Tax Competition, Public Good Provision, and Income Redistribution: The Case of Linear Capital Income Tax

Transcription

1 CIRJE-F-595 Tax Competton, Publc Good Provson, and Income Redstrbuton: The Case of Lnear Captal Income Tax Toshhro Ihor Unversty of Tokyo C.C. Yang Academa Snca Natonal Chengch Unversty October 008 CIRJE Dscusson Papers can be downloaded wthout charge from: Dscusson Papers are a seres of manuscrpts n ther draft form. They are not ntended for crculaton or dstrbuton except as ndcated by the author. For that reason Dscusson Papers may not be reproduced or dstrbuted wthout the wrtten consent of the author.

2 Tax Competton, Publc Good Provson, and Income Redstrbuton: The Case of Lnear Captal Income Tax Toshhro Ihor* Department of Economcs, Unversty of Tokyo C.C. Yang** Insttute of Economcs, Academa Snca Department of Publc Fnance, Natonal Chengch Unversty October 008 [Abstract] Ths paper consders a tax competton model n whch regonal government actvtes nclude ncome redstrbuton as well as publc good provson. To ncorporate the regonal government functon of ncome redstrbuton, we extend the tax system from the stylzed proportonal captal ncome tax to the lnear captal ncome tax: the revenue collected from captal taxaton n each regon s used not only to provde the regonal publc good but also to offer a unform lump-sum grant to each ndvdual n the regon. In contrast to Hoyt s (1991) fndng that the extent to whch publc goods are undersuppled s monotoncally ncreasng n the number of competng regons, we show that, regardless of the number of competng regons, all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods; on the other hand, the sze of ncome redstrbuton s monotoncally decreasng n the number of competng regons. JEL classfcaton: D7; F0; H41; H71 Key words: Tax competton; Publc goods; Income redstrbuton * Department of Economcs, Unversty of Tokyo, Hongo, Tokyo , Japan. E-mal: hor@e.u-tokyo.ac.jp ** Correspondng author, Insttute of Economcs, Academa Snca, Nankang, Tape 115, Tawan. E-mal: ccyang@econ.snca.edu.tw We are grateful to Jay Wlson and an anonymous referee for ther helpful comments on an earler verson of ths paper. Forthcomng: Asa-Pacfc Journal of Accountng and Economcs

3 1. Introducton A fundamental result n the lterature on tax competton s that nterregonal tax competton for moble captal generates fscal externaltes and tends to result n an undersupply of publc goods n a regon. Ths result s orgnally artculated by Oates (197) and formally modeled by Wlson (1986) and Zodrow and Meszkowsk (1986). 1 In an mportant contrbuton, Hoyt (1991) shows that the extent to whch publc goods are undersuppled s monotoncally ncreasng n the number of competng regons. Followng Wlson and Wldasn (004), an ncrease n the number of competng regons can be vewed as ncreased tax competton. Thus, Hoyt s fndng suggests that ncreased nterregonal tax competton wll worsen the undersupply of publc good provson n a regon. On the bass of hs fndng, Hoyt (1991, p. 130) concludes: The exstence of wasteful tax competton suggests that the optmal number of jursdctons s one, thereby elmnatng the externaltes created by captal taxaton. The tradtonal Tebout lterature argues that havng many ndependent jursdctons promotes effcency and taste stratfcaton by ncreasng the competton among jursdctons. Thus, a tradeoff s faced, more jursdctons ncrease the sortng of resdents but at a cost of decreasng the publc servce provson because of tax competton. Hoyt employs a standard tax competton model n whch regonal government actvtes are confned to publc good provson only. Ths setup s obvously counterfactual. Indeed, exstng data clearly ndcate that ncome redstrbuton consttutes the most dramatc rse n regonal government actvtes durng the past century (Tanz and Schuknecht, 000). In ths paper we extend the Hoyt model to a more realstc world n whch regonal government actvtes nclude not only publc good provson but also ncome redstrbuton. The stylzed tax system consdered n tax competton models s the proportonal captal 1 Ths fundamental result s stated as Proposton 4.1 n Wellsch (000, p. 64) and as Proposton 4. n Haufler (001, p. 65). See Wlson (1999), Wlson and Wldasn (004), and Fuest et al. (005) for surveys of the tax competton lterature. 1

4 ncome tax. To ncorporate the regonal government functon of ncome redstrbuton, we extend the stylzed tax system from the proportonal to the lnear captal ncome tax wth a unform lump-sum grant: the revenue collected from captal taxaton n each regon s used not only to provde the regonal publc good but also to offer a unform lump-sum grant to each ndvdual n the regon. In contrast to Hoyt s fndng, we show that, regardless of the number of competng regons, all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods; on the other hand, the sze of ncome redstrbuton s monotoncally decreasng n the number of competng regons. Our result suggests that the tradeoff wth more jursdctons s not at a cost of decreasng publc servce provson as n Hoyt (1991), but at a cost of decreasng ncome redstrbuton f more redstrbuton s desrable.. Model Our model of the economy s standard n the tax competton lterature wth the two peculartes: () there are heterogeneous rather than homogeneous ndvduals, and () regonal government actvtes nclude ncome redstrbuton as well as publc good provson. These two peculartes are obvously ntertwned. There would be no need for the government functon of ncome redstrbuton f people were homogeneous. Consder an economy n whch there are n dentcal regons, where n { 1,..., }. Each regon s nhabted by N ndvduals. There are two factors of producton: an nterregonal mmoble factor and a perfectly moble factor. Ths s a carcature of the real world stuaton n whch some factors have a much hgher nterregonal moblty than others. Followng the prevous lterature, we wll refer to the mmoble factor as labor and to the moble factor as The model s bult on Hoyt (1991). As noted by Hoyt, hs model follows that of Wldasn (1988). It s a textbook, workhorse model of tax competton; see, for example, Wellsch (000, Secton 4.1) and Haufler (001, Secton 4.3).

5 captal. Each ndvdual n each regon has the same clam to mmoble labor, but unequal clams to moble captal. Specfcally, ndvdual j n regon supples 1 / N unts of labor and k j unts of captal. Ths nequalty feature n endowment s agan a carcature of the real world stuaton n whch captal ncomes are more unequally dstrbuted than labor ncomes. 3 Let k =. Denotng the amount of captal employed n regon by k, captal k j j market clearng requres = k k. (1) All regons produce a sngle prvate good whose prce s normalzed to unty. Ths prvate good can ether be consumed drectly as a prvate commodty, c, or be used to provde the regonal publc servce, g. One unt of the prvate good produces one unt of the publc servce. The producton n each regon s gven by f k ) wth f ( k ) > 0 and f ( k ) < 0, where a unt of the labor nput n the regon s suppressed. All markets are assumed to be perfectly compettve. Each regon leves a source tax at rate t on each unt of captal employed wthn ts regon. Perfectly moble captal mples f k ) t = r( t,..., t ) () ( 1 n where r s the after-tax rate of return on captal, whch depends on ( t 1,...,tn and s equalzed across the economy. Usng (1)-() and the assumpton that all regons are dentcal, we have 4 r 1 = n (3-1) k 1 (1/ n) = f ( k ) (3-) k (1/ n) = f ( k ), (3-3) 3 For emprcal evdence, see Daves and Shorrocks (000). One may ncorporate labor as well as captal nequalty nto the model. However, t yelds few further nsghts as far as ths paper s concerned. 4 See Hoyt (1991). 3

6 where denotes any regon other than regon. Let u u c, g ) denote the preferences of ndvdual j n regon over the prvate j ( j good c and the publc servce g. We shall work wth the quas-lnear form: u c, g ) = c + v( g ) wth v > 0 and v < 0. For one thng, ths form has become ( j j standard n the lterature on publc goods. 5 Perhaps more mportantly, the quas-lnear form makes our work drectly comparable wth a large tax competton lterature on the effcency problems assocated wth the provson of publc goods. It s known that the crteron of Pareto effcency (.e., the so-called Samuelson condton) alone s unable to unquely determne the optmal level of publc goods n general when ndvduals are heterogeneous. 6 A socal welfare functon s typcally ntroduced to pn t down n such stuatons. However, ths approach may be arbtrary n our context snce dfferent socal welfare functons as a rule pont to dfferent optmal levels of publc goods. The advantage of the quas-lnear form s that t enables us to stck to the crteron of Pareto effcency and, at the same tme, unquely determne the optmal level of publc goods even n the case of heterogeneous people. The stylzed tax system consdered n tax competton models s the proportonal captal ncome tax. To ncorporate the regonal government functon of ncome redstrbuton, we extend the stylzed tax system from the proportonal to the lnear captal ncome tax wth a unform lump-sum grant. That s, the revenue collected from captal taxaton n each regon s used not only to provde the regonal publc servce, g, but also to offer a unform lump-sum grant, a, to each ndvdual n the regon. Thus the tax system nvolved conssts of two parameters: a margnal tax rate t and a lump-sum grant a. The tax system pays the lump-sum grant or demogrant a to each ndvdual n a regon, and fnances the lump-sum payment 5 See, for example, Besley and Coate (003) and Batna and Ihor (005). As n Wlson (1986) and Zodrow and Meszkowsk (1986), we focus on the fscal externalty generated by moble tax bases, leavng out the spllover effects of publc servces across regons for smplcty. 6 See Varan (199, p. 419) 4

7 and the cost of publc good provson by mposng the margnal tax rate t on all captal employed n the regon. Ths redstrbutve tax system s referred to as a demogrant polcy n Brownng and Johnson (1984) and Ballard (1988). 7 The government budget constrant n each regon mples g + Na = t k. (4) On the other hand, the ndvdual budget constrant mples c = ( 1/ N )[ f ( k ) ( r + t ) k ] + rk + a j (5) j j where f ( k ) ( r + t ) k s the wage rate n regon. By assumpton, ndvdual j n regon supples 1 / N unts of labor, k j unts of captal, and receves an a amount of the lump-sum grant. 3. Analyss Ths secton analyzes the ndvdually preferred polcy and the polcy formaton wthn each regon. Consder ndvdual j n regon who owns k j unts of captal. Gven ndvdually preferred publc servce ( g ( k j ), t ( k j g and tax polcy t satsfy g and t, the )) = arg max{ c + v( g )} (A) g, t j where g and c j follow (4) and (5), respectvely. From (1)-() and the budget constrant (4), the lump-sum grant a wll be determned resdually once g and t are chosen. 8 The frstorder condtons for program (A) wth respect to g and t are gven by 7 The redstrbuton through the demogrant polcy may be crtczed for beng unrealstc n that transfer recepts nclude the rch as well as the poor. Brownng and Johnson (1984), however, emphasze that only the net effect of the taxes and transfers s crucal for redstrbuton. They provde evdence that the the demogrant polcy can have dstrbutonal mplcatons smlar to those resultng from the entre actual tax and transfer system. 5

8 u j g u j = ( 1/ N ) + v ( g ) = 0 (6) cj = = 0 (7) where v g ) s the margnal value of the publc servce. ( 3.1. Indvdually preferred level of publc good provson Eq. (6) mmedately yelds N v ( g ) = 1 (6-1) whch s the Samuelson condton for the optmal provson of publc goods. Ths result arses because, gven t, t and hence k, the margnal rate of transformaton (MRT) between g and a equals 1 / N (see Eq. (4)) whle the margnal rate of substtuton (MRS) between g and a equals v ( g ) (see ths by substtutng (5) n the utlty functon); and each ndvdual equates MRS wth MRT f she s decsve. g = Eq. (6-1) unquely determnes the frst-best level of publc goods, g F. The fndng F ( kj ) g for all j gves rse to our frst man result: Proposton 1. Suppose that the tax system n effect s a lnear captal ncome tax. Then tax competton results n an outcome n whch all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods. 8 Note that the lump sum grant determned resdually may not be postve under some parameter values of our model. As ponted out by Inman (1987, pp ), the possblty of a negatve lump sum grant n the lnear ncome tax hghlghts the tenson between two goals of an economy: effcency and equty. Provdng publc goods more or less has to do wth correctng market falures. Ths effcency part of government actvtes may crowd out redstrbutve spendng so much so that the democratcally chosen level of redstrbutve government actvty may become zero or even negatve. Although theoretcally nterestng, we nterpret our fndngs mostly n the more realstc case where the equlbrum lump sum grant s postve. 6

9 Ths result s n stark contrast to a fundamental result n the tax competton lterature that nterregonal tax competton for moble captal generates fscal externaltes and hence tends to result n an undersupply of publc goods n a regon (see the Introducton). To understand more about Proposton 1, let us suppose that the demogrant polcy s absent so that a 0 n (4)-(5). In the absence of the demogrant polcy, program (A) wll be replaced by ~ t ( k ) = arg max{ c + v( g )} (B) j t j and the frst-order condtons (6)-(7) wll be replaced by uj cj g = + v ( g ) = 0. ~ Usng (B-1) and (3)-(5) wth a 0, t ( ) n program (B) gves k j (B-1) ~ t ( k k j j ) = (1/ n) < uj / 0 (B-) where u / < 0 s requred by the second-order condtons. The result of (B-) j ndcates that the lower the share of captal owned by an ndvdual, the hgher the tax rate preferred by the ndvdual. Ths result s ntutve. In the absence of the demogrant polcy, redstrbuton between the rch and the poor can stll be taken place through sharng the cost of the publc good dfferently. As a result, the rch prefer a lower tax rate whle the poor prefer a hgher tax rate. Usng (3)-(5) wth a 0 also yelds c j 1 k 1 = ( 1 ) kj < 0 n N n (B-3) where the frst RHS term represents the tax-nduced change n labor ncome (the same negatve effect across heterogeneous ndvduals) whle the second RHS term represents the tax-nduced change n captal ncome (vared negatve effects across heterogeneous ndvduals). Rasng t wll reduce the ndvdual captal ncome receved through the effect of (3-1) and ncrease captal flght through the effect of (3-). Rasng t wll also reduce 7

10 the ndvdual labor ncome receved because labor and captal are complementary n producton. (B-3) mples from (B-1) g > 0. (B-4) Puttng (B-) and (B-4) together, we see that the lower the share of captal owned by an ndvdual, the hgher wll be the level of publc good provson preferred by the ndvdual. However, once the demogrant polcy s avalable as n program (A), redstrbuton between the rch and the poor can be acheved through the demogrant drectly (see more elaboraton later). As a result, t s no longer necessary to redstrbute ncome ndrectly through sharng the cost of publc good provson. Puttng dfferently, heterogeneous ndvduals face dfferent personalzed margnal costs of publc good provson n program (B), whereas they all face the same margnal cost of publc good provson n program (A). The dfference can be seen by comparng (B-1) wth (6). Ths explans why all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods n our model. 3.. Indvdually preferred tax rates Gven F g = g, t s assumed that j / < 0 u so that the second-order condtons are met and there s a unque t k ) satsfyng (7). ( j Usng (3) and gven that k = k n a symmetrc Nash equlbrum, (7) leads to 9 sj ( n 1) ε τ = 1 (8) (1/ N ) where τ t /( r + t ) (the ad valorem tax rate n regon ), s j kj / k (the share of captal owned by ndvdual j n regon ), and ε k / ( r + t )][( r + t ) / k ] (the elastcty of [ 9 Techncally, there wll be a corner soluton n the case of n=1 so that (8) may not hold as an equalty. 8

11 demand for captal wth respect to the before-tax rate of return n regon ). In Eq. (8), each ndvdual trades off the margnal redstrbutve beneft from taxaton (n the form of the devaton between her own captal share s j and the regon s mean captal share 1 / N ) aganst the margnal dstortonary cost of taxaton (n the form of a tax-nduced outflow of captal ( n 1)ε τ ). The ndvdually preferred captal tax rate results from the balancng of ths tradeoff. Note that ndvduals who own captal shares hgher than the regon s mean share would lke to subsdze captal ( t < 0 ), whle ndvduals who own captal shares lower than the regon s mean share would lke to tax captal ( t > 0 ). Only those ndvduals whose captal share happens to be the regon s mean share would lke to nether subsdze nor tax captal ( t = 0 ) Poltcal equlbrum Obvously, dfferent ndvduals would lke to mpose dfferent tax rates f they are decsve. There are several possble ways to pn down tax rates n poltcal equlbrum (see Persson and Tabelln, 000). For smplcty, we consder a prmtve, but transparent way wthn our model. From the frst-order condtons (7), we have ( uj / ) dt ( cj / ) + dk k j j = 0. (9) From (3)-(5), we have cj 1 k t[1 (1/ n)] = ( kj ) + n N Nf. (10) Snce ( c / ) / k = (1/ n) by (10), Eq. (9) leads to j j ( k k j j ) = (1/ n) < uj / 0 (11) 9

12 whch mples that the lower the share of captal owned by an ndvdual, the hgher s the tax rate preferred by the ndvdual. Ths result s ntutve because redstrbuton from the rch to the poor now takes place through sharng the cost of the lump sum grant dfferently. The reasonng behnd ths result s smlar to that behnd (B-). In fact, one can show that ( a / ) > 0 n equlbrum (see Lemma 3), whch together wth (11) mples that the lower the share of captal owned by an ndvdual, the hgher wll be the level of demogrant preferred by the ndvdual. Note that the redstrbutve ncentves of the poor are qualfed n the presence of tax competton snce (11) depends on the number of competng regons n as well. In partcular, t s observed that the rch and the poor wll concur wth each other on the tax polcy f n. Ths s so because, from (3), a change n the tax rate wll not affect the after-tax rate of return on captal but wll only affect the common labor ncome once n. By the assumpton that u / < 0, the preferences of ndvduals qua voters exhbt j sngle-peakedness over tax rates t. Snce t ( k j ) s monotonc n k j accordng to (11), the ndvdual preferences for t nduce a preference orderng for k j. Ths nduced preference obvously exhbts sngle-peakedness over captal endowments k j. Then, by nvokng the medan voter theorem, we arrve at: Lemma 1. The lower the share of captal owned by an ndvdual, the hgher s the tax rate preferred by the ndvdual. The decsve voter n poltcal equlbrum s the medan voter, that s, the ndvdual who owns a medan share of k, denoted by m s j. Ths has a conventonal flavor snce t agrees wth a standard result of poltcal competton: the medan voter s decsve n determnng polcy. Employng Lemma 1 and usng (8), we have n poltcal equlbrum: 10

13 m sj ( n 1) ε τ = 1. (1) (1/ N ) Snce postvely skewed dstrbutons of captal ncome are typcally observed n the real world, we shall mpose the nequalty s m j < 1/ N. Ths then mples from (1) that τ > 0 n poltcal equlbrum Increased nterregonal tax competton It s nterestng to observe the presence of n, the number of competng regons, n Eq. (1). When n = 1 (.e., there s no tax competton or the economy s closed), the margnal dstortonary cost of taxaton (the left-hand sde of (1)) s equal to zero snce k = k holds all the tme. The balancng of the tradeoff s completely domnated by the margnal redstrbutve beneft from taxaton (the rght-hand sde of (1)). As a result, the equlbrum tax rate wll be as hgh as possble. On the other hand, when n (.e., a small open economy n whch the after-tax rate of return on captal s beyond the control of ndvdual regons), the margnal dstortonary cost of taxaton approaches nfnty. The balancng of the tradeoff s completely domnated by the margnal dstortonary cost of taxaton (the left-hand sde of (1)). As a result, the equlbrum tax rate wll be as low as possble. We consder the general case where 1 < n < n the followng. Gven F g = g, the frst-order condtons (7) gve 10 ( uj / ) dt ( cj / ) + dn = 0 n. (13) Note from (10) that ( c / ) / n = (1/ n )[ k ( k / N ) + ( t / Nf )], and hence Eq. ( 13) j j leads to 10 We treat n as a contnuous varable as n Seade (1980). 11

14 ( kj ) (1/ n = n )[ k j ( k u j / N ) + ( t / / Nf )] (14) where we have utlzed k = k n a symmetrc Nash equlbrum. Ths result mples that ( ( kj ) / n) < 0 f kj < k / N or, equvalently, s j < 1/ N. Snce s m j < 1/ N, we have from Lemma 1: Lemma. ( ( kj ) / n) < 0 holds n equlbrum n our economy. That s, the equlbrum tax rate chosen by the decsve medan voter s monotoncally decreasng n the number of competng regons. Usng (3)-(5), Eq. (7) can be expressed as c j 1 k k j a = [( 1 ) + ] + = 0 n N n. (15) Thus, from (15), we also have: Lemma 3. ( a / ) > 0 holds n equlbrum n our economy. Lemma 3 confrms the ntuton that a ratonal ndvdual wll not pursue taxaton so much so that an ncrease n the tax rate reduces the lump sum grant receved: ( a / ) 0. Puttng Lemmas -3 together yelds our second man result: Proposton. The equlbrum sze of the demogrant s monotoncally decreasng n the number of competng regons. As noted n the Introducton, Hoyt (1991) shows that the extent to whch publc goods are undersuppled s monotoncally ncreasng n the number of competng regons. Regonal government actvtes are confned to publc good provson only and the agents are dentcal n Hoyt s model. Our ncluson of ncome redstrbuton as well as publc good provson n 1

15 government actvtes leads to a dramatc change. In contrast to Hoyt s fndng, we show that, regardless of the number of competng regons, all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods (Proposton 1); on the other hand, the sze of ncome redstrbuton (measured by the sze of the demogrant) s monotoncally decreasng n the number of competng regons (Proposton ). The tradeoff wth more jursdctons emphaszed by Hoyt (1991) s not at a cost of decreasng publc servce provson, but at a cost of decreasng ncome redstrbuton f agents are heterogeneous and more redstrbuton s desrable Comparson wth Meltzer and Rchard (1981) In ther classcal work, Meltzer and Rchard (1981) consder a closed economy n whch ndvduals vote over the lnear (labor) ncome tax. They show that each ndvdual trades off the margnal redstrbutve beneft from taxaton aganst the margnal dstortonary cost of taxaton. The ndvdually preferred labor tax rate results from the balancng of ths tradeoff. The tradeoff between dstorton and redstrbuton s hghlghted n many tax models (say, the celebrated Mrrlees (1971) model) and seems to be the most mportant feature of the poltcal economy of taxaton. In vew of ths, t s not surprsng to fnd that the mechansm drvng both our result and ther result s qute smlar. However, observe that there s no role for n n the determnaton of the sze of ncome redstrbuton n the Meltzer-Rchard closed economy, whereas the role of n s mportant n the determnaton of the sze of ncome redstrbuton n our open economy. It s worth notng that the theoretcal fndng summarzed by our Proposton s consstent wth 13

16 some emprcal evdence whch suggests that the sze of regonal governments vares nversely wth the total number of competng regons Dscusson Ths paper consders the lnear tax system T ( k) = a + tk, showng that tax competton results n an outcome n whch all heterogeneous ndvduals concur wth each other on the frst-best provson of publc goods (Proposton 1). One may wonder the robustness of ths result f the tax system s extended from lnear to non-lnear. Followng Cukerman and Meltzer (1991), a smple non-lnear extenson takes the form ( k) = a + tk + t k. Unlke ) T T (k n whch the margnal tax rate s constant n k, the margnal tax rate vares wth k n T (k). It can be checked that Proposton 1 remans true wth the extenson from T (k) to T (k). The reason s that MRT (the margnal rate of transformaton between g and a ) stll equals to 1 / N wth the replacement of (k) T by T (k) and, as a result, (6) stll holds. In fact, one can make further extensons of the tax system to, say, 3 ( k) = a + tk + t k + t k or T 3 4 ( k) = a + tk + t k + t k + t k, and T show that the concluson of Proposton 1 remans true wth respect to these further extensons. Gven tax rates, an ncrease n the level of publc good provson s effectvely fnanced by a unform lump-sum tax (a reducton of the demogrant). Ths s the key to our Proposton 11 See, for example, Nelson (1987), Eberts and Gronberg (1988) and Zax (1989). Note that we do not ncorporate lesure-labor choce nto our model. Emprcally, t seems hard to recognze the dsncentve effect of ncome taxes on labor supply (Saez, 00). However, t s very clear that tax competton among regons wll sgnfcantly affect the allocaton of captal. In ths sense, t would be more useful to consder ths aspect n the analytcal framework of an open economy than to nvestgate the conventonal lesure-labor choce n a closed model. 14

17 1. As long as the non-lnear captal ncome tax contans a unform lump-sum grant such as the a term n T (k), T (k) and T (k), the concluson of Proposton 1 wll reman true. 1 In our model labor s assumed completely mmoble and hence the regonal populaton sze N remans a constant all the tme. Ths s an mportant assumpton to uphold Proposton 1. However, wth some labor moblty, a change n one regon s tax-transfer polcy mght nduce ndvdual moblty across regons. Once the regonal populaton sze s endogenously determned, Proposton 1 may no longer hold. In such a case the tradtonal Tebout result mght hold: People lve together n a homogeneous regon and the redstrbuton polcy becomes less mportant. Gven tax rates, the RHS term of (4) wll be gven as well. Snce an ncrease n the level of publc good provson s effectvely fnanced by a unform lump-sum tax, the exercse of (6) bascally represents a resource re-allocaton between the publc good provson and the lump-sum grant n terms of the LHS terms of (4). As long as the cost assocated wth labor moblty s hgh enough to domnate the net benefts or costs resultng from ths resource reallocaton, ndvduals wll not move across regons n response to the resource re-allocaton. In such stuaton, the regonal populaton sze N can de facto be treated as a constant even f allowng for some labor moblty. In our settng, captal s assumed a perfectly moble factor whle labor an nterregonal mmoble factor. Ths settng s to capture the fact that these factors have dfferent degrees of moblty n the real world. How our Proposton 1 may be modfed n the presence of some captal mmoblty and/or some labor moblty s an ssue worth further study. 1 The avalablty of a lump-sum grant s crucal to our result. If ncome redstrbuton s done n the form of a dfferent nstrument wthout a lump-sum grant or n the form of ncome-contngent transfers, the concluson of Proposton 1 would not hold. 15

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