First Nature vs. Second Nature Causes: Industry Location. and Growth in the Presence of an Open-Access Renewable Resource

Transcription

1 First Nature vs. ecod Nature Causes: Idustry Locatio ad Growth i the Presece of a Ope-Access eewable esource afael Gozález-Val a Ferado Pueyo b a Uiversidad de Barceloa & Istituto de Ecoomía de Barceloa b Uiversidad de Zaragoza Abstract: I this paper we preset a model itegratig characteristics of the New Ecoomic Geography, the theory of edogeous growth ad the ecoomy of atural resources. This theoretical framework eables us to study explicitly the effect of first ature causes i the cocetratio of ecoomic activity, more specifically, the cosequeces of a asymmetrical distributio of atural resources. The atural resource we cosider appears as a localized iput i oe of the two coutries, givig firms located i that coutry a cost advatage. I this cotext, after a decrease i trasport costs, firms decide to move to the coutry with the greatest domestic demad ad market size, where they ca take more advatage of icreasig returs, despite the cost advatage of locatig i the outh, due to the presece of the atural resource. Keywords: idustrial locatio, edogeous growth, reewable resource, geography JEL: F43, O3, Q, 1. Correspodig Address: Dpto. de Aálisis Ecoómico, Uiversidad de Zaragoza Facultad de CC. Ecoómicas y Empresariales Gra Vía, 55 Zaragoza (pai) fpueyo@uizar.es

2 1. Itroductio There are may factors ifluecig the distributio of ecoomic activity. It is traditioal to distiguish betwee characteristics liked to the physical ladscape, such as temperature, raifall, access to the sea, the presece of atural resources or the availability of arable lad, ad factors relatig to huma actios ad ecoomic icetives (for example, scale ecoomies or kowledge spillovers). The first group of factors, related to atural geographical circumstaces, are called first ature causes, ad the secod group are called secod ature causes. A great deal of effort has bee dedicated to researchig the ifluece of secod ature causes, especially after the pioeerig work of Krugma (1991), who demostrated how ecoomic forces (icreasig returs ad trasport costs) determie the distributio of activity. However, the models of New Ecoomic Geography are usually based o the assumptio that the space is homogeous, thus cotrollig the first ature causes. This meas that less work has bee ivested i the theoretical study of the effect of first ature causes, eve though may empirical studies demostrate their importat ifluece o ecoomic growth ad the cocetratio of ecoomic activity. For the case of the Uited tates, Elliso ad Glaeser (1999) state that atural advatages, such as the presece of a atural harbour or a particular climate, ca explai at least half of the observed geographic cocetratio. Glaeser ad hapiro (3) fid that i the 199s people moved to warmer, dryer places. Black ad Hederso (1998) coclude that the extet of city growth ad mobility are related to atural advatages, or geography. Beeso et al. (1) show that access to trasport etworks, either atural (oceas) or produced (railroads) was a importat source of growth durig the period , ad that climate is oe of the factors promotig populatio growth. Ad Mitcheer et al. (3) fid that some geographical characteristics accout for a high proportio of the differeces i productivity levels betwee America states. The aim of this paper is to provide a theoretical model which eables us to aalyse the ifluece of oe of the first ature causes, the presece of atural resources, o the cocetratio of ecoomic activity ad growth. To do this we will build a model i which firms ca choose to locate i oe of two coutries which trade with each other, which we will call North ad outh. This model itegrates characteristics of the New Ecoomic Geography, the theory of edogeous growth ad the ecoomy of atural resources. We will follow the model developed by Marti ad Ottaviao (1999), which combies a model of edogeous growth similar to that of omer (199), ad Grossma ad Helpma (1991), with a geographical framework like that of Helpma ad Krugma (1985), ad Krugma (1991). Ecoomic growth is supported by a edogeous framework with atioal spillovers i iovatio, causig research activities to take place i a sigle coutry, ad thus, the greater the idustrial cocetratio i that coutry, the higher the ecoomic growth rate. To this model, we add a ope access reewable atural resource, used by firms as a productive iput. This itroduces a additioal elemet that coditios firms decisios about whether to locate i the North or i the outh, besides the traditioal home market effect ad the existece of trade costs. The relative importace of these three forces determies a o-symmetrical locatio of firms. The idustrial geography here relates to the atural resource i two ways. First, the atural resource is located i oly oe of the two coutries, amely, the outh. Ad, secod, the iteratioal trade of the atural resource is subject to a trasport cost. 1

3 There are other theoretical models which study how the presece of atural resources affects iteratioal trade, focusig o factors such as comparative advatages ad relative prices (Brader ad Taylor, 1997a, 1997b, 1998a, 1998b), or differeces i property rights of the resources (Chichilisky, 1994). This paper proposes a differet approach, as the atural resource has a ifluece ot oly o iteratioal trade, but also o the distributio of firms amog coutries, which is edogeously determied. I tur, the distributio of ecoomic activity also affects the equilibrium stock of the atural resource. The followig results are obtaied. After a decrease i ay of the trasport costs, firms decide to move to the coutry with the greatest domestic demad ad market size. Despite the cost advatage of locatig i the outh due to the presece of the resource, firms prefer to move to the North, the rich coutry, where they ca take more advatage of icreasig returs. I tur, cocetratio improves the ecoomic growth rate, give the atioal ature of the spillovers. The cocetratio of firms i the North also has a positive effect o the stock of the atural resource, which icreases. This meas that i the framework of our model, secod ature causes (the home market effect), actig cetripetally, have greater weight i firm decisios tha the advatages of atural geographic circumstaces (first ature causes) which act cetrifugally. However, the outh ca icrease the importace of the first ature cause by itroducig public policies to reiforce the cost advatage of the resource s presece for firms located i the outh. We will cosider two public policies: imposig restrictios o the iteratioal trade of the resource ad promotig a techological chage to a techology which uses the resource more itesively. I both cases, after such policies the outh attracts firms from the North, producig decreases i the growth rate ad i the stock of the atural resource i equilibrium. The effect o welfare remais udetermied. The ext sectio presets the basic characteristics of the theoretical model. ectio 3 describes the market equilibrium of differetiated goods, with special attetio give to the distributio of firms i the equilibrium. ectio 4 describes the atural resource market ad solves the correspodig equilibrium. ectio 5 determies the steady state growth rate, which depeds o geography, ad also shows how ecoomic growth i tur iflueces geography through icome iequality. Oce the geeral equilibrium is described, sectio 6 aalyses the effect of chages i differetiated goods ad resource s trasport costs. These trasport costs ca also be iterpreted i terms of public policies, as see i sectio 7. Fially, the paper eds with the mai coclusios.. The model The diagram i Figure 1 describes schematically how the model works. We will cosider two coutries, North ad outh, which trade with each other. Both are idetical except for their iitial level of capital, K i the North ad K i the outh, ad the presece of a atural resource oly i the outh. Let us suppose that the North has a higher iitial icome level, such that K > K. Both coutries are ihabited by represetative households playig the part of cosumers, workers ad researchers. There are L households, both i the North ad i the outh. Labour is mobile betwee sectors but immobile betwee coutries. Give that the model is early symmetrical, we will focus o describig the ecoomy of the North (a asterisk deotes the variables correspodig to the outh).

4 The prefereces are istataeously ested CE, ad itertemporally CE, with a elasticity of itertemporal substitutio equal to the uit: U [ D( t) Y ( t) ] = log 1 e ρ t dt, < < 1, (1) where ρ is the itertemporal discout rate, Y is the umerary good ad D is a composite good which, i the style of Dixit ad tiglitz, cosists of a umber of differet varieties: N ( t) 1 D ( t) = σ D ( ) σ i t di, σ > 1. () i= N is the total umber of varieties available, both i the North ad the outh. σ is the elasticity of substitutio betwee varieties, ad is also the demad price elasticity of the demad for each variety (assumig that N is high eough). Growth comes from a icrease i the umber of varieties. Note that the atural resource does ot appear explicitly i the structure of idividual prefereces, meaig that it lacks value for them (but it might have social value, as a plaer might exist who decides to maitai a miimum level). This assumptio is restrictive, but has a double justificatio. First, the idirect utility fuctio is very difficult to aalyse eve without icludig the atural resource (see sectio 7). Icludig it would give rise to more idetermiacy (although, as we will see below, the resource does appear i the idirect utility fuctio idirectly through its price). Ad secod, idividuals caot move betwee coutries. This meas that they caot react i ay way to chages i the stock of the resource, ad so itroducig it ito its utility fuctio makes o sese. The value of per capita expediture E i terms of the umerary Y is: i p Didi τ p D dj Y E. (3) i j j = j The umber of maufactured goods produced i each coutry, ad, is edogeous, with N =. There is a trasport cost ( τ > 1) that affects iteratioal trade betwee the two coutries. Also, iteratioal tradig of the atural resource from outh to North is also subject to a trasport cost τ. τ ad τ represet iceberg-type costs, as i amuelso (1954), ad reflect the part of the good which is lost i trasit. The trasport costs operate accordig to the followig schema: 3

5 Thus, oly τ 1 < 1 of each uit of differetiated variety set from the other coutry is available for cosumptio. imilarly, the North icurs a additioal trasport cost derivig from the atural resource (oly τ 1 < 1 of each uit of the atural resource set from the outh ca be used) which the outh does ot bear. Decreases i τ or τ facilitate trade. From here we will assume that τ τ ; i other words, it is less costly or, at best, the same i terms of trasactio costs to sed uits of the atural resource tha the differetiated good 1. Meawhile, the umerary good is ot subject to ay trasactio cost. The umerary good is produced usig oly labour, subject to costat returs i a perfectly competitive sector. As labour is mobile betwee sectors, the costat returs i this sector tie dow the wage rate w i each coutry at each momet. We assume throughout the paper that the parameters of the model are such that the umerary is produced i both coutries, that is, that the total demad for the umerary is big eough so as ot to be satisfied with its productio i a sigle coutry. I this way, wages are maitaied costat ad idetical i both coutries. A uit of labour is eeded to produce a uit of Y, so free competitio i the labour market implies that w = 1 i both coutries. The differetiated goods are produced with idetical techologies, i a idustry with moopolistic competitio with icreasig scale returs i the productio of each variety. To begi to produce a variety of a good, a uit of capital is eeded; this fixed cost (FC) is the source of the scale ecoomies. Labour (L) ad atural resource () μ μ combie through a Cobb-Douglas type techology, xi = L 1 i i, with a proportio μ (,1) for the atural resource that represets how itesive the techology is i the use of the resource. This makes firm costs differet if they are located i the North or outh. If β represets the variable cost, the costs fuctio of a represetative firm i the North is as follows: c = FC βx q, while that of a firm i the outh, which does i ot have to bear trasport costs for the atural resource ( τ ), is: i c i = FC β xiq, 1 The results are maitaied eve whe trasport cost for the resource is higher tha that of the differetiated good, as log as the differece is ot too great (it is a sufficiet coditio). 4

6 where q ad q are the price idexes of the producers: q w ( ) μ = 1, ad μ τ p μ μ q = w 1 p, ad p is the market price of the atural resource. Therefore, firms i the outh ejoy a competitive advatage i costs derived from the presece of the atural resource i its territory. The stadard rule of moopolistic competitio determies the price of ay variety produced either i the North or the outh. The differece i costs implies that these σ prices are differet: β ( τ ) μ σ μ p = p i the North ad p = β p i the σ 1 σ 1 outh, where we have take ito accout that w = 1 i both coutries. pecifically, the price for ay variety fixed by firms i the North is higher tha the price fixed by firms i the outh due to the additioal trasport costs for the atural resource that they bear ( p > p as τ > 1). The operatig profits of the firms are also differet depedig o the coutry where they are located: π = i the North, ad βx p β ( τ ) μ i xi ( pi ) xi ( pi ) q = p (4) σ 1 βx μ π pi xi pi βxi pi q p σ = ( ) ( ) = (5) 1 i the outh, where x ad x are the productio scale of a represetative firm i the North ad i the outh, respectively. I order to produce a ew variety a previous ivestmet is required, either i a physical asset (machiery) or a itagible oe (patet). The cocept of capital used i this paper correspods to a mixture of both types of ivestmet. We assume that each ew variety requires oe uit of capital. Thus, the value of ay firm is the value of its uit of capital. The total umber of varieties ad firms is determied by the aggregate stock of capital at ay give time: N = = K K. Oce the ivestmet is made, each firm produces the ew variety i a situatio of moopoly ad chooses where to locate its productio, as there are o costs of relocatig the capital from oe coutry to the other. Ulike firms, households (workers/researchers/cosumers) are immobile, so their icome is geographically fixed, although the firms ca move. I other words, if a firm ower decides to locate productio i the coutry where he does ot reside, he repatriates the profits. Fially, we assume there is a safe asset which pays a iterest rate r o uits of the umerary, whose market is characterized by freedom of iteratioal movemets r = r. ( ) olvig the first order coditios of the problem of the cosumer i the North we obtai the demads for each variety produced i the North ( D i ), i the outh ( D j ), ad for the umerary good: μ ( τ p ) ) μ 1 σ ( τ p ) σ 1 E D i = (6) βσ σ μ 1 σ ( ( ) δ ( p ) ) 5

7 σ μ σ τ ( p ) E μ 1 σ μ ( τ p ) ) δ ( p ) σ 1 D j = (7) βσ 1 σ ( ) Y = )E (8) σ where δ = τ 1 is a parameter betwee ad 1 that measures the opeess of trade: δ = 1 represets a situatio i which trasport costs do ot exist, while if δ = trade would be impossible due to the high trasactio costs. The itertemporal optimizatio of cosumers implies that the growth rate of expediture is give by the differece betwee the iterest rate ad the itertemporal E E discout rate: = = r ρ. As we will show below, i the steady state, E ad E E* will be costat, so r = ρ. 3. Equilibrium i the market of differetiated goods The equilibrium i the differetiated goods market ivolves two issues. First, we have to determie x ad x, the productio scales i the equilibrium of a represetative firm located i the North or i the outh, respectively. ecod, the distributio of firms betwee both coutries is determied edogeously, depedig directly o geography ad trasport costs. The geographical part of the model refers to the locatio of firms, as the populatio does ot move betwee coutries. The locatio of firms i equilibrium is determied by four coditios. The first two refer to the fact that whe differetiated goods are produced i both coutries, total demad, from both North ad outh, for each variety (icludig trasport costs) must equal supply. Thus, from (6) ad (7): L( σ 1) x = βσ N μ ( τ p ) ) E σ μ 1 σ μ 1 σ ( ( τ p ) ) ) δ ( p ) ) N δ ( τ p ) L( σ 1) x = βσ N μ ( p ) E σ μ 1 σ μ 1 σ ( δ ( τ p ) ) )( p ) ) N ( τ p ) δe μ 1 σ μ 1 σ ( ( ) )( ) ) p δe μ 1 σ μ 1 σ ( ( ) ) δ ( ) ) p where = is the share of varieties of the maufactured good produced i the North. N The third coditio is the cosequece of the free movemets of capital betwee coutries ( r = r ), which implies a equal retributio via profits: (9) (1) E Populatio is tied to their ative coutry, but idividuals are affected by the locatio of firms, because the more firms i the coutry, the lower the price idex they have to bear. The price idexes are: 1 1 βσ μ μ σ ) P = p [ τ δ ] 1 σ σ i the North, ad βσ μ μ σ ) P = p [ δτ ] 1 1 σ i the outh. σ 1 6

8 ad, therefore, accordig to (4) ad (5), π = π, (11) x x =. Fially, the fourth coditio, already metioed, idicates that the total umber of varieties is fixed by the worldwide supply of capital at each momet: = K K = N. (1) olvig the system formed by these four equatios, we obtai the optimum size of each firm i equilibrium i the North ad i the outh: μ τ ( E E ) ( ) μ L( σ 1) x = τ βσ N p ( E E ) μ, (13) L( σ 1) x = p. (14) βσ N The equilibrium productio scales are differet i each coutry. Locatig i the North implies a additioal cost due to the trasport of the atural resource, ad the firms react by producig fewer uits of the differetiated good that they sell at a higher price. I tur, this differet behaviour is what eables profits obtaied i equilibrium to be the same i both coutries. The proportio of firms (or varieties) i the North ( = ) is give by: N = E δ φ ) δ E ) ( φ δ ), (15) E where, i tur, E = is the participatio of the North i total expediture ad E E μ σ ) φ = τ is a parameter betwee ad 1 of similar iterpretatio to δ, measurig the freedom of trade of the atural resource. It is also possible to demostrate that, as log as the North has a larger domestic market 3 1 E >, most firms are located i the 1 North >. The locatio of equilibrium of the firms depeds o atioal expediture higher local expediture or icome meas a larger domestic market, which attracts more firms watig to take advatage of icreasig returs (home market effect) ad the relatioship betwee the level of opeess of trade of differetiated goods ( δ ) ad of the atural resource ( φ ). The atural resource iflueces the distributio of firms i equilibrium via φ : the lower the trasport cost of the atural resource, the smaller the advatage for firms located i the outh. It is easy to see that ( φ δ ) > as log as τ τ. Give that most firms are cocetrated i the North, the home market effect, which we may idetify as a secod ature cause, acts cetripetally, favourig the 3 Below it is show that this coditio is always bore out as log as K, as we have supposed. > K 7

9 agglomeratio of ecoomic activity, while the cost advatage offered by the atural resource to firms located i the outh, the first ature cause, acts cetrifugally. 4. Natural resource growth The outh is edowed with a stock of atural resource ( ), characterized as i Eliasso ad Turovsky (4) or i Brader ad Taylor (1997a, 1997b, 1998a, 1998b). This atural resource has some specific characteristics. It is (i) reewable, (ii) ope access, (iii) used oly as a iput i the productio of maufactured goods, ad (iv) its exploitatio requires oly labour. These four coditios ca be cosidered as restrictive, but are ecessary to keep the model tractable. A atural resource with such characteristics is, for example, the wood from the forests of the outh. = G At ay poit of time, the et chage i the stock of the resource is give by ( ), where ( ) G describes the atural growth of the resource ad is the harvested amout. We assume that the reproductio fuctio G is a cocave fuctio depedig o the curret stock of the resource, ad positive i the iterval betwee ad, where is the miimum viable stock size ad is the maximum amout which the stock ca reach, give physical ad atural limitatios (for example, available space). G ( ) is aalogous to a productio fuctio, with the differece that the rate of accumulatio of the stock is limited. ee Brow () for a wider discussio of G ( ) ad its properties. For simplicity, we fix = ad assume that the growth of the resource, G ( ), correspods to a logistic fuctio: G( ) = γ 1, γ > (16) where γ is the itrisic growth rate of the resource (the atural growth rate). I the absece of harvestig ( = ), coverges to its maximum sustaiable stock level,. This fuctio has bee widely used i the aalysis of reewable resources, ad may be the simplest ad most empirically plausible fuctioal form of describig biological growth i a restricted eviromet. The harvest of the atural resource requires ecoomic resources; for the sake of simplicity, we will assume it requires oly labour. We assume that harvestig is carried out accordig to the chaefer harvestig productio fuctio: = BL, (17) where L is the amout of labour used i the reewable resource sector (workers i the outh, where the resource is located), is the harvested quatity offered by the producers ad B is a positive costat. If al ( ) represets the uit labour requiremet L 1 i the resource sector, (17) implies that al ( ) = =. It verifies a ( ) < L B : labour requiremet icreases as the stock of the resource decreases. Productio is carried out by profit-maximizig firms operatig uder coditios of free etry (perfect competitio). Therefore, the price of the resource good must equal its uit productio cost: 8

10 w 1 p = wal = =. (18) B B Both B ad w are i terms of the umerary good, so p is too. This price icorporates the assumptio of ope access to the resource, because the oly explicit productio cost is labour. There are o other explicit costs of usig the resource 4. The firms i the sector of the differetiated goods demad the atural resource as a iput i the productio of their varieties. Applyig hephard s lemma to the cost μ 1 fuctios we obtai the demad for the atural resource: βx μ( τ p ) for a 1 represetative firm of the North ad μ βx μp for a represetative firm of the outh. ubstitutig the equilibrium productio levels give by (13) ad (14), ad aggregatig for the firms i the North (takig ito accout the trasport cost they bear) ad i the D : outh, we obtai the worldwide demad for the resource ( ) ( E ) D 1 ( σ 1) = μp L E. (19) σ This demad depeds o some structural parameters, the price of the resource ad world L E E. aggregate icome, ( ) eplacig i (19) the price set by the producers, give by (18), we obtai the resource market equilibrium coditio, which gives us the equilibrium harvest level : ( σ 1) ( ) = μb L( E E ) Note that this harvest level is a fuctio ( ) σ. () that grows with the size of the stock. teady state is reached whe the stock evolves to a level i which the harvest G, give by of the atural resource, ( ), is equal to its capacity for reproductio, ( ) equatio 16, meaig that = G( ) ( ) = = =. The other solutio is give by: ~ ( σ 1) = 1 μb L γσ. A trivial solutio is reached whe ( E E ). (1) Figure shows how covergece is produced to the steady state level. The figure illustrates a situatio i which at the iitial stock the amout harvested, G. The stock the decreases util it reaches the ( ), exceeds atural growth, ( ) steady state level ~. This idicates that, i steady state, the quatity of the resource used by firms is costat. The steady state harvest level is obtaied by replacig ~ i ( ): ~ ( σ 1) ( σ 1) ( ) = μb L( E E ) 1 μb L( E E ) σ γσ. () 4 If there were o free access to the resource, aother cost would exist derivig from the reductio of the capacity for reproductio of the resource, which relates to Hotellig s rule. The resource would be exploited oly by firms with property rights i a situatio which would the ot be perfect competitio, makig the fial price greater tha the uit cost, ad geeratig additioal icome. 9

11 As show by Brader ad Taylor (1997a), a positive steady state solutio exists if ad oly if the term betwee brackets is positive, that is to say, if the coditio ( σ 1) γ μ B ( E E ) < holds. I this case the solutio is globally stable (for ay σ L > ). If such coditio is ot satisfied the resource would disappear ad the uique possible steady state is = =. Graphically, this coditio meas that, i the origi, the slope of the fuctio ( ) is less tha the slope of G ( ), thus esurig that they cut off at some poit for positive values of. 5. Ecoomic growth ad icome iequality 5.1 Ecoomic growth We will first examie the growth rate of the ecoomy. tartig from the solutio of the problem of the itertemporal optimizatio of the cosumer, we kow that, i E E equilibrium, = = r ρ. As the capital flows are free, r = r, ad the expediture E E growth rate will be the same i both coutries. From (15), this implies that the ratio of firms producig i the North,, is also costat i time, ad, therefore,, ad N grow at the same costat rate N g = = =. N Natioal spillovers exist i the iovatio sector, so that the more firms producig differet maufactured goods are located i the same coutry, the less costly is &D 5. This sector follows Grossma ad Helpma (1991), with η beig the cost i η terms of labour of a iovatio i the North ad i the outh. The immediate coclusio of this formulatio of the sector is that, for reasos of efficiecy, research activity will take place i oly oe of the two coutries: the oe with the most firms producig maufactured goods (which will be the rich coutry, the North, give that 1 > ). No researcher will have ay icetive to begi &D i the other coutry. This formulatio makes the aalytical treatmet of the model easier, although the results are maitaied eve if a certai degree of diffusio of the kowledge exists at the iteratioal level (Hirose ad Yamamoto, 7). The value of the firm is give by the value of its uit of capital. As the capital market is competitive, this value ( v ) will be give by the margial cost of iovatio, η η v = =, which is therefore decreasig at the rate g, the rate of iovatio N v ( = g ). As the umber of varieties icreases, the profits of each firm decrease, ad v also does its value, which ca also be iterpreted as the future flow of discouted profits 5 This type of kowledge spillovers is closer to the cocept of Jacobs (1969) tha to that of Marshall- Arrow-omer (MA). The empirical evidece for these exteral effects betwee differet idustries i the same geographical uit is documeted; see, for example, Glaeser et al. (199) ad Hederso et al. (1995). 1

12 [ ] = r ( s) r ( t) βx( s) v( t) e ds, where r represets the cumulative discout factor. t σ 1 Takig ito accout the arbitrage coditio betwee the capital market ad the safe asset market, the relatio betwee the iterest rate ad the value of the capital is give by 6 : v π r =. (3) v v O the other had, the costrait of world resources, E E = ( rη) ( ) L, where the right-had icludes the sum of labour icome ( w = 1 i the two coutries) ad capital returs, implies that worldwide expediture is costat over time, so that i steady state r = ρ, as poited above. Note that this restrictio icludes oly labour ad capital returs; the harvest of the atural resource does ot geerate additioal icome for either of the two coutries, as it is a ope access resource exploited i a competitive idustry. Fially, we must take ito accout the labour market. The world s labour is devoted to &D activities (usig oly workers from the North), ad to the productio of goods. From the latter, a proportio ( 1 ) is dedicated to the productio of the umerary good, ad a proportio to the productio of differetiated goods. I tur, give the Cobb-Douglas techology properties, from the labor used, either directly or idirectly, i the productio of maufactured goods, a proportio μ is used i the exploitatio of the resource (usig oly workers i the outh), ad a proportio 1 μ is used directly as a iput i the productio of varieties. Thus, the world labour market equilibrium coditio is give by: g σ η L( E E ) = L. (4) σ I steady state (see details i Appedix A), all the variables will grow at a costat rate. eplacig i (3) the profits obtaied i (4), the optimum size of firms i the equilibrium (13), ad cosiderig (4) ad that i steady state r = ρ, we obtai the labour ad capital markets equilibrium coditio: L σ g = ρ = g( ). (5) η σ σ where g is the growth rate of K ad K (the same for the two coutries) i steady state 7. This rate depeds o structural parameters of the model ( L, η,, σ, ρ ), but also o (the geography), lieally. 5. World icome distributio 6 This coditio is formulated i terms of the profits of the firms i the North ( π ), but applies i the same way to the outh because, although the expressios of π ad π differ (equatios 4 ad 5), oe of the coditios of equilibrium (equatio 11) requires that π = π. 7 Agai the results are preseted i terms of the variables of the North (π ad x ). Usig π ad x the same result is obtaied (the steady state ecoomic growth rate is the same for the two coutries), takig ito accout that i equilibrium π = π, meaig that x x =. μ τ 11

13 ecodly, we are iterested i how this ecoomic growth rate affects icome iequality betwee the coutries. emember that we assumed the North to be richer iitially ( K > K ). The per capita icome of each coutry is the sum of labour icome (which, as we have already see, is the uit), plus the capital icome, which is r times Kv Kv the value of per capita wealth. Thus, it will be E = 1 r = 1 ρ for ay L L idividual i the North. If we replace v from the arbitrage coditio betwee the capital market ad the safe asset market (3), the equilibrium profits (4), ad the optimum productio scale (13), it is possible to express Norther expediture as a fuctio of g : ρ K E = 1, (6) ( σ ) ρ σg K where K = is the share of capital owed by the idividuals i the North, that K K remais costat because K ad K grow at the same rate g i the steady state. imilarly, for the outh: E ρ( K ) ( σ ) ρ σg = 1. (7) 1 We have previously defied the ratio E E =, which represets the E E participatio of the North i total icome or expediture. eplacig the expressios (6) ad (7) we obtai: E = 1 σ ( ρ g) ρ( K 1). (8) σ ( ρ g) 1 If, as we have supposed, the North is richer ad K >, the 1 >. However, the E relatioship of E with the ecoomic growth rate is egative: as the umber of varieties icreases, the value of the capital is reduced, ad, as the North idividuals ow more capital, the icome differece is reduced i relative terms. Fially, to carry out the aalysis of the ext sectio, we eed to relate the geography ( ) with the growth rate g. To do this, we replace (8) i (15), obtaiig the differetiated goods market equilibrium coditio, idicatig the distributio of firms for each value of g : ( g) 1 ( )( ) ( ) ( ) ρ( k 1) 1 δ φ δ 1 δ φ 1 δ φ φ δ σ ρ g = = ( ) 5.3. Equilibrium [ ( g) ] E. (9) We have obtaied two equatios, (5) ad (9), represetig, respectively, the labour ad capital markets equilibrium coditio ad the differetiated goods market equilibrium coditio. These fuctios relate the growth rate with the spatial distributio of firms, ad defie the equilibrium values of these variables. ice the algebraic solutio is ot easy, we follow a graphical approach. 1

14 The fuctio g( ) g = is liear ad icreasig: give the ature of the techological spillovers (atioal), the greater the cocetratio of firms, the lower the costs of iovatio ad the higher the growth rate. The fuctio = ( g) is covex ad decreasig 8. emember that this equatio icorporates the iequality of icome, g, ad that this decreases as g icreases via the reductio of = [ ( )] E moopolistic profits of firms. At the same time, as the differeces i icome vaish, idustrial cocetratio ad the market size of the rich coutry decrease due to the home market effect. These fuctios are represeted i Figure 3. The itersectio poit determies the steady state locatio of firms as well as the growth rate of the ecoomy. 6. Effects of reducig trade costs As we explaied i the itroductio, the purpose of this paper is explicitly to study the effect of first ature causes o the cocetratio of ecoomic activity, aalyzig oe of the possible atural geographical characteristics, the role which may be played by a atural resource. tartig from the equilibrium situatio, a chage i differetiated goods or atural resource s trasport cost will lead to chages i the distributio of firms. Firms move accordig to two types of icetives: the North attracts firms thaks to its larger domestic market, 1 E >, which we ca idetify as oe of the secod ature causes of cocetratio of firms, while the first ature causes i our model refer to the advatage i costs ejoyed by firms i the outh thaks to the geographical presece of the atural resource i its territory. Variatios i ay type of trasactio cost do ot affect the fuctio g( ) g =, which depeds oly o the structural parameters of the model. It is the curve = ( g) which will reflect the chages i trasport costs, movig ad chagig its slope. We carry out our aalysis, first, from the perspective of the effects that decreasig trasport costs have o the idustrial localizatio ad the growth rate. The, the effect o the equilibrium stock of the resource is aalyzed. 6.1 Effects o idustrial cocetratio ad ecoomic growth Decrease i the trasport cost of differetiated goods Let us cosider first a decrease i the differetiated goods tradig cost: d τ <. After differetiatig the equatios (5) ad (9), we obtai that d dg <, < ad, dτ dτ thus, both the proportio of firms located i the North ad the ecoomic growth rate icrease. This situatio is represeted i Figure 4. The decrease i trasactio costs eables a easier access to the market of the other coutry, so some firms prefer to move to the North (remember that there are o relocatio costs). Despite the cost advatage of locatig i the outh due to the presece of the atural resource, firms prefer to move to the North, the rich coutry ad thus the 8 = ( g) is covex ad decreasig as log as ( δ ) > have bee assumig from the begiig. Additioally, ( φ δ ) φ. This coditio is verified if τ τ, as we is greater tha zero eve whe trasport cost for the resource is higher tha that of the differetiated good, as log as the differece is ot too great. 13

15 bigger market, where they ca take more advatage of icreasig returs. This meas that, i the framework of our model, the home market effect (secod ature causes), actig cetripetally, have a greater weight i firm decisios tha the advatages of atural geographic circumstaces (first ature causes), which act cetrifugally. I tur, cocetratio speeds up the ecoomic growth rate, because the more maufacturig firms are located i the North, the lower the cost of iovatio give the atioal ature of the spillovers. Decrease i the trasport cost of the resource If the trasport cost of the atural resource decreases, dτ <, we obtai that d dg <, <. Thus, both the proportio of firms located i the North ad the dτ dτ ecoomic growth rate rise: Figure 5 shows this situatio. The differece from Figure 4 is that, i this case, the slope of the curve = ( g) moves upwards rather tha dowwards. The lower trasport cost of the atural resource meas a loss i the cost advatage of the firms located i the outh, close to the atural resource, over those located i the North. At the limit, if this trasport cost did ot exist ( τ = 1) the firms could ot extract ay advatage from its locatio close to the resource ad there would be o relatioship betwee the distributio of atural resource ad the ecoomic geography. I other words, as the trasport cost of atural resources decreases, the importace of the first ature cause (i our model, the atural resource) vaishes. As a cosequece of this decrease i relative costs i the North, firms move from the outh to the North, which has a bigger domestic market ad greater demad. Moreover, as the umber of firms i the North icreases, the cost of research decreases due to atioal spillovers, ad the ecoomic growth rate icreases. 6. Effects o the stock of the atural resource Ay variatio i the distributio of firms or i the ecoomic growth rate, whether due to a chage i the trasport cost of differetiated goods or of the resource, will have a effect o the stock level of the resource i steady state. That is, chages i the geographical distributio of firms affect the market of the atural resource. Let us remember that both the harvest level, give by the resource market equilibrium coditio (equatio ), ad the stock of the resource i equilibrium (equatio 1), deped o aggregate world icome L ( E E ). I tur, world icome ca be related to ad g, replacig i (3) the profits obtaied i (4) ad the optimum size of firms i the equilibrium (13): ησ ( ρ g) L( E E ) =. (3) If we replace this expressio of world icome i () ad (1) we obtai: ( σ 1) η( ρ g) = 1 μ B, (31) γ 14

16 ( ) η( ρ g) = μ B ( σ 1). (3) From these expressios we ca aalyse the effects o the atural resource of the chages i the distributio of firms. Let us cosider chages i the trasport costs that lead to a higher proportio of firms located i the North ( d > ), that is, reductios i the trasport cost of either the itermediate goods or the atural resource. I tur, give the atioal ature of the &D spillovers, the higher cocetratio of firms i the North reduces the cost of iovatio ad raises ecoomic growth: dg >. o, by differetiatig (31), we obtai the effect of the reductio i trasport costs o the stock of the atural resource i steady state: ( σ 1) 1 1 d = μb η dg. γ This expressio eables us to idetify two opposite effects: a) Idustry localizatio effect: As the umber of firms located i the North icreases, the amout of the resource which is harvested decreases, because the firms i the North produce less uits of differetiated good ( x < x ) ad thus require less atural resource. b) Growth effect: As the umber of firms i the North icreases, the growth rate of the umber of varieties also icreases, so that the umber of firms grows faster. More firms require a higher aggregate amout of the atural resource. L However, applyig that, from (5), dg = d η, it is possible to obtai a clear sig: σ ( ρ g) d ( σ 1) 1 d = μ B η > ρ d, γ σ idicatig that the firms localizatio effect domiates: more firms i the North meas that less resource is cosumed o average, eablig the level of stock to icrease i steady state. O the other had, the effect o the harvested amout is ot clearly determied. If we differetiate (3), ad replace dg ad d with the expressios obtaied earlier, we have: d > μ B( σ 1) η ρ d <. σ = The sig of the above expressio depeds o, that is, o whether the iitial steady state stock exceeds or ot. The same coclusio ca be obtaied if we differetiate the fuctio G ( ) (equatio 16). Graphically, it depeds o whether ~ is o the icreasig or decreasig part of G ( ). Figures 6 ad 7 illustrate the two possibilities. 15

17 ~ I Figure 6 we cosider the case >, meaig that d < after the reductio i trasport costs. I this situatio, the icreasig umber of firms i the North is accompaied by a decrease i the amout harvested. This will be the most commo solutio, as it correspods to situatios where the slope of the fuctio ( ) is low. From (3), this is the more probable case whe the idustry is highly cocetrated i the North ad/or the techology of the itermediate good firms is ot very itesive i the use of the atural resource. ~ <, the amout harvested ). This case is represeted i Figure 7, ad correspods to situatios I cotrast, if the fuctio ( ) is very steep ad icreases ( d > where, despite cosumig more resource, the equilibrium stock icreases due to the G. high capacity of regeeratio of the atural resource o this side of the curve ( ) 7. Public policies: How to protect the outh s atural advatage? I the previous sectio we aalyzed the effects of decreases i trasport costs, obtaiig as a result a icrease i idustrial cocetratio i the North, the rich coutry, ad a icrease i the growth rate ad the stock level of the resource i steady state. uch lower trasport cost of the atural resource meat that the firms of the outh lost some of the cost advatage due to the closer locatio of the atural resource. That is, as the trasport cost of the resource decreases, the less importat this first ature cause becomes, cofigured as a cetrifugal force, ad the more firms cocetrate i the North. From this poit of view, there is ot much the outh ca do faced with a rich North with the home market effect i its favour, i a cotext of iteratioal trasport costs tredig dowwards over time, so that sooer or later the cost advatage will disappear. However, the outh ca cosider some public policies i order to protect the cost advatage. estrictios o iteratioal tradig of the resource A first route, the most direct, would be to ifluece τ, sice higher trasport costs for the resource icrease the cost advatage for firms i the outh. By modifyig slightly the iterpretatio of the parameter τ, we ca cosider some ways the outh could protect ad eve icrease the cost advatage give by ature. Marti ad ogers (1995) posited that the trasport costs used i the models of Ecoomic Geography ca alteratively be iterpreted as a measure of the quatity ad quality of trasport ifrastructures, ad, thus, ca be modified by public policies. From this poit of view, they defied public trasport ifrastructures as ay good or service provided by the state which ca facilitate the coectio betwee productio ad cosumptio. It is evidet that trasport ad commuicatio media ca be icluded amog these trade ifrastructures, but there are other o-physical elemets, such as the legal system or the levels of public safety, which have a equally great ifluece o trade. Good ifrastructures mea low trasactio costs; poor ifrastructures represet a situatio where trade is difficult because of the high costs icurred. From this wide sese of the term, the parameter φ becomes a idex betwee ad 1 which measures the level of ifrastructures ad/or legal restrictios related to the atural resource trade. 16

18 The best (worst) quality i trade ifrastructures is foud whe φ = 1 (). uch is also the case whe there are o legal restrictios for trade of the atural resource. I this way, the outh could act through public policies ad reiforce the cost advatage of outher firms by restrictig the iteratioal trade of the atural resource. The easiest way ca be the itroductio of exportatio tariffs. The more difficult it is to access the atural resource from outside, the more firms will decide to locate i the outh. This will eable to attract firms from the North, which would i tur cause a reductio i the growth rate ad i the stock of the atural resource i equilibrium (because the firms i the outh use more quatity of the atural resource tha those i the North). Techological chage There is aother parameter that ca ifluece the importace of the cost advatage which the atural resource gives to firms i the outh. This is μ, which measures the degree i which the techology of the differetiated goods sector is itesive i the use of the atural resource. pecifically, the more depedet the techology is o the atural resource, the greater the cost advatage of locatig productio i the outh. If the outh could use some kid of public policy, such as subsidisig firms, to promote a chage to a techology that used the resource more itesively, this would reiforce the cost advatage of its firms. This policy ca be represeted as a icrease i the parameter μ ( d μ > ). After differetiatig the equatios (5) ad (9), we fid that this leads to a decrease i the proportio of firms located i the North,, as well as i the ecoomic growth rate g, due to the atioal ature of the spillovers: d dg <,. < dμ dμ The equilibrium stock of the resource also decreases. Differetiatig (31), ad L takig ito accout that, from (5), dg = d η, we have: σ ( σ 1) 1 μ d = B η ( ρ g) dμ ρd <. γ σ The effect o the harvested amout i equilibrium is agai ot clearly determied, G. depedig o whether ~ is i the icreasig or decreasig side of the fuctio ( ) Meawhile, the effect o the variables would be the opposite if the North were to try to reduce firms techological depedece ( d μ < ) o the atural resource ot preset i its territory. I this case the cocetratio of firms i the North ad the ecoomic growth rate would icrease. It is ot difficult to fid examples of this kid of policies, carried out by coutries either to protect their advatages associated to the presece of atural resources, either to reduce the depedece i the case of importers. The case of oil, although it is ot a reewable ope access atural resource, is possibly the more represetative. O oe had, the producers try to protect the profits derived from its exploitatio by cotrollig (eve reducig) the iteratioal availability of the iput. O 17

19 the other had, the coutries which have to import the resource promote chages i the techology ad research i substitute iputs i order to reduce its depedece. What about utility? The two types of policies proposed above stregthe the ifluece of the first ature cause, leadig firms to move from the North to the outh. A questio that arises at this poit is whether such chage would be desirable. I order to try to aswer this questio, we aalyse the idirect utility fuctios. Although it is difficult to carry out a rigorous aalysis of welfare, give that ay variatio i the distributio of firms (the ratio ) has several differet effects o the idirect utility fuctio, with the global sig remaiig udetermied, we ca idetify the differet effects that cosumers would experiece i utility. The idirect utility fuctio of a household i the North is give by: V = l ρ σ 1 βσ 1 p ρη L 1 g σ 1 ρ ( σ 1) 1 k σ 1 ) 1 N ( ( φ δ ) δ ) μ e. (33) As we remarked above, although the atural resource does ot appear explicitly i cosumer prefereces (equatio 1), it iflueces the idirect utility fuctio idirectly through its price p. If we replace p from (18), the utility fuctio becomes: V = l ρ σ 1 βσ ρη L 1 g σ 1 ρ ( σ 1) 1 μ k σ 1 ) ( B ) 1 N ( ( φ δ ) δ ) e. (34) The impact of a chage i the cocetratio of firms 9 ca be obtaied by differetiatig the above fuctio with respect to, takig ito accout that, from L (5), dg = d η, ad cosiderig the expressio obtaied earlier for the chage i σ ( σ 1) 1 the atural resource stock d = μb η d ρ γ : σ V = η k L ρη k L ρ ησ ( φ δ ) ( σ 1) ρ( σ 1) ( ( φ δ ) δ ) μ ( σ 1) Bη σγ > < The effect o a Norther household welfare is udetermied. Besides the three effects obtaied by Marti ad Ottaviao (1999), i our model a fourth effect derivig from the price of the atural resource arises. Thus, if the outh maages, usig public policies, to attract firms from the North ( d < ), ot oly the ecoomic growth rate ad the level of equilibrium stock of the resource will decrease. Cosumers i the North also experiece four effects o utility: a) The first elemet of the above derivative captures the positive impact of a decrease i the growth rate o the wealth of Norther households. ice the 9 This aalysis of utility is partial, as we cosider that the chage i is exogeous. I the cocrete case that the cause of the variatio i the cocetratio of firms were a chage i effects would exist that would icrease idetermiacy. ee Appedix B. τ or i μ, additioal 18

20 cocetratio of firms i the North is reduced, the cost of &D rises ad the ecoomic growth rate decreases. This leads to a rise i itermediate firms moopolistic profits ad, thus, per capita icome icreases i the North. b) The secod elemet represets the egative impact o the reductio of the growth rate, which implies a slower rate of itroductio of ew varieties of the itermediate good, o the utility of idividuals due to their structure of prefereces ad the love-of-variety effect. c) The third term captures the decrease i welfare due to risig trade costs for cosumers i the North whe decreases, sice a higher rage of varieties have to be imported. This effect depeds o the differetial ( φ δ ). It is easy to see that ( φ δ ) > as log as τ τ, as we supposed. Thus, a lower proportio of firms located i the North, imply that Norther cosumers will bear higher trasport costs. d) The last elemet represets the egative effect of a lower cocetratio of firms i the North o the price of the atural resource. As the proportio of firms i the North decreases, so does the stock of the atural resource i equilibrium, d >, ad this leads to a icrease i its price (equatio 18). I tur, this d icrease i the price of the iput traslates to the price of the differetiated goods, with cosumers losig utility. imilarly, the idirect utility fuctio of a household i the outh is: 1 V = l ρ (35) σ 1 βσ ) ( B ) ρη 1 ) N g 1 μ σ 1 σ 1 ρ ( σ 1) K φδ )) e L Ad, by differetiatig this fuctio with respect to, we obtai a aalogous expressio to that above:. V = η L K ) L ρη ) ρ ησ ( σ 1) ρ( σ 1) K φδ ) φ δ )) μ ( σ 1) Bη σγ > < with the differece that the sig of the third effect is the opposite, sice a lower cocetratio of firms i the North causes a decrease i the trasport costs bore by cosumers i the outh, so that their welfare icreases via prices. I this situatio, i which both the cocetratio of firms i the North ad the ecoomic growth rate decrease, two egative effects o welfare are shared by the idividuals of both coutries: the love-of-variety effect (egative as the cosequece of a slower growth rate of the umber of varieties), ad the egative effect of the icreased price of the atural resource o the price of the differetiated goods. I the opposite, the reductio i the growth rate causes moopolistic profits of itermediate good producers to rise, ad thus icrease per capita icome i both coutries. Oly the tradig cost effect has a opposite impact o each coutry. While Norther cosumers lose utility because they have to import more varieties ad bear 19

21 higher trasport costs, the opposite holds for outher idividuals, which gai utility. This eables us to affirm that, whe the outh succeeds i attractig firms from the North, either cosumers i the outh lose utility, although less tha the cosumers i the North (i which case the public policy would be poitless), or they would gai utility, depedig o the cocrete values of the parameters. Therefore, i some situatios (for a certai rage of parameters), the outh will be iterested i applyig such public policies that eable it to icrease the cost advatage of the presece of the atural resource i its territory, the first ature cause, thus attractig firms from the other coutry. 8. Coclusios ad future lies of research I this paper, we preset a model itegratig characteristics of the New Ecoomic Geography, the theory of edogeous growth, ad the ecoomy of atural resources. This theoretical framework eables us to study explicitly the effect of first ature causes i the cocetratio of ecoomic activity, aalyzig oe of the possible atural geographical characteristics, the presece of a atural resource i the territory. Geography eters the model via trasport costs, which coditio the distributio of firms which attempt to take advatage of icreasig returs i a market of moopolistic competitio. Ecoomic growth is supported by a edogeous framework with atioal spillovers i iovatio, causig research activities to take place i a sigle coutry (the North), ad thus, the greater the idustrial cocetratio i that coutry, the higher the ecoomic growth rate. Ad the atural resource appears as a localized iput i oe of the two coutries (the outh), givig firms located i that coutry a cost advatage. After a decrease i ay of the trasport costs, firms decide to move to the coutry with the greatest domestic demad ad market size. Despite the cost advatage of locatig i the outh, due to the presece of the atural resource, firms prefer to move to the North, where they ca take more advatage of icreasig returs. I tur, cocetratio improves the ecoomic growth rate, give the atioal ature of the spillovers. Fially, the cocetratio of firms i the North would also have a positive effect o the stock of the atural resource i steady state, which would icrease. Despite idetifyig two opposite effects, a idustry localizatio effect ad a growth effect, the idustry localizatio effect domiates. Firms located i the North use a lower amout of atural resource, eablig the stock i steady state to icrease. This is so because the firms i the North react to the cost advatage of firms i the outh by producig a lower quatity of the differetiated good (ad thus usig less atural resource) ad sellig them at a higher price. This meas that, i the framework of our model, the home market effect (secod ature causes), actig cetripetally, have greater weight i firm decisios tha the advatages of atural geographic circumstaces (first ature causes), which act cetrifugally. However, the outh ca icrease the importace of the first ature cause by itroducig public policies to reiforce the cost advatage due to the atural resource presece i its territory. We have cosidered two differet public policies: imposig restrictios o the iteratioal trade of the atural resource ad promotig a techological chage towards a techology which uses the resource more itesively. I both cases, the outh attracts firms from the North, causig both the ecoomic growth