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1 DISCUSSION PAPER SERIES No AGGLOMERATION AND REGIONAL GROWTH Richard Baldwi ad Philippe Marti INTERNATIONAL TRADE ABCD Available olie at:

2 ISSN AGGLOMERATION AND REGIONAL GROWTH Richard Baldwi, Graduate Istitute of Iteratioal Studies, Geeva ad CEPR Philippe Marti, Uiversité de Paris1, CERAS-ENPC ad CEPR Discussio Paper No July 003 Cetre for Ecoomic Policy Research Goswell Rd, Lodo EC1V 7RR, U Tel: (44 0) , Fax: (44 0) cepr@cepr.org, Website: This Discussio Paper is issued uder the auspices of the Cetre s research programme i INTERNATIONAL TRADE. Ay opiios expressed here are those of the author(s) ad ot those of the Cetre for Ecoomic Policy Research. Research dissemiated by CEPR may iclude views o policy, but the Cetre itself takes o istitutioal policy positios. The Cetre for Ecoomic Policy Research was established i 1983 as a private educatioal charity, to promote idepedet aalysis ad public discussio of ope ecoomies ad the relatios amog them. It is pluralist ad o-partisa, brigig ecoomic research to bear o the aalysis of medium- ad log-ru policy questios. Istitutioal (core) fiace for the Cetre has bee provided through major grats from the Ecoomic ad Social Research Coucil, uder which a ESRC Resource Cetre operates withi CEPR; the Esmée Fairbair Charitable Trust; ad the Bak of Eglad. These orgaizatios do ot give prior review to the Cetre s publicatios, or do they ecessarily edorse the views expressed therei. These Discussio Papers ofte represet prelimiary or icomplete work, circulated to ecourage discussio ad commet. Citatio ad use of such a paper should take accout of its provisioal character. Copyright: Richard Baldwi ad Philippe Marti

3 CEPR Discussio Paper No July 003 ABSTRACT Agglomeratio ad Regioal Growth* We review the theoretical liks betwee growth ad agglomeratio. Growth, i the form of iovatio, ca be at the origi of catastrophic spatial agglomeratio i a cumulative process à la Myrdal. Oe of the surprisig features of the rugma (1991) model was that the itroductio of partial labour mobility i a stadard ew trade model with trade costs could lead to catastrophic agglomeratio. The growth aalog to this result is that the itroductio of edogeous growth i the same type of ew trade model ca lead to the same result. A differece with the labour mobility versio is that the results are easier to derive from the aalytical poit of view i the edogeous growth versio. We show that the relatio betwee growth ad agglomeratio depeds crucially o capital mobility betwee regios. The absece of capital mobility is at the heart of the possibility of spatial agglomeratio with catastrophe. I additio, growth alters the process of locatio eve without catastrophe. I particular, ad cotrary to the fudametally static models of the New Ecoomic Geography, spatial cocetratio of ecoomic activities may be cosistet with a process of delocatio of firms towards poor regios. Fially, the presece of localized techology spillovers implies that spatial agglomeratio is coducive to growth. JEL Classificatio: O40 ad R10 eywords: agglomeratio, capital mobility, geography ad growth Richard Baldwi Graduate Istitute of Iteratioal Studies 11A Aveue de la Paix CH-10 Geève SWITZERLAND Tel: (41 ) Fax: (41 ) baldwi@hei.uige.ch For further Discussio Papers by this author see: Philippe Marti CERAS-ENPC ENS 48 Boulevard Jourda Paris FRANCE Tel: (33 1) Fax: (33 1) marti-p@epc.fr For further Discussio Papers by this author see:

4 *This is the draft of a chapter for the Hadbook of Regioal ad Urba Ecoomics: Cities ad Geography edited by Vero Hederso ad Jacques Thisse. We are grateful to our discussat Jacques Olivier for helpful commets ad especially to Jacques Thisse for detailed suggestios. This Paper is produced as part of a CEPR Research Network o The Ecoomic Geography of Europe: Measuremet, Testig ad Policy Simulatios, fuded by the Europea Commissio uder the Research Traiig Network Programme (Cotract No: HPRN-CT ). Submitted 06 Jue 003

5 1. Itroductio: why should we care about growth ad geography?. The basic framework of growth ad agglomeratio 3. The case without localized spillovers: growth matters for geography 3.1. The growth equilibrium Edogeous growth ad the optimal savigs/ivestmet relatio The role of capital mobility 3.. Perfect capital mobility: the locatio equilibrium Stability of the locatio equilibrium 3.. Does capital flow from the rich to the poor? 3.3. No capital mobility: ew growth ad ew geography Stability of the symmetric equilibrium 3.3. The core-periphery equilibrium 3.4. Cocludig remarks 4. The case with localized spillovers: geography matters for growth (ad vice versa) 4.1. Necessary extesios of the basic model 4.. The case of perfect kowledge capital mobility 4..1 Spatial equity ad efficiecy 4.. Welfare implicatios 4.3. The case without capital mobility: the possibility of a growth take-off ad agglomeratio The log-ru equilibria ad their stability 4.3. Possibility of catastrophic agglomeratio Geography affects growth Ca the Periphery gai from agglomeratio? 4.4. The geography of goods ad ideas: stabilizig ad destabilizig itegratio 5. Other cotributios 6. Cocludig remarks Globalizatio ad the ewly idustrialized coutries 4.4. The learig-liked circular causality

6 1. INTRODUCTION Spatial agglomeratio of ecoomic activities o the oe had ad ecoomic growth o the other had are processes difficult to separate. Ideed, the emergece ad domiace of spatial cocetratio of ecoomic activities is oe of the facts that uzets associated with moder ecoomic growth. This strog positive correlatio betwee growth ad geographic agglomeratio of ecoomic activities has bee documeted by ecoomic historias (Hoheberg ad Lees, 1985 for example), i particular i relatio to the idustrial revolutio i Europe durig the ieteeth cetury. I this case, as the growth rate i Europe as a whole sharply icreased, agglomeratio materialized itself i a icrease of the urbaizatio rate but also i the formatio of idustrial clusters i the core of Europe that have bee by ad large sustaied util ow. The role of cities i ecoomic growth ad techological progress has bee emphasized by urba ecoomists (Hederso, 1988, Fujita ad Thisse, 00), developmet ecoomists (Williamso, 1988) as well as by ecoomists of growth (Lucas, 1988). At the other had of the spectrum, as emphasized by Baldwi, Marti ad Ottaviao (001), the growth takeoff of Europe took place aroud the same time (ed of eighteeth cetury) as the sharp divergece betwee what is ow called the North ad the South: growth sharply accelerated (for the first time i huma ecoomic history) at the same time as a dramatic ad sudde process of agglomeratio took place at the world level. Hece, as put by Fujita ad Thisse (00), agglomeratio ca be thought as the territorial couterpart of ecoomic growth. Less dramatically ad closer to us, Quah s results (1996) suggest also a positive relatio betwee growth ad agglomeratio. He fids that amog the Cohesio group of coutries (Greece, Spai, Portugal ad Irelad, though there are o Irish regioal data), the two coutries that have achieved a high rate of growth ad coverged i per capita icome terms towards the rest of Europe (Spai ad Portugal) have also experieced the most marked regioal divergece, This is cosistet with the results of De la Fuete ad Vives (1995), for istace, buildig o the work of Esteba (1994) who suggest that coutries have coverged i Europe but that this process of covergece betwee coutries took place at the same time as regios iside coutries either failed to coverge or eve diverged. There are however few direct empirical tests of the relatio betwee agglomeratio ad growth. Ciccoe (00) aalyses the effects of employmet desity o average labor productivity for 5 Europea coutries at the Nuts 3 regioal level. He fids that a icrease i agglomeratio has a positive effect o the growth of regios. A idirect test of the relatioship is performed i the literature o localized techology spillovers. The presece of localized spillovers has bee well documeted i the empirical literature. Studies by Jacobs (1969) ad more recetly by Jaffe et al. (1993), Coe ad Helpma (1995), Coe et al. (1997), Ciccoe ad Hall (1996) provide strog evidece that techology spillovers are either global or etirely localized. The diffusio of kowledge across regios ad coutries does exist but dimiishes strogly with physical distace which cofirms the role that social iteractios betwee idividuals, depedet o spatial proximity, have i such diffusio. A recet study by eller (00) shows that eve though techology spillovers have become more global with time, techology is to a substatial degree local, ot global, as the beefits from spillovers are decliig with distace. The fact that techology spillovers are localized should i theory lead to a positive lik betwee growth ad spatial agglomeratio of ecoomic activities as beig close to iovatio clusters has a positive effect o productivity. Hece, these empirical results 3

7 poit to the iterest of studyig growth ad the spatial distributio of ecoomic activities i a itegrated framework. From a theoretical poit of view, the iterest should also be clear. There is a strog similarity betwee models of edogeous growth ad models of the ew ecoomic geography (NEG). They ask questios that are related: oe of the objectives of the first field is to aalyze how ew ecoomic activities emerge through techological iovatio; the secod field aalyzes how these ecoomic activities choose to locate ad why they are so spatially cocetrated. Hece, the process of creatio of ew firms/ecoomic activities ad the process of locatio should be thought as joit processes. From a methodological poit of view, the two fields are quite close as they both assume (i some versios) similar idustrial structures amely, models of moopolistic competitio which reflects the role of ecoomies of scale i both fields. I this chapter, we will attempt to clarify some of the theoretical liks betwee growth ad agglomeratio. Growth, i the form of iovatio, ca be at the origi of catastrophic spatial agglomeratio i a cumulative process à la Myrdal. Oe of the surprisig features of the rugma (1991) model, was that the itroductio of partial labor mobility i a stadard ew trade model with trade costs could lead to catastrophic agglomeratio. The growth aalog to this result is that the itroductio of edogeous growth i the same type of ew trade model ca lead to the same result. A differece with the labour mobility versio is that the results are easier to derive from the aalytical poit of view i the edogeous growth versio. I additio, growth alters the process of locatio eve without catastrophe. I particular, ad cotrary to the fudametally static models of the NEG, spatial cocetratio of ecoomic activities may be cosistet with a process of delocatio of firms towards poor regios. I commo with the static models (see the chapter by Ottaviao ad Thisse i this volume), the Home Market Effect plays here a crucial role to explai agglomeratio. The relatio betwee growth ad agglomeratio depeds crucially o capital mobility. Without capital mobility betwee regios, the icetive for capital accumulatio ad therefore growth itself is at the heart of the possibility of spatial agglomeratio with catastrophe. I the absece of capital mobility, some results are i fact familiar to the NEG (Fujita, rugma ad Veables, 1999): a gradual lowerig of trade costs betwee two idetical regios first has o effect o ecoomic geography but at some critical level iduce catastrophic agglomeratio. I the model preseted i this chapter, i the absece of migratio, catastrophic agglomeratio meas that agets i the south have o more private icetive to accumulate capital ad iovate. The circular causality which gives rise to the possibility of a core-periphery structure is depicted below ad as usual i ecoomic geography models is characterized by both productio ad demad shiftig which reiforce each other. The productio shiftig takes the form of capital accumulatio i oe regio (ad de-accumulatio i the other) ad the demad shiftig takes the form of icreased permaet icome due to ivestmet i oe regio (ad a decrease i permaet icome i the other regio). 4

8 North accumulates more capital Norther firm profits ad retur to capital rises Norther permaet icome icreases Norther market size icreases Figure 1: Demad-liked circular causality Capital mobility elimiates the possibility of catastrophic agglomeratio because i this case productio shiftig does ot iduce demad shiftig as profits are repatriated. It is therefore stabilizig i this sese. This is i sharp cotrast with labor mobility which we kow to be destabilizig. However, capital mobility also makes the iitial distributio of capital betwee the two regios a permaet pheomeo so that both the symmetric ad the core-periphery equilibria are always stable. I a secod sectio of this chapter, we will cocetrate o the opposite causality ruig from spatial cocetratio to growth. For this, we will itroduce localized techology spillovers which will imply that the spatial distributio of firms will have a impact o the cost of iovatio ad therefore the growth rate. This chapter uses modified versios of Baldwi (1999), Baldwi, Marti ad Ottaviao (000) ad Marti ad Ottaviao (1999). The first two papers aalyze models of growth ad agglomeratio without capital mobility. I cotrast to the first paper which uses a exogeous growth model, this chapter aalyses edogeous growth. I cotrast to the secod paper, we restrict our attetio to the case of global techology spillovers. The last paper presets a model of growth ad agglomeratio with perfect capital mobility. Baldwi et al. (003) also treat some commo themes i their chapters 6 ad 7.. THE BASIC FRAMEWOR OF GROWTH AND AGGLOMERATION May of the most popular ecoomic geography models focus o labor, examples beig rugma (1991), rugma ad Veables (1995), Ottaviao, Tabuchi ad Thisse (00) ad Puga (1999). These are usuited to the study of growth. The key to all sustaied growth is the accumulatio of huma capital, physical capital ad/or kowledge capital with the accumulatio of kowledge capital, i.e. techological progress havig a privileged positio. We thus eed a model i which capital exists ad its stock is edogeous. 5

9 To preset the basic elemets of this literature, we orgaize the discussio with the help of a workhorse model. As Baldwi et al (003) show, itroducig capital ito a geography model is relatively simple. The simplest way is accomplished by the footloose capital model (FC model) due to Marti ad Rogers (1995). The FC model, however, takes the capital stock as give. Gettig to a growth model requires us to add i a capital-producig sector. Specifically we deote capital by ad labor by L. The capital-producig sector is referred to as the sector I (for iovatio ad ivestmet, see below) ad this comes o top of the two usual sectors, maufactures M ad traditioal-goods T. The regios (two of them) are symmetric i terms of prefereces, techology ad trade costs. The usual Dixit-Stiglitz M-sector (maufactures) cosists of differetiated goods. Aother differece is that the fixed cost is i terms of. Each variety requires oe uit of capital which ca be iterpreted as a idea, a ew techology, a patet, machiery, etc.. Productio also etails a variable cost (a M uits of labor per uit of output). Its cost fuctio, therefore, is π +w a M x i, where π is 's retal rate, w is the wage rate, ad x i is total output of a typical firm. Traditioal goods, which are assumed to be homogeous, are produced by the T-sector uder coditios of perfect competitio ad costat returs. By choice of uits, oe uit of T is made with oe uit of L. The structure of the basic growth ad agglomeratio model is i figure. Regioal labor stocks are fixed ad immobile, so that we elimiate oe possible source of agglomeratio. Each regio's is produced by its I-sector. I is a memoic for iovatio whe iterpretig as kowledge capital, for istructio whe iterpretig as huma capital, ad for ivestmet-goods whe iterpretig as physical capital. Oe possible iterpretatio of the differece betwee the situatio of capital mobility ad oe of capital immobility is that i the first case is physical capital (mobility the meas the delocatio of plats) or as kowledge capital that is marketable ad tradable through patets. The secod case, capital immobility, would be more cosistet with the iterpretatio of huma capital. I this case, labor immobility implies capital immobility. The I-sector produces oe uit of with a I uits of L, so that the margial cost of the I sector, F, is w a I. Note that this uit of capital i equilibrium is also the fixed cost F of the maufacturig sector. As oe uit of capital is required to start a ew variety, the umber of varieties ad of firms at the world level is simply the capital stock at the world * level: W = +. We ote ad * the umber of firms located i orth ad south * respectively. As oe uit of capital is required per firm we also kow that: W = +. However, depedig o the assumptio we make o capital mobility, the stock of capital produced ad owed by oe regio may or may ot be equal to the umber of firms producig i that regio. I the case of capital mobility, the capital may be produced i oe regio but the firm that uses this capital uit may be operatig i aother regio. Hece, the umber of firms located i oe regio is, i the case of capital mobility, differet from the stock of capital owed by this regio. 6

10 L, umeraire, w=1 T sector (traditioal) - Walrasia (CRS& Perf. Comp.) - uit labor cost M-sector (Maufactures) - Dixit-Stiglitz moopolistic competitio - icreasig returs: fixed cost, 1 uit of - variable cost = a M uits of L No trade costs? p T =p T = w=w*=1 Iceberg trade costs North &ad South markets I-sector (Iovatio, Ivestmet ) - perfect competitio -itertemporal spillovers ( cases: global or localized) - variable cost for oe uit of = a I Trade i capital, cases: -perfect capital mobility - o capital mobility Figure : The basic structure of the growth ad agglomeratio model To idividual I-firms, the iovatio cost a I is a parameter. However, followig Romer (1990) ad Grossma ad Helpma (1991), a sector-wide learig curve is assumed. That is, the margial cost of producig ew capital declies (i.e., a I falls) as the sector's cumulative output rises. May justificatios of this itertemporal exterality, classic i the edogeous growth literature, are possible. Romer (1990), for istace, ratioalizes it by referrig to the o-rival ature of kowledge. We ca summarize these stadard assumptios of this literature by the followig: L & = a W W ; F = wa ; a = 1/ ; = I I I + I where ad * are the orther ad souther cumulative I-sector productio levels. Note that spillovers are global: the North lears as much from a iovatio made i the South tha i the North. Below, we itroduce localized techological spillovers. Followig Romer (1990) ad Grossma ad Helpma (1991), depreciatio of kowledge capital is igored. Fially, the regioal 's represet both regio-specific capital stocks ad regio-specific cumulative I-sector productio. Because the umber of firms, varieties ad capital uits is equal, the growth rate of the umber of varieties, o which we will focus, is therefore: & W W / = g. We assume a ifiitely-lived represetative cosumer (i each coutry) with prefereces: * (1) U * + ρt 1 α α 1 1 / σ = l ; ; C e Qdt Q = CT C M M = ci t= 0 i= 0 di / σ () See Baldwi et al. (003) for a similar aalysis with depreciatio. 7

11 where ρ is the rate of time preferece, σ is the costat elasticity of substitutio amog varieties, ad the other parameters have the usual meaig. Utility optimizatio implies that a costat fractio α of total orther cosumptio expediture E falls o M-varieties with the rest spet o T. Optimizatio by agets i the North also yields uitary elastic demad for T ad the CES demad fuctios for M varieties. The optimal orther cosumptio path also satisfies the stadard Euler equatio with log utility which requires 3 E & / E = r ρ (r is the orth's rate of retur o ivestmet) ad a trasversality coditio. Souther optimizatio coditios are isomorphic. O the supply side, free trade i T equalizes omial wage rates as log as both regios produce some T (i.e. if α is ot too large). Takig orther labor as umeraire the w=w*=1. As for the M-sector, uits are chose such that a M =1-1/σ so that producer prices of varieties are also ormalized to 1. With moopolistic competitio, equilibrium operatig profit is the value of sales divided by σ. Usig the goods market equilibrium ad the optimal pricig rules, the operatig profits are give by: E π = bb w w E π * = bb * ; w w ; B s B* s se + φ(1 s φse + φ(1 s φ(1 se ) + ) φs + 1 s 1 se + ) φ s + 1 s ; α b σ, φ τ where s E E/ E w is orth s share of world expediture E w ; s = /(+*) is the share of firms which are located i the orth, ad 0 = φ = 1 is the usual trasformatio of trade costs such that φ measures the free-ess (phi-ess of trade), with φ=0 implyig zero free-ess ad φ=1 implyig perfect free-ess (zero trade costs). Whe capital is immobile, this share is the share of capital owed by the Norther regio: s. Also, B is a memoic for the 'bias' i orther M-sector sales sice B measures the extet to which the value of sales of a orther variety exceeds average operatig profit per variety worldwide (amely, be w / w ). 1 σ (3) 3 See Barro ad Sala-I-Marti 1995 for a derivatio usig the Hamiltoia approach. Ituitively, the margial cost of postpoig cosumptio is ρ plus the rate of declie of margial utility which, give the log prefereces is just, E & / E. The margial beefit is r, the rate of retur o ivestmet. The optimal cosumptio path must be such that the two are equalized so that agets are idifferet to a small itertemporal reallocatio of cosumptio. 8

12 3. THE CASE WITHOUT LOCALIZED SPILLOVERS: GROWTH MATTERS FOR GEOGRAPHY We start with the simple extreme case cosidered by Grossma ad Helpma (1991) where spillovers are perfectly global. This assumptio is already embedded i equatio (1) The growth equilibrium Sice the locatio of iovatio ad productio are irrelevat to the iovatio process (kowledge spillovers are global ad deped oly o past I-sector productio), the worldwide equilibrium growth rate ca be determied without piig dow the spatial distributio of idustry (the locatio equilibrium). The easiest ad most ituitive way of solvig for growth equilibria is to use Tobi s q (Baldwi ad Forslid 000). The essece of Tobi's approach is to assert that the equilibrium level of ivestmet is characterized by the equality of the stock market value of a uit of capital which we deote with the symbol v ad the replacemet cost of capital, F. Tobi takes the ratio of these, so what micro ecoomists would aturally call the M-sector free-etry coditio (amely v=f) becomes Tobi's famous coditio q =v/f=1. Calculatig the umerator of Tobi's q (the preset value of itroducig a ew variety) requires a discout rate. I steady state, E & / E = 0 i both regios 4, so the Euler equatios imply that r=r * =ρ. Moreover, the preset value of a ew variety also depeds upo the rate at which ew varieties are created. I steady state, the growth rate of the capital stock (or of the umber of varieties) will be costat ad will either be commo (g=g* i the iterior case) or orth's g (i the core-periphery case). I either case, the steady-state values of ivestig i ew uits of are: π v = ρ + g ; v * * π = ρ + g It ca be checked that the equality, v=f, is equivalet to the arbitrage coditio preset i edogeous growth models such as Grossma ad Helpma (1991). The free etry coditio i the iovatio sector esures that the growth rate of the value v of capital is equal to growth rate of the margial cost of a iovatio, F, which due to itertemporal spillovers is g. With r =ρ, ad usig the defiitio of F we get the regioal q's: q = π ρ w + g ; q * * w π = ρ + g I the case of global spillovers, the commo growth rate is easy to fid because it does ot deped o geography. The reaso is simply that the cost of iovatio ad the total size of the market do ot deped o the locatio of firms. Hece, we ca just use the special case of the symmetric equilibrium where s E = s = 1/ to fid the growth rate. (5) (4) 4 w w To see this, use the world labour market equilibrium: L = ae (1 1/ σ ) + ( 1 a)e + g which says that world labour supply ca be used either i the maufacturig sector, the traditioal sector or the iovatio sector. It implies that a steady state with costat growth oly exists if E w itself is costat. 9

13 3.1.1 Edogeous growth ad the optimal savigs/ivestmet relatio Usig equatio (3) i that case ad imposig that Tobi's q is 1 i equatio (5), we get the followig relatio betwee growth ad world expediture E w : be w = g + ρ where b α/σ as is stadard i the growth literature. It just says that higher expediture by icreasig profits iduces more etry i the maufacturig sector, which implies a higher growth rate. The other equilibrium relatio betwee growth ad world expediture is give by the world labor market w w equilibrium: L = ae ( 1 1/ s ) + ( 1 a)e + g, which states that labor ca be used either i the maufacturig sector (recall the uit labor requiremet i this sector is ormalized to 1-1/σ), i w the traditioal sector or i the iovatio sector ( & is the productio of the sector per uit of time ad F=1/ w is the labor requiremet i the iovatio sector). Here the relatio is egative as higher expediture implies that labor resources are diverted from the iovatio sector to the maufacturig ad traditioal sector. Combiig the two we fid that the world level of expediture is simply give by: E w = L + ρ. Usig these equatios, the growth rate of the umber of varieties ad of the world capital stock is give by: g = Lb (1 b) ρ ; b α σ g depeds positively o the size of the world ecoomy (as measured by the edowmet of the primary factor) ad egatively o the discout rate as i ay edogeous growth model. Importatly, whe kowledge spillovers are global i scope, the equilibrium growth rate g does ot deped o geography. Fially, a simple equilibrium relatio exists betwee s E ad s, the orther share of expeditures ad the orther share of capital owership. It ca be show that optimizig cosumers set expediture at the permaet icome hypothesis level i steady state. That is, they cosume labor icome plus ρ times their steady-state wealth, F= s, ad, F*= (1- s ) i the orth ad i the south respectively. Hece, E = L+ρ s, ad E* = L+ρ(1-s ). Note that this is w aother way to check the level of world expediture as: E + E* = E = L + ρ. Thus, we get: s E E E w L + ρ s = L + ρ = 1 ρ + s L + ρ 1 This relatio betwee s E ad s, ca be thought as the optimal savigs/expediture fuctio sice it is derived from itertemporal utility maximizatio. The ituitio is simply that a icrease i the orther share of capital icreases the permaet icome i the orth ad leads therefore to a icrease i the orther share of expeditures The role of capital mobility Havig worked out the equilibrium growth rate, ad thus implicitly defied the amout of resources devoted to cosumptio, we ca tur to workig out the spatial divisio of idustry, i.e., the locatio equilibrium. From ow o two roads are ope: 1) we ca let capital owers decide where to locate productio. Capital is mobile eve though capital owers are ot, so that profits are repatriated i the regio where capital is owed. (6) (7) 10

14 I this case, s, the share of firms located i the orth ad s, the share of capital owed by the orth, may be differet. s is the edogeous ad determied by a arbitrage coditio that says that locatio of firms is i equilibrium whe profits are equalized i the two regios. Because of capital mobility, the decisio to accumulate capital will be idetical i both regios so that the iitial share of capital owed by the orth, s, is permaet ad etirely determied the iitial distributio of capital owership betwee the two regios. ) a secod solutio is to assume that capital is immobile. Presumably, this would be the case if we focus o the iterpretatio of capital beig huma (coupled with immobile agets). I this case, the locatio of productio, s, is pied dow by capital owership: s = s. As we shall see i detail below, the capital mobility assumptio is pivotal. Why is this? I stadard termiology, allowig capital mobility elimiates demad-liked circular causality (backward likages); capital moves without its owers, a shift i productio leads to o expediture shiftig because profits are repatriated. Whe capital is immobile, ay shock which favours productio i oe regio is satisfied by the creatio of ew capital i that regio. Sice the icome of the ew capital is spet locally, the productio shiftig leads to expediture shiftig. Of course, expediture shiftig fosters further productio shiftig (via the famous home market effect), so without capital mobility, the model features demad-liked circular causality. As is well kow, this form of likage is de-stabilizig, so as we shall see i detail below capital mobility i a growth model is a stabilizig force. Because the case of capital mobility is simpler, we start with it. 3.. Perfect capital mobility: the locatio equilibrium With capital mobility, a obvious questio arises: where does capital locate? Capital owed i oe regio ca be located elsewhere. Agai, the arbitrage coditio, which implies that profits across regios eed to be equal for firms to be idifferet betwee the two locatios, pis dow the equilibrium locatio of firms. Usig equatio (3), ad imposig the equality of profits, we get that there is o more icetive for relocatio whe the followig relatio betwee s ad s E is satisfied: s 1 1+ φ 1 = + se, 0 s 1 φ 1 where the equilibrium s equals uity or zero whe the s implied by (8) is outside the zero-uity rage. This is a example of the home market effect. Sice (1+φ)/(1-φ) is greater tha oe, this relatioship tells us that a chage i market size leads to a more tha proportioal chage i the spatial allocatio of idustry. Combiig equatios (7) ad (8), we get the equilibrium relatio betwee the share of firms located i the orth, s, ad the share of capital owed by the orth, s : s 1 ρ 1+ φ 1 = + s 0 s L + ρ 1 φ Note also that if the iitial distributio of capital i the orth is such that s > ½, the more firms will be located i the orth tha i the south: s > ½. A icrease i the share of capital i the orth, s, iduces relocatio to the orth as it icreases expediture ad market size there. Note also that lower trade costs (higherφ) will reiforce the home market effect, implyig that a 1 (8) (9) 11

15 uequal distributio of capital owership will traslate i a eve more uequal distributio of firms Stability of the locatio equilibrium It is easy to see that the divisio of idustry described above will ot chage over time. With perfect capital mobility, operatig profits have to be the same i both regios which also implies that the value of capital has to be the same i both regios. Hece, π =π* ad q=q*=1. This, together with the assumptio of costat returs to scale, ad the assumptio of global spillovers (implyig that the cost of iovatio is the same i both regios) meas that the two regios will accumulate capital at the same costat rate so that ay iitial distributio of capital is stable. Moreover, sice either backward or forward likages operatig i this model with capital mobility, o catastrophic agglomeratio sceario ca ufold (see Marti ad Ottaviao 1999). Hece, the equilibrium described by (9) is always stable. I particular, the symmetric equilibrium where s = s = 1/, is always stable for ay level of trade costs. To see this poit i more detail, oe ca aalyze the effect of a small icrease i s ad check the impact of this perturbatio o the ratio of profits i the orth to profits i the south. That is, we ask the questio whether a icrease i geographic cocetratio i the orth decreases or icreases the icetive to relocate i the orth. The symmetric equilibrium is stable if ad oly if (π/π*)/ s is egative. Ideed this is the case for all positive levels of trade costs sice, evaluated at the equilibrium geography: ( π ) ( 1 φ ) π * = s ( 1+ φ ) s E 1 (1 s E < 0 ) Evaluated at the equilibrium give by (9), a exogeous icrease i the share of firms located i the orth always decreases relative profits there, so that it leads firms to go back to the south. The locatio equilibrium determied i (9) is always stable. The reaso is that whe more firms locate i the orth, this icreases competitio there (ad decreases it i the south). 3.. Does capital flow from rich to poor? A iterestig questio that ca be aalyzed i this framework is: Do firms relocate towards the orth or towards the south? I ecoomic geography models without growth, idustrial cocetratio implies that firms are destroyed i the south ad built i the orth. Here, the relocatio story is richer because of the costat creatio of ew firms. To see what is the directio of relocatio we eed to look at the differece betwee the share of capital owed by the orth ad the share of firms located i orth. The expressio is easier takig ratios, so: s s L(1 φ) ρφ 1 = s ( 1 φ )(L + ρ) I the symmetric equilibrium, where both regios are edowed origially with the same amout of capital there is o relocatio of course. If the iitial distributio of capital is such that s >1/, so that the orth is richer tha the south, the the directio of the capital flows is ambiguous; it depeds o the sig of L(1-φ)-ρφ. If this expressio is positive, the s > s so that some of the capital owed by the orth relocates to the south. (10) 1

16 The ambiguity of the directio of capital flows stems from the fact that it is govered by two opposite effects, amely the market crowdig effect (which is a dispersio force that makes the poor capital regio attractive because firms istalled there face less competitio), ad the market access effect (which is a agglomeratio force that makes the rich regio attractive because of its high level of icome ad expediture). The first effect domiates whe trade is quite closed (φ is low). Note that whe the rate of time preferece is high or more geerally whe the retur to capital is high, the capital rich regio becomes more attractive because the market access effect is reiforced. There is a threshold level of trade costs that determies the directio of capital flows. It is give by: φ CP L = L + ρ Whe trade costs are below this level, relocatio takes place towards the south ad vice-versa. The reaso why we attach CP (for core-periphery) to this threshold will become clear later whe we aalyze the case of capital immobility, as we will see that this threshold value is the oe for which the symmetric equilibrium becomes ustable. A iterestig feature here is that cocetratio of wealth ad of ecoomic activities i the orth (s ad s >½), is compatible with relocatio of firms from orth to south (s <s ) whe φ <φ CP. This comes from the itroductio of growth ad the fact that a larger umber of ewly created firms are created ad owed by the orth tha by the south No capital mobility: "ew growth" ad "ew geography" The previous sectio described a growth ad geography equilibrium where agglomeratio forces were preset, 5 but where o "catastrophe" could take place sice all circular causality had bee ruled out. As discussed above, elimiatig capital mobility i a growth model is actually destabilizig sice aythig that chages the spatial allocatio of idustry ad thus capital will simultaeously chage that spatial allocatio of expediture. Ad, as is well kow, the home market effect meas that ay chage i expediture s spatial allocatio iduces a kock-o chage i the locatio of idustry. More formally, restrictig capital mobility (together with the assumptios of labor immobility) has two implicatios. First, the umber of firms ad the umber of uits of capital owed i a regio are idetical: s = s. Secod, because the arbitrage coditio of the previous sectio does ot hold, profits may be differet i the two regios. This i tur implies that, cotrary to the previous sectio, the two regios may ot have the same icetive to accumulate capital so that the iitial owership of capital does ot eed to be permaet. This meas that the aalysis will be quite differet from the previous sectio. We will ask the followig questios which are the usual oes i the NEG models. Startig from a equal distributio of capital, the symmetric equilibrium, we will determie uder which circumstaces it remais a stable equilibrium. The we will look at the core-periphery equilibrium ad agai ask whe this equilibrium is stable. (11) 5 We defie agglomeratio as the pheomeo where the cocetratio of ecoomic activity creates forces that foster the cocetratio of ecoomic activity. The home market effect, which did operate i the pervious sectio, shows agglomeratio forces are preset sice a divisio where s L =s >½ would ot be a equilibrium. Due to the home market effect, such a divisio would ecourage further cocetratio of ecoomic activity i the orth. 13

17 3.3.1 Stability of the symmetric equilibrium We first cosider iterior steady states where both regios are ivestig, so q =1 ad q * =1. Usig (3) ad (5) i (6), q = q * =1 ad imposig s = s we get: 1 1+ φ 1 s = + s E 1 φ which of course is just (8) with s replaced by s. I other words, it ow determies the locatio of capital owership as well as the locatio of productio. Together with equatio (7) which implied that productio shiftig led to expediture shiftig, this defies a secod positive relatio betwee s E ad s, i.e. expediture shiftig leads to productio shiftig. The ituitio is that a relative icrease i orther demad icreases profits i the orth ad therefore the margial value of a extra uit of capital. I other words, the umerator of Tobi s q icreases i the orth. Hece, this raises the icetive to iovate there ad the orth ideed icreases its share of capital s. The ituitio is therefore very close to the home market effect except that it iflueces here the locatio of capital accumulatio. Together with the optimal savig relatio of (7), it is easy to check that the symmetric solutio s E = s = ½ is always a equilibrium, i particular it is a equilibrium for all levels of trade costs. The symmetric equilibrium is the uique equilibrium for which both regios accumulate capital (q = q* =1). However, the fact that there are two positive equilibrium relatios betwee s E ad s, the share of expeditures ad the share of capital i the orth, should war us that the symmetric equilibrium may ot be stable. Ideed, i this model a 'circular causality' specific to the presece of growth ad capital immobility teds to de-stabilize the symmetric equilibrium because of the demad-liked cycle i which productio shiftig leads to expediture shiftig ad vice versa. The particular variat preset here is based o the mechaism first itroduced by Baldwi (1999) i a eo-classical growth model. There are several ways to study the symmetric equilibrium's stability. We ca first graph the two equilibrium relatios betwee s E ad s,, the Permaet Icome relatio (call it PI) give by equatio (7) ad the Optimal Ivestmet relatio (call it OI) give by equatio (1). I the case where the slope of the PI relatio is less tha the OI relatio we get the left-pael of Figure 3. At the right of the permaet icome relatio, s E, the share of expeditures i the orth, is too low give the high share of capital owed by the orth (agets do ot cosume eough). The opposite is true at the left of the PI relatio. At the right of the optimal ivestmet relatio, s, the share of capital i the orth, is too high give the low level of s E, the share of expeditures i the orth (agets ivest too much). The opposite is true is at the left of the OI relatio. This graphical aalysis suggests that i this case the symmetric equilibrium is stable. I the case where the slope of the PI relatio is steeper tha the OI the the same reasoig leads to the right-pael of the diagram. This suggests that i this case, the symmetric equilibrium is ustable. Accordig to this graphical aalysis, the trade cost below which the symmetric equilibrium becomes ustable is exactly the oe for which the slope of the PI curve equals the slope of OI curve. The slope of the PI curve is ρ/(l+ρ) which is the share of capital icome i total icome. The slope of the OI curve is: (1-φ)/(1+φ). The two slopes are equal for a level of trade costs which we saw above: it turs out to be the threshold level, which we defie as φ CP, give by equatio (11), amely φ CP =L/(L+ρ). Whe the "free-ess" of trade is higher tha this level, our graphical aalysis suggests that the stable equilibrium is ot stable. (1) 14

18 s E OI s E PI PI 0I 1/ 1/ 1/ s 1/ s Figure 3: The orther shares of expediture ad capital, stable ad ustable cases To gai more ituitio o this result, we ca also study the symmetric equilibrium's stability i a differet ad more rigorous way. We ca aalyze the effect of a exogeous icrease s, by a small amout ad check the impact of this perturbatio o Tobi s q, allowig expediture shares to adjust accordig to (7). The symmetric equilibrium is stable if ad oly if q/ s is egative: i this case, a icrease i the share of orther capital lowers Tobi's q i the orth (ad therefore the icetive to iovate) ad raises it i the south (by symmetry q/ s ad q * / s have opposite sigs). Thus whe q/ s <0, the perturbatio geerates self-correctig forces i the sese that the icetive to accumulate more capital i the orth falls ad icreases i the south. If the derivative is positive, the icrease i the share of capital i the orth reiforces the icetive to accumulate more capital i the orth: the symmetric equilibrium is ustable i this case. Differetiatig q with respect to s, we have: q / q s s = 1/ 1 φ s = 1 + φ s E s = 1/ 1 φ 1+ φ This expressio illustrates the two forces affectig stability. The first term is positive, so it represets the destabilizig force, amely the demad-liked effect. This effect was abset of the stability aalysis i the case of capital mobility because a icrease i profits i oe regio led to delocatio of capital but ot to more local capital accumulatio. I the case of capital immobility, the oly adjustmet mechaism whe profits icrease i oe regio is that agets i that regio accumulate more capital up to poit where the profits of accumulatig capital are drive to zero. This "local" accumulatio process geerates a higher permaet icome ad a higher level of expediture i oe regio oly which is the reaso for the circular causality. The egative secod term reflects the stabilizig market crowdig effect, which was the oly oe preset i the capital mobility case. Clearly, reducig trade costs (a icrease i φ) erodes the stabilizig force more quickly tha it erodes the destabilizig demad-likage. (14) 15

19 Usig (7) to fid s E / s = ρ/(l+ρ ), the critical level of φ at which the symmetric equilibrium becomes ustable is defied by the poit where (13) switches sig. It is easy to check that agai this critical level is give by φ CP of equatio (11). Whe trade costs are high the symmetric equilibrium is stable ad gradually reducig trade costs produces stadard, static effects more trade, lower prices for imported goods, ad higher welfare. There is, however, o impact o idustrial locatio, so durig a iitial phase, the global distributio of idustry appears uaffected. As trade free-ess moves beyod φ CP, however, the equilibrium eters a qualitatively distict phase. The symmetric distributio of idustry becomes ustable, ad orther ad souther idustrial structures begi to diverge; to be cocrete, assume idustry agglomerates i the orth. Sice s caot jump, crossig φ CP triggers trasitioal dyamics i which orther idustrial output ad ivestmet rise ad souther idustrial output ad ivestmet fall. Moreover, i a very well defied sese, the south would appear to be i the midst of a 'vicious' cycle. The demad likages would have souther firms lowerig employmet ad abstaiig from ivestmet, because souther wealth is fallig, ad souther wealth is fallig sice souther firms are failig to ivest. By the same logic, the orth would appear to be i the midst of a 'virtuous' cycle The core-periphery equilibrium I additio to the symmetric equilibrium, a core-periphery outcome (s = 0 or 1, but we will focus oly o the secod oe where the orth gets the core) ca also exist. For s =1 to be a equilibrium, it must be that q = v/f = 1 ad q* = v*/f* <1 for this distributio of capital owership: cotiuous accumulatio is profitable i the orth sice v=f, but v*<f* so o souther aget would choose to setup a ew firm. Defiig the core-periphery equilibrium this way, it implies that it is stable wheever it exists. Usig (3), (5) ad (6), (7), q* with s =1 simplifies to: (1 + φ ) L + φ q* = (L + ρ) φ ρ (14) If q* is less tha 1 whe s =1, the the core-periphery equilibrium exists ad is stable as there is o icetive for the south to iovate i this case. The threshold φ that solves q*=1 defies the startig poit of the core-periphery set. Agai, this threshold is φ CP of equatio (11). This implies that at the level of the trade costs for which the symmetric equilibrium becomes ustable, the core-periphery becomes a stable equilibrium. Whe trade costs are high eough, the core-periphery equilibrium is ot a stable equilibrium: i this case the south would have a icetive to iovate because the profits i the south are high eough. This is because eve though the souther market is small i this case (it has o capital icome i the core-periphery equilibrium), it is protected from orther competitio thaks to high trade costs. Whe trade costs are low eough, this protectio dimiishes ad the fact that the market i the south is small becomes more importat: i this case, above the threshold φ CP, it becomes o profitable to operate a firm i the south. Usig s =1, the remaiig aspects of the core-periphery steady state are simple to calculate. I particular, sice s =1, q=1, ad q*<1, we have that o labor is used i the iovatio or maufacturig sectors i the south ad all iovatio is made i the orth. 16

20 Note that the core-periphery outcome (s =1) is reached oly asymptotically. This is because we preset a simpler versio of the model where the stock of capital i the south does ot depreciate ad oce the level of φ CP is crossed, stays costat, whereas the stock of capital i the orth keeps growig at rate g. Figure 4 summarizes the model s stability properties i a diagram with φ ad s o the axes: 1 s Symmetric (stable) Core-Periphery (stable) 1/ Symmetric (ustable) 0 (o trade) φ CP 1 (free trade) φ Figure 4: Stability properties of the core-periphery equilibrium Followig the traditio of the NEG we have aalyzed here the existece ad stability coditios of the symmetric ad core-periphery equilibria. I this simple model we ca go further ad aalyze what would happe if we started from a situatio i which the orth had more capital tha the south (1/ <s <1). It ca be checked, usig equatios (3), (5) ad (6) that i this case q <1 (ad q*>1) if: 1 ( 1 s )( s )( 1 φ )[ ρ φ L( 1 φ )] < 0 that is, if φ <φ CP. Hece, i this case, the orth would ot iovate (the large stock of capital implies a high degree of market crowdig) ad the south would iovate. Hece, if we start from such a iterior asymmetric equilibrium the oe would coverge back to the symmetric equilibrium as log as trade costs are high eough. If φ > φ CP, the the ecoomy coverges to the core-periphery equilibrium Cocludig remarks Comparig perfect capital mobility to o capital mobility, we coclude that: - whe trade costs are high, the absece of capital mobility leads to covergece betwee the two regios: if oe regio starts with more capital tha the other the, the two regios coverge to the symmetric equilibrium. O the cotrary, with capital mobility, ay iitial distributio of capital owership becomes permaet. However, some of the firms owed by the orth will relocate ad produce i the south. This will produce some sort of covergece i terms of GDP but ot i terms of GNP. 17

21 - whe trade costs are low, the absece of capital mobility leads to divergece betwee the two regios: asymptotically, whatever the iitial distributio of capital, all the capital is accumulated ad owed by oe regio. 7 With capital mobility, as log as all the capital is ot etirely owed by the orth, some firms will still produce i the south. However, some of the souther capital will delocate to the orth. Hece, i the case of mobile capital (physical or tradable iovatios such as patets), the key parameter for regioal icome distributio is the iitial distributio of capital. I the case of immobile (huma) capital, the key parameter is the level of trade costs. The regioal distributio of capital affects the log term regioal icome distributio oly to the extet that it determies which regio becomes the core, through a small iitial advatage i capital edowmets for example. To simplify matters we have used a model where oly oe type of capital exists. To make it more realistic, i particular for the Europea case, it would be iterestig to exted it ad take ito accout the differet atures of capital so that part of the capital is mobile ad part is ot. Ca we derive some policy implicatios from this aalysis? Oe strikig result is that whe regios are ot well itegrated (high trasport/trade costs) capital immobility is coducive to regioal covergece. 9 However, whe regios are well itegrated, the opposite result is true. To the extet that public policies ca alter capital mobility, the policy implicatio is clear: capital mobility, both physical ad huma, should be facilitated betwee coutries which are well itegrated o the trade side. I the Europea cotext, this suggests that the "sigle market" was right to foster free movemet of goods ad capital at the same time. 7 This result however is ot geeral. Urba (00) itegrates a eo-classical growth model ito a static geography model without physical capital mobility. Cotrary to the models preseted here, he shows that lower trade costs lead to covergece betwee the poor ad the rich coutry. The reaso is that the classic local decreasig returs effect implies that there is more icetive to accumulate capital i the poor coutry ad i his model this effect does ot deped o trade costs. O the cotrary, the home market effect, the divergece force, decreases as trade costs dimiish. 9 Basevi ad Ottaviao (00) modify this type of model to ivestigate the itermediate situatio i which capital mobility is either abset or perfectly free. 18