Agglomeration and Growth with EndogenousExpenditure Shares�

Fabio CerinaCRENoS and University of Cagliari

Francesco Muredduy

CRENoS and University of Cagliari

Abstract

We develop a New Economic Geography and Growth model which, byusing a CES utility function in the second-stage optimization problem,allows for expenditure shares in industrial goods to be endogenously de-termined. The implications of our generalization are quite relevant. Inparticular, we obtain the following novel results: 1) catastrophic agglom-eration may always take place, whatever the degree of market integration,provided that the traditional and the industrial goods are su¢ ciently goodsubstitutes; 2) the regional rate of growth is a¤ected by the interregionalallocation of economic activities even in the absence of localized spillovers,so that geography always matters for growth and 3) the regional rate ofgrowth is a¤ected by the degree of market openness: in particular, depend-ing on whether the traditional and the industrial goods are good or poorsubstitutes, economic integration may be respectively growth-enhancingor growth-detrimental.

Key words : new economic geography, endogenous expenditure shares,substitution e¤ect

JEL Classi�cations: R10, O33, O41

1 Introduction

The recent Nobel Prize assigned to Paul Krugman �for his analysis of tradepatterns and location of economic activity�witnesses the important role thatthe scienti�c community gives to the insights of the so-called New EconomicGeography (NEG) literature. This �eld of economic analysis has always beenparticularly appealing to policy makers, given the direct link between its results

�We would like to thank Gianmarco Ottaviano and Francesco Pigliaru for their usefulsuggestions. All remaining errors are our own.

yCorresponding author: Francesco Mureddu, Viale Sant�Ignazio 78 - 09123 - Cagliari(Italy). E-mail: francescomureddu@hotmail.com

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and regional policy rules. For the same reason it is useful to deepen the analysisof its most important outputs by testing the theoretical robustness of some ofits more relevant statements. This paper tries to o¤er a contribution in thisdirection by focusing on a particular sub-�eld of NEG literature, the so-calledNew Economic Geography and Growth (NEGG, henceforth), which basicallyadds endogenous growth to a version of Krugman�s celebrated core-peripherymodel (Krugman 1991).In this paper, we develop a NEGG model which deviates from the standard

approach in two respects: 1) we explicitly consider the love of variety parameterseparating it from the intrasectoral elasticity of substitution between the dif-ferent varieties within the industrial sector; 2) we use a more general ConstantElasticity Function (henceforth CES) instead of a Cobb-Douglas utility func-tion in the second-stage optimization problem, thereby allowing the elasticity ofsubstitution between manufacture and traditional good (intersectoral elasticityhenceforth) to diverge from the unit value.The main e¤ect of these departures is that the share of expenditure on

manufactures is no longer exogenously �xed (as in the Cobb-Douglas approach)but it is endogenously determined via agents�optimization. By endogenizing theexpenditure shares in manufacturing goods, we are able to test the robustnessof several well-established results in the NEGG literature and we show thatthe validity of such results, and of the associated policy implications, cruciallydepends on the particular Cobb-Douglas functional form used by this class ofmodels.Our generalizations of the standard NEGG literature act at two di¤erent

levels: a) the dynamic pattern of equilibrium allocation of economic activitiesand b) the equilibrium growth prospect. As for the �rst level, the main resultof our analysis is the emergence of a new force, which we dub as the substitu-tion e¤ect. This force, which is a direct consequence of the dependence of theexpenditure shares on the location of economic activities, is neutralized in thestandard NEGG model by the unitary intersectoral elasticity of substitution.Our model "activates" this force and the associated new economic mechanismopens the door to a series of novel results. First we show that this substitutione¤ect acts as an agglomeration or a dispersion force depending on whether thetraditional and the di¤erenciated goods are respectively good or poor substi-tutes. Then we analyze the implications of this new force and we show that,unlike the standard model, catastrophic agglomeration may always take placewhatever the degree of market integration may be, if the substitution e¤ect isstrong enough. This result, which is a novelty in the NEGG literature, has im-portant implications in two respects: �rst, policy makers should be aware of thefact that policies a¤ecting the degree of market integration can a¤ect the equi-librium location of economic activities only for a restricted set of values for theparameters describing the economy. Second, the emergence of the substitutione¤ect suggests that the intersectoral elasticity of substitution has a crucial rolein shaping the agglomeration or the dispersion process of economic activities.As for the equilibrium growth prospect, results are even more striking. We

show that, due to the endogenous expenditure shares: 1) the regional rate of

2

growth is a¤ected by the interregional allocation of economic activities even inthe absence of localized spillovers, so that geography always matters for growthand 2) the regional rate of growth is a¤ected by the degree of market openness:in particular, according to whether the intersectoral elasticity of substitution islarger or smaller than unity, economic integration may be respectively growth-enhancing or growth-detrimental. These results are novel with respect to thestandard NEGG literature according to which geography matters for growthonly when knowledge spillovers are localized and, moreover, trade costs nevera¤ect the growth rate in a direct way. This second set of results is characterizedby even more important policy implications: �rst, our results suggests thatinterregional allocation of economic activity can always be considered as aninstrument able to a¤ect the rate of growth of the economy. In particular,when the average interregional expenditure share on industrial goods are higherin the symmetric equilibrium than in the core-periphery one, then each policyaiming at equalizing the relative size of the industrial sector in the two regionswill be good for growth, and vice-versa. Second, each policy a¤ecting economicintegration will also a¤ect the rate of growth and such in�uence is cruciallylinked to the value of the intersectoral elasticity of substitution.As already anticipated, the literature we refer to is basically the so-called

New Economic Geography and Growth (NEGG) literature, having in Baldwinand Martin (2004) and Baldwin et. al (2004) the most important theoreticalsyntheses. These two surveys collect and present in an uni�ed framework theworks by Baldwin, Martin and Ottaviano (2001) - where capital is immobile andspillovers are localized - and Martin and Ottaviano (1999) where spillovers areglobal and capital is mobile. Other related papers are Baldwin (1999) which in-troduces forward looking expectations in the so-called Footloose Capital modeldeveloped by Martin and Rogers (1995); Baldwin and Forslid (1999) whichintroduces endogenous growth by means of a q-theory approach; Baldwin andForslid (2000) where spillovers are localized, capital is immobile and migration isallowed. Some more recent develpments in the NEGG literature can be groupedin two main strands. One takes into consideration factor price di¤erences inorder to discuss the possibility of a non-monotonic relation between agglomera-tion and integration (Bellone and Maupertuis (2003) and Andres (2007)). Theother one assumes �rms heterogeneity in productivity (�rst introduced by Eatonand Kortum (2002) and Melitz (2003)) in order to analyse the relationship be-tween growth and the spatial selection e¤ect leading the most productive �rmsto move to larger markets (see Baldwin and Okubo (2006) and Baldwin andRobert-Nicoud (2008)). These recent developments are related to our paper inthat they introduce some relevant departures from the standard model.All the aforementioned papers, however, work with exogenous expenditure

shares. A �rst attempt to introduce endogenous expenditure shares in a NEGGmodel has been carried out by Cerina and Pigliaru (2007), who focused on thee¤ects on the balanced growth path of introducing such assumption. The presentpaper can be seen as an extension of the latter, considering that we deepen theanalysis of the implications of endogenous expenditure shares by fully assessingthe dynamics of the model, the mechanisms of agglomeration and the equilibria

3

growth rate.We believe that the results obtained in this paper are important considering

at least three di¤erent perspectives: 1) a purely theoretical one: a tractableendogenous expenditure share approach, being more general than an exogenousone, represents a theoretical progress in the NEG literature and enables us toconsider the standard NEGG models as a special case of the one developed here;2) a descriptive perspective: the endogenous expenditure share approach, byintroducing some new economic mechanisms, might be empirically tested and itcan be extended to several other NEG models in order to assess their robustness;3) a policy perspective: our paper suggests that policy makers should not trusttoo much on implications drawn from standard NEGG models because of theirlimited robustness.The rest of the paper is structured as follows: section 2 presents the an-

alytical framework, section 3 deals with the equilibrium location of economicactivities, section 4 develops the analysis of the growth rate and section 5 con-cludes.

2 The Analytical Framework

2.1 The Structure of the Economy

The model structure is closely related to Baldwin, Martin and Ottaviano (2001).The world is made of 2 regions, North and South, both endowed with 2 factors:labour L and capital K: 3 sectors are active in both regions: manufacturing M;traditional good T and a capital producing sector I: Regions are symmetric interms of: preferences, technology, trade costs and labour endowment. Labour isassumed to be immobile across regions but mobile across sectors within the sameregion. The traditional good is freely traded between regions whilst manufactureis subject to iceberg trade costs following Samuelson (1954). For the sake ofsimplicity we will focus on the northern region1 .Manufactures are produced under Dixit-Stiglitz monopolistic competition

(Dixit and Stiglitz, 1975, 1977) and enjoy increasing returns to scale: �rms facea �xed cost in terms of knowledge capital2 and a variable cost aM in terms oflabour. Thereby the cost function is � + waMxi; where � is the rental rate ofcapital, w is the wage rate and aM are the unit of labour necessary to producea unit of output xi:Each region�s K is produced by its I-sector which produces one unit of K

with aI unit of labour. So the production and marginal cost function for theI-sector are, respectively:

_K = QK =LIaI

(1)

F = waI (2)

1Unless di¤erently stated, the southern expressions are isomorphic.2 It is assumed that producing a variety requires a unit of knowldge interpreted as a blue-

print, an idea, a new technology, a patent, ora a machinery.

4

Note that this unit of capital in equilibrium is also the �xed cost F of themanufacturing sector. As one unit of capital is required to start a new variety,the number of varieties and of �rms at the world level is simply equal to thecapital stock at the world level: K + K� = Kw. We denote n and n� as thenumber of �rms located in the north and south respectively. As one unit ofcapital is required per �rm we also know that: n + n� = nw = Kw. As inBaldwin, Martin and Ottaviano (2001), we assume capital immobility, so thateach �rm operates, and spends its pro�ts, in the region where the capital�s ownerlives. In this case, we also have that n = K and n� = K�. Then, by de�ningsn =

nnw and sK =

KKw ; we also have sn = sK : the share of �rms located in one

region is equal to the share of capital owned by the same region3 .To individual I-�rms, the innovation cost aI is a parameter. However, fol-

lowing Romer (1990), endogenous and sustained growth is provided by assumingthat the marginal cost of producing new capital declines (i.e., aI falls) as thesector�s cumulative output rises. In the most general form, learning spilloversare assumed to be localised. The cost of innovation can be expressed as:

aI =1

AKw(3)

where A � sK + � (1� sK), 0 < � < 1 measures the degree of globalizationof learning spillovers and sK = n=nw is share of �rms allocated in the north.The south�s cost function is isomorphic, that is, F � = w�=KwA� where A� =�sK +1� sK : However, for the sake of simplicity, we focus on the case of globalspillovers, i.e., � = 1 and A = A� = 14 . Moreover, in the model version weexamine, capital depreciation is ignored5 .Because the number of �rms, varieties and capital units is equal, the growth

rate of the number of varieties, on which we focus, is therefore:

g �_K

K; g� �

_K�

K�

Finally, traditional goods, which are assumed to be homogenous, are pro-duced by the T -sector under conditions of perfect competition and constantreturns. By choice of units, one unit of T is made with one unit of L.

3We highlight that our results on the equilibrium growth rate holds even in the case ofcapital mobility.

4Analysing the localised spillover case is possible, but it will not signi�cantly enrich theresults and it will obscure the object of our analysis.

5See Baldwin (1999) and Baldwin et al. (2004) for similar analysis with depreciation butwith exogenous expenditure shares.

5

2.2 Preferences and consumers�behaviour

The preferences structure of the in�nitely-lived representative agent is given by:

Ut =

Z 1

t=0

e��t lnQtdt; (4)

Qt =

��

�nw

v+ 11��

CM

��+ (1� �)CT �

� 1�

;� � 1; v > 0 (5)

CM =

"Z n+n�

i=0

c1�1=�i di

# 11�1=�

;� > 1

where v is the degree of love for variety parameter, � is the elasticity parame-ter related to the elasticity of substitution between manufacture and traditionalgoods and � is the elasticity of substitution across varieties.Following Cerina and Pigliaru (2007), we deviate from the standard NEGG

framework in two respects:1) As in Benassy (1996) and Smulders and Van de Klundert (2003), the

degree of love for variety parameter is esplicitly considered. In the canonicalNEGG framework the love for variety parameter takes the form 1

��1 ; beingtied to the elasticity of substitution across varieties � (intrasectoral elasticityhenceforth). By contrast, in the present model v is not linked to � but it isindependently assessed6 .2) We use a more general CES second-stage utility function instead of a

Cobb-Douglas one, thereby allowing the elasticity of substitution between man-ufacture and traditional good (intersectoral elasticity henceforth) to divergefrom the unit value: indeed the intersectoral elasticity is equal to 1

1�� whichmight be higher or lower than unity (albeit constant) depending on whether �is respectively negative or positive. The main e¤ect of this modi�cation is thatthe share of expenditure on manufacture is no longer constant but it is a¤ectedby changes in the price indices of manufacture. This consequence is the sourceof most of the result of this paper.Allowing for a larger-than-unity intersectoral elasticity of substitution, re-

quires the introduction of a natural restriction on its value relative to the one

6Take an utility function U (CT :CM ) where CM = Vn (c1;:::; cn) is homogeneous of degreeone, with n being the number of varieties. By adopting the natural normalization V1 (q1) = q1,we can de�ne the following function:

(n) =Vn(c; :::; c)

V1(nc)=Vn(1; :::; 1)

n

with (n) representing the gain in utility derived from spreading a certain amount of ex-penditure across n varieties instead of concentrating it on a single one. The degree of love forvariety v is just the elasticity of the (n) function:

v(n) =n 0(n)

(n)

In the standard NEGG framework CM =

�R n0 c

��1�

i di

� ���1

hence (n) = 1��1 :

6

of the intrasectoral elasticity of substitution. The introduction of two distinctsectors would in fact be useless if substituting goods from the traditional to themanufacturing sector (and vice-versa) was easier than substituting goods withinthe di¤erentiated industrial sectors. In other words, in order for the representa-tion in terms of two distinct sectors to be meaningful, we need goods belongingto di¤erent sectors to be poorer substitutes than varieties coming from the samedi¤erenciated sector. The formal expression of this idea requires that the inter-sectoral elasticity of substitution 1

1�� is lower than the intrasectoral elasticityof substitution �:

1

1� � < �

This assumption, which will be maintained for the rest of the paper, statesthat � cannot not be too high. It is worth to note that this assumption isautomatically satis�ed in the standard Cobb-Douglas approach where 1

1�� = 1and � > 1:The in�nitely-lived representative consumer�s optimization is carried out in

three stages. In the �rst stage the agent intertemporally allocates consumptionbetween expenditure and savings. In the second stage she allocates expenditurebetween manufacture and traditional goods, while in the last stage she allocatesmanufacture expenditure across varieties. As a result of the intertemporal opti-mization program, the path of consumption expenditure E across time is givenby the standard Euler equation:

_E

E= r � � (6)

with the interest rate r satisfying the no-arbitrage-opportunity conditionbetween investment in the safe asset and capital accumulation:

r =�

F+_F

F(7)

where � is the rental rate of capital and F its asset value which, due toperfect competition in the I-sector, is equal to its marginal cost of production.In the second stage the agent chooses how to allocate the expenditure be-

tween manufacture and the traditional good according to the following opti-mization program:

maxCM ;C T

Qt = ln

��

�nw

v+ 11��

CM

��+ (1� �)CT �

� 1�

(8)

s:t:PMCM + pTCT = E

By setting v = 1��1 and � = 0 the maximization program boils down to

the canonical CD case. As a result of the maximization we obtain the followingdemand for the manufactured and the traditional goods:

PMCM = �(nw; PM )E (9)

7

pTCT = (1� �(nw; PM ))E (10)

where pT is the price of the traditional good, PM =hRK+K�

i=0pi1��

i 11��

is

the Dixit-Stiglitz perfect price index and �(nw; PM ) is the share of expenditurein manufacture which, unlike the CD case, is not exogenously �xed but it isendogenously determined via the optimization process and it is a function ofthe total number of varieties (through v) and of the M� goods price index(through �). This feature is crucial to our analysis.The northern share of expenditure in manufacture is given by:

�(nw; PM ) =

0B@ 1

1 + P�

1��M

�1���

� 11��

�nw

11���v

� �1��

1CA (11)

while the symmetric expression for the south is:

�(nw; P �M ) =

0B@ 1

1 + P� �1��

M

�1���

� 11��

�nw

11���v

� �1��

1CA (12)

so that northern and southern expenditure shares only di¤er because of thedi¤erence between northern and southern manufacture price index, PM and P �Mrespectively.Finally, in the third stage, the amount ofM� goods expenditure �(nw; PM )E

is allocated across varieties according to the a CES demand function for a typ-

ical M -variety cj =p��jP 1��M

�(nw; PM )E; where pj is variety j�s consumer price.

southern optimization conditions are isomorphic.

2.3 Specialization Patterns, Love for Variety and Non-Unitary Elasticity of Substitution

Due to perfect competition in the T -sector, the price of the agricultural goodmust be equal to the wage of the traditional sector�s workers: pT = wT : More-over, as long as both regions produce some T; the assumption of free trade inT implies that not only price, but also wages are equalized across regions. It istherefore convenient to choose home labour as numeraire so that:

pT = p�T = wT = w

�T = 1

As it is well-known, it�s not always the case that both regions produce someT . An assumption is actually needed in order to avoid complete specialization: asingle country�s labour endowment must be insu¢ cient to meet global demand.Formally, the CES approach version of this condition is the following:

L = L� < ([1� �(nw; PM )] sE + [1� �(nw; P �M )] (1� sE))Ew (13)

8

where sE = EEw is northern expenditure share and Ew = E + E�:

In the standard CD approach, where �(nw; PM ) = �(nw; P �M ) = �; thiscondition collapses to:

L = L� < (1� �)Ew:The purpose of making this assumption, which is standard in most NEGG

models7 , is to maintain the M -sector and the I-sector wages �xed at the unitvalue: since labour is mobile across sector, as long as the T - sector is presentin both regions, a simple arbitrage condition suggests that wages of the threesectors cannot di¤er. Hence,M� sector and I-sector wages are tied to T -sectorwages which, in turn, remain �xed at the level of the unit price of a traditionalgood. Therefore:

wM = w�M = wT = wT = w = 1 (14)

Finally, since wages are uniform and all varieties� demand have the sameconstant elasticity �; �rms�pro�t maximization yields local and export pricesthat are identical for all varieties no matter where they are produced: p =waM

���1 : Then, imposing the normalization aM = ��1

� and (14), we �nallyobtain:

p = w = 1 (15)

As usual, since trade in the M�good is impeded by iceberg import barriers,prices for markets abroad are higher:

p� = �p; � � 1

By labeling as pijM the price of a particular variety produced in region i andsold in region j (so that pij = �pii) and by imposing p = 1, the M�goods priceindexes might be expressed as follows:

PM =

"Z n

0

(pNNM )1��di+

Z n�

0

(pSNM )1��di

# 11��

= (sK + (1� sK)�)1

1�� nw1

1��

(16)

P �M =

"Z n

0

(pNSM )1��di+

Z n�

0

(pSSM )1��di

# 11��

= (�sK + 1� sK)1

1�� nw1

1��

(17)where � = �1�� is the so called "phi-ness of trade" which ranges from 0

(prohibitive trade) to 1 (costless trade).A quick inspection of condition (13) and expressions (16) and (17) reveals

that the introduction of the no-specialization assumption in our model is sen-sibly more problematic than in the standard CD case and these di¢ culties arecrucially linked to the role of the love for variety parameter v: In order to seethis in detail, we need to dwell a little bit deeper on the role of the expenditureshare and of the love for variety parameter.

7See Bellone and Maupertuis (2003) and Andrés (2007) for an analysis of the implicationsof removing this assumption.

9

2.3.1 Love of variety and expenditure shares

Substituting the new expressions for theM�goods price indexes in the northernand southern M�goods expenditure shares, yields:

�(nw; sK ; �) =

0B@ 1

1 +�1���

� 11��

�nw

� v�1�� (sK + (1� sK)�)

�(1��)(1��)

�1CA (18)

��(nw; sK ; �) =

0B@ 1

1 +�1���

� 11��

�nw

� v�1�� (�sK + 1� sK)

�(1��)(1��)

�1CA : (19)

As we can see the shares of expenditure in manufactures now depends onthe localization of �rms sK , the parameter � and the overall number of �rms inthe economy nw:We can make a number of important observations from analysing these two

expressions.First, when the elasticity of substitution between the two goods is di¤erent

from 1, (i.e. � 6= 0), north and south expenditure shares di¤er (�(nw; sK ; �) 6=��(nw; sK ; �)) in correspondence to any geographical allocation of the manu-facturing industry except for sK = 1=2 (symmetric equilibrium). In particular,we �nd that8

� > (<) 0, @�

@sK=

� (1� �)� (1� �)(1� �) (� � 1) ((sK + (1� sK)�))

> (<) 0 (20)

� > (<) 0, @��

@sK=

� (�� 1)�� (1� ��)(1� �) (� � 1) ((sK + (1� sK)�))

< (>) 0 (21)

Hence, when � > 0, production shifting to the north (@sK > 0) leads to arelative increase in the southern price index for the M goods because southernconsumers have to buy a larger fraction of M goods from the north, whichare more expensive because of trade costs. Unlike the CD case, where thisphenomenon had no consequences on the expenditure shares for manufactureswhich remained constant across time and space, in the CES case expenditureshares on M goods are in�uenced by the geographical allocation of industriesbecause they depend on relative prices and relative prices change with sK :Secondly, the impact of trade costs are the following:

� > (<) 0) @�

@�=

�(1� sK)� (1� �)(1� �) (� � 1) ((sK + (1� sK)�))

> (<) 0 (22)

� > (<) 0) @��

@�=

�sK�� (1� ��)

(1� �) (� � 1) ((sK + (1� sK)�))> (<) 0 (23)

8For simplicity�s sake we omit the arguments of the functions � and ��:

10

so that, when the two kinds of goods are good substitutes (� > 0) economicintegration gives rise to an increase in the expenditure share for manufacturedgoods in both regions: manufactures are now cheaper in both regions and sincethey are good substitutes of the traditional goods, agents in both regions willnot only increase their total consumption, but also their shares of expenditure.Obviously, the smaller the share of manufacturing �rms already present in thenorth (south), the larger the increase in expenditure share for the M good inthe north (south). The opposite happens when the two kinds of goods arepoor substitutes: in this case, even if manufactures are cheaper, agents cannoteasily shift consumption from the traditional to the di¤erentiated good. Inthis case, even if total consumption on manufactures may increase, the share ofexpenditure will be reduced.Finally, the impact of the number of varieties is the following:

� > (<) 0) @�

@nw=

�v

1� �(1� �)�nw

� (� 0)

� > (<) 0) @��

@nw=

�v

1� �(1� ��)��

nw� (� 0)

Therefore, when goods are good (poor) substitutes (� > 0), and individualslove variety (v > 0) ; the expenditure share for the M� goods in both regionsis an increasing (decreasing) function of the total number of varieties. In theanalytical context of the NEGG models, this result (which is a feature of theCES utility function we have chosen) has highly unwelcome e¤ects from theviewpoint of the formal dynamics of the model. In particular, since along thebalanced growth path the number of total varieties is increasing ( _n

w

nw = g � 0),the expenditure shares � and �� will asymptotically approach to 1 or 0 accordingto whether � is positive or negative. This result is a consequence of the interplaybetween non-unitary intersectoral elasticity of substitution and love for variety.Consider the case when � is positive: when agents love variety, an increase inthe number of total variety is su¢ cient to let their perceived price index for themanufactured goods decrease. As a consequence, because of the elasticity ofsubstitution larger then 1, they will devote a larger share of total expenditureto the M�goods. Since the role of the M -goods expenditure shares is crucial inthe NEGG models, their non-constancy has a series of important and correlatedconsequences. Some of them are the following:

1. The real growth rate of the two regions never reach a constant value in a�nite time and might di¤er as the agglomeration process takes place.

2. Since when � > 0; � and �� go to 1; the no-specialization condition cannothold forever: there comes a (�nite) time when the expenditure shares forthe traditional good become so small that a single country will be able toproduce everything necessary to meet the global demand.

The �rst result is particularly relevant for policy implications. However, wewill not focus on it: for a detailed analysis of this issue please refer to Cerina and

11

Pigliaru (2007). The second result also triggers some new important mechanismsinvolving the role of wage di¤erentials, but makes the analysis highly intractable.Since the aim of this paper is to focus on the e¤ects that "geography" (i.e.:

interregional �rms�allocation and trade costs) has on a NEGG model when aCES second-stage utility function is considered, we henceforth abstract from thetwo previous consequences by imposing v = 0, that is, we assume no love forvariety. From now on, the second stage maximization program is then:

maxCM ;C T

Qt = ln

��

�nw

11��

CM

��+ (1� �)CT �

� 1�

(24)

s:t:PMCM + pTCT = E

giving rise to the following expressions for the northern and southern expen-diture shares:

�(sK ; �) =

0B@ 1

1 +�1���

� 11��

�(sK + (1� sK)�)

�(1��)(1��)

�1CA (25)

��(sK ; �) =

0B@ 1

1 +�1���

� 11��

�(�sK + 1� sK)

�(1��)(1��)

�1CA (26)

where the in�uence of the argument nw has been neutralized by the conditionv = 0 so that � and �� are only a¤ected by �rms�allocation (sK) and by thefreeness of trade (�). Since the latters are constant along the balanced growthpath, � and �� are constant too.What are the drawbacks of eliminating the love for variety on the descriptive

relevance of our model? We believe they are not so signi�cant for several reasons.First, from the theoretical point of view, the assumption v = 0 is just as

general as the standard NEGG assumption according to which v = 1��1 .

Second, from an empirical perspective, there are several empirical analysisassessing a value for the v parameter lower than that assumed in standardNEGG models (see for instance Ardelean 2007). In this case the impact ofthe product variety on economic growth and industrial agglomeration is smallerthan what is typically assumed and, therefore, closer to 0:Third, several other NEGG studies abstract from the love for variety. Murata

(2008) for instance uses a similar but more restrictive (because � = 0) functionutility to investigate the relation between agglomeration and structural change.This assumption can also be found in the �new Keynesian economics�literature(see Blanchard and Kiyotaki (1987), for example), which is another strand ofliterature based on the model of monopolistic competition by Dixit and Stiglitz(1977).Fourth, from the point of view of the generality of our model, the introduc-

tion of the restriction according to which v = 0 is compensated by the introduc-tion of the parameter � which, unlike the standard NEGG models, allows theelasticity of substitution to deviate from the unit value.

12

The analytical gains of introducing this restrictions are by contrast veryrelevant.First, By eliminating the love for variety we are able to maintain a version

of the typical assumption in NEGG models which states that a single country�slabour endowment must be insu¢ cient to meet global demand. We are entitledto do this because, when v = 0; both � and �� cannot reach the unit value. Theno-specialization condition should be modi�ed as follows:

L < ([1� �(sK ; �)] sE + [1� ��(sK ; �)] (1� sE))Ew; 8 (sK ; �) 2 (0; 1) � R2:(27)

Since sE has to be constant by de�nition and even9 :

Ew(sE ; sK ; �) =(2L� LI � L�I)�

sE (� � �(sK ; �)) + (1� sE) (� � ��(sK ; �))(28)

is constant in steady state, (27) can be accepted without any particular lossof generality. Our analysis can be developed even without the no-specialisationassumption.Second, by imposing v = 0, we are able to focus on the e¤ect that a non-

unitary value of the intersectoral elasticity of substitution has on the equilibriumoutcomes of the model. By allowing for this elasticity parameter to deviate fromthe unit value, we obtain some novel results on the agglomeration and growthprospects of the model. In the next two session we will extensively describethese results.

3 Equilibrium and stability analysis

This section analyses the e¤ects of our departures from the standard NEGGliterature on the equilibrium dynamics of the allocation of northern and southern�rms.Following Baldwin, Martin and Ottaviano (2001), we assume that capital

is immobile. Indeed, capital mobility can be seen as a special case of capitalimmobility (a case where @sE

@sK= 0). Moreover, as we shall see, capital mobility

does not provide any signi�cant departure from the standard model from thepoint of view of the location equilibria (the symmetric equilibrium is alwaysstable). However, it should be clear that our analysis can be carried on evenin the case of capital mobility. In particular, the results of the growth analysisdeveloped in section 4 holds whatever the assumption on the mobility of capital.In models with capital immobility the reward of the accumulable factor (in

this case �rms�pro�ts) is spent locally. Thereby an increase in the share of�rms (production shiftings) leads to expenditure shiftings through the perma-nent income hypothesis. Expenditure shiftings in turn foster further productionshiftings because, due to increasing returns, the incentive to invest in new �rms

9The expression for Ew can be found by using an appropriate labour market-clearingcondition.

13

is higher in the region where expenditure is higher. This is the so-called demand-linked circular causality.This agglomeration force is counterbalanced by a dispersion force, the so-

called market-crowding force, according to which, thanks to the unperfect sub-stitutability between varieties, an increase in the number of �rms located inone region will decrease �rms�pro�ts and then will give an incentive for �rmsto move to the other region. The interplay between these two opposite forceswill shape the pattern of the equilibrium location of �rms as a function of thetrade costs. Such pattern is well established in NEGG models (Baldwin, Martinand Ottaviano 2001, Baldwin at al. 2004, Baldwin and Martin 2004): in theabsence of localized spillovers, since the symmetric equilibrium is stable whentrade costs are high and unstable when trade costs are low, catastrophic ag-glomeration always occur when trade between the two countries is easy enough.That happens because, even though both forces decreases as trade costs becomelower, the demand-linked force is lower than the market crowding force (in ab-solute value) when trade costs are low, while the opposite happens when tradecosts are high.By adopting the CES approach we are able to question the robustness of

such conclusions. In particular our model displays a new force, that we callsubstitution e¤ect. This force fosters agglomeration or dispersion dependingon whether the T and the M�commodities are respectively good or poor sub-stitutes. By introducing this new force, which acts through the northern andsouthernM -goods expenditure shares, we show that, depending on the di¤erentvalues of the intersectoral elasticity of substitution, the symmetric equilibriummight be unstable for every value of trade costs. These results have severalimplications. First, when the intersectoral elasticity of substituion is allowedto vary from the unit value, the location patterns of �rms may not be a¤ectedby the market integration process: catastrophic agglomeration will or will notoccur regardless trade costs so that policy-makers should not be concerned withthe e¤ect of market integration. Second, the intersectoral elasticity of substitu-tion becomes a crucial parameter in the analysis of the location pattern of �rmsand, hence, on the relative welfare of northern and southern agents. We willnow explore such implications in detail.

3.1 Tobin�s q and Steady-state Allocations

Before analysing the equilibrium dynamics of �rms�allocation, it is worth re-viewing the analytical approach according to which such analysis will be carriedon. As in standard NEGG models, we will make use of the Tobin q approach(Baldwin and Forslid 1999 and 2000). We know that the equilibrium level ofinvestment (production in the I sector) is characterized by the equality of thestock market value of a unit of capital (denoted with the symbol V ) and thereplacement cost of capital, F . With E and E� constant in steady state, theEuler equation gives us r = r� = �: Moreover, in steady state, the growth rateof the world capital stock Kw (or of the number of varieties) will be constantand will either be common (g = g� in the interior case) or north�s g (in the

14

core-periphery case)10 . In either case, the steady-state values of investing innew units of K are:

Vt =�t�+ g

;V �t =��t�+ g

:

Firms� pro�t maximization and iceberg trade-costs lead to the followingexpression for northern and southern �rms�pro�ts:

� = B(sE ; sK ; �)Ew

�Kw(29)

�� = B�(sE ; sK ; �)Ew

�Kw(30)

whereB(sE ; sK ; �) =h

sEsK+(1�sK)��(sK ; �) +

�(1�sE)�sK+(1�sK)�

�(sK ; �)iandB�(sE ; sK ; �) =h

sE�sK+(1�sK)��(sK ; �) +

1�sE�sK+(1�sK)�

�(sK ; �)i: Notice that this expression dif-

fers from the standard NEGG in only one respect: it relies on endogenousM�good expenditure shares which now depend on sE ; sK and �.By using (2), the labour market condition and the expression for northern

and southern pro�ts, we obtain the following expression for the northern andsouthern Tobin�s q:

q =VtFt= B(sE ; sK ; �)

Ew

(�+ g)�(31)

q� =VtFt= B�(sE ; sK ; �)

Ew

(�+ g)�(32)

Where will investment in K will take place? Firms will decide to invest inthe most-pro�table region, i.e., in the region where Tobin�s q is higher. Since�rms are free to move and to be created in the north or in the south (eventhough, with capital immobility, �rm�s owners are forced to spend their pro�tsin the region where their �rm is located), a �rst condition carachterizing anyinterior equilibria (g = g�) is the following:

q = q� = 1 (33)

The �rst equality (no-arbitrage condition) tells us that, in any interior equi-librium, there will be no incentive for any �rm to move to another region. Whilethe second (optimal investment condition) tells us that, in equilibrium, �rms willdecide to invest up to the level at which the expected discounted value of the

10By time-di¤erentiating sK = KKw ; we obtain that the dynamics of the share of manufac-

turing �rms allocated in the north is

_sK = sK (1� sK) _K

K�

_K�

K�

!so that only two kinds of steady-state ( _sK = 0) are possible: 1) a steady-state in which the

rate of growth of capital is equalized across countries (g = g�); 2) a steady-state in which themanufacturing industries are allocated and grow in only one region (sK = 0 or sK = 1).

15

�rm itself is equal to the replacement cost of capital. The latter is crucial in or-der to �nd the expression for the rate of growth but it will not help us in �ndingthe steady state level of sK : Hence, we focus on the former. By using (29), (30),(31) and (32) in (33) we �nd the steady-state relation between the northernmarket size sE and the northern share of �rms sK which can be written as:

sE =1

2+1

2

���(sK ; �) (sK + (1� sK)�)� �(sK ; �) (�sK + (1� sK))�(sK ; �) (�sK + (1� sK)) + ��(sK ; �) (sK + (1� sK)�)

�(34)

The other relevant equilibrium condition is given by the de�nition of sE whenlabour markets clear. This condition, also called permanent income condition,gives us a relation between northern market size sE and the share of �rms ownedby northern entrepeneurs sK :

sE =E

Ew=L+ �sK2L+ �

=1

2+� (2sK � 1)2 (2L+ �)

(35)

By equating the right hand side of these two equations we are able to �ndthe relation between sK and sK that has to hold in every interior steady state:

��(sK ; �) (sK + (1� sK)�)� �(sK ; �) (�sK + (1� sK))�(sK ; �) (�sK + (1� sK)) + ��(sK ; �) (sK + (1� sK)�)

=� (2sK � 1)(2L+ �)

(36)

so that the steady state level of sK is one which satis�es the last condition.It is easy to see that the symmetric allocation, sK = 1

2 ; is always an interiorequilibrium. In this case, in fact, the latter condition becomes an indentity. Inthe appendix, we also show that the assumption according to which 1

1�� < �;assures that the symmetric equilibrium is also the unique interior equilibrium.As for the core-periphery equilibria, things are much simpler. We know that

_sK = 0 also when sK = 0 or sK = 1: For simplicity, we focus on the lattercase keeping in mind that the other is perfectly symmetric. The core-peripheryoutcome is an equilibrium if �rms in the north set the investment to the optimallevel (q = 1) while �rms in the south have no incentive to invest (q� < 1).To sum up, as in the standard CD approach with global spillovers, we only

have three possible equilibria: a symmetric equilibrium (sK =12 ) and two core-

periphery equilibria (sK = 0 or sK = 1). We will now study the stabilityproperties of such equilibria.

3.2 Stability Analysis of the symmetric equilibrium

Following Baldwin and Martin (2004) we consider the ratio of northern andsouthern Tobin�s q:

q

q�=B(sE ; sK ; �)

B�(sE ; sK ; �)=

hsE

sK+(1�sK)��(sK ; �) +�(1�sE)

�sK+(1�sK)��(sK ; �)

ih

sE�sK+(1�sK)��(sK ; �) +

1�sE�sK+(1�sK)�

�(sK ; �)i = (sE ; sK ; �)

(37)

16

Starting from an interior (and then symmetric) steady-state allocation where (sE ; sK ; �) = 1; any increase (decrease) in (sE ; sK ; �) will make invest-ments in the north (south) more pro�table and thus will lead to a productionshifting to the north (south). Hence the symmetric equilibrium will be stable(and catastrophic agglomeration will not occur) if a production shifting, say,to the north (@sK > 0) will reduce (sE ; sK ; �). By contrast, if (sE ; sK ; �)will increase following an increase in sK ; then the equilibrium is unstable andcatastrophic agglomeration becomes a possible outcome.We remind that this method is the same employed by standard NEGG mod-

els. The only and crucial di¤erence is that, in our framework, the northernand southern expenditure shares � (sK ; �) and �� (sK ; �) play a crucial role be-cause their value is not �xed but depends on geography and trade costs. Thekey variable to look at is then the derivative of (sE ; sK ; �) with respect tosK :evaluated at sK = 1

2 : This derivative can be written as:

@ (sE ; sK ; �)

@sK

����sK=sE=

12

=(1� �)(1 + �)

1

��12 ; �

� � @�

@sK� @��

@sK

��4�1� �1 + �

�2+4@sE@sK

(1� �)(1 + �)

(38)The stability of the symmetric equilibrium is then determined by the inter-

play of three forces given by:

� (1��)(1+�)

1

�( 12 ;�)

�@�@sK

� @��

@sK

�� �4

�1��1+�

�2� 4 @sE@sK

(1��)(1+�)

The last two forces are the same we encounter in the standard NEGG modeland they are the formal representation of, respectively, the market-crowding ef-fect and the demand-linked e¤ect. In the standard model, the stability of theequilibrium is the result of the relative strenght of just these two forces. The�rst force represents the novelty of our model. In the standard case, where�� (sK ; �) = � (sK ; �) = � and then

@�@sK

= @��

@sK= 0; this force simply doesn�t

exist. We dub this force as the substitution e¤ect in order to highlight the linkbetween the existence of this force and a non-unitary value of the intersectoralelasticity of substitution. As we will see in detail below, the substitution e¤ectmight be a stabilizing (when negative) or destabilizing one (when positive) de-pending on whether the manufactured and the traditional good are respectivelypoor (� < 0) or good (� > 0) substitutes.But what is the economic intuition behind this force? Imagine a �rm moving

from south to north (@sK � 0). For a given value of �; this production shifting,via the home-market e¤ect, reduces the manufactured good price index in thenorth and increases the one in the south. In the standard case, where the man-ufactured and the traditional goods are neither good nor poor substitutes, thisrelative change in the price levels has no e¤ect on the respective expenditure

17

shares. By contrast when the intesectoral elasticity of substitution is allowed tovary from the unitary value, the shares of expenditure change with theM�priceindex and hence with sK : In particular, when the manufactured and the tra-ditional goods are good substitutes (� > 0), a reduction in the relative price

level in the north leads to and increase�@�@sK

� 0�in the northern expenditure

shares and a decrease�@��

@sK� 0

�in the southern expenditure shares, then in-

creasing the relative market size in the north and then providing an (additional)incentive to the southern �rms to relocate in the north. The opposite ( @�@sK � 0and @��

@sK� 0) happens when the manufactured and the traditional goods are

poor substitutes (� < 0): in this case, southern relative market size increasesand this gives and incentive for the moving �rm to come back home. This iswhy, when the M and the T goods are good substitutes the substitution e¤ectacts as an destabilizing force, while the opposite happens when the M and theT goods are poor substitutes.We can re-write (38) by using (20) and (21) which reveals that @�

@sK= � @��

@sK.

Hence:

@ (sE ; sK ; �)

@sK

����sK=sE=1=2

= 4

�1� �1 + �

�2� (1� � (1=2; �))(� � 1) (1� �)z }| {

Substitution

�4�1� �1 + �

�2z }| {Market-crowding

+4(1� �)(1 + �)

@sE@sKz }| {

Demand-linked

Where, using the permanent income condition (35), we have @sE@sK

= �2L+� :

The symmetric equilibrium will be stable or unstable according to whether theprevious expression is positive or negative. Again, the only di¤erence withrespect to the standard case is the presence of the �rst term in the left-handside, the substitution e¤ect, which is in fact zero when � = 0:It is easy to show that, since 1

1�� < �; we always have:

4

�1� �1 + �

�2� (1� � (1=2; �))(� � 1) (1� �)

Substitution e¤ect

�4�1� �1 + �

�2Market-crowding e¤ect

� 0 for any � 2 [0; 1] (39)

so that the substitution e¤ect will never o¤set the market-crowding e¤ect11 .Moreover, in a similar way to the other two forces, the substitution e¤ect willbe decreasing in the freeness of trade. Hence, the dynamic behaviour of theagglomeration process as a function of � will not be qualitatively di¤erent fromthe standard case: as � decreases, each forces will reduce their intensity (inabsolute value) but the decrease of the Demand-linked e¤ect will be slower.Nevertheless, the presence of our additional force will introduce the possibil-

ity of an additional outcome which was exluded from the standard CD case. In11From this result, we can derive a corollary for the capital mobility case. In this case, sn

should not equal sK and, above all, there is no permanent income condition so that @sE@sn

= 0:

Hence the stability condition reduces to (39) and, just as in the standard case, the symmetricsteady-state is always stable when capital is mobile.

18

order to do that, we recall the notion of break-point, that is the value of � abovewhich the stability of the interior equilibria is broken, and then an in�nitesimalproduction shifting in the north (south) will trigger a self-reinforcing mechanismwhich will lead to a core-periphery outcome. In the standard CD case, since� = 0, we have that:

@ (sE ; sK ; �)

@sK

����sK=sE=1=2

� 0, � � �CDB

where �CDB = LL+� is the break-point level of the trade costs. Since �

CDB 2

(0; 1) ; there is always a feasible value of the trade costs above which the interiorequilibrium turns from stable to unstable and then agglomeration will take place.In our model, it is not possible to calculate an explicit value for the break-

point. That�s because � enters the expression for � (1=2; �) as a non-integerpower. Nonetheless, we can draw several implications from the existence ofthe substitution e¤ect. Let�s re-write the condition according to which the

symmetric equilibrium is unstable�@ (sE ;sK ;�)

@sK

���sK=sE=1=2

� 0�in this way:

� (1� � (1=2; �))(� � 1) (1� �) � 2 (L+ �)

(1� �) (2L+ �)

��CDB � �

�(40)

We can notice that the sign of the left-hand side, as 2(L+�)(1��)(2L+�) is always

non-negative, is completely determined by��CDB � �

�. First, note that in the

standard case, when � = 0; this condition reduces to:

� > �CDB

so that, by de�nition, the equilibrium is unstable when the freeness of tradeis larger than the break-point level.Secondly, note that in our model the right-hand side of (40) might be strictly

positive or negative depending on whether � is positive or negative. That meansthat the break-point in our model (call it �CESB ) may be higher or lower than�CDB depending on whether the intersectoral elasticity of substitution is largeror smaller than 1: Formally:

�CESB > �CDB , � > 0

�CESB < �CDB , � < 0

In other words, and quite intuitively, the presence of an additional agglomerationforce (the substitution e¤ect when � > 0), shifts the break-point to a lower levelso that catastrophic agglomeration is more likely and it occurs for a larger setof values of �: By contrast, when the substitution e¤ect acts as a dispersionforce (� < 0), the break-point shifts to an upper level so that catastrophicagglomeration is less likely as it occurs for a smaller set of values of �:Thirdly, and most importantly, there is a set of parameters such that �CESB <

0 and so catastrophic agglomeration may always occur for any value of �. To see

19

this we should �nd two sets of parameters such that the symmetric equilibriumis unstable even for � = 0. That is, by rewriting (40) for � = 0 and using thefact that �CDB = L

L+� ; this condition reduces to:

� (1� � (1=2; 0))(� � 1) (1� �) >

2L

2L+ �

which, expressing it in terms of �; becomes:

� >2L (� � 1)

(1� � (1=2; 0)) (2L+ �) + 2L (� � 1) > 0

which is a possible outcome, provided that 2L(��1)(1��(1=2;0))(2L+�)+2L(��1) <

��1�

and so:

� (1=2; 0) <�

2L+ �=@sK@sE

In this case, therefore, the symmetric equilibrium is unstable and thencatastrophic agglomeration always takes place for any feasible value of �:For the sake of precision, note that we are not able to show the opposite,

i.e., that when � is negative enough the break-point level of � is larger than 1and then agglomeration may never take place. To see this, just notice that the

substitution e¤ect (4�1��1+�

�2�(1��(1=2;�))(��1)(1��) ) decreases with � at the same speed

as the market-crowding e¤ect. Hence, for � close enough to 1; the agglomerationforce (4 �

2L+�(1��)(1+�) ) will always be larger in absolute value than the sum of the

two dispersion forces because it decreases at a lower speed12 .

3.3 Stability analysis of the Core-Periphery Equilibrium

The northern share of �rms is constant ( _sK = 0) even when sK = 1 or sK = 0:Since the two core-periphery equilibria are perfectly symmetric, we just focuson the �rst where the north gets the core. By following Baldwin and Martin(2004), for sK = 1 to be an equilibrium, it must be that q = v=F = 1 and q� =V �=F � < 1 for this distribution of capital ownership: continuous accumulationis pro�table in the north since v = F , but V � < F so no southern agent wouldchoose to setup a new �rm. De�ning the core-periphery equilibrium this way, itimplies that it is stable whenever it exists. By using (35) and (32) we concludethat, at sK = 1 implies:

12For catastrophic agglomeration never to occur, we need that condition (40) never holdeven when � is very close to 1: Formally, this condition can be written as

lim�!1

� (1� � (1=2; �))(� � 1) (1� �)

< lim�!1

� 2�

2L+ �

1

1� �= �1

Which can never be true for any negative �nite value of � because the left-hand side alwaystakes a �nite value.

20

q (sK ; sE ; �)jsK=1 =[(L+ �)�(1; �) + L��(1; �)]

(�+ g)�= 1

q� (sK ; sE ; �)jsK=1 =

�(L+ �)�2�(1; �) + L��(1; �)

��� (�+ g)

< 1

From the �rst we can derive the value of the growth rate of world capitalin the core-periphery outcome gCP which, in this case, coincides with north�scapital:

gCP =L (�(1; �) + ��(1; �))� � (� � �(1; �))

�(41)

By substituting in q� < 1; this condition collapses to:

� >L

L+ �

��(1; �)

� (1; �)(42)

The solution of this inequality yields the sustain point of our model (call it�S), i.e., the value of the freeness of trade � above which the core-peripheryequilibrium exists and it is stable. Even though this inequality cannot be solvedexplicitly, yet we can draw several useful observation by analysing it.First notice that, when � = 0, we have that ��(1; �) = � (1; �) = � and this

condition reduces to:

� > �CDS =L

L+ �

as in the standard case (where �CDS = �CDB = LL+� ).

Secondly, if we allow � to be di¤erent from 0; we conclude that:

� > 0, �S < �CDS =

L

L+ �

� < 0, �S > �CDS =

L

L+ �

These results represent a con�rmation of our previous intuitions related to thesymmetric equilibrium. When the substitution e¤ect behaves as an additionalagglomeration force (� > 0), then catastrophic agglomeration is more likely andthe core-periphery equilibrium becomes stable for lower values of the freenessof trade. By contrast, when the substitution e¤ect behaves as an additionaldispersion force, then catastrophic agglomeration is less likely to occur and thecore-periphery equilibrium becomes stable for higher values of the freeness oftrade.

4 Geography and Integration always matter forGrowth

A well-established result in the NEGG literature (Balwin Martin and Ottaviano2001, Baldwin and Martin 2004, Baldwin et al. 2004) is that geography mat-

21

ters for growth only when spillovers are localized. In particular, with localizedspillovers, the cost of innovation is minimized when the whole manufacturingsector is located in only one region. If this is the case, innovating �rms have ahigher incentive to invest in new units of knowledge capital with respect to a sit-uation in which manufacturing �rms are dispersed in the two regions. Therebythe rate of growth of new units of knowledge capital g is maximized in the core-periphery equilibrium and "agglomeration is good for growth". When spilloversare global, this is not the case: innovation costs are una¤ected by the geograph-ical allocation of �rms and the aggregate rate of growth is identical in the twoequilibria being common in the symmetric one (g = g�) or north�s g in thecore-periphery one. Moreover, in the standard case, market integration haveno direct in�uence on the rate of growth which is not dependent on �. Whenspillovers are localized, trade costs may have an indirect in�uence on the rateof growth by a¤ecting the geographical allocation of �rms: when trade costsare reduced below the break point level, the symmetric equilibrium becomesunstable and the resulting agglomeration process, by lowering the innovationcost, is growth-enhancing. But even this indirect in�uence will not exist whenspillovers are global.In what follows, we will question these conclusions. We will show that in

our more general context (i.e. when the intersectoral elasticity of substitution isnot necessarily unitary), geography and integration always matters for growth,even in the case when spillovers are global. In particular we show that

1. Market integration has always a direct e¤ect on growth: when the inter-sectoral elasticity of substitution is larger than 1, then market integration(by increasing the share of expenditures in manufactures) is always goodfor growth. Otherwise, when goods are poor substitutes, integration isbad for growth.

2. The geographical allocation of �rms always matters for growth: the rate ofgrowth in the symmetric equilibrium di¤ers from the rate of growth in thecore-periphery one. In particular, growth is faster (slower) in symmetryif the share of global expenditure dedicated to manufactures is higher(lower) in symmetry than in the core-periphery. If this is the case, thenagglomeration is bad (good) for growth

4.1 Growth and economic integration

We now look for the formal expression of the growth rate in both the symmetricand the core-periphery equilibrium. As we have seen, the expression for thegrowth rate can be found by making use of the optimal investment condition(33). By using (31), (32) we �nd that, in the interior equilibrium we shouldhave:

gS = B(sE ; sK ; �)Ew

�� � = B�(sE ; sK ; �)

Ew

�� �

In the symmetric equilibrium we have sK = sE =12 ; so that, by using (29)

22

and (30) we know that B( 12 ;12 ; �) = B

�( 12 ;12 ; �) = �

�12 ; �

�and therefore:

gS = �

�1

2; �

�Ew

�� �

Finally, we know that Ew = 2L+ � so that we can write:

gS =2L�

�12 ; �

�� �

�� � �

�12 ; �

���

(43)

It is easy to see that:

@gS@�

=@��12 ; �

�@�

2L+ �

�

and by (22) and (23) we conclude that:

@gS@�

> 0, � > 0

@gS@�

< 0, � < 0

@gS@�

= 0, � = 0

so that integration is good for growth if and only if the traditional and themanufacturing goods are good substitutes. In the standard approach, the specialcase when � = 0, integration has no e¤ect on growth.In the core-periphery equilibrium, innovation takes place in only one region

(say, the north) so that sK = 1 and g > g� = 0: The expression of the growthrate is the same we have encoutered in the previous section (41):

gCP =L (�(1; �) + ��(1; �))� � (� � �(1; �))

�

The relation between growth and integration is not qualitatively di¤erentfrom the symmetric equilibrium. In particular we have:

@gCP@�

=L

�

�@�(1; �)

@�+@��(1; �)

@�

�+�

�

@�(1; �)

@�(44)

so that, similarly to the symmetric case:

@gCP@�

> 0, � > 0

@gCP@�

< 0, � < 0

@gCP@�

= 0, � = 0

23

We conclude that the relation between growth and market integration is notqualitatively a¤ected by the geographical location of �rms: both in symmetryand in core-periphery this relation is only a¤ected by the value of �: In bothequilibria, when � is positive, so that the intersectoral elasticity of substitutionis larger than unity, the policy maker should promote policies towards marketintegration in order to maximize the (common) growth rate. By contrast, if weaccept that the two kinds of goods are poor substitutes, then policies favoringeconomic integration are growth-detrimental and if the policy-maker is growth-oriented then he should avoid them. In any case, the growth rate in the standardcase (where growth is una¤ected by � and is identical in the symmetric and core-periphery equilibrium) is obtained as a special case (� = 0).What is the economic intuition behind this result? We should �rst consider

that growth is positively a¤ected by the total expenditure share in manufac-turing goods at the world level: an increase in this variable would increasemanufacturing pro�ts, raising Tobin�s q and then incentives to invest. As a re-sult, growth would be higher. Then, any policy instrument able to increase totalexpenditure on manufacturing goods at the world level will accelerate economicgrowth. The issue is then: what are the determinants of the total expenditureshare on manufactures at the world level? From our previous analysis we knowthat, with CES intermediate utility function, northern and southern expenditureshares depend on the geographical location of �rms (sK) and on the degree ofeconomic integration �: We leave the �rst determinant aside for a moment andwe concentrate on the second. A reduction in the cost of trade will always bringto a reduction in the price index for the manufacturing goods in both regions.However, this reduction will have opposite e¤ect on � (�) and �� (�) dependingon whether the intersectoral elasticity of substitution is larger or smaller than 1.In the �rst case, since the traditional good (which is now relatively more expen-sive) can be easily replaced by the industrial goods, the expenditure shares onthe latters will increase in both regions, and this will also increase the growthrate. By contrast, when the traditional good cannot be easily replaced by theindustrial goods, a reduction in the price index of industrial goods may increasetotal expenditure but it will decrease their share of expenditure in both regions.As a result, any integration-oriented policy will also reduce growth.

4.2 Growth and �rms�location

Since the only two possible kinds of equilibria are the symmetric and the core-periphery allocation, in order to �nd the relation between geographical locationof �rms and growth, we just need to compare (43) with (44). We then have:

gS > gCP , �

�1

2; �

�> scpE � (1; �) + (1� s

cpE )�

� (1; �) (45)

where scpE = L+�2L+� is the market size of the north when the whole industry is

concentrated in this region (sK = 1). In other words, growth in the symmetricequilibrium will be faster than in the core-periphery equilibrium if and only if

24

the industrial-goods�expenditure share in manufactures in the symmetric equi-librium (which is common in the two regions), is larger than a weighted averageof the industrial goods�expenditure share in the core-periphery equilibrium inthe two regions, where the weights are given by the reciprocal regional marketsizes. What is signi�cant in this case is then the relative importance of theindustrial goods in the consumption bundle at the world level. If at the worldlevel the industrial good is relatively more important in the symmetric equilib-rium than in the core-periphery one, then agglomeration is bad for growth anda growth-oriented policy-maker should promote policies which favor dispersionof economic activities. It is worth noting that this condition is not trivial at allsince we have:

� > 0, � (1; �) > �

�1

2; �

�> �� (1; �)

� < 0, �� (1; �) > �

�1

2; �

�> � (1; �)

A further analysis of condition (45), e.g. by using (25) and (26), will notprovide any signi�cant insight. The validity of condition (45) is highly depen-dent on the curvature of � (�) and �� (�) with respect to sK and its analysis doesnot provide any relevant economic intuition.

5 Conclusions

This paper is a �rst attempt to introduce endogenous expenditure shares ina New Economic Geography and Growth model. We do this by allowing theintersectoral elasticity of substitution to be di¤erent from the unit value andwe show how this slight change in the model assumptions leads to di¤erentoutcomes in terms of the dynamics of the allocation of economic activities, theequilibrium growth prospect and the policy insights.Concerning the dynamics of the allocation of economic activities, our model

displays three main results: 1) when the modern and the traditional goodsare poor substitutes, the substitution e¤ect acts as dispersion force, hence theagglomeration outcome can be reached for level of trade openness which arehigher than the standard case; 2) when the traditional and the industrial goodsare good substitutes, the substitution e¤ects acts as an agglomeration force andagglomeration is reached for lower degrees of market openness; 3) there arevalues of parameters such that the degree of integration is irrelevant becauseagglomeration can be reached for whatever level of trade costs.From the growth perspective, results are even more relevant: 1) unlike the

standard NEGG models, the growth rate is in�uenced by the allocation of eco-nomic activities even in absence of localized knowledge spillovers and 2) thedegree of economic integration always a¤ects the rate of growth, being growth-detrimental if the intersectoral elasticity of substitution is lower than unityand being growth-enhancing in the opposite case. We are then able to pro-

25

vide a rationale for the rather counterintuitive conclusion according to whichan integration-oriented policy rule is bad for growth.The policy implications of our analysis are signi�cant. A �rst message of

our model is that policy makers should not blindly rely on standard NEGGmodels� suggestions because some of their main results are highly dependenton the underlying assumptions. A typical example is the well-established resultstating that policy makers should not try to avoid the agglomeration of economicactivities because the concentration of the innovative and the increasing returnssectors will increase growth at a global level when spillovers are localized. Thisconclusion does not take into account the fact that the incentive to invest innew units of capital (and thereby the growth rate) depends on the Dixit-Stiglitzoperating pro�ts of manufacturing �rms, that in our model are in�uenced by theshare of expenditure in the modern goods. If the average regional expenditureshare in this sector is higher in the symmetric equilibrium than in the case ofagglomeration, then �rms�pro�ts are higher when the economic activities aredispersed among the two regions and concentrating them in only one region willreduce economic growth.A second message of our paper is that policies should take into account the

crucial role of the intersectoral elasticity of substitution. To our knowledge, thereare no empirical studies assessing the value of this parameter in the context of aNEG model. An empirical analysis of the intersectoral elasticity of subtstitutionwould be an expected follow-up of our analysis and would be highly needed inorder to assess the relative empirical relevance of the theoretical results we haveobtained.

26

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[2] Ardelean, A., (2007), "How Strong is Love for Variety?", Working Paper,Leavey School of Business, University of Santa Clara, California.

[3] Baldwin, R., (1999), "Agglomeration and endogenous capital" EuropeanEconomic Review, 43: 253-280,

[4] Baldwin, R., Forslid R., (1999), "Incremental trade policy and endogenousgrowth: A q-theory approach", Journal of Economic Dynamics and Con-trol, 23: 797-822.

[5] Baldwin, R., Forslid, R., (2000), "The Core-Periphery Model and Endoge-nous Growth: Stabilizing and De-Stabilizing Integration", Economica 67:307-324.

[6] Baldwin, R., Martin, P., (2004), "Agglomeration and Regional Growth,"in J. V. Henderson and J. F. Thisse (ed.), Handbook of Regional and UrbanEconomics volume 4: 2671-2711, Elsevier.

[7] Baldwin, R., Forslid, R., Martin, P., Ottaviano, G., Robert-Nicoud, F.,(2004), Economic Geography and Public Policy, Princeton University Press.

[8] Baldwin, R., Martin, P., Ottaviano, G., (2001), "Global Income Divergence,Trade, and Industrialization: The Geography of Growt Take-O¤s", Journalof Economic Growth, 6: 5-37.

[9] Baldwin, R., Robert-Nicoud, F., (2008), "Trade and growth with heteroge-nous �rms", Journal of International Economics, 74: 21-34.

[10] Baldwin, R., Okubo, T., (2006), "Heterogeneous �rms, agglomeration andeconomic geography: spatial selection and sorting", Journal of EconomicGeography , 6: 323-346.

[11] Bellone, F., Maupertuis, M., (2003), "Economic Integration and RegionalIncome Inequalities: Competing Dynamics of Regional Wages and Innova-tive Capabilities", Review of International Economics, 11: 512-526.

[12] Benassy, J., (1996), "Taste for variety and optimum production patternsin monopolistic competition", Economic Letters, 52: 41-47.

[13] Blanchard, O., Kiyotaki, N., (1987), "Monopolistic Competition and theE¤ects of Aggregate Demand", American Economic Review, 77: 647-66

[14] Cerina. F., Pigliaru, F., 2007, "Agglomeration and Growth: a critical as-sessment" Bernard Fingleton (ed.), 2007, New Directions in Economic Ge-ography, Edward Elgar, Chelthenam

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[15] Dixit, A.K., Stiglitz, J.E., (1975), "Monopolistic Competition and Opti-mum Product Diversity," The Warwick Economics Research Paper Series(TWERPS) 64, University of Warwick.

[16] Dixit, A.K., Stiglitz, J.E., (1977), "Monopolistic Competition and optimumproduct diversity", American Economic Review 67: 297-308.

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6 Appendix

Proposition 1 sK = 12 is the only interior equilibrium.

Proof. Consider the right-hand side of (36). The right hand side is a lin-ear function f (sK) in sK taking values from the real interval [0; 1] to the

real intervalh� �2L+� ;

�2L+�

iand having constant positive derivative given by

f 0 (sK) =�

2L+� > 0: In particular, this function is strictly positive when sK >12 ;

strictly negative when sK < 12 and is zero when sK =

12 : Consider now the left

hand side:

g (sK) =��(sK ; �) (sK + (1� sK)�)� �(sK ; �) (�sK + (1� sK))�(sK ; �) (�sK + (1� sK)) + ��(sK ; �) (sK + (1� sK)�)

since the denominator of this function is always positive, the sign of g (�)is completely determined by the numerator. By substituting for the value of� (sK ; �) and �� (sK ; �) ; the numerator of g (�) can be written as:�1� ��

� 11�� �

(�sK + 1� sK)�

(1��)(1��)+1 � (sK + (1� sK)�)�

(1��)(1��)+1��(2sK � 1) (1� �)

28

In order to study the sign of this expression, we now remind our additionalrestriction on the relative values of the intersectoral and intrasectoral elasticitiesaccording to which:

1

1� � � �

Thanks to this assumption, we are able to conclude that the previous expressionis strictly negative when sK > 1

2 , strictly positive when sK <12 and zero when

sK =12 : Hence sK =

12 is the unique interior equilibrium.

29