Local public good, regional integration and fiscal competition : an economic geography model

Transcription

1 Local public good, regional integration and fiscal competition : an economic geography model Catherine Billard Programme doctoral ESSEC LAEP, Université Paris I Panthéon-Sorbonne c.billard@tiscali.fr March 2004 Preliminary version Abstract The purpose of this paper is to explain how the public provision of local public good, like public infrastructures, transport network or legal system, acts upon agglomeration forces and how these forces, in back, affect tax competition. In this paper, we introduce a local public good, which influences productivity of firms in an economic-geography framework. We show that localization choice, for the mobile factor, depends on tax differential but also on effectiveness of public good provision in two regions. Introducing this new parameter changes the equilibrium between agglomeration and dispersion forces and affects conditions at witch a core-periphery pattern is possible. JEL codes: F12, H41, H72, R10 1

2 1 Introduction The creation of monetary union, in absence of a common fiscal policy in Europe, brings up the question of the fiscal competition between member states. The greater mobility of the factors and the economic integration in Europe should lead to convergence of the tax rates between various States. According to the traditional vision of fiscal competition, this convergence is inevitable: the differential of rate will be reduced thanks to a joint action of States or by the game of competition which entails the governments in a fiscal race. This point of view is that of traditional paradigm of fiscal competition (Baldwin and Krugman, 2000). This last one regards the fiscal game between governments as a non cooperative Nash game where States are brought to offer an attractive combination tax-public good. The fiscal game entails States in a spiral in the decline of tax rates which leads to levels of tax and public spending lower than the optimal levels. The necessity of harmonizing tax results from the fact that, ceteris paribus, producers are going to assign their capital in regions offering the weakest rate of tax so forcing the other States to align their tax policies with this rate. Thus, these models recommend coordination of the national fiscal policies or implementation of a supranational State to be able to take into account fiscal externalities generated by the fiscal decisions of the nearby States. In the literature, we find many papers analysing these questions with very different hypothesis and developments. Nevertheless, although very active, this literature doesn t explain why differential of tax persists in Europe and why governments offer public goods without being too much constrained. The question is then to know for which reasons, countries as France or Germany, in spite of a differential of tax, retain firms, capital or skilled labour. The objective is then not to consider only tax rates but also the other factors entering the choice of localization of mobile factors. It is exactly the field of Economic Geography which explains why certain economic activities choose to localize in particular places, and which studies the impact that these multiple decisions have on the territorial organization of Economy. The spatial configuration of activities is the result of a process implying two opposite forces: the centripetal forces which encourage the spatial concentration of activities and dispersion forces that oppose such concentration. In 1920, Alfred Marshall 1 identified three reasons with the fact that an entrepreneur chooses to localize near the other firms exercising the same type of 1 MARSHALL A. (1920), Principles in Economics, London Macmillan. 2

3 activity: the spatial concentration encourages a bigger availability of inputs (possessions and workers), it allows training of a highly qualified workforce resulting from a better accumulation of the human resources, finally it facilitates the exchange of information and so encourages headways in research and development. It is so a question of reasoning in terms of positive externality engendered by concentration of the activities in certain regions. The spatial configuration of the activities is the result of a process implying two types of opposite forces: the centripetal force which encourages the spatial concentration of the activities and the centrifugal force playing the other way around. Contrary to traditional models which suppose a situation of pure and perfect competition and the constant returns, the recent developments of the New Geographic Economy analyze a manufactured sector subjected to increasing returns which play the role of agglomeration force. Based on the model of Krugman (1991), these analyses show that game between the two forces can create trend to spatial concentration of production around a manufactured core. This new approach thus has strong implications in term of fiscal competition because it can justifies the existence of diverserateoftaxwithintheemu. Baldwin and Krugman (2000) show that spatial structure of economy can evolve towards concentrated equilibrium where existence of positive rent to agglomeration allows the core regions to tax more strongly the mobile factor. Andersson and Forslid (1999) develop a similar model in which they introduce a public good but they didn t widen their thought to the impact of public good on decisions of localization. Nevertheless, even if recent analyses considered the existence of a public good, they did not spread specifically their reflection to the impact of public good on the decisions of localization of mobile factor. These papers study effect of tax on the determination of the equilibrium but neglect the role of public sector as supplier of public utilities as education or public infrastructures in the fiscal choice of localization for mobile factors. The purpose of the paper is to show that localization decisions of capital (physical or human) take place not only according to the net return of capital but also according to a public factor like public infrastructures, transport network, quality of administrative department, legal system or facilities of communicationthe objective is to integrate both aspects of public policies: fiscal policy and public spending policy. With European integration, countries should reduce tax rates but try to attract firms and capital with a public investment appropriate and which offer a favourable environment for 3

4 the development of firms. The aim of paper is to explain how the public provision of local public good acts upon agglomeration forces and how these forces, in back, affect tax competition. We address these issues within a particular model where fiscal competition is analyze within the monopolistic competition framework in which we consider increasing returns and positive externalities generated by the supply of a local public good. In this paper, we introduce a local public good which influences productivity of firms via the cost function. The section 1 presents the hypotheses of model and the equilibrium conditions of short term. The section 2 introduces the supply of local public good and tax. This section determines the equilibrium conditions of long term and impact of public good on the decisions of localization. 2 The model Increasing returns is modelled within framework developed by Dixit-Stiglitz ( 1977 ) and transformed by Krugman ( 1991 ). We suppose two regions (1 et 2), two sectors (agricultural and manufactured, A et M) and two factors, unskilled labour (L) and skilled labour (human capital, K). Only skilled labour is mobile between regions. L=L 1 +L 2,L 1 represents the number of unskilled workers in the region 1thatpaysw L 1. The agents have the same preferences represented by the utility function: U = C µ M C1 µ A \ µ µ (1 µ) 1 µ (1) µ (0, 1) is a constant and represents the part of manufactured goods in expenses of consumption. -C A represents the consumption of an homogeneous good A produced by the agricultural sector. This sector is supposed in situation of pure and perfect competition and present constant returns on scale. The good A is produced without human resources and is exchanged in absence of transportation costs. This good is used as numeraire thus p A =w L =1,a single unit of work is used in production of one unity of good A. This allows to concentrate on the determination of return on human capital which is one of the key variables of model. Indeed, as the qualified work is mobile 4

5 between regions, the holders of capital are going to arbitrate between the various returns to choose their location. -C M is the consumption of differentiated goods produced by the manufactured sector. The firms of this sector are in situation of imperfect competition because of increasing returns. C M represents a sub-utility function defined on a continuum of differentiated goods. It is described by CES function where σ represent the elasticity of substitution between varieties, σ 1. n C M = j=1 x σ 1/σ i σ 1 σ (2) x i represent the consummate quantity of variety i, n is the number of available varieties. 2.1 The consumer behaviour The representative consumer determines his possibilities of consumption of the various goods under constraint of income. Let us suppose, Y the given aggregated income, p A =1 the price of agricultural good and p(i) the price of vaiety i produced by M sector. The program of maximisation of consumer under budgetary constraint spells: Max U = C µ M C1 µ A \ µ µ (1 µ) 1 µ sc Y = p A C A + n i=1 p(i)x(i) We determine demand functions for agricultural sector and for manufactured sector: C M = µy 1 H (3) C A = Y (1 µ) (4) The term ( H ) represents the price index of all varieties produced by the manufactured sector. Both stages of maximisation allow us to change equation of demand for the variety i in region 1: 5

6 x(i) =µy p(i) σ H1 σ 1 (5) Let us note that for H constant, the price-elasticity of demand for available variety is constant and equals σ. 2.2 Producer behaviour in manufactured sector The goods of M sector are produced in a context of monopolistic competition with increasing returns. The cost function presents fixed costs in human capital and identical variable costs between regions and corresponding to the amount of unskilled work necessary to produce one unity of good. We suppose that only one unit is necessary. Let us consider the cost function of a firm producing in region 1. c 1 = α 1 r 1 + x 1 (6) r 1 is the return of human capital and x 1 the number of produced units. The profit of firm in region 1 spells: Π 1 = p 1 x 1 [α 1 r 1 + x 1 ] (7) As we are in monopolistic competition, the maximisation of the profit is made according to the hypotheses of Chamberlin ( 1933 ). Every firm decides on the level of production and defines the price according to marginal recipe = marginal cost. p σ i =( σ 1 ) (8) We suppose that there is free entrance on market, thus profits tighten towards zero. By substituting the equation of price in that of profit, we find the equilibrium quantity offered by a company producing the variety i in the region 1: x i =(σ 1)α 1 r 1 (9) x i = (σ 1) σ µy 1 ( + φµy 2 ) (10) n 1 + φn 2 φn 1 + n 2 6

7 Because of equilibrium conditions on human capital market, the number of firms in each regions (n 1 et n 2 ) is a function of the elasticity of substitution and of the fixed cost: n 1 = K 1 = λk (11) σα 1 σα 1 n j = K 2 (1 λ)k = (12) σα 2 σα 2 With K 1 = λk and K 2 =(1 λ)k Before determining the equilibrium conditions of sector M, we are going to introduce transportation costs. The manufactured good can be exchanged between places but this has a cost. Indeed, the prices of manufactured goods differ between regions because they include transportation costs ( T ). So, the price index of manufactured goods ( H ) varies according to regions. We suppose iceberg type 2 of transportation costs (T), for which the cost is included in the transported good. If one unity of good is exchanged, only afractionτ 1 really arrive at destination. The rest is consumed during the transport. This particular shape of transportation costs implies that variety i produced in the region 1 is sale to a price p 1 i in region 1 and at a price p 2 i =p1 i + T12 i in region 2. The fraction τ is then equals to inverse of transportation cost. The same good will thus have different price according to regions. We define φ = T 1 σ which represents the degree of economic opening of locality. 0 φ 1, whenφ =1, the cost of transport is equal to zero, it is a situation of free exchange. If φ =0, it corresponds to the total autarky of region. With n 1 the number of firms in region 1. The price index of sector M for region 1 spells: H 1 =(p 1 σ 1 n 1 + φp 1 σ 2 n 2 ) 1 1 σ (13) σ H 1 = (σ 1) (n 1 + φn 2 ) 1 1 σ (14) A locality with a sector M very developed will have a lower price index because only a small part of consumption will support costs of transport. 2 Ce type de coûts de transport a été introduit par Samuelson (1952). 7

8 Besides, workers migration in the region 1 will entail an increase of the number of available variety in this region. This increase has the effect of reducing the price index and thus of increasing the real wage of workers. This relation, generally spells forward linkage, will be studied more in detail in the following section. The demand for variety i, produced in the region 1, is then the sum of the domestic demand and the outside demand. In the equilibrium, we equalize the offer and the demand to define the equilibrium return of human capital. p σ 1 p 1 x 1 = α 1 σr 1 = µy 1 H1 1 σ + µy φp σ 1 2 H2 1 σ 1 µy 1 r 1 = + φµy 2 σα 1 n 1 + φn 2 φn 1 + n 2 (15) (16) 2.3 Long-term equilibriums We find, here, the main results of the simplified version of core-periphery model proposed by Ottaviano (2003). In short run, we consider that the human capital endowment of both villages is fixed. This endowment, in qualified workers, determines the size of manufactured sector. L 1 and K 1 are respectively the endowments in unskilled workers and in human capital in region 1. We suppose that unskilled workers are distributed in a symmetric way between regions: L 1 = L 2 = L/2. Besides, we suppose that labour markets of each locality fit immediately. To determine the return on human capital in both regions (1 and 2), we suppose: Y 1 = L/2+r 1 (λ, φ)λk (17) Y 2 = L/2+r 2 (λ, φ)(1 λ)k (18) By substituting these incomes in the equation of r 1 : µ r1 L/2+r1 λk = σα 1 n 1 + φn 2 + φ(l/2+r 2(1 λ)k) φn 1 + n 2 (19) 8

9 By supposing α 1 = α 2, for this moment, we obtain a system of equations allowing us to express the returns on equilibrium: r 1(λ,φ)= Lµ(σ(λ(φ 1) 2 φ 2 1) + (λ 1)(φ 2 1)µ) 2K(µ σ)( σφ λ(φ 1) + µ(1 + φ)) + λ 2 (φ 1)(σ(φ 1) + µ(1 + φ))) (20) r 2(λ,φ)= Lµ(σ2φ + λ(φ 1)(σ(φ 1) + µ(1 + φ))) 2K(µ σ)( σφ λ(φ 1) + µ(1 + φ)) + λ 2 (φ 1)(σ(φ 1) + µ(1 + φ))) (21) The derivation of the ratio r 1 (λ,φ) r2 (λ,φ), with regard to lambda, allows us to define a value threshold for the costs of transport. Indeed, as long as the value of transportation costs is higher than the value threshold (φ r (0, 1)), the region with the best endowed in human capital will also be the one who offers the best return. φ r = σ µ σ + µ In longer term, the skilled workers migrate between regions according to the relative utility proposed by the various places. To determine this relative utility, we build the indirect utility function of a representative individual resulting from his consumer s choices. With v 1 (λ), the indirect utility function of representative agent in region 1 expressed according with Y and H : v 1 = µy H µ (1 µ) Y p A 1 µ \ µ µ (1 µ) 1 µ (22) It is preferable here to argue directly in term of differential and to express the indirect utility function of skilled workers under the shape: v(λ, φ) [ r 1(λ, φ) H µ 1 r 2(λ, φ) H µ ] (23) 2 9

10 When v(λ) is negative (when λ =0), we attend a migratory movement of the region 1 towards the region 2. The situations where all the sector M is concentrated in only one place (λ =0et λ =1) are equilibriums if and only if, respectively v(0, φ) 0 et v(1, φ) 0. We can rewrite v(λ, φ) and isolate the parameters independent of φ so as to work on a reduced shape of v(λ, φ). This expression, handier, will allow us to determine the equilibriums. v(λ, φ) B V (λ, φ) (24) V (λ, φ) = 2φλ +[1 µ/σ +(1+µ/σ)φ2 ](1 λ) [λ + φ(1 λ)] µ 1 σ - 2φ(1 λ)+[1 µ/σ +(1+µ/σ)φ2 ]λ [φλ +(1 λ)] µ 1 σ (25) The function of indirect utility, on which depends the decisions of localization, allows to put in light the game between concentration and dispersion forces: a region with better endowed in human capital, with more firms and more workers, offers a vaster market and thus be more attractive for companies and holders of human capital, it is the home market effect. Besides, towards the offer, more qualified workers amounts to more varieties and thus to a weaker price index. From then on, the region offers a more attractive real wage to skilled workers, it is the price index effect. These two effects have a central place in circular causality in the spatial concentration of firms and workers. Given the consumers preference for variety, when numerous varieties of good is produced in region 1, it increases the real income of the workers (for a given nominal income) thus more workers-consumers settledowninregion1. Thishasaneffect of increasing the size of market and allows numerous firms, benefiting from economies of scale, to become established in the region 1... Now, the question is to determine the conditions for which the concentrated equilibrium exists and those where it becomes necessary, that is when the symmetric equilibrium stops being stable. These two critical points (φ s et φ b ) express the levels of transportation costs thresholds for the equilibriums. For high costs, there is a stable equilibrium where the human capital is distributed between both regions. When these costs fall and pass below the critical threshold (φ b )thesymmetricequilibrium becomes unstable. 10

11 Finally, a reduction of the costs of transport below a second critical point allows the emergence of a new equilibrium with a concentration of capital in only one region Stability of concentrated equilibrium To determine the threshold point where the core-periphery equilibrium is bearable, we study the case where all sector M is concentrated in region 1 (what corresponds in λ =1). It is then a question of comparing the level of the returns between both regions. We replace λ by 1 in function V (λ, φ): V (1, φ) =2φ φ µ µ 1 σ (1 σ +(1+µ σ )φ2 ) (26) So, in term of transportation costs, the stability of core-periphery pattern is guaranteed for levels superior to the sustain point, φ sustain, defines by the equation: µ 1 σ 2φ s φs (1 µ σ +(1+µ σ )φ2 s)=0 (27) The bearable value of transportation costs (φ sustain ) is thus an increasing function of µ and decreasing of σ Stability of symmetric equilibrium The symmetric distribution of firms and human capital is a stable equilibrium for relatively high levels of transportation costs. On the other hand, if these costs pass below a certain threshold (φ b ), the equilibrium becomes unstable. We estimate, for λ =1/2, the partial derivative of V (λ, φ) with regard to lambda and we study its sign. If derivative of V (1/2, φ) is negative then the symmetric equilibrium is stable. We determine then the break point where the symmetric equilibrium stops being stable. It is the case if the costs of transport become too weak. Indeed, for intermediate levels of transportation costs, both effects (price index and home market) play and a migration of capital towards the region 1 increases the return on capital in this region and puts in danger the stability of the symmetric equilibrium. We define φ break : φ b µ(1 + µ)+σ σ2 +2µσ µ(1 µ) σ + σ 2 +2µσ (28) 11

12 The break point of symetric equilibrium (φ break ) is growing with µ and decreasing with σ. So, more the manufactured sector is important and more the substitutability of products is weak, more the sustain point of the equilibrium core-periphery is situated at high levels of transportation costs. According to the analysis of Krugman (1991), φ sustain φ break. The symmetric equilibrium becomes stable for a value of transportation costs lower than the value for which the concentrated equilibrium stops being stable. Indeed, if we are in core-periphery pattern, the costs of transport have to pass above thebreakpoint(φ break ), so that the concentrated equilibrium has to become unstable and what appears the symmetric equilibrium. 3 Public provision of local public good and localization decisions Nevertheless, in this type of model àlakrugman, the treatment of public sector remains partial because only taxes are integrated into the model whereas the role of public spending is totally ignored. Indeed, with the European integration, States undertake in a greater fiscal competition but also try to attract capital in their region by assigning their fiscal receipts to the creation of public infrastructures be able to fulfil at the needs of firms. Taxes serve to finance public infrastructures generating pecuniary externalities and the effects of which can limit the movement of relocation of activities. The tax system is thus at the origin of a decline of the return on capital but also generates positive externalities for firms. It is then a question of integrating into traditional model both aspects of the public action: taxation and public spending policy. These two aspects are modelled by two types of opposite forces. Indeed, a high tax rate reduces rent of agglomeration and so acts as force of dispersal. On the other hand, an increase of public investments favours the spatial concentration of companies if they increase the attractiveness of the region. So, we can think that high rates of taxes imply better public infrastructures. Nevertheless, it s important to study relations between these two forces and estimating which one dominates in arbitrage of localization. The object of this section is to integrate a local public good, be able to create positive externality for firms. 12

13 3.1 The treatment of local public good The governments of both regions, supply each a local public good (G 1 et G 2 ) financed from a tax on return of human capital (t 1 et t 2 ). The budget constraint of governments spells: G = trk (29) The object of this section is to integrate a public good, benefiting to firms, into arbitrage of localization for mobile factor. We suppose that the supply of local public good affects the productivity of firms via the cost function: public infrastructures favor the business connections via the quality of networks (transport, telecom...). Indeed, the positive externality engendered by this good reduces the fixed cost of the company in term of human capital. This hypothesis allows reporting the impact of public good on production. The fixed cost depends on the supply of local public good which is function of level of tax. We suggest here to define the parameter of the fixed cost α according to thetaxe(t)andtodegreeofefficiency of the public spending (β). Thefixed cost (α(t, β) (0, 1)) falling with t and vary according to regions. We suppose a firm in region 1: α 1 = α 1 (t 1, β 1 ) (30) α 1 =1 β 1 t 1 (31) c 1 = α 1 (t 1 )r 1 + x 1 =(1 β 1 t 1 )r 1 + x 1 (32) β 1 and β 2 ( (0, 1)) represent, respectively, the degree of efficiency of the public spending in region 1 and in region 2. The parameter of the fixed cost α is decreasing function of βand t. As the efficiency of the public spending increases (decline of beta), the fixed cost supported by firms in term of human capital decrease. The market clearing conditions on human capital market gives the number of companies in both regions also according to α 1 (t 1 ): 13

14 λk n 1 = σ(1 β 1 t 1 ) (33) (1 λ)k n 2 = σ(1 β 2 t 2 ) (34) We can, at the moment, express equilibrium conditions in manufactured sector with the following system: r1 = r2 = µ L/2+r1 λk σ(1 β 1 t 1 ) n 1 +φn 2 + φ(l/2+r 2(1 λ)k) φn 1 +n 2 µ φ(l/2+r1 λk) σ(1 β 2 t 2 ) n 1 +φn 2 + L/2+r 2(1 λ)k φn 1 +n 2 (35) This system allows us to determine equilibrium values of r 1 et r 2 : r 1 = L(1 β 2 t 2 )µ(2(1 β 2 t 2 )σλφ (1 β 1 t 1 )(λ 1)((φ 2 1)µ+σ(φ 2 +1) 2K(µ σ)((1 β 1 t 1 ) 2 (λ 1) 2 σφ+(1 β 2 t 2 ) 2 λ 2 σφ (1 β 1 t 1 )(1 β 2 t 2 )(λ 1)λ(µ(φ 2 1)+(σ(φ 2 +1))) (36) r 2 = Lα 1 µ( 2α 1 (λ 1)σφ (1 β 2 t 2 )λ((φ 2 1)µ+σ(φ 2 +1) 2K(µ σ)((1 β 1 t 1 ) 2 (λ 1) 2 σφ+(1 β 2 t 2 ) 2 λ 2 σφ (1 β 1 t 1 )(1 β 2 t 2 )(λ 1)λ(µ(φ 2 1)+(σ(φ 2 +1))) (37) The return of human capital become a function of elasticity of substitution, of transportation costs, of the part of manufactured goods in expenses of consumption, of the spatial distribution of human capital, of level of fiscality fixed by local authorities and of degree of efficiency of public spendings. As the tax and efficiency of public spendings differ from a region in the other one, it affects the produced quantities and thus the number of present firms in localities because it appear at the level of fixed costs supported by the firm. 14

15 3.1.1 Stability of concentrated equilibrium Let us resume the expression of the indirect utility in the differential form: v(λ, φ) [ r 1(λ, φ) H µ 1 r 2(λ, φ) H µ ] (38) 2 The indirect utility of skilled worker subjected to tax spells: v(λ, φ) [ (1 t 1)r 1 (λ, φ) H µ (1 t 2)r 2 (λ, φ) 1 H µ ] (39) 2 We simplify this function and we obtain this reduced form: v(λ, φ) B V (λ, φ) (40) V = [(t 1 1)(1 t 2 β 2 )( 2λσφ(t 2 β 2 1)+(t 1 β 1 1)(λ 1)(σ µ+φ 2 (µ+σ)) [(t 1 β 1 1) 2 (λ 1) 2 σφ+(t 2 β 2 1) 2 λ 2 σφ (t 1 β 1 1)(t 2 β 2 1)(λ 1)λ(σ µ+φ 2 (µ+σ))] (41) + (1 t 2 )(1 t 1 β 1 )(2σφ(t 1 β 1 1)(λ 1)+λ(1 t 2 β 2 )(σ µ+φ 2 (µ+σ)) (42) [(t 1 β 1 1) 2 (λ 1) 2 σφ+(t 2 β 2 1) 2 λ 2 σφ (t 1 β 1 1)(t 2 β 2 1)(λ 1)λ(σ µ+φ 2 (µ+σ))] With t 1,t 2 and β 1, β 2 (0, 1). The decision of localization depends on traditional parameters but also ontaxratesandonefficiency of public spendings in both regions, via the fixed cost. V represents the migration equation, as V =0no migration occurs. We take place, at the moment, in the framework where all industrial activity is concentrated in the region 1 (λ =1)andthefirst ask is thus to define the sustain point of transportation cost above which the core pattern is sustainable. As long φ > φ s (T < T s ), capital stay agglomerated in region 1. As we made it previously, we are interested by the sustain value of transportation costs for the stability of core-periphery pattern. To determine this equilibrium, we look for the value of φ which solve the equation V (1, φ) =0 Here, we can find a analytical solution which is the new point threshold φ s : 15

16 φ s = 2σ(t 1 1)(t 2 β 2 1)+ 4σ 2 (t 1 1) 2 (t 2 β 2 1) 2 +4(t 2 1) 2 (t 1 β 1 1) 2 (µ σ)(µ+σ) 2(t 2 1)(t 1 β 1 1)(µ+σ) (43) Introduction of tax rates and efficiency of public spendings affects conditions and stability of equilibrium. The sustain point for transportation cost and for concentrated equilibrium is a decreasing function of t 1,t 2, β 1 and β 2. When tax rate increases, φ s falls, the sustainable level of transportation costs for core-periphery pattern is higher. 3.2 Tax competition The modelling allowed us to put in evidence the role of public spendings and taxation in decisions of localization. We show while the fiscal arbitrage of localization is not only made according to tax differential but also according to the efficiency of public spendings. In second time, we have to be interested in reactions of state in the face of fiscal variable and of fiscal arbitrages of localization. The objective of this section is to show how the government takes into account the impact of its offer of public good on the fixed cost supported by firms and on their decisions of localization. The stake is to know if tax rates can remain, in Europe, at different levels as long as the disparities are not too important, because of existence of a concentrated equilibrium. This equilibrium is characterized by the agglomeration of firms in the industrial area of core where levels of taxes and public good are higher than levels in peripheral region. In view of tax competition, we are specially interested by the core-periphery outcome because it is better reflected the European situation. As Baldwin and Krugman (2000), we suppose a three stage game where human capital is concentrated in region 1 (λ =1). In the first stage, the region core sets its tax rate, in the second stage government of region 2 decides its tax rate. In the third stage, production and migrations are set up. Using backward induction, the third stage is describes by the equilibrium conditions and we focus on the second stage. Government of region 2 sets its tax rate by taking the rate of region 1 as given. He can set its tax rate to a level enough low to attract firms/entrepreneurs of the core or he can determine its tax rate only according to its domestic economy and no migratory movement will take place. We can then define the critical tax rate of region 2 below which the human resources migrates of the core region to the periphery. This critical point (t b 2 ) is obtained in solving the delocation condition 3. 3 See BALDWIN R.E. and P.KRUGMAN (2004) 16

17 This condition is a condition of no-migration when all human capital is agglomerated in region 1 and corresponds in case where the indirect utility function equals to zero or: [ (1 t 1)r 1 (λ, φ) H µ 1 = (1 tb 2 )r 2(λ, φ) H µ ] (44) 2 To determine the critical point for tax rates in region 2, we look for the value of t 2 which solve the equation V (1, φ) =0 t b 2 = µ(t 1 β 1 1)(φ 2 1) + σ[ (φ 1) 2 + t 1 (β 1 2φ + β 1 φ 2 )] µ(t 1 β 1 1)(φ 2 1) + σ[2β 2 φ 1 φ 2 + t 1 (β 1 2β 2 φ + β 1 φ 2 )] t b 2 is an increasing function of t 1. Given the number of variables and the complexity of analytical resolution of model, we proceed by numeric simulations. For a tax rate given in the core region, we observe variations of the rate threshold for the region 2. If the tax rate of region 2 exceeds this critical rate, we attend a migration of the core towards the periphery. In absence of efficiency of public spendings (β 1 = β 2 =0), critical point for region 2 is a linear function of t 1.We observe that for a rate given in the region 1, a variation in the decline of the costs of transport (increase of φ) create an increase in tax rate threshold for region 2. In case of UEM, we think more realistic to consider a low level of transportation cost. In this case and if efficiency of public spendings is positive in region 1, we see that for very high level of tax rate in region 1, the critical value for tax rate in periphery is very low. If the efficiency of public spendings is high, the core region can also keep human capital in despite of tax differential with region Conclusion We have seen that if the forces of agglomeration dominate, skilled workers will encourage to join the core. The government of core can thus tax human capital at a higher level than level of tax rate in periphery because of a positive rent of agglomeration which comes to compensate the difference of taxation. The government of core region then set a tax rate enough low so that the peripheral region does not try to attract industry. In this analysis, the fiscal competition is transformed because the peripheral region knows 17

18 that she cannot compete, as long as the differential of tax remains acceptable for skilled workers. The government of peripheral region thus fixes its tax rate mainly according to its domestic economics. On the other hand, the eventuality of a fiscal competition coming from the periphery, force the core region in its fiscal choices. The central question is now to study the impact of externality generated by local public good on government behaviour. How governments of both regions take into account their influence on decisions of localization of capital? The stake is to define a situation where the economic integration would not be translated by the fiscal race and by the sub-optimal supply of public utilities. The modelling proposed by the New Economic Geography allows to arrest the question of fiscal competition thanks to the presence of agglomeration and dispersion forces which can bring to the existence of a coreperiphery equilibrium. This equilibrium appears when externality of concentration, due to increasing returns on scale and to presence of the local public good, dominates the dispersion force. The idea is then to consider the supply of certain type of public good as a new agglomeration force likely to influence human capital in its decisions of localization. 18

19 References [1] ANDERSSON F. et R.FORSLID (1999), Tax Competition and Economic Geography, CEPR Discussion Paper n [2] BALDWIN R. et P.KRUGMAN (2000), Agglomeration, integration and tax harmonization, CEPR Discussion Paper n [3] BALDWIN R. et P.KRUGMAN (2004), Agglomeration, integration and tax harmonization, European Economic Review, vol. 48, pages1-23 [4] CHARLOT S. (2000), Des infrastructures de transport à la concurrence fiscale, Revue d Economie Régionale et Urbaine, volume 0(1), pages [5] DIXIT A.K. et J.E.STIGLITZ (1977), Monopolistic Competition and Optimum Product Diversity, American Economic Review, volume 67, pages [6] FORSLID R. (1999), Agglomeration with human and physical capital: An analytically solvable case, CEPR Discussion Paper n [7] FORSLID R. et I.WOOTON (1999), Comparative Advantage and the Location of Production, CEPR Discussion Paper n 2118 [8] FUJITA M., KRUGMAN P. et A.J.VENABLES (1999), The Spatial Economy. Cities, Regions and International Trade. MIT Press. [9] KRUGMAN P. (1991), Increasing Returns and Economic Geography, Journal of Political Economy, volume 99 n 3,pages [10] LUDEMA R.D. et I.WOOTON (1998), Economic Geography and the Fiscal Effects of Regional Integration, CEPR Discussion Paper n [11] MASSIMILIANO M. (2002), Some stylised facts on non-systematic fiscal policy in the euro area, CEPR Discussion Paper n 3635 [12] OTTAVIANO G.I.P et J.F. THISSE (2003), Agglomeration and economic geography, CEPR Discussion Paper n 3838 [13] OTTAVIANO G.I.P et T.V. YPERSELE (2002), Market access and tax competition, CEPR Discussion Paper n 3638 [14] RIEBER A. (2000), Intégration régionale, mobilité du capital et concurrence fiscale, Economie Internationale n 81, pages