lo-cations, firms are eager to locate themselves in less competitivemarkets. This negative effect of a larger number of competitors on afirm's location choice is called the local market competition effect.

If trade costs are very high and firms are agglomerating in countryA, a firm can almost monopolize the domestic market in country B byrelocating there alone. Hence, the firm will be motivated to do justthat, at the cost of the larger market and lower production coststhat the firm enjoys in country A. That is, the local market competitioneffect dominates the forward and backward linkage effects and destabi-lizes the agglomeration. When trade costs fall, the domestic market inthe country with a smaller number of firms becomes less protectedfrom imports. A firm would rather locate in the country with a largernumber of firms. Thus, the manufacturing sector stably agglomeratesin the country where it is expected to agglomerate.6

To cope with complexities in multiple equilibria, the following as-sumption is made concerning where the manufacturing sector ag-glomerates. As long as Eq. (12) holds, even if Eq. (13) holds, themanufacturing sector keeps agglomerating in the country where ithas been agglomerating (country A in this case). That is, in order forthe current peripheral country B to attract the manufacturing sector,it must offer sB that is high enough not only to satisfy Eq. (13) (andthe agglomeration in country B potentially stable), but also to violateEq. (12) (and the current agglomeration in country A unstable). SuchsB is much higher than sA. In this sense, I assume that the location ofthe manufacturing sector has some persistency.

Therefore, if the manufacturing sector agglomerates in country Abut from now on sA and sB take constant values that satisfy Eq. (13)and violate Eq. (12), then R&D shifts to country B in period t. The growthrate in the number of differentiated manufacturing firms from now tothe next period is λg(sB) reflecting the handicap in dynamic technologicalexternal effects. From the next period onward, the manufacturing sectorconcentrates in country B and the growth rate is g(sB), as long as sA

and sB take constant values from now on.

4. R&D subsidy game

4.1. Setup

So far, I have treated the subsidy rate as an exogenously constant variable. In this section, I consider how subsidy rates are determined in theR&D subsidy game by governments.

Governments maximize the welfare of households in their own countries. That is, the government and households in a country maximize thehouseholds' intertemporal utility by choosing, respectively, the sequence of subsidy rate, and those of consumption and savings. In this paper, Irestrict the governments' strategy to a Markov strategy. That is, a government chooses its subsidy rate as a function of its current state: whetherits state is the core (denoted by state C) or the periphery (denoted by state P), and the number of differentiated goods nt.

Households, on the other hand, maximize their intertemporal utility expecting that the subsidy rates that governments choose nowwill con-tinue permanently. That is, I assume that households form a static expectation of the subsidy rate.7

Consequently, a household's consumption expenditure in a period and the growth rate from that period to the next depend on the R&D sub-sidy rates only in that period as in Section 3. A household's instantaneous utility in each period also depends on the R&D subsidy rate only in thatperiod.

Governments know that when R&D subsidy rates change, households will redo their intertemporal utility maximization expecting that thenew subsidy rates will continue. The households' consumption expenditure, growth rate, and instantaneous utility in that period will be deter-mined as functions of the new subsidy rates. Therefore, a government expects that its choice of the sequence of the subsidy rates determines ahousehold's instantaneous utility in each period as a function of the subsidy rate in the corresponding period as discussed above. Thus it

B alone, a decrease in the profits from country A's market also becomes less prominent.o shift its location to country B. It should also be noted, however, that τ near τ⁎ in Fig. 1tly large profits from the domestic market for a firm in country B. On the other hand, itThen, locating in country B is the most disadvantageous when τ=τ⁎. When τ becomesarns. Hence, the agglomeration force becomes less prominent. However, agglomeration

of the subsidy rates. Unfortunately, in such general settings, analysis is impossibly com-e constant values under rational expectations. Starting with the static expectation for-to be determined in more general settings.


determines a household's intertemporal utility, as the discounted sum of the instantaneous utilities. The intertemporal utility can be describedas a Bellman functional formation. It can be converted as:

Ui Cð Þ ¼ MAXsi Cð Þ

"ln E C; si Cð Þ; sj Pð Þ

� �þ 1−γ

γ

� �α

1−a

� � 1ρ

� �ln g si Cð Þ

� �þ 1

1þ ρ

� �Ui Cð Þ;

ln E P; si Cð Þ; sj Pð Þ� �

þ 1−γγ

� �α

1−a

� � 1ρ

� �ln λg sj Pð Þ

� �þ 1

1þ ρ

� �Ui Pð Þ

#;

ð14Þ

Ui Pð Þ ¼ MAXsi Pð Þ

"ln E C; si Pð Þ; sj Cð Þ

� �−α ln τ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �ln λg si Pð Þ

� �þ 1

1þ ρ

� �Ui Cð Þ;

ln E P; si Pð Þ; sj Cð Þ� �

−α ln τ þ 1−γγ

� �α

1−a

� � 1ρ

� �ln g sj Cð Þ

� �þ 1

1þ ρ

� �Ui Pð Þ

#:

ð15Þ

Their derivations are in Appendix A.2. In these expressions, E(C,si,sj) and E(P,si,sj) are consumption expenditures in the core country i and inthe peripheral country j, respectively. Their expressions are in Appendix A.1. In Eqs. (14) and (15), Ui (C) is the value function, the maximumintertemporal utility starting from the initial state of the core (denoted by state C). Also, Ui (P) are the value function in the case where the initialstate is the periphery (denoted by state P). Furthermore, si(C) and si(P) are the corresponding R&D subsidy rate decisions.

I let ϕ(si,λ,τ) denote a lower bound of sj which guarantees h(C, si, sj,λ,τ)b1. When country i is the core, with si(C) high enough to sat-isfy sj(P)≤ϕ(si(C),λ,τ), country i can continue hosting the manufacturing sector. In this case, Ui (C) is equal to the first component on theright side of Eq. (14). In contrast, when si(C) is lower, all of the R&D activities are attracted to the other country, and Ui (C) is equal to thesecond component in Eq. (14). When country i is the periphery, with si(P) high enough to satisfy si(P)>ϕ(sj(C),λ,τ), country i can attractR&D activities. Then Ui(P) is equal to the first component on the right side of Eq. (15). However, if si(P) is lower, then Ui(P) is equal to thesecond component in Eq. (15).

Let Ui and si (i=A, B) denote the vectors (Ui=(Ui(C),Ui(P)) and si=(si(C), si(P)). Let si ¼ H sj�

denote si, which solves Eqs. (14) and (15)given country j's choice of sj. If the pair sA and sB satisfies sA ¼ H sB

� and sB ¼ H sA

� , then that pair is a Nash equilibrium. Here I focus on the

symmetric Nash equilibrium sA ¼ sB ¼ s, which is the fixed point of s=H(s).

4.2. Incentives for R&D subsidies

Before analyzing strategic interaction and equilibrium in R&D subsidy competition, I will consider the incentives for a country to subsidizeR&D, given the other country's R&D subsidy policy. First, I discuss what the optimum subsidy rate when country i continues to host themanufacturing sector. Next, I consider which is preferable, to be the core or to be the periphery. If one state is strongly preferable to theother, a country i has an extra incentive to take up an R&D subsidy policy to change its state.

First, I consider country i's incentives for R&D subsidies, assuming that the country is initially the core and chooses to remain the core, hostingthe manufacturing sector. The government in the core has an incentive to enhance R&D by subsidizing it. R&D investments bring about not onlyprivate know-how inmanufacturing for a firm incurring R&D investment costs, but also public knowledgewhichmakes future R&Dmore efficient(dynamic technological external effects). R&D activities in the market are insufficient, as the dynamic public benefits are not taken into account.

I let s denote the R&D subsidy rate which produces the maximum value for Eq. (14) in which the left side is equal to the first component inthe right side. This is calculated as follows:

s ¼1−aγð Þ 1þ ρð Þ −2γρþ 1−aγð Þ 1þ ρð Þð Þ−α 1−γð Þ ρ2 1−γð Þ þ 1−aγð Þ 1þ 2ρð Þ

� �1−α þ αγ−aγð Þ 1þ ρð Þ α 1−γð Þ þ 1−aγð Þ 1þ ρð Þð Þ : ð16Þ

If the rival country j's R&D subsidy rate is not very high, the maximum utility of being the core is attained at the rate of s. In contrast, if theR&D subsidy rate of the rival country j's is high enough to satisfy sj Pð Þ > ϕ s;λ; τð Þwhile country i still chooses to be the core, country iwill choosea si(C) high enough to satisfy sj(P)=ϕ(si(C),λ,τ). In either case, country i will subsidize R&D once it has decided to remain the core.

Next, I consider which is preferable, to be the core or to be the periphery. If there is a large gap between the maximized utility of being thecore and that of being the periphery, the country will take up an R&D subsidy policy to change its state. Whether being the core is preferable tobeing the periphery, or vice versa, is not obvious. Therefore, it is difficult to anticipate how fierce the R&D subsidy game will be.

The main disadvantage of being the periphery is the trade costs it must pay to import all of the differentiated goods, as reflected in the term−αlnτb0 in Eq. (15). The larger this disadvantage is, the more a country is eager to attract the manufacturing sector even if it requires the pay-out of huge R&D subsidies. As a consequence, the R&D subsidy game tends to get much fiercer.

Being the periphery also has an advantage, however. The periphery can free-ride on the core's R&D subsidies. Countries may be eager to re-lease the manufacturing sector by choosing very small subsidies or even taxation on R&D. Consequently, the R&D subsidy game may get muchless fierce.

4.3. Trade costs in middle sizes

Thus far I have considered one country's incentives for R&D subsidies given the other country's R&D subsidy policy. The analysis becomesmuch more complicated when I also take into account the strategic interaction between the countries. To find a symmetric Nash equilibrium,I firstly consider the conditions under which a country's strategy of choosing s when it is the core and offering no subsidy when it is the periph-ery (sA ¼ sB ¼ s;0ð Þ) is a Nash equilibrium. That is, I consider under which conditions a country has no incentive to take up an R&D subsidy pol-icy to change its state, and only the basic incentive to subsidize R&D to cope with dynamic technological external effects survives. The followingproposition states such conditions.

Area III

λ

Area II

Area I

τ

1

0.95

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.51 1.2 1.4 1.6 1.8 2 2.2 2.4

Fig. 3. Area I shows the area of τ and λ that satisfy the conditions in Proposition 2. If τ and λ are in Area II, R&D subsidy competition becomes fiercer. If they are in Area III, it becomesless fierce. α=0.16, a=0.54, ε=3.8, γ=0.74, and ρ=1.


Proposition 2. A country's strategy of choosing s when it is the core and offering no subsidy when it is the periphery (sA ¼ sB ¼ s;0ð Þ) is a Nashequilibrium when

(i) trade costs τ are in middle sizes, and(ii) the scope of dynamic technological external effects is less global (λ is closer to zero).


The Area I in Fig. 3 shows (τ,λ) that satisfy the conditions in Proposition 2. If (τ,λ) is in Area II, R&D subsidy competition becomes fiercer. And if(τ,λ) is in Area III, it becomes less fierce. I consider these cases in sub-sections 4.4 and 4.5, respectively.

-1 -0.75 -0.5 -0.25 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0.1

-1 - 0.75 -0.5 - 0.25 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0 .1

(CU i

(Csi

s

(PU i

)

)

)

)(Psi

),,ˆ( τλφ s

Fig. 4. Ui(C) and Ui(P) as functions of si(C) and si(P) given that the strategy of the rival country j is sj ¼ s ;0ð Þ when trade costs are in a middle size. α=0.16, a=0.54, ε=3.8,γ=0.74, ρ=1, b=0.075, λ=0.85 and τ=1.4. Under the numerical example, s ¼ 0:388. With si(C)b−0.896 the core loses the manufacturing sector. The periphery can attractmanufacturing and become the new core with si Pð Þ ¼ ϕ s;λ; τð Þ > 0:669.

-1 - 0.75 -0.5 - 0.25 0.25 0.5 0.75

-0.1

-0.05

0

0.05

0.1

-1 -0.75 -0.5 - 0.25 0.25 0.5 0.75

-0.14

-0.12

-0.1

-0.08

-0.06

(CU i

(Csi

s

(PU i

)

)

)

)(Psi

),,ˆ( τλφ s

Fig. 5. Ui(C) and Ui(P) as functions of si(C) and si(P) given that the strategy of the rival country j is sj ¼ s ;0ð Þ when trade costs are high. α=0.16, a=0.54, ε=3.8, γ=0.74, ρ=1,b=0.075, λ=0.85 and τ=2.2. Under the numerical example, s ¼ 0:388. With si(C)b−0.398 the core loses the manufacturing sector. The periphery can attract manufacturing andbecome the new core with si Pð Þ ¼ ϕ s;λ; τð Þ > 0:547.


In a numerical example with τ and λ included in Area I in Figs. 3 and 4(i) plots the initial core country's intertemporal utility as a function ofits choice of the R&D subsidy rate si(C). Similarly, Fig. 4(ii) shows the initial periphery country's intertemporal utility as a function of si(P). Inthese figures, the rival county's strategy is given. It is sj ¼ s;0ð Þ. Fig. 5(i) and (ii) plots the intertemporal utility of the initial core country as afunction of si(C) and of the initial periphery country as a function of si(P), respectively, when trade costs τ are as high as those in Area II inFig. 3. Fig. 6(i) and (ii) plots the intertemporal utilities when the trade costs τ are as low as those in Area III.

Trade costs τ affect a country's incentive to take up an R&D subsidy policy to change its state, determining the gap between the attainableutility when a country is the core and that when it is the periphery.

Unless the trade costs are extremely high, the initial periphery is unwilling to become the core by paying out huge costs to attract themanufacturing sector. As we have seen, the main disadvantage of being the periphery is the trade costs it must bear to import all of the differ-entiated goods. Yet the periphery also has an advantage, in that it can free-ride on the R&D subsidies of the core. The lower the trade costs are,the less likely it is that the periphery's disadvantage outweighs its advantage. Therefore, the less likely it is that the periphery has an incentive tobecome the core, as we can see comparing between Figs. 4(ii) and 6(ii).

And unless the trade costs are extremely low, the initial core country will prevent relocation by providing an R&D subsidy at rate s. The initialcore country i can impose the manufacturing sector cluster on country j by choosing a very small subsidy or even taxation on R&D. Then it canfree-ride on the R&D subsidy of the new core country j at rate sj Cð Þ ¼ s from the next period onward. On the other hand, it will have to importmanufactured goods, thereby incurring trade costs. Unless the trade costs falls to extremely low levels, the advantage of becoming the peripherycannot outweigh its disadvantage, as we can see comparing between Figs. 4(i) and 5(i).

To sum up, when trade costs are middle-sized, both countries will remain in their initial states. This is the intuition behind Proposition 2(i)and Fig. 3.

Local in scope dynamic technological external effects discourage both the core and the periphery to change their status. The process of shiftingthe state – the relocation of the manufacturing sector – follows the R&D activities in the periphery. The more local in scope is the work of thedynamic technological external effect, the less efficient the R&D in the periphery is and the more serious a temporary drop in growth rate g is.Hence, the process of shifting the state cost both the core and the periphery too much. This is the intuition behind Proposition 2(ii) and Fig. 3.

4.4. High trade costs

When trade costs are as high as those in Area II in Fig. 3, being the core is attractive for both countries. The periphery's disadvantage ofimporting all the differentiated goods outweighs its advantage of free-riding on the R&D subsidy of the core. Hence, the initial periphery iseager to attract manufacturing even at the cost of huge R&D subsidies, as clearly shown in Fig. 5(ii). The initial core will prevent the relocationof manufacturing even by choosing an R&D subsidy rate that is higher than s.

-1 - 0.75 -0.5 - 0.25 0.25 0.5 0.75

0.02

0.04

0.06

0.08

0.1

-1 - 0.75 -0.5 - 0.25 0.25 0.5 0.75

0

0.05

0.1

0.15

0.2

(CU i

(Csi

s

(PU i

(Psi

)

)

)

)

),,ˆ( τλφ s

Fig. 6. Ui(C) and Ui(P) as functions of si(C) and si(P) given that the strategy of the rival country j is sj ¼ s ;0ð Þ when trade costs are low. α=0.16, a=0.54, ε=3.8, γ=0.74, ρ=1,b=0.075, λ=0.85 and τ=1.05. Under the numerical example, s ¼ 0:388. With si(C)b−0.328 the core loses the manufacturing sector. The periphery can attract manufacturing andbecome the new core with si Pð Þ ¼ ϕ s;λ; τð Þ > 0:538.


As a result of such a fiercer competition, a Nash equilibrium has the core choose an R&D subsidy rate higher than s, and has the peripherychoose a much higher R&D subsidy rate. The manufacturing sector never relocates. The growth rate is higher than that when trade costs areat a medium level, g sð Þ. The higher the subsidy rate the core chooses, the less attractive for the periphery becoming the core, because a muchhigher rate of R&D subsidy is required for the periphery to become the core. In addition, the periphery gains more of an advantage from free-riding on the R&D subsidy of the core.

Let �s denote theminimum of the R&D subsidy rates with which the core can discourage the periphery from becoming the core. See Appendix B.3for the derivation of�s. Fig. 7(i) and (ii) shows country i's intertemporal utilitywhen it is the core andwhen it is the periphery, respectively, given thatthe rival country j's strategy is sj ¼ �s;ϕ �s;λ; τð Þð Þ. We can see that country i has no incentive to deviate from the strategy si ¼ �s;ϕ �s;λ; τð Þð Þ and thussA ¼ sB ¼ �s;ϕ �s;λ; τð Þð Þ is the Nash equilibriumwhen trade costs are very high. Unlike the case of Fig. 5(ii), in the case of Fig. 7(ii) the periphery hasno incentive to attractmanufacturing, as the rival core chooses a higher rate of R&D subsidy and the subsidy rate required to attractmanufacturing ismuch higher. The initial periphery country i will choose to remain the periphery by choosing an R&D subsidy rate that is equal to or lower thanϕ �s; λ; τð Þ, rather than to attract manufacturing by setting an R&D subsidy rate that is strictly higher than ϕ �s; λ; τð Þ. For the core, the minimumR&D subsidy rate required to continue hosting manufacturing in Fig. 7(i) is �s and it is higher than that in Fig. 6(i), as the rival periphery chooses amuch higher rate of R&D subsidy in Fig. 7(i) than in Fig. 6(i). However, being the core is attractive and thus the initial core is willing to choose �s,though it is higher than s.

4.5. Low trade costs

Lastly, I consider the case where trade costs are as low as those in Area III in Fig. 3. In this case, both countries are willing to be the periphery.The periphery's advantage of free-riding on the R&D subsidy of the core outweighs its disadvantage of importing all the differentiated goods.Hence, the core is eager to become the periphery by taxing on R&D as we can see in Fig. 6(i).

As a result of a less fierce competition, in a Nash equilibrium the core chooses a sufficiently high rate of R&D subsidy s and the periphery taxeson R&D. The manufacturing sector never relocates, and the growth rate equals g sð Þ. When the initial periphery taxes on R&D, the initial core isless eager to become the periphery. The shift in state is accompanied by the R&D in the initial periphery. The periphery's taxation on R&D dis-courages its R&D, reduces growth rate and suffers the initial core as well as the periphery.

Let ~s denote the maximum of the R&D subsidy rates with which the periphery can discourage the core from imposing its manufacturing sec-tor to the periphery. See Appendix B.3 for the derivation of ~s. Fig. 8(i) and (ii) shows country i's intertemporal utility when it is the core and thatwhen it is the periphery, respectively, given that the strategy of the rival country j is sj ¼ s;~sð Þ. From these figures we can check that sA ¼ sB ¼s;~sð Þ is the Nash equilibriumwhen trade costs are very high. For the core country i becoming the periphery is less attractive in Fig. 8(i) where the

0 0.4 0.6 0.8

-0.1

-0.05

0

0.05

0.1

-0.75 -0.5 -0.25 0.25 0.5 0.75

-0.14

-0.12

-0.1

-0.08

-0.06

(CU i

(Csi

s

(PU i

)

)

)

)(Psi

),,( τλφ s

Fig. 7. Ui(C) and Ui(P) as functions of si(C) and si(P) given that the strategy of the rival country j is sj ¼ �s;ϕ �s;λ; τð Þð Þ when trade costs are high. α=0.16, a=0.54, ε=3.8, γ=0.74,ρ=1, b=0.075, λ=0.85 and τ=2.2. Under the numerical example, �s ¼ 0:415 and ϕ �s;λ; τð Þ ¼ 0:566.


rival peripheral country j taxes on R&D at a rate sj Pð Þ ¼ ~sb0 than in Fig. 6(i). The initial core country i will remain the core and subsidize R&D atthe rate of s to cope with dynamic technological external effects, rather than to release manufacturing by taxing R&D at the rate−si Cð Þ > −ϕ−1 ~s;λ; τð Þ.

5. Policy cooperation

To maximize the sum of the intertemporal utilities of the twocountries, there should be no relocation of the manufacturing sector.That is because the relocation of the manufacturing sector is accom-panied by R&D in the periphery with lower R&D efficiencies andcauses a temporary drop in the growth rate g. Both countries shouldremain in their initial statuses: the initial core country should staythe core and the initial periphery should stay the periphery. I let s⁎

denote the core's R&D subsidy rate which maximizes the sum of theintertemporal utilities of the two countries.

In the real world, however, the core will choose s that is lower thans⁎, given that it will choose to remain the core, as we have seen in sub‐section 4.2. The core takes no notice of how its R&D subsidy willbenefit the periphery through a boosting of the growth rate g. Thus, Iconsider the following policy cooperation. The core chooses the R&Dsubsidy rate that is as high as s⁎. And the peripherymakes the transferto the core in the amount TR. This subsidy and transfer must enableboth the core and periphery to enjoy higher intertemporal utilitiesthan they do in the Nash equilibrium shown in Section 4.

This type of cooperation, however, is not necessarily stable. Thecore can enjoy higher utilities by choosing s, if the transfer by the pe-riphery to the core is high. The periphery can also enjoy higher utili-ties by choosing zero transfer, if the core subsidizes R&D at rate s⁎. Idiscuss the stability of the cooperative policy by considering the trig-ger strategy. If the core and periphery have respectively chosen sub-sidy rate s⁎ and some positive transfer thus far, they will choose the

same policy in the current period. But once either country deviatesfrom the policy cooperation, from the current period onward both be-have uncooperatively, and the Nash equilibrium situation in Section 4takes place.

Let TR∈ [TRmin,TRmax] denote the range of TR under which the pol-icy cooperation is stable. The following proposition states that therange depends on the size of trade costs.

Proposition 3.

(i) As long as trade costs are in middle or low, TRmax and TRmin takeconstant values.

(ii) When trade costs are higher, TRmax and TRmin are lower thanthose where trade costs are in middle or low.


As we have seen in Section 4.4, when trade costs are high, bothcountries are eager to attract the manufacturing sector and thusR&D subsidy competition becomes fierce. In the Nash equilibrium,the core's R&D subsidy rate is higher and its intertemporal utility islower than those when trade costs are middle or low. Therefore, theshift from policy cooperation to the Nash equilibrium reduces theutilities of the core more plausibly and dramatically. Hence, even ifthe transfer from the periphery is only modest, the core is willing tocooperate. And if only a modest amount of transfer is required, theperiphery also chooses to cooperate.

-1 -0.75 -0.5 -0.25 0.25 0.5 0.75

0.02

0.04

0.06

0.08

-1 - 0.75 -0.5 - 0.25 0.25 0.5 0.75

0

0.05

0.1

0.15

0.2

(CU i

(Csi

s

(PU i

)

)

)

)(Psi

s~),,ˆ( τλφ s

0.1

Fig. 8. Ui(C) and Ui(P) as functions of si(C) and si(P) given that the strategy of the rivalcountry j is sj ¼ s; ~sð Þ when trade costs are low. α=0.16, a=0.54, ε=3.8, γ=0.74,ρ=1, b=0.075, λ=0.85 and τ=1.05. Under the numerical example, s ¼ 0:388 and~s ¼ −0:032. With si(C)b−0.388 the core loses the manufacturing sector.


6. Conclusion

I considered the effects of globalization on international speciali-zation patterns and growth, when the intensiveness of R&D subsidycompetition among countries endogenously varies. When tradecosts are higher, the less industrialized countries are more willing tochoose higher R&D subsidies to attract manufacturing. The more in-dustrialized countries thus choose much higher R&D subsidies to pre-vent the relocation of manufacturing. As a result, manufacturingnever relocates and the growth rate is very high. When internationaltrade costs become lower, countries are less willing to hostmanufacturing. The R&D subsidy game becomes less intense, andthe growth rate becomes much lower.

I assumed that households maximize their intertemporal utilityunder static expectations of the governments' subsidy policies.When we assume households' rational expectation formation, analy-sis becomes impossibly difficult. If initially there is no gap in the fi-nancial assets between countries and if households form a staticexpectation, the gap in the financial assets never emerges, as wehave seen in Section 3. In contrast, if households rationally expect achange in R&D subsidy rate, the gap can emerge. This is becausehouseholds will improve their intertemporal utility by adjustingsavings and assets to even out consumption. Therefore, value functionUi(), and corresponding subsidy rate si() and consumption level Ei()depend not only on the status (core country or periphery country)but also on the asset levels Wi. However, the propensities by whichthe subsidy rates are determined will not fundamentally differ fromthe discussions in Section 4. R&D subsidy rates and consumptionlevels will keep constant values. The constant subsidy rates and thesize of the trade costs τ and the scope of the technological externaleffects λ to which the discussions in sub-sections 4.3, 4.4 and 4.5apply will be a bit different from those in Fig. 3.8

This study also assumes that knowledge capital depreciates at a100% rate after one period of use, as is often the case in basic econom-ic growth and real business cycle models. This assumption drasticallychanges the distribution of differentiated goods firms among coun-tries, simplifying the problem of analyzing value functions over dis-crete binary states (core and periphery countries). However, instandard settings for new economic geography models, the distribu-tion of firms changes continuously as a result of the gap in R&D inten-sity or by the movements of firms between countries. However, if weintroduce more general settings together with rational expectations,we must analyze value function Ui() and policy function si(), whichdepend continuously on the international distribution of firms ni aswell as the asset levels Wi. Analyzing such multi-dimensional andcontinuous functional equations is impossible. However, the resultsof this paper offer many clues for further research using more generalsettings.

Many empirical studies have found that trade openness increaseseconomic growth, as Lopez (2005) has recently surveyed. This paper,in contrast, shows that globalization reduces economic growth. Yetapart from the endogenously determined subsidy competition chan-nel on which I focus, there are many other channels through whichglobalization may affect economic growth, such as the scale effects

8 For instance, as we have seen in sub-section 4.4, when trade costs are higher, thecore chooses a higher subsidy rate, and the periphery chooses to remain the peripheryrather than to pay huge R&D subsidies to attract manufacturing. If a household forms arational expectation, the R&D subsidy rate with which the core can discourage the pe-riphery from being the core will be a bit higher. Suppose that the households in the pe-riphery rationally expect that the government in that country will pay huge R&Dsubsidies to be the core in the current period, and it will choose a lower subsidy ratefrom the next period. A household will smooth out its consumption expenditure bysaving less in the current period, and saving more in the future. Therefore, comparedwith the case where a household forms a static expectation, the intertemporal utilityis slightly larger. For the core to discourage the periphery from being the core, it hasto choose a subsidy rate that is a little higher than that we have seen in sub-section 4.4.

of market size or (and) competition effects. To focus on the R&D sub-sidy competition game, I introduce some of these channels in simplesettings without considering the others.

This paper employs a simple version of endogenous growth andnew economic geography models. In the frameworks of endogenousgrowth and new economic geography models, reduced trade costslead to industrial agglomeration and higher growth rates. In a simpleversion of these models, however, further decreases in trade costs donot continue to enhance the growth rate, given that the policy stanceremains unchanged. Once full agglomeration emerges, resource allo-cation across sectors and countries no longer changes.9 However, fur-ther decreases in trade costs may change the incentives for policyintervention and affect the growth rate. Based on this simple versionof endogenous growth and new economic geography models, I ab-stract the effects of globalization on growth through changes in thefierceness of the R&D subsidy competition among governments foragglomeration rents.

Also, I do not taken into account the competition effects. Aw et al.(2000) and Bernard and Jensen (1999) find that firms are very het-erogeneous even in narrowly defined industries. They exhibit largeand persistent differences in productivity and are more likely to

9 In Baldwin, Martin, and Ottaviano (2001), when trade costs fall below a critical val-ue, industries agglomerate and the economic growth rate rises, yet the gap in economicwelfare among countries becomes persistent. However, when trade costs fall further,growth rate no longer rises but the gap in economic welfare diminishes. In contrast,in Gao (2005), even after agglomeration emerges, further decreases in trade costs con-tinues to enhance the growth rate. FDI makes resources shift from the traditional sec-tor to the manufacturing production process in less industrialized countries, and itmakes more resources shift to the R&D process in more industrialized countries.


export when they becomemore productive. Melitz (2003) shows thatglobalization leads to economic growth enhancing average productiv-ity within an industry. Globalization induces the more productivefirms to enter the international market, forces the less productiveones to exit, and shifts resources from the latter to the former (self-selection effects).

The productivity of a firm in this model is determined by the num-ber of other firms located nearby. A firm in a country with a smallernumber of firms is less productive. When trade costs decrease, sucha firm is less protected and will soon exit. Consequently, firms ag-glomerate only in one country. However, there is nothing other thanthe number of firms within a country that determines a firm's

productivity in that country. Hence, there is no heterogeneity in pro-ductivity among firms in the same sector in one country. Therefore,once agglomeration emerges, further reduction in trade costs causesno more self-selection effects. To focus on the agglomeration thatleads the differences in productivity and the subsidy competition forthe agglomeration rent, I choose not to introduce the other possiblefactors of heterogeneity among firms.

If we introduce these channels more explicitly, the overall effect ofglobalization on growth is difficult to clearly determine, as it dependson the relative impacts of several channels all at once. However, thenegative effect of globalization on growth through the incentives forR&D subsidies.

Appendix A

A.1. The derivations of the growth rate, consumption, and profit per firm

The unit costs in producing a differentiated good in country i are (Pi)a(wi)1− a. Hence, when a differentiated good κ is produced in theamount of q(κ), the total costs are (Pi)a(wi)1−aq(κ). Applying the Shepard's Lemma to it yields demands for labor and a differentiated goodκ′ by a differentiated good firm κ located in country i:

1−að Þ Pi� �a

q κð Þ; i ¼ A;B; ðA1Þ

a Pi� �a

q κð ÞpDi κ ′ð Þ� �−�

Pi� 1−�

i ¼ A;B: ðA2Þ

A differentiated good firm κ faces the demand of a(Pi)aq(κ′)(pDi(κ))−�/(Pi)1−� by each firm and of (4) per consumer. Since in each countryall firms face the same factor prices and demand function, all choose the samemill price pi and production amount qi. Thus, from Eqs. (A1), (A2),and pi=(Pi)a/γ, the demands for labor, a differentiated in that country and that in the other country by a firm in country i are:

γ 1−að Þpiqi; i ¼ A;B; ðA1′Þ

γapiqipi� �−�

Pi� 1−�

; i ¼ A;B; ðA2′Þ

γapiqiTpj� �−�

Pi� 1−�

; i; j ¼ A;B; i≠j: ðA2″Þ

The shares of (1−a)γ and aγ of total revenue piqi are paid for labor and intermediate inputs, respectively, and the rest 1−γ is retained asprofits:

πi ¼ 1−γð Þpiqi; i ¼ A;B: ðA3Þ

From Eqs. (A2′), (A2″) and (4), the condition that a differentiated good's market is cleared is written as:

qi ¼ αEi þ γanipiqi� � pi

� �−�

Pi� 1−�

þ αEj þ γanjpjqj� �T1−� pi

� �−�

Pj� 1−�

; i; j ¼ A;B; i≠j:

The total revenue of the manufacturing sector in each country can be written as:

nipiqi ¼ αEi þ γanipiqi� �

Ωii þ αEj þ γanjpjqj� �

Ωij; i; j ¼ A;B; i≠j; ðA4Þ

whereΩii≡ni(pi/Pi)1−� andΩij≡ni(τpi/Pj)1− ε are the share of the expenditure by a household in country j for the differentiated goods producedin country i out of the household's total expenditure for differentiated goods (Ωii+Ωji=1). Solving (A4) for nipiqi (i=A,B) yields:

nipiqi ¼ αΩii−aγ ΩAAΩBB−ΩABΩBAð Þf gEi þΩijE

j

1−aγ ΩAA þΩBBð Þ− aγð Þ2 ΩABΩBA−ΩAAΩBBð Þ

" #; i; j ¼ A;B; i≠j: ðA5Þ


Inserting Eqs. (A5) into (A3) and (A1′), we can derive the profits per firm and the total labor force employed in the differentiated goodssector in country i as:

πi ¼ 1−γð Þαni

� � Ωii−aγ ΩAAΩBB−ΩABΩBAð Þf gEi þΩijEj


" #; ðA6Þ

liX ¼ 1−að Þγα Ωii−aγ ΩAAΩBB−ΩABΩBAð Þf gEi þΩijEj


" #; i; j ¼ A;B; i≠j: ðA7Þ

I consider the case where the manufacturing sector has been concentrating in country A: n=nA. Eq. (A6) is calculated as:

πA ¼ 1−γð Þαn

� �EA þ EB

1−aγ

!; ðA8Þ

πB ¼ 1−γð Þ αEA þ αaγ1−aγ

� �EA þ EB� ��

n−1τ 1−�ð Þτ−a �−1ð Þ þ 1−γð ÞαEBn−1τ �−1ð Þτ−a �−1Þ;ð ðA9Þ

and rearranging Eq. (8) yields:

gt ¼lAR&Dt

b

!: ðA10Þ

By aggregating the households' demand for traditional goods Eq. (5) and inserting Eq. (7) into it, we can derive the labor force devoted to theagricultural goods sector in each country as:

liY ¼ siY 1−αð Þ EA þ EB� �

; i ¼ A;B; ðA11Þ

where sYi denotes the market share of country A in the production of traditional goods. I assume that the preference for agricultural goods is

sufficiently large for the sector to operate in both countries, and thus wages are equal between the two countries. Thus, after I calculate g andEi by using (A11), I must check that sYi ∈(0,1). That is, the employment in the manufacturing sector is not so large as to exhaust the laborendowment in one country (lR&DA + lX

Ab1), and the employment in the agricultural sector is too large to be absorbed by one country (lYA+ lYB=

(1−α)(EA+EB)>1).The labor market clearing condition in each country is:

lAR&D þ lAX þ lAY ¼ 1; lBY ¼ 1: ðA12Þ

Under the assumption that wages are equalized, we can write the condition that g and Ei in equilibrium must satisfy by inserting Eqs. (A7),(A10) and (A11) into Eq. (A12) and summing them for i=A,B:

bgt þ1−að Þγα 1−aγ ΩAAΩBB−ΩABΩBAð Þf g

1−aγ ΩAA þΩBBð Þ− aγð Þ2 ΩABΩBA−ΩAAΩBBð Þ þ 1−αð Þ� �

EAt þ EBt� �

¼ 2; i; j ¼ A;B; i≠j:

Since Ωii+Ωji=1 holds, 1−aγ(ΩAAΩBB−ΩABΩBA) can be rewritten as (1+aγ)−aγ(ΩAA+ΩBB), and 1−aγ(ΩAA+ΩBB)−(aγ)2(ΩABΩBA−ΩAAΩBB) can be rewritten as (1−aγ){(1+aγ)−aγ(ΩAA+ΩBB)}. Then the condition can be written as:

bgt þ1−að Þγα1−aγ

þ 1−αð Þ� �

EAt þ EBt� �

¼ 2:

In the second term on the left side, 1−að Þγα1−aγ

h iEAt þ EBt� �

is the labor force devoted in the production of differentiated goods, and (1−α)(EtA+

EtB) is that of agricultural goods. This can be simplified as:

bgt þ1−aγ−α þ αγ

1−aγ

� �EAt þ EBt� �

¼ 2: ðA13Þ

As both 1−að Þγα1−aγ and (1−α) are positive, the sum of them 1−aγ−αþαγ

1−aγ

� �is positive. As the denominator 1−aγ is positive, the numerator

(1−aγ−α+αγ) is also positive.For R&D to be active in country A, Eq. (10) must be bind for that country: vA=b(1− sA)/nA. Using Eqs. (9) and (A8), this can be rewritten as

1−sAð Þbgt ¼1

1þ rt

� �1−γð Þα1−aγ

� �EAtþ1 þ EBtþ1

� �: ðA14Þ


From Eq. (6) we can see that consumption expenditures grow at a rate of (1+rt)/(1+ρ):

1EAt þ EBt

¼ 1þ rt1þ ρ

� �1

EAtþ1 þ EBtþ1

!: ðA15Þ

Solving Eqs. (A13), (A14) and (A15) yields interest rate, growth rate and consumption expenditures in equilibrium. The interest rate rt isequal to the subjective discount rate ρ, the growth rate is Eq. (11) and the total consumption expenditure is:

EA þ EB ¼ 2 1−aγð Þ 1þ ρð Þ 1−sAð Þ1−γð Þα þ 1−aγ−α þ αγð Þ 1þ ρð Þ 1−sAð Þ : ðA16Þ

As we have seen, (1−aγ−α+αγ)>0. Then, from Eq. (11), we can see that ∂g/∂sA>0. As the interest rate rt equals to the subjective dis-count rate ρ in equilibrium, from Eq. (6), the consumption expenditure in each country Ei as well as the total consumption expenditure(Eq. A16) is constant. From the facts that Ei is constant, wi=1, r=ρ and Ti accompanied by a constant rate of R&D subsidy si and the transferfrom the periphery to the core TR are also constant, and the intertemporal budget constraint (Eq. 2), we can derive Ei as:

Ei ¼ ρWit−1 þwi−Ti

: ðA17Þ

In country A, R&D activities take place and government subsidize them at a constant subsidy rate sA. To finance the R&D subsidy, the govern-ment taxes sAbg>0 on the households in that country. Then the net tax burden per capita in country A is TA=sAbg−TR. In contrast, in country B,there is no R&D subsidy and thus no tax accompanied by that. Then, TB=TR. As wage income wi=1 and taxation Ti are constant over time,households will keep financial assets Wi at a constant amount to even out the consumption expenditure Ei. I have assumed that initiallythere is no gap in the amount of financial assets between countries. Then the gap in Wi never emerges, and the gap in Ei comes only from thedifference in Ti:

EB−EA ¼ TA−TB ¼ sAbg−TR−TR ¼ sAbg−2TR: ðA18Þ

From Eqs. (11), (A16) and (A18), we can derive EA and EB as:

EA ¼ 1−aγð Þ 1þ ρð Þ 1−sAð Þ− 1−γð ÞαsA1−γð Þα þ 1−aγ−α þ αγð Þ 1þ ρð Þ 1−sAð Þ þ TR; ðA19Þ

EB ¼ 1−aγð Þ 1þ ρð Þ 1−sAð Þ þ 1−γð ÞαsA1−γð Þα þ 1−aγ−α þ αγð Þ 1þ ρð Þ 1−sAð Þ−TR: ðA20Þ

I let E(C,si,sj,TR) denote the consumption expenditure in the core country i (country A in this case). And I let E(P,sj,si,−TR) denote the con-sumption expenditure in the peripheral country j (country B in this case). (In sections 3 and 4, TR=0 and I express these function as E(C,si,sj)and E(P,sj,si).) By substituting EA and EB in Eq. (A8) using E(C,sA,sB) and E(P,sB,sA), we can express the profits per differentiated good firm inthe core country A as a function of subsidy rates. I let π(C,sA,sB,τ) express it. Similarly, by substituting EA and EB in (Eq. A9) using E(C,sA,sB)and E(P,sB,sA), we can express the profit that a firm would earn if it locate in country B alone as a function of subsidy rates and trade costs. Ilet π(P,sB,sA,τ) express it.

I must check whether sYi ∈(0,1) holds. From Eqs. (A11) and (A16), we can derive the condition under which sYi ∈(0,1) holds as:

2 1−αð Þ 1−aγð Þ 1þ ρð Þ 1−sAð Þ1−γð Þα þ 1−aγ−α þ αγð Þ 1þ ρð Þ 1−sAð Þ > 1: ðA21Þ

Finally, I must consider the condition under which R&D is active only in country A. In this case, Eq. (10) is bind for country A, while it is not forcountry B. By dividing vA/b(1−sA)(nA+λnB) on the left-hand side of Eq. (10) by vB/b(1− sB)(nB+λnA) and replacing vi with Eq. (9), we obtainthe function h(C,sA,sB,λ,τ) in Eq. (12). Therefore, h(C,sA,sB,λ,τ) means the relative the advantage in R&D in the core country A to that inthe peripheral country B. If h(C,sA,sB,λ,τ) is larger than unity as in Eq. (12) and if Eq. (10) is bind for country A, Eq. (10) is not binding forcountry B.

A.2. Derivations of Eqs. (14) and (15)

Suppose that the manufacturing sector has agglomerated in country i and the subsidy rates in the current period satisfy sj≤ϕ(si,λ,τ). Thenhouseholds expect that the manufacturing sector will continue to agglomerate in country i and grow at the rate g(si). Consumption expendituresin the current period are E(C,si,sj) in country i and E(P,sj,si) in country j. Then, from Eqs. (1), (3), (4), (5), (7), pi=(Pi)a/γ, nti=nt and nj=0,the utilities in the current period in country i (the core) and in country j (the periphery) are lnE(C,si,sj)+((1−γ)/γ)αlnnt and lnE(P,sj,si)−αlnτ+((1−γ)/γ)αlnnt, respectively.

In contrast, when subsidy rates “unexpectedly” change in the current period to satisfy sj>ϕ(si,λ,τ), then R&D shifts to country j. The growthrate brought about by such a shift is λg(sj). Households expect that themanufacturing sectorwill continue to agglomerate in country j and grow atthe rate g(sj) From the next period onward. Household consumption expenditures are E(P,si,sj) in country i and E(C,sj,si) in country j.Then, the utilities in the current period in country i (the core) and in country j (the periphery) are lnE(P,si,sj)+((1−γ)/γ)(α/(1−a))lnnt andlnE(C,sj,si)−αlnτ+((1−γ)/γ)(α/(1−a))lnnt, respectively. The gap in the quantity of financial assets never emerges.


A government knows that its choice of the sequence of the subsidy rates determines household's instantaneous utility in each period asabove, and affects household's intertemporal utility, the discounted sum of the instantaneous utilities. Therefore, the optimization problem ofthe government in each country can be constructed as the following recursive Bellman functional formation:

ui C;ntð Þ ¼ MAXsi C;ntð Þ

"lnE C; si C;ntð Þ; sj P;ntð Þ� �

þ 1−γγ

� �α

1−a

� �lnnt þ

11þ ρ

� �ui C;ntþ1�

;

lnE P; si C;ntð Þ; sj P;ntð Þ� �

þ 1−γγ

� �α

1−a

� �lnnt þ

11þ ρ

� �ui P;ntþ1� #

;

ðA22Þ

ui P;ntð Þ ¼ MAXsi P; ntð Þ

"lnE C; si P;ntð Þ; sj C;ntð Þ� �

−αlnτ þ 1−γγ

� �α

1−a

� �lnnt þ

11þ ρ

� �ui C;ntþ1�

;

lnE P; si P;ntð Þ; sj C;ntð Þ� �

−αlnτ þ 1−γγ

� �α

1−a

� �lnnt þ

11þ ρ

� �ui P;ntþ1� #

;

ðA23Þ

where ui(C,nt) and ui(P,nt) are the value functions that give the maximum intertemporal utility starting from the initial states in which country iis the core (denoted by state C), and in which country i is the periphery (denoted by state P), respectively. Furthermore, si(C,nt) and si(P,nt) arecountry i's corresponding R&D subsidy rate decisions, given country j's decisions sj(C,nt) and sj(P,nt).

When country i is the core, with si(C,nt) high enough to satisfy sj(P,nt)≤ϕ(si(C,nt),λ,τ), then country i can continue hosting themanufacturing sector and thus ui(C,nt) is equal to the first component on the right side of Eq. (A22) in which nt+1=g(si)nt. With si(C,nt)so low as in sj(P,nt)>ϕ(si(C,nt),λ,τ), all of the R&D activities shift to the other country, and ui(C,nt) is equal to the second component inEq. (A22) in which nt+1=λg(sj)nt.

In contrast, when country i is the periphery and si(P,nt) is so high as to satisfy si(P,nt)>ϕ(sj(C,nt),λ,τ), then country i can attract R&D activ-ities and Ui(P) is equal to the first component on the right side of (A23) in which nt+1=λg(si)nt. However, if si(P,nt) is lower, then ui(P,nt) isequal to the second component in (A23) in which nt+1=g(sj)nt.

The maximized intertemporal utilities ui(C,nt) and ui(P,nt) depend on the number of differentiated goods firms (nt) and whether or notcountry i hosts them (C or P). The value function can be expressed as the sum of these two elements' functions. I guess that the value functionstake the form of ui(C,nt)=Ui(C)+μlnnt, and ui(P,nt)=Ui(P)+μlnnt and verify μ. The partial derivative of the value function with respect to statevariable nt is equal to the partial derivative of the right side in which nt+1 is substituted by using nt+1=gnt (in the case that there is norelocation of manufacturing from t to t+1) or nt+1=λgnt (in the case that there is a relocation of manufacturing from t to t+1)(Benveniste and Scheinkman, 1979). By using this fact, we can verify μ ¼ 1þρ

ρ

� �1−γγ

� �α. Using ui C;ntð Þ ¼ Ui Cð Þ þ 1þρ

ρ

� �1−γγ

� �αlnnt and

ui P; ntð Þ ¼ Ui Pð Þ þ 1þρρ

� �1−γγ

� �αlnnt , we can rewrite Eqs. (A22) and (A23) as Eqs. (14) and (15), respectively.

Appendix B

B.1. Proof of Proposition 1

(i): With Eqs. (A8) and (A9), Eqs. (12) and (13) can be rewritten as:

h C;0;0;λ; τð Þ ¼ π C;0;0; τð Þπ P;0;0; τð Þ� �

1λ

� �¼ E C;0;0ð Þ þ E P;0;0ð Þ

τ 1það Þ 1−�ð ÞE C;0;0ð Þ þ 1−aγð Þτ −1það Þ 1−�ð Þ þ aγτ 1það Þ 1−�ð Þ �E P;0;0ð Þ

1λ

� �:

and

h P;0;0;λ; τð Þ ¼ π C;0;0; τð Þπ P;0;0; τð Þ� �

λ ¼ E C;0;0ð Þ þ E P;0;0ð Þτ 1það Þ 1−�ð ÞE C;0;0ð Þ þ 1−aγð Þτ −1það Þ 1−�ð Þ þ aγτ 1það Þ 1−�ð Þ �

E P;0;0ð Þλ:

The lower λ is, the more likely it is that h(C,0,0,λ,τ)≥1 holds. Then, the manufacturing can agglomerate in one country. In contrast,h(P,0,0,λ,τ)≥1 is less likely hold. That is, once the manufacturing sector agglomerates in one country, it never relocates. It continues to agglom-erate in that country.

(ii) and (iii): In h(C,0,0,λ,τ) and h(P, 0,0,λ,τ), the part (π(C,0,0,τ)/π(P, 0,0,τ)) is common. The derivative of the denominator with τ is:

1−�ð Þτ 1það Þ 1−�ð Þ−1 1þ að Þ E C;0;0ð Þ þ aγE P;0;0ð Þð Þ þ −1þ að Þ 1−aγð ÞE P;0;0ð Þτ−2 1−�ð Þh i:

I let τ⁎ denote τ which makes it zero:

τ⁎ ¼ 1þ a1−a

� �E C;0;0ð Þ þ aγE P;0;0ð Þ

1−aγð ÞE P;0;0ð Þ� �

:

When τ=1 (no trade costs), π(C,0,0,τ)/π(P,0,0,τ)=1. For τ∈ [1,τ⁎], π(C, 0,0,τ)/π(P,0,0,τ) is increasing function and thus larger than unity.With τ higher than τ⁎, π(C,0,0,τ)/π(P,0,0,τ) is decreasing function yet with τ that is a bit higher than τ⁎ it is still higher than unity. Therefore,


when τ is low, π(C,0,0,τ)/π(P,0,0,τ) is necessarily larger than unity. Hence, h(C,0,0,λ,τ)≥1 necessarily holds, and the manufacturing sector canagglomerate in one country. When τ is close to τ⁎ and λ is close to unity, h(P,0,0,λ,τ)≥1 as well as h(C,0,0,λ,τ)≥1 holds. Hence, themanufacturing sector can potentially agglomerate in either of the two countries.

Q.E.D.


When country j's strategy is sj ¼ s;0ð Þ and country i is the core, country i never chooses anything other than si Cð Þ ¼ s if the first component islarger than the second component on the right side of Eq. (14) with si Cð Þ ¼ s and sj(P)=0:

lnE C; s;0ð Þ þ 1−γγ

� �α

1−a

� � 1ρ

� �lng sð Þ þ 1

1þ ρ

� �Ui Cð Þ

≥ lnE P; s;0ð Þ þ 1−γγ

� �α

1−a

� � 1ρ

� �lnλg 0ð Þ þ 1

1þ ρ

� �Ui Pð Þ:

ðB1Þ

If (B1) is satisfied, Ui(C) is equal to the first component of Eq. (14) (the left side of (B1)), and calculated as:

Ui Cð Þ ¼ 1þ ρρ

� �lnE C; s;0ð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �: ðB2Þ

When it is the periphery, country i has no incentive to choose anything other than si(P)=0 if the second component is larger than the firstcomponent on the right side of Eq. (15) with sj Cð Þ ¼ s and si Pð Þ ¼ ϕ s;λ; τð Þ:

lnE C;ϕ s;λ; τð Þ; sð Þ−αlnτ þ 1−γγ

� �α

1−a

� � 1ρ

� �lnλg ϕ s;λ; τð Þð Þ þ 1

1þ ρ

� �Ui Cð Þ

≤ lnE P;0; sð Þ−αlnτ þ 1−γγ

� �α

1−a

� � 1ρ


1þ ρ

� �Ui Pð Þ:

ðB3Þ

If Eq. (B3) is satisfied, Ui(P) is equal to the second component of Eq. (15) (the right side of Eq. (B3)) and calculated as:

Ui Pð Þ ¼ 1þ ρρ

� �lnE P;0; sð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �: ðB4Þ

By substituting value functions Ui(C) and Ui(P) using Eqs. (B2) and (B4), I can express the conditions (B1) and (B3) as:

− α 1−γð Þγρ 1−að Þ� �

lnλþ αρ

� �lnτ þ α 1−γð Þ þ γρ 1−að Þ

γρ 1−að Þ� �

lnα 1−γð Þ þ 1−aγ−α þ αγð Þ 1þ ρð Þ

α 1−γð Þ þ 1−sð Þ 1−aγ−α þ αγð Þ 1þ ρð Þ� �

þln −sα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þð Þ− 1ρ

� �ln

sα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þ−sα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þ� �

−ln 1−aγð Þ 1þ ρð Þ ≥ 0;

ðB5Þ

and

− α 1−γð Þγρ 1−að Þ� �

lnλ− αρ

� �lnτ þ α 1−γð Þ þ γρ 1−að Þ

γρ 1−að Þ� �

lnα 1−γð Þ þ 1−ϕ s;λ; τð Þð Þ 1−aγ−α þ αγð Þ 1þ ρð Þ

α 1−γð Þ þ 1−sð Þ 1−aγ−α þ αγð Þ 1þ ρð Þ� �

þlnsα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þ

−ϕ s;λ; τð Þα 1−γð Þ þ 1−ϕ s;λ; τð Þð Þ 1−aγð Þ 1þ ρð Þ� �

þ 1ρ

� �ln

sα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þ−sα 1−γð Þ þ 1−sð Þ 1−aγð Þ 1þ ρð Þ� �

≥0:ðB6Þ

The lower λ is, the more likely both Eq. (B5) and (B6) hold. The higher τ is, the more likely Eq. (B5) holds yet the less likely Eq. (B6) holds.That is, when both Eqs. (B5) and (B6) hold, τ is in a middle size. Q.E.D.

B.3. Derivations of �s and ~s

The minimum of the R&D subsidy rates with which the core can discourage the periphery from being the core, �s, together with Ui(C) andUi(P), can be obtained by simultaneously solving the followings:

lnE C;ϕ �s;λ; τð Þ; �sð Þ−αlnτ þ 1−γγ

� �α

1−a

� � 1ρ

� �lnλg ϕ �s;λ; τð Þð Þ þ 1

1þ ρ

� �Ui Cð Þ

¼ lnE P;ϕ �s;λ; τð Þ;�sð Þ−αlnτ þ 1−γγ

� �α

1−a

� � 1ρ

� �lng �sð Þ þ 1

1þ ρ

� �Ui Pð Þ;

ðB7Þ

Ui Cð Þ ¼ 1þ ρρ

� �lnE C; �s;ϕ �s;λ; τð Þð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng �sð Þ

� �; ðB8Þ


and

Ui Pð Þ ¼ 1þ ρρ

� �lnE P;ϕ �s;λ; τð Þ; �sð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �: ðB9Þ

The maximum of the R&D subsidy rates with which the periphery can discourage the core from imposing its manufacturing sector ~s satisfies:

lnE C; s;~sð Þ þ 1−γγ

� �α

1−a

� � 1ρ


1þ ρ

� �Ui Cð Þ ¼ lnE P;ϕ−1 ~s;λ; τð Þ;~s

� �þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lnλg ~sð Þ þ 1

1þ ρ

� �Ui Pð Þ; ðB10Þ

where Ui(C) and Ui(P) are equal to Eqs. (B2) and (B4), respectively.


For both countries not to have incentives to deviate, the transfer from the periphery to the core TR must satisfy the following:

1þ ρρ

� �lnE C; s⁎;0; TRð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng s⁎ð Þ

� �≥ lnE C; s;0; TRð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �þ 1

1þ ρ

� �Ui Cð Þ; ðB11Þ

1þ ρρ

� �lnE P;0; s⁎;−TRð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng s⁎ð Þ−αlnτ

� �≥ lnE P;0; s⁎;0ð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng s⁎ð Þ−αlnτ

� �þ 1

1þ ρ

� �Uj Pð Þ:

ðB12Þ

When trade costs are in middle or low, Ui(C) and Uj(P) on the Nash equilibrium are Eqs. (B2) and (B4), respectively. Then, conditions (B11)and (B12) become:

1þ ρρ


γ

� �α

1−a

� � 1ρ


� �≥ lnE C; s;0; TRð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �

þ 1ρ

� �lnE C; s;0;0ð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �;

ðB13Þ

1þ ρρ

� �lnE P;0; s⁎;−TRð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �≥ lnE P;0; s⁎;0ð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �

þ 1ρ

� �lnE P;0; s;0ð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �:

ðB14Þ

The term−αlnτ in both sides in Eq. (B14) is canceled out. As long as τ is in middle or low, the conditions that TR should satisfy are the sameas Eqs. (B13) and (B14), and they are independent from τ.

When trade costs are higher, Ui(C) and Uj(P) on the Nash equilibrium are Eqs. (B8) and (B9), respectively. Then, conditions (B11) and (B12)in this case are:

1þ ρρ


γ

� �α

1−a

� � 1ρ


� �≥ lnE C; s;0; TRð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ

� �lng sð Þ

� �

þ 1ρ

� �lnE C;�s;ϕ �s;λ; τð Þ;0ð Þ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �;

ðB15Þ

1þ ρρ

� �lnE P;0; s⁎;−TRð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �≥ lnE P;0; s⁎;0ð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �

þ 1ρ

� �lnE P;ϕ �s;λ; τð Þ;�s;0ð Þ−αlnτ þ 1−γ

γ

� �α

1−a

� � 1ρ


� �:

ðB16Þ

The left sides of Eqs. (B13) and (B15) increase as the transfer that the core receives TR increases. The right side of Eq. (B15) is smaller thanthat of Eq. (B13). Therefore, TRmin under which Eq. (B15) binds is smaller than TRmin under which Eq. (B15) binds. The left sides of Eqs. (B14) and(B16) decrease as the transfer that the periphery gives to the core TR increases. The right side of Eq. (B16) is larger than that of Eq. (B14).Therefore, TRmax under which Eq. (B16) binds is smaller than TRmax under which Eq. (B14) binds. Q.E.D.


Appendix C. Setting parameter values for numerical examplesin figures

To set plausible parameter values α, a, and γ, I abstract an industryor group of industries which correspond to the manufacturing sectorin the model in this paper from the input–output tables released byOECD in the year 2000. These OECD tables cover 48 industrial sectorsbased on the international standard industrial classification (ISIC),Revision 3. Industries which correspond to manufacturing in ISICRev. 3 are grouped into the manufacturing block; agriculture, hunt-ing, forestry and fishing, and mining and quarrying are grouped intothe agricultural block; and the remaining industries are groupedinto the service block. This service block therefore includes the con-struction and electricity, gas, and water supply industries.

Significant interdependence can be observed among the indus-tries within the manufacturing block. Many industries in themanufacturing block spend more than 40% of the value of their re-spective outputs to purchase intermediate inputs from other indus-tries in the same block. And the manufacturing sector, as a block,spends nearly 40% of the value of its total output to purchase itsown outputs as intermediate inputs. Specifically, the ratio of themanufacturing sector's payment for intermediate inputs from itsown block to the value of its total output is 34.7% in the US, 40.5%in Japan, 34.0% in the UK, 40.8% in France, 40.0% in Germany, 40.6%in Canada, and 39.7% in Italy.

Note, however, that some industries in the manufacturing block,namely, food products, beverages, and tobacco, purchase fewer oftheir intermediate inputs from their own block than many of theother industries in the block. Though grouped in the manufacturingblock, they procure their intermediate inputs from the agriculturalblock. Therefore, I remove these industries from the manufacturingblock and add them to the agricultural block.10

As a result, the ratio of the payment for the intermediate inputs ofthe new manufacturing block from its own block to the value of thetotal output of the new manufacturing block increases. Specifically,the value increases to 36.1% in the US, 42.6% in Japan, 35.2% in theUK, 43.3% in France, 41.8% in Germany, 42.0% in Canada, and 40.7%in Italy.

The ratio of the value of intermediates from the agricultural blockto the value of the total output of the same block also increases, yetonly to about 20%, a ratio much smaller than that in the manufactur-ing block. And the manufacturing block and agricultural block be-come more independent from one another. The service blockprovides intermediate inputs to the manufacturing block, agriculturalblock, and service block itself. The ratio of the payment for intermedi-ate inputs from the service block to the value of the total output in themanufacturing block is about 20%, and that in the agricultural block isabout the same. The ratio of the payment for intermediate inputsfrom the service block itself to the value of total output in the serviceblock is nearly 30%. The service block, however, does not have signif-icant demand for intermediate inputs from the manufacturing andagricultural blocks. Moreover, few of the service sector products canbe traded. Thus, the industries in the service block do not concentratethemselves in a self-enforced manner.

Hence, I consider this manufacturing block (manufacturing in ISICRev. 3 minus food products, beverages, and tobacco industries) asthe manufacturing sector in this theoretical model. In this theoreticalmodel, the total revenue of the manufacturing sector is disbursed forlabor, intermediate inputs, and stockholders in shares of (1−a)γ, aγ,and 1−γ, respectively. Thus, I set aγ=0.4. Following Bernard et al.(2003) and Ghironi and Melitz (2005), I set the elasticity of demand

10 Other industries besides food products, for example, petroleum products, also haveweak links to the other industries in the manufacturing block. I choose, however, tokeep these industries in the manufacturing block, as only very small impacts areobtained by removing them.

for differentiated goods to =3.8 (γ=0.74). As I have set aγ=0.4,a=0.54. Household's expenditure for products of the manufacturingblock accounts for 15% of the total consumption expenditure byhouseholds (14.3% in the US, 11.5% in Japan, 20.0% in the UK, 16.7%in France, 17.9% in Germany, 14.3 in Canada, and 19.1 in Italy).Thus, I set α=0.16.

The length of time it takes the initial periphery to become the newcore corresponds to one period in this model. I have assumed thatknowledge capital depreciates at the rate of 100% after one periodof use. The length of time that it takes a firm to succeed at R&D isthe same as the length of time for which a firm can operate and pro-vide a good it has invented. Therefore, the distribution of differentiat-ed goods firms between the two countries undergoes drastic changes.(I have discussed on this point in Conclusion.)

In the real world, however, a good is provided for a longer time.Moreover, a firm's exit is caused by obsolescence or patent expirationof its product. In this model, I have assumed CES types of utility andproduction functions, where all the goods are equally preferred. Inthe real world, newly invented goods are preferred and, thus, the pre-viously invented ones become obsolete. I assume that a differentiatedgood exits within 20 years, owing to either obsolescence or expiry ofthe product's patent. Therefore, the distribution of differentiatedgoods firms changes continuously. If R&D keeps being conductedonly in the initial periphery, it takes 20 years for the initial peripheryto host all the differentiated goods firms in the world within its bor-der and become the new and complete core country. However, inless than 20 years, the initial periphery leapfrogs the initial core inthe number of differentiated goods firms, which I consider as a shiftin state. Therefore, this length of time corresponds to one period inthis model, which is about 10 years, half of the 20 years period duringwhich all the present differentiated goods exit the market.

Hence, if I set ρ=1, the annual discount factor ρannual is obtainedby solving 1/(1+ρannual)10=1/(1+1). It equals 0.072 and is almostequal to that employed by Mehra and Prescott (1985) after observingthe US stock market.

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International R&D subsidy competition, industrial agglomeration and growth

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