DISCUSSION PAPER SERIES. No SUBSIDIES TO POOR REGIONS AND INEQUALITIES: SOME UNPLEASANT ARITHMETIC. Vincent Dupont and Philippe Martin

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1 DISCUSSION PAPR SRIS No SUBSIDIS TO POOR RGIONS AND INQUALITIS: SOM UNPLASANT ARITHMTIC Vicet Dupot ad Philippe Marti INTRNATIONAL TRAD ABCD Available olie at:

2 ISSN SUBSIDIS TO POOR RGIONS AND INQUALITIS: SOM UNPLASANT ARITHMTIC Vicet Dupot, Uiversité des Scieces et Techologies de Lille (USTL) Philippe Marti, CRAS-NPC ad Uiversité de Paris I ad CPR Discussio Paper No November 2003 Cetre for coomic Policy Research Goswell Rd, Lodo C1V 7RR, UK Tel: (44 20) , Fax: (44 20) mail: cepr@cepr.org, Website: This Discussio Paper is issued uder the auspices of the Cetre s research programme i INTRNATIONAL TRAD. Ay opiios expressed here are those of the author(s) ad ot those of the Cetre for coomic Policy Research. Research dissemiated by CPR may iclude views o policy, but the Cetre itself takes o istitutioal policy positios. The Cetre for coomic Policy Research was established i 1983 as a private educatioal charity, to promote idepedet aalysis ad public discussio of ope ecoomies ad the relatios amog them. It is pluralist ad o-partisa, brigig ecoomic research to bear o the aalysis of medium- ad log-ru policy questios. Istitutioal (core) fiace for the Cetre has bee provided through major grats from the coomic ad Social Research Coucil, uder which a SRC Resource Cetre operates withi CPR; the smée Fairbair Charitable Trust; ad the Bak of glad. These orgaizatios do ot give prior review to the Cetre s publicatios, or do they ecessarily edorse the views expressed therei. These Discussio Papers ofte represet prelimiary or icomplete work, circulated to ecourage discussio ad commet. Citatio ad use of such a paper should take accout of its provisioal character. Copyright: Vicet Dupot ad Philippe Marti

3 CPR Discussio Paper No November 2003 ABSTRACT Subsidies to Poor Regios ad Iequalities: Some Upleasat Arithmetic This paper aalyses the effect of differet types of regioal subsidies to poor regios o idustrial locatio, employmet, icome iequality betwee ad iside regios ad welfare. We show that the impact o locatio of such subsidies is stroger whe trade costs are low. Whe firms are mobile, regioal subsidies that take the form of tax breaks or subsidies to the fixed cost lead to higher profits for all firms, eve those ot located i the regio that gives the subsidy. If fiaced at the atioal level, such subsidies give to firms i the poor regio icrease regioal icome iequality as the rich regio ows more capital. Hece, eve though they costitute a official fiacial trasfer from the rich to the poor regio, they actually lead to a icome trasfer from the poor to the rich regio. It also leads to higher iequality withi regios. Whe fiaced at the local level, subsidies succeed i attractig firms. Besides, as regioal subsidies to firms of the maufacturig sector i the poor regio alter local competitio ad firm size, they may actually lead to a decrease of regioal employmet ad productio of that sector i the poor regio. Fially, with relocatio costs, such regioal subsidies may hurt the poor regio. JL Classificatio: H2, H7 ad R0 Keywords: ecoomic geography, regioal iequalities ad regioal subsidies Vicet Dupot Uiversité des Scieces et Techologies de Lille, USTL Cité Scietifique Villeeuve d Ascq Cedex FRANC Tel: (33 3) mail: dupotvi@voila.fr For further Discussio Papers by this author see: Philippe Marti CRAS-NPC NS 48 Boulevard Jourda Paris FRANC Tel: (33 1) Fax: (33 1) mail: marti-p@epc.fr For further Discussio Papers by this author see:

4 We thak Richard Baldwi, Giamarco Ottaviao ad Frederic Robert- Nicoud for helpful commets, as well as participats at the NBR Summer Istitute 2003 ad the A This Paper is produced as part of a CPR research etwork o The coomic Geography of urope: Measuremet, Testig ad Policy Simulatios, fuded by the uropea Commissio uder the Research Traiig Network Programme (Cotract No: HPRN-CT ). Submitted Tuesday, September 23, 2003

5 I. Itroductio Oe third of the U budget goes to regioal policies. This is the secod item o the budget just after the Commo Agricultural Policy ad will accout for 213 billio for the period. O top of this, atioal govermets themselves also sped large amouts o regioal policies ad subsidies or State Aid which are allowed by the U up to a certai degree, which depeds o how disadvataged the regio is. A substatial share of the budget of regioal policies at the U or at the atioal level, cosists of direct or idirect subsidies to private firms located i poor regios. I the Uited States, Bartik (2002) estimates that roughly $20 30 billio i state ad local govermet spedig is devoted to such ecoomic developmet programs aually, mostly i the form of tax breaks, with perhaps aother $6 billio aually i support from the federal govermet. The prime objective of the subsidies i the U is to attract ecoomic activities i poor regios based o the assumptio that this will decrease regioal iequality, icrease employmet, wages, ad productivity i those regios. I the U jargo, they are also supposed to ehace social cohesio meaig that they are supposed to reduce iequalities i a more geeral sese 1. The aim of this paper is to show that regioal policies may have other less obvious effects that are less welcome from a political poit of view. For this, we aalyze differet types of subsidies ad their effects o idustrial locatio, regioal icome iequality, profits, employmet ad iequalities betwee workers ad capital owers. This aalysis is doe i a very simple geeral equilibrium model with agglomeratio forces. Several isights arise from the study of subsidies i the presece of agglomeratio forces whe firms are mobile. 1 The extet to which uropea regioal policies have bee successful is the subject of a lively empirical debate: the Commissio (1999) has foud a positive effect of regioal policies o regioal growth over the short term, i.e. over a five- or six-year period. But those macroecoomic studies look at the macroecoomic effect at the coutry level oly, ot the regioal level. Combes ad Overma (2003) amog others have show that, eve if icome per capita has slightly coverged betwee Member States, it has diverged at the regioal level durig the same period. Boldri ad Caova (2001) fid o effect of regioal policies o regioal covergece. More precisely, they fid o evidece (with the exceptio of Irelad) that regios which received U fuds grew faster tha others. De la Fuete (2000) fids a more positive impact of the U policies for Spaish regios. Fially, Midlefart-Karvick ad Overma ( 2002) foud that the geography of maufacturig remaied very stable at the atioal level, while becomig more cocetrated at the regioal level sice the 1980s. 2

6 Regioal subsidies do attract firms a result that would hold i almost ay model, icludig models without agglomeratio forces. Our first isight is that the impact of the regioal subsidies becomes greater the higher is the level of goods-market itegratio. This is just a corollary of the home market effect, preset i ew trade models, but it has implicatios for regioal itegratio. For example, if regioal itegratio i the U or amog developig coutries (MRCOSUR) ad more geerally if the decrease i trasport costs cotiues to lower trade barriers without chagig the level of permissible subsidies to firms i remote regios, the subsidies will lead to a icreased distortio of the spatial allocatio for idustry. The secod isight is that whe firms are mobile, regioal subsidies to firms i oe regio lead to higher operatig profits i all regios as the equilibrium geography is such that profits are equalized across regios. Thus, eve firms that do ot directly beefit from regioal subsidies gai idirectly through the distortio o regioal competitio: as firms relocate to the regio that provides the subsidies, competitio becomes weaker i the other regio so that profits icrease there too. This raises iterestig questios o the relatio betwee spatial iequalities ad idividual iequalities, especially betwee immobile workers ad owers of mobile capital ad the impact of regioal policies o these types of iequalities. Implicitly or explicitly, regioal policies are based o the belief that if spatial iequalities are decreased the iequalities i geeral will be decreased. I a situatio where capital is mobile but workers are ot (or less so), this is ot true. Not oly do such subsidies icrease iequalities betwee workers ad capital owers. A subsidy give to firms that locate i the poor regio ca actually worse omial icome iequality betwee the poor ad the rich regio: if profits icrease due to the subsidy ad most capital owers are i the rich regio the these capital owers will disproportioately beefit from the subsidy iteded to the poor regio, ad so will the rich regio too. Hece, the subsidy to the poor regio actually leads to a trasfer from the poor to the rich regio eve whe the subsidy is fiaced by a atioal proportioal tax o icome which falls therefore more heavily o the rich regio. Aother way to say this is that eve though there is a official et trasfer from the rich to the poor regio, the et effective trasfer of icome is from the poor to the rich regio. For this result to hold, it is ot ecessary that capital owers of the rich regio ow the firms that beefit from the subsidy i the poor regio but simply that firms be mobile. The third isight cocers the effect of the way subsidies are fiaced. Fiacig the subsidy requires a tax that reduces market potetial, ad so firms profits. Regioal subsidies that 3

7 are fiaced at the atioal level have the largest effect o relocatio. Whe the subsidy is fiaced by the regio itself, the local tax that satisfies the budget costrait decreases local demad, ad so reduces the iitial impact of subsidy o relocatio. ve whe fiaced locally, regioal subsidies lead to relocatio i the regio that gives the subsidy. Aother way to put it is that the egative effect of taxig regioal expediture is more tha compesated by the subsidies to regioal productio. A fourth isight is that whatever the way the subsidy is fiaced, ad eve though it targets firms of the maufacturig sector, it may lead to a decrease of employmet ad output of that sector i the poor regio. The reaso is that as firms relocate to the poor regio, the icrease i competitive pressure implies a decrease i their size. Fially, we aalyze the effect of relocatio costs. If they are high eough so that subsidies for firms located i the poor regio lead to o or little relocatio, the the subsidy actually hurts the poor regio because it geerates a trasfer from the poor to the rich regio. I what follows we will aalyze the effects of a local subsidy to firms producig i poor regios i a geeral equilibrium model of edogeous locatio. Three types of subsidy are successively studied: 1) a subsidy to profits of firms that locate i the poor regio, that ca be iterpreted as a tax break 2) a lump sum subsidy to firms that locate i the poor regio. This ca be iterpreted as lump sum tax break or a subsidy to the fixed cost, such as whe lad is give (or sold below market price) to the firm to build the plat. 3) a subsidy to productio of firms located i the poor regio, such as subsidies proportioal to the umber of jobs created by the firms. They work as a decrease of the variable cost of productio. This is for example the case i Frace with the mai istrumet of regioal policy, the Prime d Améagemet au Territoire (PAT) which gives to firms located i poor regios a subsidy of aroud 10000$ per job created. Because the subsidy is give oce ad for all ad that it ca also fiace R&D of those firms, the PAT has also the characteristic of a lump sum subsidy. Frace however appears as a exceptio i urope. Most coutries subsidize ivestmet rather tha employmet at the regioal level ad this traslates ito subsidies to capital rather tha labor (see Yuill et al, 1994 ad Fuest ad Huber, 2000). A importat example is the subsidy program provided to aster Germay. Accordig to Fuest ad Huber (2000), 90% of the subsidies to firms locatig i aster Germay take the form of ivestmet subsidies. At the uropea level, more tha 400 types of subsidies exist that ca help firms i poor regios. They take so may forms that it is difficult to put them i oe of these three categories. It seems quite safe to characterize them as a complicated mix of the three. 4

8 The existig papers most related to ours aalyze the effect of taxes ad subsidies i ecoomic geography models. This is the case of Baldwi et al. (2003) who show that the impact of subsidies or taxes is subject to threshold effects, discotiuities ad hysteresis which come directly from the catastrophic ature of the ew ecoomic geography models started with Krugma (1991). They also revisit the aalysis of tax competitio i geography models with agglomeratio effects. This is also the case of Haufler ad Wooto (1999), Ludema ad Wooto (2000) ad Baldwi ad Krugma (2003). The closest paper is the oe by Robert-Nicoud ad Sbergami (2002) who aalyze the effect of subsidies o locatio i a political ecoomy model. The political structure they study is much richer tha ours but they do ot focus o the redistributive cosequeces of regioal subsidies ad assume lump sum taxes. Also, Forslid (2003) aalyses similar issues i a three-regio model. Fially, Owes ad Sarte (2002) aalyze i a very differet model the impact of regioal subsidies i a model with movig costs ad market power to show that these subsidies ca be used to reach a more efficiet spatial allocatio of firms. The ext sectio presets the framework, based o a model with capital mobility, labor immobility, icreasig returs, the existece of operatioal profits ad trade costs. To build up ituitio we the aalyze i sectio III a partial equilibrium versio of the model where the issue of fiacig is overlooked. The geeral equilibrium aalysis is preseted i sectio IV: both subsidies to profits ad lump sum subsidies, which are similar i their effects, are studied. Sectio V shows that regioal subsidies to productio have quite differet effects o locatio ad icome iequality. Welfare ad idividual iequality issues are studied i sectio VI. Fially, we aalyze the effect of relocatio costs i sectio VII. II. Basic Framework We will aalyze the effect of regioal subsidies i the footloose capital model developed by Marti ad Rogers (1995) ad further aalyzed i Baldwi et al. (2003). This model features agglomeratio, if we defie agglomeratio as the tedecy of ecoomic activity to geerate forces that ecourage further cocetratio of ecoomic activity. Agglomeratio stems from the home-market effect, which implies that a more tha proportioate share of idustry locates i the larger market. Agglomeratio i the footloose capital model, 5

9 however, is ot self-reiforcig : there is o circular causality as i Core-Periphery models (Krugma 1991, Veables 1996), as there is either labor mobility or vertical likages. I the footloose capital model, locatio of mobile capital is determied by a arbitrage coditio that equalizes profits across regios. We will oly aalyze the case of perfect capital mobility so that issues of stability ad catastrophic agglomeratio are igored. It meas that capital icomes must ot be cosumed i the regio where capital is located : profits ca be repatriated ad firms ca relocate without costs. I this case the stock of capital is exogeous, ad the value of capital is give by profits. II.1. Assumptios There are two regios (North ad South), two sectors, ad two productive factors. Regios are symmetric i terms of tastes, techology, opeess to trade, ad labor edowmets. The two sectors are referred to as maufacturig ad traditioal sector, ad maufacturig is marked by icreasig returs, moopolistic competitio ad iceberg trade costs. The traditioal sector is assumed to produce a homogeeous good uder Walrasia coditios (costat returs ad perfect competitio) ad its output is traded costlessly. The product factors are physical capital K ad labor L, with K beig the mobile factor ad labor beig the immobile factor. Physical capital ca be employed i oe regio while its ower speds its reward i the other regio somethig that is clearly impossible whe factors are associated with people as i the core-periphery model of Krugma (1991). Moreover, capital is oly employed as a fixed cost of idustrial firms; the variable cost oly ivolves labor. 2 Importatly, the footloose capital model assumes that capital owers are completely immobile across regios. Thus, whe pressures arise to cocetrate productio i oe regio, physical capital will move, but all of its reward will be repatriated to its coutry of origi. Total supplies of capital ad labor are fixed, with the world s edowmet deoted as K w ad 2L. Because physical capital ca be separated from its owers, the regio i which capital s icome is spet may differ from the regio i which it is employed. We must therefore distiguish the share of world capital owed by Norther residets (we deote this as s K K/K w ) 6

10 from the share of world capital employed i the North. Because we assume that each idustrial variety requires oe uit of capital (see below), the share of the world capital stock employed i a regio exactly equals the regio s share of world idustry. Cosequetly, we ca use North s idustry share, i.e. s /(+), to represet the share of capital employed i the North ad the share of all varieties made i the North ( is the umber of firms producig i the North, asterisk refers to the South). The cost fuctio of a typical idustrial firm (the icreasig-returs sector) is ohomothetic; the factor itesity of the fixed cost differs from the factor itesity of the variable cost. To keep thigs simple, we make the extreme assumptio that the fixed cost ivolves oly capital ad the variable cost oly ivolves labor. More specifically, each idustrial firm requires oe uit of K ad a m uits of labor per uit of output. The implied cost fuctio is: π + w a where π ad w L are the rewards to capital ad labor, a m is the variable uit iput requiremet, ad x is firm-level output. Techology i the traditioal sector is kept as simple as possible. Producig traditioal goods requires oly labor, specifically, it takes oe uit of labor to make oe uit of this good. Note that this meas that the icreasig returs sector is itesive i the use of the mobile factor. The represetative cosumer i each regio has prefereces give by: L m x 1/( 1-1/ σ ) w µ µ 1 1-1/ σ (2.1) U = C; C C MCT, CM < µ < < σ c, 0 1 i = 0 i di where C M ad C T are, respectively, cosumptio of the composite of maufacturig sector varieties ad cosumptio of the traditioal sector. Also, w is the mass (roughly speakig, the umber) of idustrial varieties available worldwide, µ is the expediture share o idustrial varieties, ad σ is the costat elasticity of substitutio betwee ay two varieties. The idirect utility for the prefereces i (2.1) is: (2.2) V P w 1 µ = ; P pt i = 0 p 1 σ i di µ /( σ 1) 2 Viewig K as physical capital, we ca thik of the fixed cost i the M-sector as a factory. We ca also iterpret it as a patet required to start the productio of a variety. 7

11 where is Norther expediture (i.e. after-tax disposable icome), P is perfect price idex, p T is the price of the traditioal good, p i is the cosumer price of idustrial variety i (the variety subscript is dropped where clarity permits). 3 Aalogous defiitios hold for Souther variables, all of which are deoted by a asterisk. II.2. quilibrium without subsidies Traditioal Sector Results Utility optimizatio implies that the demad fuctio for the traditioal good is C T =(1-µ)/p T. Perfect competitio i this sector forces margial cost pricig, i.e. p T = w L ad p T =w L. I additio, costless trade equalizes Norther ad Souther prices ad thus idirectly equalizes wage rates iteratioally: w L =w L as log as some traditioal good is produced i both regios. This coditio the so-called o-full-specializatio (NFS) coditio requires that o regio has eough labor to satisfy world demad for the traditioal good. The exact coditio is that total world spedig o this good, amely (1-µ) w, where w is world expediture, is greater tha the maximum value of productio that is possible by either regio, amely p T L. This is assumed to hold heceforth. Assumig workers are perfectly mobile betwee sectors, we get that wages are equalized i all sectors. Takig traditioal good as umeraire, we get that wages are equal i both regio to oe : p T =w L =p T =w L =1. Maufacturig Sector Results Utility optimisatio yields a costat divisio of expediture betwee sectors, ad CS demad fuctios for idustrial varieties implies: (2.3) σ pj µ cj w ; = π K + wl L p di i= 0 1 σ i where is regio-specific expediture (ad icome whe there is o taxatio), π is the Norther retal rate of capital, K is the Norther stock ok capital, w L is the Norther wage rate. 3 Usig stadard termiology, P is perfect sice real icome defied with P measures utility. 8

12 As usual, Dixit-Stiglitz moopolistic competitio ad (2.3) imply that mill pricig is optimal for idustrial firms, so the ratio of the price of a Norther variety i its local ad export markets is just τ. Thus: (2.4) p wlam τwla, p = 1 1/ σ 1 1/ σ = M Normalizig a M σ 1 =, ad replacig w L by oe, we get the pricig rules of firms i the σ icreasig-sector : domestic price is oe, ad export price is τ. The Mobile Factor s Reward Sice physical capital is used oly i the fixed cost compoet of idustrial productio, the reward to capital is the Ricardia surplus of a typical variety, i.e. the operatig profit of a typical variety. Sice each uit of capital ca be used to produce oe idustrial variety, the reward to capital would be bid up to the poit where it equalled operatig profit. Uder Dixit-Stiglitz competitio, this operatig profit is simply the value of sales divided by σ. I symbols, this meas π=x/σ, where x is the scale of productio, ad a aalogous expressio holds for the Souther operatig profit, π. Usig the demad fuctio ad mill pricig, we ca write these equilibrium expressios for π ad π as: (2.5) w s φ (1 s) µ π = b ; b 1; w + < φ τ K s + φ(1 s) sφ + 1 s σ w sφ (1 s) π = b w + K s + φ(1 s ) s φ + 1 s 1-σ where w is world icome, with s ad s 1-s beig the North s ad the South s share of expediture ; s is the North s share of idustry, ad s is the North s share of expediture. Note that with oe uit of capital per variety, s is both the North s share of idustry ad its share of world capital employed i the North while w = K w. Fially φ is the usual trasformatio of trasactio costs, reflectig the freeess of trade: φ equals 0 whe trasactio costs are ifiite, ad equals 1 whe trasactio costs are ull. 9

13 The case without subsidies: The total level of icome of the coutry is the sum of labor ad capital icome: w (2.6) = 2L+ π where we assume that the two regios are of equal size ad ormalize the total stock of capital K w to 1. I the log ru, with free relocatio, profits are equalized across regios so that π = b W ad W 2L =. 1 b The spatial distributio of capital owership is exogeous ad give by s K. With the assumptio that regios are of equal size, we ca defie North s icome as = L + s K π. The Norther share of total expediture is therefore give by (2.7) s 1 b(2sk 1) = The North s share of idustry s correspod to the geographical equilibrium, that is whe profits are equalized across regio. Solvig π = π, we fid (2.8) s 1 (1 + φ)(2s 1) = + 2 2(1 φ) We assume that the differeces i icome shares ad therefore capital owership are ot too large so that locatio is always at a iterior equilibrium with s <1. III. The Locatio ffect of Regioal Subsidies: partial equilibrium III.1. Regioal subsidies proportioal to operatig profits We start the aalysis of the locatio effect of these policies by overlookig the fiacig issue: hece this is oly a partial equilibrium aalysis. We first look at the effect of subsidies o the locatio of firms i the maufacturig sector give icome shares. To simplify further we aalyze i this sectio oly a subsidy proportioal to operatig profits for firms located i the 10

14 South. This ca be iterpreted as a tax break o profits for firms located i the South 4. Such a tax break i the traditioal sector does ot chage aythig, as this sector has zero operatig profits. This particular form of subsidy has o impact o wages ad therefore o labor icome. I the sectio where we aalyze the effects of subsidies i geeral equilibrium, we also study the effects of a lump sum subsidy, ad the case of a subsidy to productio to firms locatig i the South. The coditio that operatig profits must be equalized for locatio of firms to be a equilibrium becomes i the case of subsidies to profits: π = (1 + z ) π where z deotes the subsidy proportioal to operatig profits for firms located i the South ad π ad π are the operatig profits give by equatio (2.5). Usig the equality of operatig profits ad for a give distributio of expediture s (the share of expeditures i the North), which as we will see i the ext sectio may be iflueced by the subsidy itself, we get that the share of firms located i the North is: (3.1) s 2 (1 φ ) φ(1 + z φ) z zs s = 0< s < 1 (1 φ)1 + φ (1 + φ) As usual i geography models, the share of firms locatig i a regio is a icreasig fuctio of the share of expediture of that regio. Quite ituitively also, for a give distributio of expediture s, a icrease i subsidies to firms located i the South decreases spatial cocetratio i the North as: (3.2) ( 1 + φ ) 2 s(1 s) 2 s z = < 0 s costat 1 + z φ sz (1 + φ) Note that lower iterregioal trade costs (higher φ) magify the relocatio effect of the subsidy. The reaso is that whe those costs are low, firms are more willig to relocate to take advatage of a small differetial i profits (whether due to market size or subsidies), as they ca easily export to the regio they leave. Profits i the North ad i the South are give by: 4 I the US, tax breaks, most otably reduced property taxes o ew or expaded maufacturig facilities are the mai istrumet used for regioal developmet (Bartik, isiger, ad rickcek 2003). 11

15 (3.3) π = + = (1 z ) π ( ) w b w K 1 φ(1 + z ) 1+ z φ 1 + z φ s z (1 + φ) 1 + z (1 φ) It ca be checked that for a give level of total expediture w, ad expediture shares s, firms profits icrease i both regios. I the South the reaso is of course the subsidy. I the North, the reaso is that as firms relocate i the South competitio becomes less fierce ad profits icrease. Hece, the profit subsidy, i the case where capital is mobile, beefits firms i both regios. III.2 Regioal subsidies ad regioal icome iequality If profits icrease the regioal icome iequality may be affected by a regioal subsidy because of possible regioal iequalities i capital stocks owership. Suppose that the U fuds a regioal subsidy to attract firms i the South of Italy. If firms are mobile across the coutry, the the subsidy will raise profits for all firms i Italy so that capital owers, wherever they are located, will be the mai beeficiaries of the policy. If most of the capital owers are i the North, which is quite plausible, the the subsidy whose objective is to help the South may actually icrease icome iequality betwee the two regios. We derive this somewhat paradoxical result here i a partial equilibrium framework where the issue of the fiacig of the subsidy is ot cosidered. The ext sectio coducts the aalysis i geeral equilibrium. The total level of icome ad expediture of the coutry is the sum of labor ad capital icome: = +. The share of icome of the North is: ( π ) / w 2L π s L s w = + K where K s is the share of capital owed by Northerers which we assume to be more tha 1/2, so that we take the North to be the rich regio. We ask the followig questio: what does a small subsidy to firms located i the South do to regioal icome iequality which ca be measured by s? It ca first be show that evaluated at z =0, a small icrease i profits icreases icome iequality as log as where s K >1/2, usig the fact that π = 2Lb 1 b for z=0 : (3.4) s π z = 0 2 ( 1 b) ( s ) = 2 K 1 > 0 4L The subsidy is give to the South but it actually worses omial icome iequality because Northerers beefit more from the subsidy tha the Southerers. This is ot due to the fact that Northerers ow some firms located i the South but oly to the assumptio that the 12

16 North ows more capital tha the South ad that capital is mobile. Itroducig a subsidy distorts local competitio ad icreases capital ower s icome, who are more umerous i the North. Hece, ay icrease i profits will raise regioal icome iequality because of uequal edowmet i capital. IV. Geeral equilibrium aalysis IV.1. A local subsidy to profits fiaced by a atioal proportioal icome tax quatio (3.1) tells us how the locatio of firms depeds o the regioal market size. Now we eed to determie how the world distributio of expediture is altered by chages i geography. The geeral equilibrium model accouts for four edogeous variables: the share of firms producig i the North s, the Norther share i total expediture s, the equilibrium level of profits π ad that of the equilibrium tax rate t. We therefore eed to solve four equatios: the arbitrage equatio which requires that profits are equalized across regios at geographical equilibrium, the budget costrait which just says the reveues of taxatio o icome must fiace the subsidies, the resource costrait at the atioal level (of the labor market i this case), whereby labor supply is equal to labor demad which comes from the traditioal ad the maufacturig sectors, ad fially the Norther share of total expediture s. We first look at the case i which the subsidy i the South is fiaced by a atioal proportioal icome tax. I this case, the share of expeditures i the North, s, is ot affected directly as both icomes ad expeditures i the two regios are proportioately affected: (4.1) s (1 t)( L + πsk ) = (1 t)(2l + π ) w It remais true that = 2L+ π if we iterpret it as pre-tax icome. The govermet budget costrait implies: (4.2) z t(2 L+ π ) = z (1 s) π = (1 s ) 1+ z π 13

17 which says that atioal icome taxatio equals the subsidy rate (z) multiplied by the umber of firms i the South (1-s ) ad the equilibrium level of profits (et of the subsidy) π. The resource costrait at the atioal level (of the labor market i this case) implies: (4.3) 2 L= (1 t)(2 L+ π )1 ( b) This equatio says that labor supply (2L) is equal to labor demad which comes from the traditioal ad the maufacturig sectors, which themselves come from the equilibrium o the goods market. This relatio already uses the fact that i equilibrium, geography must be such that profits are equalized across regios. This the implies that as wages are ot affected by the subsidies, profits must rise i both regios. This is because taxes are effectively a trasfer from workers to capital owers. quatio (4.3) idicates that total expediture must remai costat. Also equatio (3.4) tells us how a chage i profits affects regioal icome iequality. Fially, the locatio of firms is still determied by the arbitrage equatio (3.1). Puttig these equatios together, we get the followig expressio for the share of Norther expediture: (4.4) s b(1 + z)(2sk 1) 1/2= 21 + bz1 ( s) + z s This equatio (we call it o figure 1 below) shows that for a give locatio of firms, the subsidy to Souther firms will icrease icome iequality i favour of the North as log as the North is richer tha the South i.e. 2 s 1 > 0. Also, with positive subsidies, the share of K icome i the North decreases with spatial cocetratio i the North as less Souther located firms receive the subsidy. quatio (3.1), the curve o figure 1 below, correspods to the home market effect. The equilibrium locatio ad icome iequality is show o figure 1 ad is the solutio to a quadratic equatio too cumbersome to be revealig. A icrease i subsidies to the South shifts both equilibrium relatios. I equilibrium, icome iequality rises ad it ca be show that the et effect of the subsidy is a relocatio towards the South. 14

18 Figure 1: the effect of a subsidy to firms i the South o firm locatio ad icome iequality s s I the rest of the paper, we cocetrate o the effects of small subsidies, i.e. we do comparative statics at z = 0. Profits (iclusive of the subsidy i the South) icrease i both regios as: dπ dz z = 0 = dπ (1 + z dz ) z = 0 = π (1 s ) > 0 For icome iequality, we get: (4.5) ds dz (1 b)( s = z = 0 1 1/ 2)(1 s + φ )(1 φ) which says that regioal omial icome iequality icreases with the subsidy as log as the North has iitially more firms tha the South (s >1/2) which meas that the North has more capital tha the South (s K >1/2 ). This is because the icrease i profits mostly beefits the Norther regio, which has more capital tha the South. Note agai that for this to be true, it is 15

19 ot ecessary for firms producig i the South ad receivig the subsidy to be owed by Northerers. I geeral equilibrium, all that is required is that capital be mobile. The policy implies a official fiacial trasfer from the North to the South as the subsidy to Souther firms is fiaced by a proportioal icome tax: t is the share fiaced by the North ad t for the South. As the South is poorer tha the North, more of the subsidy is fiaced by the North tha by the South. From this poit of view, the regioal policy looks redistributive towards the South. The geeral equilibrium aalysis shows that the icidece of the subsidy is actually a et trasfer of resources from the South to the North as the share of total icome (which remais costat) that goes to the North icreases. Agai, capital mobility coupled with iitial iequality of capital edowmets (which presumably is the reaso for the subsidy i the first place) explais that the subsidy is actually captured by Northerers.. At the same time, subsidies alter geography of productio accordig to two opposite effects: first, firms relocate where icome ad expeditures rise because of the Home Market ffect; secod, firms relocate where profit subsidies exist. The et effect is give by: ds dz 1 2 (4.6) = 1 s ) ( 1 b) ( + bs < 2 φ ( 1 φ ) Usig the restrictio that s < 1 (the equilibrium is a iterior oe so that ot all firms are located i the North), (4.6) is egative. Hece, the regioal subsidy fiaced by a atioal proportioal icome tax leads to relocatio of firms to the South. It ca be checked that the effect of the subsidy of locatio icreases with trade itegratio as measured byφ. The ituitio is the same as i partial equilibrium. It ca also be show that the effect of the subsidy o relocatio icreases with trade itegratio (with φ). Fially, because the regio that receives the subsidy is poor ad that regioal icome iequality icreases with the subsidy, it ca be checked that the geeral equilibrium effect is less tha the partial equilibrium oe (i.e. the absolute value of 4.6 is less tha 3.2.). It is importat to ote however that the size of firms of the maufacturig sector located i the South decreases (ad icreases i the North) as: 0. dx dz z = 0 = s x < 0 16

20 As the subsidy leads firms to relocate i the South, local competitio itesifies which reduces demad for each variety produced i the South. Hece, each firm produce less i the South. Also, the subsidy effectively implies a lower expediture share i the South if it is poor which further reduces demad for varieties produced i the South. More firms of the maufacturig sector produce i the South but at a smaller scale. This is the reaso why the subsidy has a ambiguous effect o employmet (ad output) i the maufacturig sector This effect is give by the combied effect o the umber of firms ad their size ad reduces to: dl dz M (4.7) x ( 1 b)( 1 s )( s 1/2) z = 0 σ 1 = + σ φ ( 1 φ ) Hece, for a poor regio (so that s K ad therefore s >1/2), the effect of the subsidy to firms of the maufacturig sector o productio ad employmet of this sector is ambiguous. It may be egative if trade itegratio betwee the two regios is low eough, i.e. if φ is low eough. This result is at first sight paradoxical. Note that it does ot hold if the subsidy was give to a rich regio (if s K ad therefore s 1/2). The ituitio is simply that ifφ is low the few firms will relocate i the South. The reaso why the ambiguity oly holds for the poor regio is that the subsidy leads to a reallocatio of expediture ad therefore demad to the capital rich regio. 2 L M. IV.2. A local subsidy to profits fiaced by a local proportioal icome tax Regioal subsidies are ot always fiaced at the atioal level. Some are fiaced at the regioal level. I this case, the effect of subsidies o locatio of firms is ot so clear. O the oe had, firms will be attracted by such subsidies. O the other had, the icrease i the local tax o icomes will lead to a smaller market size, which will hamper firms profits. We ow assume that oly Southerers are taxed, so that the share of expeditures i the North s icreases automatically via a tax effect: (4.8) s = W, t where, ad w still defie respectively Norther icome, Souther icome ad the world icome before the tax, as give i the previous sectio. 17

21 The locatio of firms is still determied by equatio (3.1). The Souther govermet budget costrait ow implies: (4.9) z tl ( + π (1 sk)) = z (1 s) π = (1 s ) 1+ z π Ad the resource costrait (of the labor market agai) is: (4.10) 2 = ( 1 )[ 2 + π ( + π(1 ))] L b L tl s K By costructio (taxes ad subsidies are pure trasfers) we kow that total expediture ( w -t) must remai costat ad equal to 2L. Fially from equatio (4.8) ad usig (4.9) 1 b ad (4.10) we get that regioal omial icome iequality icreases with the subsidy : ds (4.11) = b(1 s ) s K dz z = 0 Agai, eve though the subsidy is give oly to Souther firms, capital mobility implies that i geeral equilibrium the icome iequality must rise i favour of the North. The subsidy is effectively captured by ortherers. Quite ituitively, it ca be checked that the icrease i icome iequality is larger i the case of local fiacig tha i the case of a atioal proportioal tax. icome tax : Fially, we get the relocatio effect of the local subsidy fiaced by a local proportioal (4.12) ds 1 1+ φ φ = (1 ) 1 < 0 s b dz 1 z = φ ( 1 φ ) which ca be proved to be egative. Hece, eve though the locally fiaced subsidy leads to a decrease i expediture i the poor regio (the tax effect) ad to icreased icome iequality (the effect o profits), it attracts firms i the poor regio. Whe subsidies are fiaced locally, oly Southerers pay the tax, so that the equilibrium tax rate is higher tha i the atioally fiaced case. The icrease i profits is the same, whereas the icrease i regioal icome disparity s is greater, which yields fewer firms to relocate to the South. Agai, the effect o maufacturig employmet ad output i the poor regio is ambiguous. If egative, the effect is more importat 18

22 because less firms relocate to the South ad the decrease i each firms size is the same uder both forms of fiacig. IV.3. A lump sum subsidy fiaced by a atioal proportioal icome tax Regioal subsidies ca take the form of a lump sum trasfer to firms of the maufacturig sector which locate i the poor regio. This may be the case for example if, as ofte happes, lad is give to the firm to build the plat, if a lump sum tax break is give or if R&D is subsidized for firms located i the poor regio. As the aalysis ad results are quite similar we oly aalyze the case of a subsidy fiaced at the atioal level ad do ot repeat all the steps. The arbitrage equatio ow becomes (4.13) π = π + F where F is the lump sum subsidy give to firms located i the South. The govermet budget costrait becomes: (4.14) t L F s (2 + π ) = (1 ) The resource costrait ad the share of expeditures i the North are still give respectively by equatios (4.3) ad (4.1). Differetiatig this system aroud a equilibrium where F is zero, we we get the variatio of regioal icome disparity with respect to profit of maufacturig firms, which is the same expressio as equatio(3.4). We fid that all these results are proportioal to the oes we obtai with a subsidy to profits fiaced by a atioal proportioal icome tax. Chages iduced by a lump sum subsidy o our four edogeous variables (the share of firms producig i the North s, the share of expediture i the North s, the equilibrium profits π ad the tax rate o icome t) are just proportioal to the effects of a subsidy to profits. The multiplyig factor is the equilibrium value 2 of profit : π = Lb 1 b. Hece, for example, s 2Lb s = F 1 b z F = 0 z = 0 We thus coclude that a lump sum subsidy leads to a decrease i spatial cocetratio of firms together with a icrease i regioal icome disparity, as i the case of a subsidy to profits. 19

23 V. A local subsidy to firms productio Regioal subsidies ca also cosist of a subsidy proportioal to productio or to the umber of jobs created by firms. I this sectio we study the case of a atioally fiaced subsidy to both sectors productios i the South. As the traditioal sector is perfectly competitive, margial-cost pricig ad zero profit coditio imply: w = (1+z). Hece, such a subsidy acts as a icrease i labor productivity ad raises the equilibrium wage i the South, as the labor markets are perfectly competitive. As for the maufacturig sector, profit maximizatio uder moopolistic competitio amσ x yields: π = p x(1 + z) am (1 + z) x p = ad π = (1 + z). Hece, a subsidy to σ 1 σ both sectors productio lets prices uchaged, whereas profits ad wages i the South are multiplied by (1+z). The arbitrage equatio that determies the optimal locatio of firms is still give by: π = ( 1+ z) π The defiitio of the Norther share of expediture is: (5.1) s ( 1 t)( L+ π sk ) t [ L + z + π ] = (1 ) (2 ) The resource costrait becomes: (5.2) 2 (1 )(1 ) ( 2 ) L = t b L + z + π Fially the govermet budget costrait whe subsidies are fiaced by a atioal proportioal icome tax ca be show to be: W (5.3) t = z (1 s ) π + z L Puttig all this together, we fid that the subsidy has a positive effect o profits i both regios (the same as i the case of a subsidy to profits) despite the wage icrease i the South: (5.4) dπ dz z = 0 2Lb = (1 s) > 0 1 b However, this type of subsidy o employmet decreases regioal after tax icome ad expediture iequality as: 20

24 ds dz (1 b) 4 (5.5) = [ b(2s 1)(2s 1) + 1 s ] 0 2 K K < z = 0 Aother implicatio is that relocatio to the South is more importat i the case of a productio subsidy tha i the case of a tax break (subsidy proportioal to profits) for firms located i the South. Ideed, the effect of the subsidy o geography of productio, usig equatio (3.2), is give by : (5.6) ds dz ( 1+ φ ) (1 + b) 4(1 φ) φ (1 φ) 2 = φ K K 2 z = 0 [ 1 s + b(2s 1)(2s 1) ] s (1 s )(1 ) which ca be show to be larger i absolute value tha (4.12). Agglomeratio is decreased to a larger extet with this kid of subsidy as the market size of the poor regio is icreased due to the positive effect o Souther wages. I the case of local fiacig however, the impact of a subsidy o employmet is exactly the same tha a subsidy o profits: icome iequality icreases betwee the two regios (the impact is give by 4.11) ad firms relocate as i (4.12). The reaso is that i this case the icrease i wages is paid locally so that o fiscal trasfer occurs from the North to the South. The oly et trasfer that takes place is the oe through profit repatriatio which beefits the North as profits icrease ad the North more capital tha the South. VI. Welfare ad iequality The ext issue to cosider is the impact of subsidies o real et icome i both regios. Chages i real icome i this model may differ from chages i omial icomes because subsidies have a impact o the price idex through their effect o idustry locatio. Whe firms relocate i a regio, this leads to a decrease of the price idex for agets located there. The reaso is that less goods eed to be imported from the other regio so that trade costs have to be paid o a lower umber of goods. A related questio is the impact o real et icomes for workers ad capital owers. 21

25 VI.1. Welfare ad regioal iequalities Real et icome i both regios reflects regioal welfare level, ad is obtaied by dividig the after-tax ad subsidy expediture by the perfect price idex. Both levels deped o the evolutio of world distributio of expediture betwee regios, give that total expediture remais costat. Welfare levels also deped o chages i price idices, because of the relocatio of firms. Whatever the type of subsidy, chages i regioal real et icome are give by : dv 1 2L ds 2µ L(1 φ) ds (6.1) = P + dz = 0 1 = 0 (1 )( 1)(1 + ) z b dz z b σ φ dz z = 0 dv 1 2L ds 2µ L(1 φ) ds (6.2) = P + dz = 0 1 = 0 (1 )( 1)(1 + ) z b dz z b σ φ dz z = 0 Results i terms of regioal welfare will be obvious i the case of a local subsidy to productio fiaced at the federal level. As both regioal icome disparity ad agglomeratio of firms decrease, the North loses ad the South wis i terms of real icome ad welfare. However for other types of subsidies we studied, North experieces a icrease i both regioal icome ad regioal price idex, whereas it is the opposite chages for the South. We thus have to determie the et effect of subsidies to profit ad lump sum subsidy o regioal welfare. From equatio (6.1) ad (6.2) it ca be checked that chages i regioal welfare are qualitatively symmetric: they chage i opposite directio. Whe the subsidy is fiaced with a atioal tax, we fid that welfare i the rich (poor) regio always decreases (icreases). However, with local fiacig ad if the capital owership is very uequally distributed, ad trade costs are high eough, we fid examples where welfare may decrease i the poor regio. This is so eve though firms do relocate i the poor regio. The same results hold for the lump sum subsidy. VI.2. Iequality iside regios Idividual welfare correspods to idirect utility as defied earlier, which is also equivalet to idividual real disposable icome. For the Norther regio for example, it depeds o factor rewards, price idices ad the tax level: i i (1 t ) V = P 22

26 where i is idividual i s omial icome, t is the tax level, ad P is North price idex. We follow the traditio of iteratioal trade theory by aalysig the effect of a subsidy o labor ad capital icomes. Table 1 provides the relative icrease or decrease of both factors omial et reward, followig the impact of the differet subsidies, takig ito accout the effect of fiacig. This allows us to determie the evolutio of itra-regioal iequality, assumig that the capital is uequally distributed. As idividuals livig i the same regio face the same price idex ad tax rate, we say that itra-regioal idividual iequality icreases if capital omial et icome icreases relative to labor. Itra-regioal idividual iequality icreases i both regios whe subsidies to profits or lump sum subsidies are give to firms, wheever they are fiaced by a atioal or a local proportioal icome tax, because these subsidies effectively lead to a trasfer of resources from workers to capital owers. O the cotrary, itraregioal idividual iequality decreases i the South whe a subsidy to productio, fiaced at the is give i firms producig i this regio. This higes o the fact that labor icome icreases, while capital et-of-tax icome decreases 5. However, workers i the North loose ad proportioally more so tha capital owers so that i this sese iequality icreases i the North. I the case of local fiacig, iequality icreases i the North ad decreases i the South. 5 Profits ad capital icome icrease, but ot eough to compesate the icrease i taxes. 23

27 Table 1 : Relative evolutio of capital ad labor et-of-tax omial icomes: 1 i R dri ; R = i dz icome of factor i Subsidy to profits Labor i both regios -b(1-s ) < 0 fiaced by a atioal proportioal icome tax 6 Capital i both regios (1-b)(1-s ) > 0 Labor i the North 0 Subsidy to profits fiaced by a local proportioal icome tax Capital i the North 1-s > 0 Labor i the South π (1 s ) < 0 L(1 s Capital i the South [ 1+ b( 2s 1) ] 0 (1 b) Labor i the North ( s ) ) > K 1 b 1 b+ < 0 2 Subsidy to productio fiaced by a atioal proportioal icome tax Labor i the South Capital i both regios 1 b + bs > s ( 1 ) 0 b < 2 Labor i North 0 Subsidy to productio fiaced by a local proportioal icome tax Capital i North 1-s > 0 Labor i South ½(1-b)+b s > 0 Capital i South 1 s ( 1 ) 0 b < 2 6 The lump sum subsidy has a qualitatively similar result. 24

28 VII. Relocatio costs Up to ow we have assumed that firms ca relocate costlessly betwee regios. This certaily implies that we overestimated the impact of regioal subsidies o firms relocatio decisios. mpirical studies usually fid that those policies have very small effects. This is the case i the US (see for example Mills, 1997). This is also the case i urope: Crozet, Mayer ad Muchielli (2003) show that regioal policies have o or very little effect o the locatio choice of FDI i Frace. Oe atural reaso may be relocatio costs. We itroduce relocatio costs i a very simple way followig Baldwi et al. (2003). We assume that a firm that relocates from oe regio to aother pays a proportioal relocatio cost of (1- k), where 0 k 1 is a measure of the freeess of capital mobility. To simplify further, we assume that it is a oe time cost ad aalyze situatios where it already has bee icurred so that curret icome is uaffected. Also, to keep the aalysis short we will focus o the case of a subsidy to profits (or a tax rebate) for firms located i the South fiaced by a atioal proportioal icome tax. The aalysis is similar for other types of subsidies. The first effect of relocatio costs is that if they are high eough, o relocatio will occur so that a o-relocatio bad exists. To see this, we ask the followig questio: startig from a situatio without subsidies (z=0), how much relocatio costs eed to be for firms i the North to decide ot to relocate if a subsidy is give i the South? To aswer this questio we eed to fid k such that: k < k = π / π (1 + z ) where π adπ are evaluated at s = s with o subsidy (i.e. as give by equatio (2.8). We also assume that before the experimet, agets are fully diversified i their portfolio, so that all firms are owed by all agets proportioally to their capital owership. This just meas that fiacial market is perfect ad there exists o domestic bias i ivestmet. This implies that the chage i profits i the North ad the South affects agets proportioally to their capital owership. I this case, profits (icludig subsidies) are ot ecessarily equalized across regios, ad the share of expediture i the North is: (7.1) s (1 t ) L+ ss Kπ + (1 s) skπ (1 + z ) w t L+ sπ + s π + z = = (1 ) 2 (1 ) (1 ) 25