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A Tax Competition Analysis of Congestible Public Inputs
Journal of Urban Economics 48, 242᎐259 Ž2000. doi:10.1006rjuec.1999.2165, available online at http:rrwww.idealibrary.com on
A Tax Competition Analysis of Congestible Public Inputs Mutsumi Matsumoto* Faculty of Economics, Ritsumeikan Uni¨ ersity 1-1-1 Noji-higashi, Kusatsu 525-8577, Japan E-mail: [email protected] Received January 5, 1998; revised November 9, 1999 This paper investigates the provision of congestible local public inputs within a tax competition framework. Public input provision is financed by a business capital tax and by a profits tax on firms as a congestion tax. With this tax system, local tax and expenditure policies are inefficient because of potential capital outflows. The tax mix is inefficient in that the profits tax rate is too high relative to the capital tax rate. The level of public input provision is inefficiently low. Focusing on expenditure inefficiency, this analysis of public inputs is compared with Wilson’s analysis Ž Journal of Urban Economics, 1995, 38, 333᎐356. of congestible public goods. 䊚 2000 Academic Press
Key Words: congestion; public inputs; tax competition.
1. INTRODUCTION In the study of tax competition, substantial attention has been devoted to inefficient local public policies in the presence of distortionary taxes on business capital. Many papers have shown that when capital taxation is imposed to provide local public services, local governments hold down tax rates to avoid capital outflows and set inefficiently low levels of public services. Related studies include Braid w2x, Bucovetsky and Wilson w3x, Hoyt w5x, Keen and Marchand w6x, Wildasin w15, 16x, Wilson w17x, Wrede w19x, and Zodrow and Mieszkowski w20x. While this argument focuses mainly on public goods benefiting residents, underprovision is also the expected consequence of tax competition in the case of public inputs into the production process. The possibility of overprovision of public inputs cannot be completely excluded because they benefit local business and *I am indebted to James Feehan, Nobuo Akai, Ming Chung Chang, Takao Ohkawa, Robert Parry, and Matthias Wrede for helpful comments on earlier drafts of this paper. The comments and suggestions from the editor and referees of this journal were helpful in revising my imperfect arguments. I am solely responsible for all remaining errors. 242 0094-1190r00 $35.00 Copyright 䊚 2000 by Academic Press All rights of reproduction in any form reserved.
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increase the productivity of mobile capital Žsee Bayindir-Upmann w1x, Noiset w9x, and Noiset and Oakland w10x.. However, this possibility is a largely irrelevant exception. Matsumoto w7x shows that capital-tax financing leads to underprovision of public inputs under fairly general specifications of production technology.1 This paper extends the tax competition studies of local public inputs by introducing the congestion costs involved in the use of these inputs. Previous studies of tax competition have often overlooked problems relating to congestion externalities. An exception is Wilson w18x, but his analysis is limited to congestible public goods. In general, the use of local public services, including public inputs, will entail congestion costs. It is wellknown that the tax measures needed for the efficient provision of congestible public services are a congestion tax and a land tax. For public inputs, Richter w11x shows that a profits tax on user-firms serves as a first-best congestion tax when the number of firms is endogenous to jurisdictions. This tax rate should be set equal to the marginal cost of congestion in the use of public inputs. If the congestibility of public inputs is incomplete, the profits tax is insufficient to raise funds for public expenditure, so that a non-distortionary land tax is used. This argument is analogous to the Žgeneralized. Henry George theorem regarding the provision of congestible public goods under population mobility.2 Following the tax competition literature, this paper investigates how capital tax distortion influences the provision of congestible public inputs. For this study, the Richter w11x model is extended to a tax competition framework, where a profits tax and a capital tax are imposed to finance public input provision. In addition to expenditure inefficiency, this paper identifies an inefficient tax mix caused by capital tax distortion. It is demonstrated that the capital tax rate is inefficiently low in equilibrium, distorting local tax and expenditure policies. The equilibrium tax mix is inefficient in that there is too much reliance on the profits tax. The equilibrium level of public input provision is inefficiently low. As the tax competition literature points out, the fear of capital outflows is responsible for these outcomes. Local governments, competing for mobile capital, 1 In Matsumoto w7x, underprovision of public inputs occurs because of capital-tax financing if production technology is characterized by constant returns to scale in private factors or all factors, including public inputs. These two possibilities of the returns to scale have been frequently examined in previous studies of public input provision. Feehan w4x reviews alternative specifications of public inputs, which are based on the degree of homogeneity of the production functions. 2 The efficient provision of congestible public goods is supported by a land tax and a head tax on mobile residents as a congestion tax. See Mieszkowski and Zodrow w8x and Wildasin w13, 14x for comprehensive surveys of related studies.
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MUTSUMI MATSUMOTO
attempt to prevent capital outflows by lowering the capital tax rate relative to the profits tax rate. Also, they have an incentive to reduce their expenditure levels because capital-tax financing of public inputs discourages business investment. These inefficiencies can be mitigated by a coordinated increase in all jurisdictions’ capital taxes. As may be expected, this paper is closely related to Wilson’s w18x analysis of congestible public goods. Although tax competition does not give rise to underprovision in his model, the difference in results between his study and this paper is simply due to the specification of local tax bases. While Wilson w18x assumes that capital and land are uniformly taxed Žproperty taxation., this paper exempts immobile factors from taxation, as in traditional models of tax competition such as that of Zodrow and Mieszkowski w20x.3 Furthermore, Wilson w18x includes an analysis of a distortionary congestion tax, but the profits tax in this paper is first-best as a congestion tax. It is shown that, once these differences are taken into account, his analysis of public goods can be reconciled with this paper’s analysis of public inputs. This paper is organized as follows. The model is described in Sect. 2. Section 3 clarifies the second-best tax and expenditure rules under capital taxation. Section 4 examines the welfare impact of coordinated policy changes made by all jurisdictions, and identifies how tax competition affects local public policies. A comparison between public goods and public inputs is drawn in Sect. 5. Section 6 gives concluding remarks. 2. THE MODEL The basic structure of the model is based on Richter w11x. Consider a national economy with competitive identical jurisdictions. In the economy, a numeraire output is produced by competitive firms using immobile land, mobile capital, and a local public input. Let M be the number of local firms in a representative jurisdiction. As formalized later, M is endogenously determined by profit-maximizing behavior. Output per firm is F Ž QrM, KrM, b . where Q, K, and b are the jurisdiction’s land, capital, and public input, respectively. Marginal products are positive and diminishing. All factors are complements in the sense that the second-order cross derivatives of F Ž⭈. are positive. The local supply of land is constant. While the total capital stock is exogenous to the economy, the local supply of capital is variable due to mobility. Each jurisdiction has a single immobile 3 As in Wilson w18x, a uniform tax on capital and land is called ‘‘property taxation’’ when his analysis is compared with this paper. In the tax competition literature, property taxation is ordinarily defined as a tax on business capital.
CONGESTIBLE PUBLIC INPUTS
245
resident who owns local land.4 All residents in the economy are equally endowed with capital stock. They spend factor income on consumption, which is the sole source of utility Žthere is no public good in the model.. The output produced can be transformed into a certain amount of either the public input or a private good. In terms of output, the cost of public input provision is C Ž M, b .. With respect to this function, the following conditions are assumed: CM ) 0,
Cb ) 0,
and ⭸ Ž CrM . r⭸ M - 0.
Ž 1.
Throughout this paper, subscripts of a function indicate partial derivatives of that function Že.g., ⭸ Cr⭸ M s CM .. Given the amount of output used to produce b, a rise in M reduces the public input supply to each firm, representing congestion externalities. This treatment of congestion has been frequently used in the study of local public finance. 5 The last inequality in Ž1. means that the congestibility of b is incomplete because the per-firm cost of public input provision declines as M rises Žscale economies in the provision of b .. This assumption appears to be reasonable in the context of regional economics. The nature of production technology is crucial to the study of public inputs Žsee Footnote 1.. Following Richter w11x, this paper assumes that F Ž⭈. exhibits constant returns to scale in all factors, including b. With this specification of technology, the benefit of public input provision accrues not only to private factors as increased productivity, but also to firms because there is a rent on the provision. Unlike Matsumoto w7x, this paper does not include the case of constant returns to scale in private factors. My analysis in this paper is founded on the idea that if public inputs are congestible, the number of user-firms will be a non-trivial variable. As Feehan w4x points out, the literature on public input provision often argues that the case of constant returns to scale in private factors is more reasonable in the presence of public inputs. With this degree of linear homogeneity, however, congestion externalities cannot be modeled satisfactorily because the optimal number of firms is always unity in each jurisdiction regardless of any other tax distortions. 4
Mobile residents who supply labor in the jurisdiction of their residence can be introduced into the model without affecting any results in this paper. In this case, it must be assumed, as in Wilson w18x, that each resident has an equal share of land in each and every jurisdiction. 5 Alternatively, congestion externalities can be directly incorporated into the production function. Suppose that output per firm is F Ž QrM, KrM, brM ␥ . where 0 - ␥ - 1. The degree of congestion is measured by ␥ . The cost of public input provision is C s b. All results in this paper are obtained from this setting, but the analysis becomes considerably more complex.
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MUTSUMI MATSUMOTO
For convenience, my analysis is carried out in terms of the aggregate level of production. Since the production function was characterized by constant returns to scale in all factors, the total output in a single jurisdiction equals MF Ž QrM, KrM, b . s F Ž Q, K , Mb . .
Ž 2.
From Eq. Ž2., the total output increases with a rise in M. This raises a problem of unbounded production possibilities even if b is congestible.6 To determine M endogenously at a finite level, it is assumed, as in Richter w11, Sect. 5x, that the formation of a new firm entails a fixed setup cost. This assumption ensures that first-best optimum and competitive equilibrium are well-defined. This paper is concerned with a long-run analysis with free entry.7 Local public expenditure is financed by a profits tax on firms and by a capital tax. Taking market prices, the tax rates, M, and b as given, firms choose the amount of private factors to maximize profits. Given the presence of the rent on public input provision equal to b⭸ F Ž Q, K, Mb.r⭸ Mb per firm, market entry continues up to the point where the rent equals the sum of the profits tax and the fixed cost of creating a new firm. The public budget constraint and the conditions for profit maximization are
M q tK s C Ž M, b . ,
Ž 3.
FK Ž Q, K , Mb . s r q t ,
Ž 4.
bFB Ž Q, K , Mb . s S q ,
Ž 5.
and
where is the profits tax rate, t is the capital tax rate, r is the net return on capital, S is the fixed cost in terms of output, and FB s ⭸ Fr⭸ Mb. In what follows, subscript B of F Ž⭈. indicates partial differentiation with respect to Mb, in order to simplify notation. Because of capital mobility, competitive jurisdictions take r as given. Equation Ž3. represents the public budget constraint. Equation Ž4. is the condition for capital investment. Equation Ž5. shows that net profits dissipate as a result of free entry. 6
For example, if congestion is modeled as in Footnote 5, the total output still increases as M rises. 7 To bound production possibilities, one can assume that the national economy has a fixed number of mobile firms. Richter w11x deals mainly with this short-run case, rather than the long-run case with free entry, since he analyzes the locational efficiency of mobile firms. The difference between the short run and the long run is irrelevant to Matsumoto’s w7x study of pure public inputs. Still, it has an important implication in the current model with a congestible public input. ŽSee also Footnote 11..
CONGESTIBLE PUBLIC INPUTS
247
Unlike Richter w11x, where profits taxation is proportional to profits, this tax is defined as a poll tax on firms. The proportional tax and the poll tax are equivalent in the current model. With the former tax Ž M ., market entry implies that Ž1 y M . FB b s S in equilibrium. This equation can be reduced to Eq. Ž5. by defining s M SrŽ1 y M .. From Eqs. Ž4. and Ž5., consumption in each jurisdiction amounts to F Ž Q, K , Mb . y Ž r q t . K y Ž S q . M q rK *,
Ž 6.
where K * is the endowment of capital. The amount F y Ž r q t . K y Ž S q . M represents income from the ownership of local land. Local governments set policy variables to maximize Ž6. subject to Eqs. Ž3. ᎐ Ž5.. In the current model with competitive jurisdictions and a single output, utility maximization is equivalent to rent maximization. 3. SECOND-BEST RULES FOR LOCAL PUBLIC POLICIES As argued in Sect. 1, a profits tax and a land tax constitute an efficient tax system in models with congestible local public inputs when the number of local firms is variable. The profits tax covers the marginal cost of congestion in the use of bŽ s CM .. If public input provision exhibits scale economies, it must be financed by the land tax. With this first-best tax system, the provision level would be set such that the sum of the marginal product of b over firms equals the marginal cost of providing bŽ MFB s Cb ., which corresponds to the Samuelson rule for public good provision.8 This section investigates the second-best conditions for tax and expenditure policies under capital tax distortion. The analysis starts with the derivation of the first-order conditions for policy variables. Equations Ž4. and Ž5. determine K and M as functions of t, , and b. Inserting them into Ž3. and Ž6., the Lagrangean of the maximization problem is F Ž Q, K Ž t , , b . , M Ž t , , b . b . y Ž r q t . K Ž t , , b . y Ž S q . M Ž t , , b . q rK * q M Ž t , , b . q tK Ž t , , b . y C Ž M Ž t , , b . , b . ,
Ž 7.
See Richter w11x for detailed arguments regarding this first-best policy. Additionally, he shows that even if the Žproportional. profits tax rate is exogenously fixed at a level that does not equal the marginal cost of congestion, an efficient allocation is possible when: Ži. a poll tax on firms is available, Žii. profits tax revenue is earmarked for public input provision, and Žiii. budget deficits are financed by a land tax. To achieve efficiency, the sum of the poll tax and the proportional profits tax per firm must equal the marginal cost of congestion. However, since these taxes are equivalent Žsee Sect. 2., this argument eventually implies that each firm pays for the marginal cost of congestion in first-best optimum. 8
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MUTSUMI MATSUMOTO
where is the Lagrange multiplier on Ž3.. Using Eqs. Ž4. and Ž5., the first-order conditions are
Ž t . Ž 1 y . K s Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . ,
Ž 8.
Ž . Ž 1 y . M s Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ t . ,
Ž 9.
Ž b . MFB s Cb y Ž y CM . Ž ⭸ Mr⭸ b . y t Ž ⭸ Kr⭸ b . .
Ž 10 .
and
Equilibrium public policies in the model are determined by Eqs. Ž8. ᎐ Ž10.. Equations Ž8. and Ž9. show that, because of the impact of t and on the tax bases, the marginal welfare impact of tax revenue does not equal that of private income; that is, / 1.9 The first-order condition for b includes the impact of b on the tax bases as distortionary benefits or costs. The examination of the derivatives of K and M plays an important role in this paper. Differentiating Ž4. and Ž5. yields
⭸ Kr⭸ t s b 2 FB Br⍀ ;
Ž 11a .
⭸ Mr⭸ t s ybFK Br⍀ ;
Ž 11b .
⭸ Kr⭸ s ybFK Br⍀ ;
Ž 11c .
⭸ Mr⭸ s FK Kr⍀ ;
Ž 11d.
⭸ Kr⭸ b s bFB FK Br⍀ ;
Ž 11e .
⭸ Mr⭸ b s yFB FK Kr⍀ y Mrb;
Ž 11f .
where ⍀ ' Ž FK K FB B y FK2 B . b 2 . In what follows, it is assumed that ⍀ ) 0; that is, F Ž⭈. is strictly concave in K and Mb. Using Eqs. Ž8. ᎐ Ž11., the properties of equilibrium public policies are derived. The following proposition summarizes the results: PROPOSITION 1. Under the assumption that ⭸ Ž CrM .r⭸ M - 0, Ža. The capital tax rate is positi¨ e Ž t ) 0. and the profits tax rate exceeds the marginal cost of congestion in the use of bŽ ) CM . in equilibrium, and Žb. The sum of the marginal product of b o¨ er firms exceeds its marginal cost Ž MFB ) Cb . in equilibrium. 9
It can be shown that ) 1 if there are scale economies in public input provision and if the Laffer effect of taxes does not exist.
CONGESTIBLE PUBLIC INPUTS
249
Proof. Ža. The first-order conditions for tax policy, Eqs. Ž8. and Ž9., imply that
Ž 1 y . r s Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . rK s Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ . rM.
Ž 12 .
This equation can be rewritten as
Ž y CM . ⌬ , t M q t⌬ , t K s 0,
Ž 13 .
⌬ , t K ' ⭸ Kr⭸ y Ž ⭸ Kr⭸ t . Ž MrK . ;
Ž 14a .
⌬ , t M ' ⭸ Mr⭸ y Ž ⭸ Mr⭸ t . Ž MrK . .
Ž 14b .
where
As shown later, ⌬ indicates the impact of balanced-budget policy changes on the tax bases. From Eqs. Ž11a. ᎐ Ž11d., ⌬ , t K and ⌬ , t M are, respectively, equal to ⌬ , t K s yb Ž KFK B q MbFB B . r Ž ⍀ K . ) 0;
Ž 15a .
⌬ , t M s Ž KFK K q MbFK B . r Ž ⍀ K . - 0.
Ž 15b .
The signs of Ž15a. and Ž15b. are derived from complementarity among factors Ž Fi j ) 0. and the linear homogeneity of F Ž⭈., i.e., Ý j Fi j j s 0, where j s Q, K, and MbŽ B .. Note that CM s M⭸ Ž CrM .r⭸ M q CrM and y Ž CrM . s yt Ž KrM .. Substituting these into Ž13. and manipulating terms gives yM ⭸ Ž CrM . r⭸ M ⌬ , t M q t ⌬ , t K y Ž KrM . ⌬ , t M s 0. Ž 16 . By Ž15a., Ž15b., and Ž16., t is positive if ⭸ Ž CrM .r⭸ M - 0. This, together with Ž13., proves that ) CM . Žb. From Eqs. Ž11c. ᎐ Ž11f., the policy-induced changes in K and M satisfy the following relations:
⭸ Kr⭸ b s yFB Ž ⭸ Kr⭸ . ;
Ž 17a .
⭸ Mr⭸ b s yFB Ž ⭸ Mr⭸ . y Mrb.
Ž 17b .
Inserting Ž17a. and Ž17b. into Ž10. yields MFB s Cb q Ž y CM . Ž Mrb . q FB Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ . .
Ž 18 .
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MUTSUMI MATSUMOTO
Equation Ž9. implies that the third term on the RHS equals Ž1 y . MFB . Thus, Eqs. Ž18. is reduced to a simple rule for public input provision: MFB s Cb q Ž y CM . Ž Mrb . , which, combined with Ža., proves that MFB ) Cb .
Ž 19 . Q.E.D.
Proposition 1 shows that public policies are affected by capital tax distortion. Consider first the tax structure. As in a first-best setting, the profits tax is not enough to finance public input provision under scale economies. As a result of using the capital tax, congestion pricing is too high Ž ) CM .. This is because, at any given level of public expenditure, local capital stock can be increased by lowering the capital tax rate relative to the profits tax rate. Local governments use the profits tax as a means of expanding the capital tax base. Formally, Eq. Ž13. gives the optimal condition for tax policy in which the second term represents the distortionary impact of the capital tax. The positive term, ⌬ , t K, is the impact of an increase in on K, with t decreasing to balance the public budget. ŽThe same argument applies to ⌬ , t M.. ⌬ , t K s ⭸ Kr⭸ q Ž ⭸ Kr⭸ t . Ž ⭸ tr⭸ . ,
Ž 20 .
where ⭸ tr⭸ s yMrK wsee Ž14a.x. The balanced-budget relations between policy variables are derived by differentiating Ž3. and using Ž8. ᎐ Ž10.: Md q Kdt y MFB db s 0.
Ž 21 .
I turn next to a consideration of public expenditure. Equation Ž19., which is based on the first-order conditions for and b, is the second-best rule for public input provision when a marginal increase in b is financed by the profits tax. With this financing of expenditure, the number of local firms declines while local capital stock does not change. Since ) CM under capital tax distortion, the decline in M reduces the fiscal surplus associated with the profits tax base, creating a distortionary cost of public input provision. Thus, MFB ) Cb in equilibrium. These arguments can be seen using Ž17a., Ž17b., and Ž21.. Since ⭸r⭸ b s FB from Eqs. Ž21., Ž17a. and Ž17b. imply that ⭸ Kr⭸ b q Ž ⭸ Kr⭸ .Ž ⭸r⭸ b . s 0 and ⌬ b , M ' ⭸ Mr⭸ b q Ž ⭸ Mr⭸ . Ž ⭸r⭸ b . s yMrb - 0.
Ž 22 .
Note that profits-tax financing of b does not affect the aggregate level of public input provision Ž Mb., so that the total output remains unchanged. Using Ž22., Ž19. is expressed as MFB s Cb y Ž y CM . ⌬ b , M.
Ž 23 .
CONGESTIBLE PUBLIC INPUTS
251
A similar argument can be established when the additional b is financed by the capital tax. In this case, the marginal benefit of public input provision exceeds its marginal cost because of policy-induced capital outflows. The capital-tax financing rule for b is MFB s Cb y Ž y CM . ⌬ b , t M y t⌬ b , t K ,
Ž 24 .
where ⌬ b, t K and ⌬ b, t M are, respectively, the impact of capital-tax financing of b on K and M we.g., ⌬ b, t K ' ⭸ Kr⭸ b q Ž ⭸ Kr⭸ t .Ž ⭸ tr⭸ b .x.10 Like Ž15., using Eqs. Ž11a., Ž11e., and Ž21., one has ⌬ b , t K s bFB Ž KFK B q MbFB B . r Ž ⍀ K . - 0.
Ž 25 .
Although the sign of ⌬ b, t M is ambiguous, equilibrium public policies must be such that the profits tax rate and the capital tax rate are set so as to equate the marginal excess burden of use of these financing measures. Part Žb. of Proposition 1 thus implies that the decrease in capital tax revenue in Eq. Ž24. is greater than the possible increase in the fiscal surplus arising from M. 4. FISCAL EXTERNALITY In the previous section, the properties of equilibrium public policies were analyzed by solving the optimization problem of a representative jurisdiction. This section investigates inefficient public policies from the viewpoint of the economy as a whole. As the tax competition literature argues Že.g., Wildasin w16x., the source of inefficiency in this paper is an interjurisdictional fiscal externality caused by capital mobility. Each local government regards policy-induced capital movements as distortionary benefits or costs due to tax competition. Given that the total capital stock is constant, however, the induced changes in local capital stock are not distortions from the viewpoint of the entire economy, because the tax revenues of other jurisdictions increase or decrease. Ignoring these external impacts gives rise to inefficient outcomes. In the current model, where congestion pricing is distorting under capital taxation, local public policies affect fiscal surplus by changing the number of local firms. But, if jurisdictions are perfectly competitive and if 10
The derivation of Eq. Ž24. is as follows. Using ⌬ b, t K and ⌬ b, t M, Eq. Ž10. can be rewritten as MFB s w Cb y Ž y CM . ⌬ b , t M y t⌬ b , t K x q w Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . x Ž ⭸ tr⭸ b . . Since ⭸ tr⭸ b s MFB rK from Ž21., Eq. Ž8. implies that the second bracketed term on the RHS equals Ž1 y . MFB . Substituting this yields Eq. Ž24..
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MUTSUMI MATSUMOTO
market entry is possible, any policy-induced change in the profits tax base in a single jurisdiction has no external impact. It merely alters the total number of firms in the economy, leaving the fiscal surplus of other jurisdictions unchanged. The entire economy, as well as local jurisdictions, faces an infinitely elastic supply of firms. Accordingly, in this paper, the sole source of externalities is policy-induced capital movements. The fiscal externality theory suggests that equilibrium public policies are inefficient relative to the available tax system. As demonstrated in Sect. 3, local governments have an incentive to transfer tax burdens from capital to profits in order to expand the capital tax base. This creates a negative externality on other jurisdictions, implying that the tax mix is inefficient in that there is too much reliance on the profits tax. With respect to public input provision, while profits-tax financing has no impact on business investment, capital-tax financing causes capital outflows and gives rise to benefits to other jurisdictions. As a result, underprovision of public inputs occurs because of undertaxation of capital.11 To verify these arguments, the rest of this section investigates the welfare impact of coordinated policy changes made by all jurisdictions from equilibrium. The intuition behind this approach is that any public policy creating positive externalities should be encouraged, and vice versa.12 Since jurisdictions were assumed to be identical, this paper deals with symmetric equilibrium. In such an equilibrium, capital stock is uniformly distributed across jurisdictions, so that K equals the endowment of capital, K *. Applying this to Ž6., consumption equals ⌽ ' F Ž Q, K *, Mb . y tK * y Ž S q . M.
Ž 26 .
Unlike the optimization problem in Sect. 3, any coordinated policy changes keep local capital stock unchanged at K *. Thus, the impact on ⌽ depends on the change in policy variables and M. The relations between these 11
If the economy has a fixed number of mobile firms, fiscal externality due to firm mobility is relevant. This short-run case is discussed here for later reference. All results in Sect. 3 remain unchanged Ž ) CM and MFB ) CB .. But, their implications differ from the case of free entry. Without market entry, the equilibrium tax mix is efficient relative to the available taxes. Although a single jurisdiction’s tax policy creates fiscal externalities by causing movements of firms and capital, these externalities are exactly offset. Inefficiency is thus limited to public input underprovision. In the short-run case, a rise in the public input supply creates a positive externality regardless of the method of financing Žthe profits tax or the capital tax.. 12 In the tax competition literature, welfare-improving policy changes are analyzed to identify how local public policies are distorted. See, for example, Bucovetsky and Wilson w3x, Keen and Marchand w6x, and Wilson w17, 18x.
CONGESTIBLE PUBLIC INPUTS
253
variables are given by the following system of equations:
M q tK * s C Ž M, b .
Ž 27 .
bFB Ž Q, K *, Mb . s S q .
Ž 28 .
and
The net return on capital is also altered according to FK Ž Q, K *, Mb. s r q t, but this equation is irrelevant to the analysis because ⌽ does not depend on r. Using Ž26. ᎐ Ž28., the direction of welfare-improving policy changes is considered. PROPOSITION 2. Starting from a symmetric equilibrium, Ža. A marginal decrease in all jurisdictions’ is welfare-impro¨ ing if t is adjusted to maintain the public budget constraint, and Žb. A marginal increase in all jurisdictions’ b is welfare-impro¨ ing under capital-tax financing, but profit-tax financing has no welfare impact. Proof. Ža. From Ž26. and Ž28., a coordinated change in the tax mix alters ⌽ by
␦ ⌽r␦ < b , constant s yK * Ž ␦ tr␦ . y M,
Ž 29 .
where ␦ is the symbol of differentiation in the case of coordinated policy changes made by all jurisdictions. Differentiating Eq. Ž27. and inserting the result into Ž29. yields
␦ ⌽r␦ < b , constant s Ž y CM . Ž ␦ Mr␦ . .
Ž 30 .
Equation Ž28. shows that ␦ Mr␦ - 0 at a given b. Since ) CM in equilibrium, the policy change stated in Ža. is welfare-improving. Žb. Suppose that all jurisdictions uniformly increase b by capital-tax financing. From Ž26. and Ž28., the resultant change in ⌽ equals
␦ ⌽r␦ b < , constant s MFB y K * Ž ␦ tr␦ b . .
Ž 31 .
The term, ␦ tr␦ b, can be derived by differentiating Eqs. Ž27. and Ž28. with respect to M, t, and b:
y CM ; 2
b FB B ;
K *; ␦ M Cb s ␦ b. ␦t y Ž FB q MbFB B . 0;
Ž 32 .
Solving Ž32. and substituting y CM s Ž brM .Ž MFB y Cb . from Eq. Ž19. yields
␦ tr␦ b s MFBrK * q FB Ž MFB y Cb . r Ž MbK*FB B . .
Ž 33 .
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MUTSUMI MATSUMOTO
Inserting Ž33. into Ž31. shows that the welfare impact of capital-tax financing is
␦ ⌽r␦ b < , constant s yFB Ž MFB y Cb . r Ž MbFB B . .
Ž 34 .
Since MFB ) Cb in equilibrium, Ž34. is positive. Profit-tax financing can be examined in a similar manner. The change in ⌽ is
␦ ⌽r␦ b < t , constant s MFB y M Ž ␦r␦ b . .
Ž 35 .
Differentiating Eqs. Ž27. and Ž28. with respect to M, , and b gives
y CM ; 2
b FB B ;
M;
Cb ␦M s ␦ b. ␦ y Ž FB q MbFB B . y1;
Ž 36 .
This equation, together with Eq. Ž19., yields ␦r␦ b s FB . Thus, ␦ ⌽r␦ b < t, constant s 0. Q.E.D. One can confirm from Eqs. Ž27. and Ž28. that ␦ tr␦ - 0 and ␦ tr␦ b ) 0 when a rise in in all jurisdictions increases fiscal surplus at a given t and b. Under this reasonable condition, Proposition 2 makes it clear that undertaxation of capital is responsible for inefficient tax and expenditure policies. A welfare improvement can be achieved by increasing all jurisdictions’ capital taxes and using the revenue to reduce their profits taxes and raise their expenditures. In particular, Part Žb. of Proposition 2 shows that no coordinated decrease in public expenditure can ever improve welfare. The equilibrium level of public input provision is thus too low. Note also that although profits-tax financing of expenditure has no welfare impact under market entry,13 there is a close relation between this tax and expenditure inefficiency. In Eq. Ž34., the welfare impact of capital-tax financing is positive if and only if ) CM . This reflects the fact that the marginal excess burdens of both financing measures are equalized Žsee Sect. 3.. From the viewpoint of the entire economy, overpricing of congestion costs is closely related to fiscal externalities due to capital mobility. 5. COMPARISON BETWEEN PUBLIC GOODS AND PUBLIC INPUTS This section compares my study of congestible public inputs and Wilson’s w18x study of congestible public goods. These studies outwardly yield different conclusions regarding expenditure inefficiency. Still, they can be reconciled under an appropriate comparison. 13 If, as in the short-run case stated in Footnote 11, the total number of firms is exogenous, a coordinated rise in the public input supply financed by the profits-tax is welfare-improving, as it is with capital-tax financing.
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In the Wilson w18x model with three factors of production Žmobile labor, mobile capital, and immobile land., a property tax is imposed on capital and land when public good provision exhibits scale economies, which are defined as declining per capita cost of the provision. Two cases are examined according to the specification of congestion taxation: a head tax and a labor tax. While each resident supplies a fixed amount of labor in the case of head taxation, the case of labor taxation allows for endogenous labor᎐leisure choice. In both cases, there is no tendency toward public good underprovision. Yet this section argues that if labor᎐leisure distortions are incorporated into Wilson’s w18x case of head taxation, a similarity between his analysis and this paper is obtained in terms of expenditure inefficiency. To make the similarity complete, the use of capital taxation instead of property taxation must be assumed under scale economies. This replacement of taxation is necessary to derive underprovision. On the other hand, this paper does not parallel Wilson’s w18x case of labor taxation, because there may not be underprovision in the presence of this distortionary congestion tax, regardless of whether property taxation or capital taxation is used under scale economies. In what follows, these discussions are summarized. ŽThe derivations are available from the author upon request.. It is useful, for my comparison, to describe the impact of a single jurisdiction’s head-tax financing of public goods. With mobile residents, an important characteristic of this financing is that it does not affect the local supply of labor and capital. It turns out that if each resident’s labor supply is endogenous, local population Žthe head tax base. alters to offset labor᎐leisure distortions. ŽA jurisdiction’s labor supply equals its population times the labor supplied per capita.. As long as the head tax rate does not equal the marginal cost of congestion, the change in local population affects the fiscal surplus associated with the head tax base, creating a distortionary cost of public good provision. In contrast, the fact that the local supply of labor and capital remains unchanged implies that head-tax financing has no impact on mobile tax bases without labor᎐leisure distortions. For this reason, public good provision follows the first-best rule in Wilson’s w18x case of head taxation, even if congestion pricing is distorting in the presence of scale economies Žsee his Proposition 1..14 This argument is related to Richter and Wellisch w12, Proposition 4.1x. In their model with a land tax and a head tax, the provision of congestible public goods under labor mobility follows the first-best rule, even if the land tax is fixed at a suboptimal level. Their result is due to the absence of a labor᎐leisure choice. Note also that, in Wilson w18x, a single jurisdiction’s labor-tax financing of public goods has no impact on the local supply of labor and capital, as in the case of head taxation. The neutrality to the labor tax base implies that the provision rule for public goods does not depend on congestion pricing Žsee Proposition 2 in Wilson w18x.. 14
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The impact of head-tax financing under labor᎐leisure distortions resembles that of profits-tax financing in this paper. The profits-tax financing rule for public inputs, Eq. Ž23., shows that the policy-induced decline in the number of local firms represents a distortionary cost of public expenditure. Similarly, head-tax financing of public goods reduces local population if leisure is a normal good and if the utility function is separable between private commodities and public goods. Under these assumptions, a coordinated increase in the public good supply improves welfare if and only if the head tax rate exceeds the marginal cost of congestion Žoverpricing of congestion costs., in which case the marginal benefit of expenditure exceeds its marginal cost because of the policy-induced population outflows. This necessary and sufficient condition for underprovision is satisfied when a capital tax is used under scale economies. As in this paper’s analysis of public inputs, the resultant inefficiency can be explained in terms of fiscal externalities due to capital mobility. A single jurisdiction’s capital-tax financing of public goods reduces its capital stock and generates a positive externality on other jurisdictions.15 On the other hand, underprovision may not occur when, as in Wilson w18x, the capital tax is replaced with a property tax on capital and land, because the impact of this tax on local capital stock is obscure. The same qualification applies to this paper. The impact of the tax mix and public inputs on business investment is obscure under property taxation, so that my results regarding the sign of externalities may be reversed. However, given that most of the studies in the tax competition literature have examined capital taxation, this argument is not surprising. In Matsumoto w7x, underprovision of pure public inputs depends on the assumption of capital taxation. ŽThis should not be confused with potential overprovision in Bayindir-Upmann w1x, Noiset w9x, and Noiset and Oakland w10x referred to in Sect. 1, since they assume the use of capital taxation.. Under labor mobility, a similar argument carries over to pure public goods if the sole source of local tax revenue is either a capital tax or a property tax. While capital-tax financing of public expenditure causes capital outflows and
15 Strictly speaking, the case of head taxation under labor᎐leisure distortions yields a result similar to the short-run case argued in Footnote 11. With the total number of residents being constant, labor mobility is also a source of fiscal externalities. As a result, the equilibrium tax mix is efficient while public good provision is inefficient. Local tax policy creates externalities through mobility of residents and capital, but these externalities are offset in equilibrium. This result regarding the mix of taxes holds regardless of whether capital taxation or property taxation is used. ŽA similar result applies to the short-run case in this paper..
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leads to underprovision, property-tax financing may increase local capital stock. ŽThe sign of fiscal externalities is obscure..16 Lastly, Wilson’s w18x case of labor taxation is discussed. In this case, inefficient public policies are due to policy-induced labor᎐leisure distortions. Unlike the case of head taxation with a labor᎐leisure choice, however, these distortions are not related to fiscal externalities due to capital mobility, even if business investment is subject to taxation. As a result, the case of labor taxation differs in its implications from those in this paper. A close look at the welfare impact of coordinated policy changes makes this clear Žsee Propositions 3 and 4 in Wilson w18x.. Although welfare is improved under plausible conditions if all jurisdictions’ public goods are increased by property-tax financing, labor-tax financing may not be welfare-improving because labor-leisure distortions increase.17 Due to the ambiguity of the welfare impact of labor-tax financing, the direction of welfare-improving changes in expenditure cannot be easily identified. Interestingly, these results hold even if capital taxation is used instead of property taxation. Despite the negative impact of capital-tax financing of public goods on business investment, this tax does not necessarily lead to underprovision in the case of labor taxation. 6. CONCLUDING REMARKS In the tax competition literature, a large number of studies have been made on the impact of competition for mobile capital on local public expenditure. While that literature has mostly clarified public good provision, several papers have recently been devoted to the study of public input provision. This paper has extended the study of public input provision by introducing the congestion costs involved in the use of public inputs. Local public expenditure is financed with the revenue raised by a profits tax on firms and by a capital tax. In addition to the profits tax as a congestion tax, the capital tax is used when the congestibility of public inputs is incomplete because of scale economies. The dependence on the capital tax causes inefficient local tax and expenditure policies. As the standard tax competition argument shows, fiscal externalities due to capital mobility are 16
If residents cannot migrate, both property taxation and capital taxation cause public good underprovision Žsee Braid w2x.. Wilson w18, Appendixx shows that even if residents are mobile, underprovision results from property taxation in the absence of scale economies. In the Wilson model, property-tax financing of public goods may increase local capital stock, but a labor inflow occurs so that the property tax base per capita declines. 17 Wilson w18x shows that the direction of welfare-improving changes in public expenditure is clearly determined under labor-tax financing if public goods are either pure public or pure private. Without this assumption, however, the welfare impact of labor-tax financing of public goods is obscure. In contrast, regardless of the degree of scale economies in public good provision, property-tax financing improves welfare.
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ignored in decentralized decision making. With hopes of gaining an advantage over other jurisdictions in competition for mobile capital, local governments attempt to keep their capital tax rates low. Consequently, they rely too heavily on the profits tax and choose inefficiently low levels of public inputs. In comparing Wilson’s w18x analysis of congestible public goods and this paper, their different assumptions of local tax bases should be taken into account. In principle, this paper is the counterpart of his case of head taxation when labor᎐leisure distortions are incorporated. Once his property tax is replaced with a capital tax, the familiar underprovision result applies to congestible public goods if a head tax serves as a congestion tax. The intuition underlying expenditure inefficiency is similar to that in this paper Žwith the proviso stated in Footnote 15.. On the other hand, Wilson’s w18x case of labor taxation does not parallel my analysis of public inputs. Under this distortionary congestion tax and labor mobility, there may not be underprovision even if capital taxation is used, because inefficient public polices are no longer related to policy-induced capital movements.
REFERENCES 1. T. Bayindir-Upmann, Two games of interjurisdictional competition when local governments provide industrial public good, International Tax and Public Finance, 5, 471᎐487 Ž1998.. 2. R. M. Braid, Symmetric tax competition with multiple jurisdictions in each metropolitan area, American Economic Re¨ iew, 86, 1279᎐1290 Ž1996.. 3. S. Bucovetsky and J. D. Wilson, Tax competition with two tax instruments, Regional Science and Urban Economics, 21, 333᎐350 Ž1991.. 4. J. P. Feehan, Pareto-efficiency with three varieties of public input, Public Finance, 44, 237᎐248 Ž1989.. 5. W. H. Hoyt, Property taxation, Nash equilibrium, and market power, Journal of Urban Economics, 30, 123᎐131 Ž1991.. 6. M. Keen and M. Marchand, Fiscal competition and the pattern of public spending, Journal of Public Economics, 66, 33᎐53 Ž1997.. 7. M. Matsumoto, A note on tax competition and public input provision, Regional Science and Urban Economics, 28, 465᎐473 Ž1998.. 8. P. Mieszkowski and G. R. Zodrow, Taxation and the Tiebout Model: The differential effects of head taxes, taxes on land rents, and property taxes, Journal of Economic Literature, 27, 1098᎐1146 Ž1989.. 9. L. Noiset, Pigou, Tiebout, property taxation, and the underprovision of local public goods: A comment, Journal of Urban Economics, 38, 312᎐316 Ž1995.. 10. L. Noiset and W. Oakland, The taxation of mobile capital by central cities, Journal of Public Economics, 57, 296᎐316 Ž1995.. 11. W. F. Richter, The efficient allocation of local public factors in Tiebout’s tradition, Regional Science and Urban Economics, 24, 323᎐340 Ž1994..
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12. W. F. Richter and D. Wellisch, The provision of local public goods and factors in the presence of firm and household mobility, Journal of Public Economics, 60, 73᎐93 Ž1996.. 13. D. E. Wildasin, ‘‘Urban Public Finance,’’ Harwood Academic Publishers, New York Ž1986.. 14. D. E. Wildasin, Theoretical analysis of local public economics, in ‘‘Handbook of Regional and Urban Economics Vol. 2’’ ŽE. S. Mills, Ed.., North-Holland, Amsterdam Ž1987.. 15. D. E. Wildasin, Nash equilibria in models of fiscal competition, Journal of Public Economics, 35, 241᎐249 Ž1988.. 16. D. E. Wildasin, Interjurisdictional capital mobility: Fiscal externality and a corrective subsidy, Journal of Urban Economics, 25, 193᎐212 Ž1989.. 17. J. D. Wilson, A theory of interregional tax competition, Journal of Urban Economics, 19, 296᎐315 Ž1986.. 18. J. D. Wilson, Mobile labor, multiple tax instruments, and tax competition, Journal of Urban Economics, 38, 333᎐356 Ž1995.. 19. M. Wrede, Tax competition and federalism: The underprovision of public goods, Finanzar¨ hi¨ , 54, 494᎐515 Ž1997.. 20. G. R. Zodrow and P. Mieszkowski, Pigou, Tiebout, property taxation, and the underprovision of local public goods, Journal of Urban Economics, 19, 356᎐370 Ž1986..
A Tax Competition Analysis of Congestible Public Inputs Mutsumi Matsumoto* Faculty of Economics, Ritsumeikan Uni¨ ersity 1-1-1 Noji-higashi, Kusatsu 525-8577, Japan E-mail: [email protected] Received January 5, 1998; revised November 9, 1999 This paper investigates the provision of congestible local public inputs within a tax competition framework. Public input provision is financed by a business capital tax and by a profits tax on firms as a congestion tax. With this tax system, local tax and expenditure policies are inefficient because of potential capital outflows. The tax mix is inefficient in that the profits tax rate is too high relative to the capital tax rate. The level of public input provision is inefficiently low. Focusing on expenditure inefficiency, this analysis of public inputs is compared with Wilson’s analysis Ž Journal of Urban Economics, 1995, 38, 333᎐356. of congestible public goods. 䊚 2000 Academic Press
Key Words: congestion; public inputs; tax competition.
1. INTRODUCTION In the study of tax competition, substantial attention has been devoted to inefficient local public policies in the presence of distortionary taxes on business capital. Many papers have shown that when capital taxation is imposed to provide local public services, local governments hold down tax rates to avoid capital outflows and set inefficiently low levels of public services. Related studies include Braid w2x, Bucovetsky and Wilson w3x, Hoyt w5x, Keen and Marchand w6x, Wildasin w15, 16x, Wilson w17x, Wrede w19x, and Zodrow and Mieszkowski w20x. While this argument focuses mainly on public goods benefiting residents, underprovision is also the expected consequence of tax competition in the case of public inputs into the production process. The possibility of overprovision of public inputs cannot be completely excluded because they benefit local business and *I am indebted to James Feehan, Nobuo Akai, Ming Chung Chang, Takao Ohkawa, Robert Parry, and Matthias Wrede for helpful comments on earlier drafts of this paper. The comments and suggestions from the editor and referees of this journal were helpful in revising my imperfect arguments. I am solely responsible for all remaining errors. 242 0094-1190r00 $35.00 Copyright 䊚 2000 by Academic Press All rights of reproduction in any form reserved.
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increase the productivity of mobile capital Žsee Bayindir-Upmann w1x, Noiset w9x, and Noiset and Oakland w10x.. However, this possibility is a largely irrelevant exception. Matsumoto w7x shows that capital-tax financing leads to underprovision of public inputs under fairly general specifications of production technology.1 This paper extends the tax competition studies of local public inputs by introducing the congestion costs involved in the use of these inputs. Previous studies of tax competition have often overlooked problems relating to congestion externalities. An exception is Wilson w18x, but his analysis is limited to congestible public goods. In general, the use of local public services, including public inputs, will entail congestion costs. It is wellknown that the tax measures needed for the efficient provision of congestible public services are a congestion tax and a land tax. For public inputs, Richter w11x shows that a profits tax on user-firms serves as a first-best congestion tax when the number of firms is endogenous to jurisdictions. This tax rate should be set equal to the marginal cost of congestion in the use of public inputs. If the congestibility of public inputs is incomplete, the profits tax is insufficient to raise funds for public expenditure, so that a non-distortionary land tax is used. This argument is analogous to the Žgeneralized. Henry George theorem regarding the provision of congestible public goods under population mobility.2 Following the tax competition literature, this paper investigates how capital tax distortion influences the provision of congestible public inputs. For this study, the Richter w11x model is extended to a tax competition framework, where a profits tax and a capital tax are imposed to finance public input provision. In addition to expenditure inefficiency, this paper identifies an inefficient tax mix caused by capital tax distortion. It is demonstrated that the capital tax rate is inefficiently low in equilibrium, distorting local tax and expenditure policies. The equilibrium tax mix is inefficient in that there is too much reliance on the profits tax. The equilibrium level of public input provision is inefficiently low. As the tax competition literature points out, the fear of capital outflows is responsible for these outcomes. Local governments, competing for mobile capital, 1 In Matsumoto w7x, underprovision of public inputs occurs because of capital-tax financing if production technology is characterized by constant returns to scale in private factors or all factors, including public inputs. These two possibilities of the returns to scale have been frequently examined in previous studies of public input provision. Feehan w4x reviews alternative specifications of public inputs, which are based on the degree of homogeneity of the production functions. 2 The efficient provision of congestible public goods is supported by a land tax and a head tax on mobile residents as a congestion tax. See Mieszkowski and Zodrow w8x and Wildasin w13, 14x for comprehensive surveys of related studies.
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attempt to prevent capital outflows by lowering the capital tax rate relative to the profits tax rate. Also, they have an incentive to reduce their expenditure levels because capital-tax financing of public inputs discourages business investment. These inefficiencies can be mitigated by a coordinated increase in all jurisdictions’ capital taxes. As may be expected, this paper is closely related to Wilson’s w18x analysis of congestible public goods. Although tax competition does not give rise to underprovision in his model, the difference in results between his study and this paper is simply due to the specification of local tax bases. While Wilson w18x assumes that capital and land are uniformly taxed Žproperty taxation., this paper exempts immobile factors from taxation, as in traditional models of tax competition such as that of Zodrow and Mieszkowski w20x.3 Furthermore, Wilson w18x includes an analysis of a distortionary congestion tax, but the profits tax in this paper is first-best as a congestion tax. It is shown that, once these differences are taken into account, his analysis of public goods can be reconciled with this paper’s analysis of public inputs. This paper is organized as follows. The model is described in Sect. 2. Section 3 clarifies the second-best tax and expenditure rules under capital taxation. Section 4 examines the welfare impact of coordinated policy changes made by all jurisdictions, and identifies how tax competition affects local public policies. A comparison between public goods and public inputs is drawn in Sect. 5. Section 6 gives concluding remarks. 2. THE MODEL The basic structure of the model is based on Richter w11x. Consider a national economy with competitive identical jurisdictions. In the economy, a numeraire output is produced by competitive firms using immobile land, mobile capital, and a local public input. Let M be the number of local firms in a representative jurisdiction. As formalized later, M is endogenously determined by profit-maximizing behavior. Output per firm is F Ž QrM, KrM, b . where Q, K, and b are the jurisdiction’s land, capital, and public input, respectively. Marginal products are positive and diminishing. All factors are complements in the sense that the second-order cross derivatives of F Ž⭈. are positive. The local supply of land is constant. While the total capital stock is exogenous to the economy, the local supply of capital is variable due to mobility. Each jurisdiction has a single immobile 3 As in Wilson w18x, a uniform tax on capital and land is called ‘‘property taxation’’ when his analysis is compared with this paper. In the tax competition literature, property taxation is ordinarily defined as a tax on business capital.
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resident who owns local land.4 All residents in the economy are equally endowed with capital stock. They spend factor income on consumption, which is the sole source of utility Žthere is no public good in the model.. The output produced can be transformed into a certain amount of either the public input or a private good. In terms of output, the cost of public input provision is C Ž M, b .. With respect to this function, the following conditions are assumed: CM ) 0,
Cb ) 0,
and ⭸ Ž CrM . r⭸ M - 0.
Ž 1.
Throughout this paper, subscripts of a function indicate partial derivatives of that function Že.g., ⭸ Cr⭸ M s CM .. Given the amount of output used to produce b, a rise in M reduces the public input supply to each firm, representing congestion externalities. This treatment of congestion has been frequently used in the study of local public finance. 5 The last inequality in Ž1. means that the congestibility of b is incomplete because the per-firm cost of public input provision declines as M rises Žscale economies in the provision of b .. This assumption appears to be reasonable in the context of regional economics. The nature of production technology is crucial to the study of public inputs Žsee Footnote 1.. Following Richter w11x, this paper assumes that F Ž⭈. exhibits constant returns to scale in all factors, including b. With this specification of technology, the benefit of public input provision accrues not only to private factors as increased productivity, but also to firms because there is a rent on the provision. Unlike Matsumoto w7x, this paper does not include the case of constant returns to scale in private factors. My analysis in this paper is founded on the idea that if public inputs are congestible, the number of user-firms will be a non-trivial variable. As Feehan w4x points out, the literature on public input provision often argues that the case of constant returns to scale in private factors is more reasonable in the presence of public inputs. With this degree of linear homogeneity, however, congestion externalities cannot be modeled satisfactorily because the optimal number of firms is always unity in each jurisdiction regardless of any other tax distortions. 4
Mobile residents who supply labor in the jurisdiction of their residence can be introduced into the model without affecting any results in this paper. In this case, it must be assumed, as in Wilson w18x, that each resident has an equal share of land in each and every jurisdiction. 5 Alternatively, congestion externalities can be directly incorporated into the production function. Suppose that output per firm is F Ž QrM, KrM, brM ␥ . where 0 - ␥ - 1. The degree of congestion is measured by ␥ . The cost of public input provision is C s b. All results in this paper are obtained from this setting, but the analysis becomes considerably more complex.
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For convenience, my analysis is carried out in terms of the aggregate level of production. Since the production function was characterized by constant returns to scale in all factors, the total output in a single jurisdiction equals MF Ž QrM, KrM, b . s F Ž Q, K , Mb . .
Ž 2.
From Eq. Ž2., the total output increases with a rise in M. This raises a problem of unbounded production possibilities even if b is congestible.6 To determine M endogenously at a finite level, it is assumed, as in Richter w11, Sect. 5x, that the formation of a new firm entails a fixed setup cost. This assumption ensures that first-best optimum and competitive equilibrium are well-defined. This paper is concerned with a long-run analysis with free entry.7 Local public expenditure is financed by a profits tax on firms and by a capital tax. Taking market prices, the tax rates, M, and b as given, firms choose the amount of private factors to maximize profits. Given the presence of the rent on public input provision equal to b⭸ F Ž Q, K, Mb.r⭸ Mb per firm, market entry continues up to the point where the rent equals the sum of the profits tax and the fixed cost of creating a new firm. The public budget constraint and the conditions for profit maximization are
M q tK s C Ž M, b . ,
Ž 3.
FK Ž Q, K , Mb . s r q t ,
Ž 4.
bFB Ž Q, K , Mb . s S q ,
Ž 5.
and
where is the profits tax rate, t is the capital tax rate, r is the net return on capital, S is the fixed cost in terms of output, and FB s ⭸ Fr⭸ Mb. In what follows, subscript B of F Ž⭈. indicates partial differentiation with respect to Mb, in order to simplify notation. Because of capital mobility, competitive jurisdictions take r as given. Equation Ž3. represents the public budget constraint. Equation Ž4. is the condition for capital investment. Equation Ž5. shows that net profits dissipate as a result of free entry. 6
For example, if congestion is modeled as in Footnote 5, the total output still increases as M rises. 7 To bound production possibilities, one can assume that the national economy has a fixed number of mobile firms. Richter w11x deals mainly with this short-run case, rather than the long-run case with free entry, since he analyzes the locational efficiency of mobile firms. The difference between the short run and the long run is irrelevant to Matsumoto’s w7x study of pure public inputs. Still, it has an important implication in the current model with a congestible public input. ŽSee also Footnote 11..
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Unlike Richter w11x, where profits taxation is proportional to profits, this tax is defined as a poll tax on firms. The proportional tax and the poll tax are equivalent in the current model. With the former tax Ž M ., market entry implies that Ž1 y M . FB b s S in equilibrium. This equation can be reduced to Eq. Ž5. by defining s M SrŽ1 y M .. From Eqs. Ž4. and Ž5., consumption in each jurisdiction amounts to F Ž Q, K , Mb . y Ž r q t . K y Ž S q . M q rK *,
Ž 6.
where K * is the endowment of capital. The amount F y Ž r q t . K y Ž S q . M represents income from the ownership of local land. Local governments set policy variables to maximize Ž6. subject to Eqs. Ž3. ᎐ Ž5.. In the current model with competitive jurisdictions and a single output, utility maximization is equivalent to rent maximization. 3. SECOND-BEST RULES FOR LOCAL PUBLIC POLICIES As argued in Sect. 1, a profits tax and a land tax constitute an efficient tax system in models with congestible local public inputs when the number of local firms is variable. The profits tax covers the marginal cost of congestion in the use of bŽ s CM .. If public input provision exhibits scale economies, it must be financed by the land tax. With this first-best tax system, the provision level would be set such that the sum of the marginal product of b over firms equals the marginal cost of providing bŽ MFB s Cb ., which corresponds to the Samuelson rule for public good provision.8 This section investigates the second-best conditions for tax and expenditure policies under capital tax distortion. The analysis starts with the derivation of the first-order conditions for policy variables. Equations Ž4. and Ž5. determine K and M as functions of t, , and b. Inserting them into Ž3. and Ž6., the Lagrangean of the maximization problem is F Ž Q, K Ž t , , b . , M Ž t , , b . b . y Ž r q t . K Ž t , , b . y Ž S q . M Ž t , , b . q rK * q M Ž t , , b . q tK Ž t , , b . y C Ž M Ž t , , b . , b . ,
Ž 7.
See Richter w11x for detailed arguments regarding this first-best policy. Additionally, he shows that even if the Žproportional. profits tax rate is exogenously fixed at a level that does not equal the marginal cost of congestion, an efficient allocation is possible when: Ži. a poll tax on firms is available, Žii. profits tax revenue is earmarked for public input provision, and Žiii. budget deficits are financed by a land tax. To achieve efficiency, the sum of the poll tax and the proportional profits tax per firm must equal the marginal cost of congestion. However, since these taxes are equivalent Žsee Sect. 2., this argument eventually implies that each firm pays for the marginal cost of congestion in first-best optimum. 8
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where is the Lagrange multiplier on Ž3.. Using Eqs. Ž4. and Ž5., the first-order conditions are
Ž t . Ž 1 y . K s Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . ,
Ž 8.
Ž . Ž 1 y . M s Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ t . ,
Ž 9.
Ž b . MFB s Cb y Ž y CM . Ž ⭸ Mr⭸ b . y t Ž ⭸ Kr⭸ b . .
Ž 10 .
and
Equilibrium public policies in the model are determined by Eqs. Ž8. ᎐ Ž10.. Equations Ž8. and Ž9. show that, because of the impact of t and on the tax bases, the marginal welfare impact of tax revenue does not equal that of private income; that is, / 1.9 The first-order condition for b includes the impact of b on the tax bases as distortionary benefits or costs. The examination of the derivatives of K and M plays an important role in this paper. Differentiating Ž4. and Ž5. yields
⭸ Kr⭸ t s b 2 FB Br⍀ ;
Ž 11a .
⭸ Mr⭸ t s ybFK Br⍀ ;
Ž 11b .
⭸ Kr⭸ s ybFK Br⍀ ;
Ž 11c .
⭸ Mr⭸ s FK Kr⍀ ;
Ž 11d.
⭸ Kr⭸ b s bFB FK Br⍀ ;
Ž 11e .
⭸ Mr⭸ b s yFB FK Kr⍀ y Mrb;
Ž 11f .
where ⍀ ' Ž FK K FB B y FK2 B . b 2 . In what follows, it is assumed that ⍀ ) 0; that is, F Ž⭈. is strictly concave in K and Mb. Using Eqs. Ž8. ᎐ Ž11., the properties of equilibrium public policies are derived. The following proposition summarizes the results: PROPOSITION 1. Under the assumption that ⭸ Ž CrM .r⭸ M - 0, Ža. The capital tax rate is positi¨ e Ž t ) 0. and the profits tax rate exceeds the marginal cost of congestion in the use of bŽ ) CM . in equilibrium, and Žb. The sum of the marginal product of b o¨ er firms exceeds its marginal cost Ž MFB ) Cb . in equilibrium. 9
It can be shown that ) 1 if there are scale economies in public input provision and if the Laffer effect of taxes does not exist.
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Proof. Ža. The first-order conditions for tax policy, Eqs. Ž8. and Ž9., imply that
Ž 1 y . r s Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . rK s Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ . rM.
Ž 12 .
This equation can be rewritten as
Ž y CM . ⌬ , t M q t⌬ , t K s 0,
Ž 13 .
⌬ , t K ' ⭸ Kr⭸ y Ž ⭸ Kr⭸ t . Ž MrK . ;
Ž 14a .
⌬ , t M ' ⭸ Mr⭸ y Ž ⭸ Mr⭸ t . Ž MrK . .
Ž 14b .
where
As shown later, ⌬ indicates the impact of balanced-budget policy changes on the tax bases. From Eqs. Ž11a. ᎐ Ž11d., ⌬ , t K and ⌬ , t M are, respectively, equal to ⌬ , t K s yb Ž KFK B q MbFB B . r Ž ⍀ K . ) 0;
Ž 15a .
⌬ , t M s Ž KFK K q MbFK B . r Ž ⍀ K . - 0.
Ž 15b .
The signs of Ž15a. and Ž15b. are derived from complementarity among factors Ž Fi j ) 0. and the linear homogeneity of F Ž⭈., i.e., Ý j Fi j j s 0, where j s Q, K, and MbŽ B .. Note that CM s M⭸ Ž CrM .r⭸ M q CrM and y Ž CrM . s yt Ž KrM .. Substituting these into Ž13. and manipulating terms gives yM ⭸ Ž CrM . r⭸ M ⌬ , t M q t ⌬ , t K y Ž KrM . ⌬ , t M s 0. Ž 16 . By Ž15a., Ž15b., and Ž16., t is positive if ⭸ Ž CrM .r⭸ M - 0. This, together with Ž13., proves that ) CM . Žb. From Eqs. Ž11c. ᎐ Ž11f., the policy-induced changes in K and M satisfy the following relations:
⭸ Kr⭸ b s yFB Ž ⭸ Kr⭸ . ;
Ž 17a .
⭸ Mr⭸ b s yFB Ž ⭸ Mr⭸ . y Mrb.
Ž 17b .
Inserting Ž17a. and Ž17b. into Ž10. yields MFB s Cb q Ž y CM . Ž Mrb . q FB Ž y CM . Ž ⭸ Mr⭸ . q t Ž ⭸ Kr⭸ . .
Ž 18 .
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MUTSUMI MATSUMOTO
Equation Ž9. implies that the third term on the RHS equals Ž1 y . MFB . Thus, Eqs. Ž18. is reduced to a simple rule for public input provision: MFB s Cb q Ž y CM . Ž Mrb . , which, combined with Ža., proves that MFB ) Cb .
Ž 19 . Q.E.D.
Proposition 1 shows that public policies are affected by capital tax distortion. Consider first the tax structure. As in a first-best setting, the profits tax is not enough to finance public input provision under scale economies. As a result of using the capital tax, congestion pricing is too high Ž ) CM .. This is because, at any given level of public expenditure, local capital stock can be increased by lowering the capital tax rate relative to the profits tax rate. Local governments use the profits tax as a means of expanding the capital tax base. Formally, Eq. Ž13. gives the optimal condition for tax policy in which the second term represents the distortionary impact of the capital tax. The positive term, ⌬ , t K, is the impact of an increase in on K, with t decreasing to balance the public budget. ŽThe same argument applies to ⌬ , t M.. ⌬ , t K s ⭸ Kr⭸ q Ž ⭸ Kr⭸ t . Ž ⭸ tr⭸ . ,
Ž 20 .
where ⭸ tr⭸ s yMrK wsee Ž14a.x. The balanced-budget relations between policy variables are derived by differentiating Ž3. and using Ž8. ᎐ Ž10.: Md q Kdt y MFB db s 0.
Ž 21 .
I turn next to a consideration of public expenditure. Equation Ž19., which is based on the first-order conditions for and b, is the second-best rule for public input provision when a marginal increase in b is financed by the profits tax. With this financing of expenditure, the number of local firms declines while local capital stock does not change. Since ) CM under capital tax distortion, the decline in M reduces the fiscal surplus associated with the profits tax base, creating a distortionary cost of public input provision. Thus, MFB ) Cb in equilibrium. These arguments can be seen using Ž17a., Ž17b., and Ž21.. Since ⭸r⭸ b s FB from Eqs. Ž21., Ž17a. and Ž17b. imply that ⭸ Kr⭸ b q Ž ⭸ Kr⭸ .Ž ⭸r⭸ b . s 0 and ⌬ b , M ' ⭸ Mr⭸ b q Ž ⭸ Mr⭸ . Ž ⭸r⭸ b . s yMrb - 0.
Ž 22 .
Note that profits-tax financing of b does not affect the aggregate level of public input provision Ž Mb., so that the total output remains unchanged. Using Ž22., Ž19. is expressed as MFB s Cb y Ž y CM . ⌬ b , M.
Ž 23 .
CONGESTIBLE PUBLIC INPUTS
251
A similar argument can be established when the additional b is financed by the capital tax. In this case, the marginal benefit of public input provision exceeds its marginal cost because of policy-induced capital outflows. The capital-tax financing rule for b is MFB s Cb y Ž y CM . ⌬ b , t M y t⌬ b , t K ,
Ž 24 .
where ⌬ b, t K and ⌬ b, t M are, respectively, the impact of capital-tax financing of b on K and M we.g., ⌬ b, t K ' ⭸ Kr⭸ b q Ž ⭸ Kr⭸ t .Ž ⭸ tr⭸ b .x.10 Like Ž15., using Eqs. Ž11a., Ž11e., and Ž21., one has ⌬ b , t K s bFB Ž KFK B q MbFB B . r Ž ⍀ K . - 0.
Ž 25 .
Although the sign of ⌬ b, t M is ambiguous, equilibrium public policies must be such that the profits tax rate and the capital tax rate are set so as to equate the marginal excess burden of use of these financing measures. Part Žb. of Proposition 1 thus implies that the decrease in capital tax revenue in Eq. Ž24. is greater than the possible increase in the fiscal surplus arising from M. 4. FISCAL EXTERNALITY In the previous section, the properties of equilibrium public policies were analyzed by solving the optimization problem of a representative jurisdiction. This section investigates inefficient public policies from the viewpoint of the economy as a whole. As the tax competition literature argues Že.g., Wildasin w16x., the source of inefficiency in this paper is an interjurisdictional fiscal externality caused by capital mobility. Each local government regards policy-induced capital movements as distortionary benefits or costs due to tax competition. Given that the total capital stock is constant, however, the induced changes in local capital stock are not distortions from the viewpoint of the entire economy, because the tax revenues of other jurisdictions increase or decrease. Ignoring these external impacts gives rise to inefficient outcomes. In the current model, where congestion pricing is distorting under capital taxation, local public policies affect fiscal surplus by changing the number of local firms. But, if jurisdictions are perfectly competitive and if 10
The derivation of Eq. Ž24. is as follows. Using ⌬ b, t K and ⌬ b, t M, Eq. Ž10. can be rewritten as MFB s w Cb y Ž y CM . ⌬ b , t M y t⌬ b , t K x q w Ž y CM . Ž ⭸ Mr⭸ t . q t Ž ⭸ Kr⭸ t . x Ž ⭸ tr⭸ b . . Since ⭸ tr⭸ b s MFB rK from Ž21., Eq. Ž8. implies that the second bracketed term on the RHS equals Ž1 y . MFB . Substituting this yields Eq. Ž24..
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MUTSUMI MATSUMOTO
market entry is possible, any policy-induced change in the profits tax base in a single jurisdiction has no external impact. It merely alters the total number of firms in the economy, leaving the fiscal surplus of other jurisdictions unchanged. The entire economy, as well as local jurisdictions, faces an infinitely elastic supply of firms. Accordingly, in this paper, the sole source of externalities is policy-induced capital movements. The fiscal externality theory suggests that equilibrium public policies are inefficient relative to the available tax system. As demonstrated in Sect. 3, local governments have an incentive to transfer tax burdens from capital to profits in order to expand the capital tax base. This creates a negative externality on other jurisdictions, implying that the tax mix is inefficient in that there is too much reliance on the profits tax. With respect to public input provision, while profits-tax financing has no impact on business investment, capital-tax financing causes capital outflows and gives rise to benefits to other jurisdictions. As a result, underprovision of public inputs occurs because of undertaxation of capital.11 To verify these arguments, the rest of this section investigates the welfare impact of coordinated policy changes made by all jurisdictions from equilibrium. The intuition behind this approach is that any public policy creating positive externalities should be encouraged, and vice versa.12 Since jurisdictions were assumed to be identical, this paper deals with symmetric equilibrium. In such an equilibrium, capital stock is uniformly distributed across jurisdictions, so that K equals the endowment of capital, K *. Applying this to Ž6., consumption equals ⌽ ' F Ž Q, K *, Mb . y tK * y Ž S q . M.
Ž 26 .
Unlike the optimization problem in Sect. 3, any coordinated policy changes keep local capital stock unchanged at K *. Thus, the impact on ⌽ depends on the change in policy variables and M. The relations between these 11
If the economy has a fixed number of mobile firms, fiscal externality due to firm mobility is relevant. This short-run case is discussed here for later reference. All results in Sect. 3 remain unchanged Ž ) CM and MFB ) CB .. But, their implications differ from the case of free entry. Without market entry, the equilibrium tax mix is efficient relative to the available taxes. Although a single jurisdiction’s tax policy creates fiscal externalities by causing movements of firms and capital, these externalities are exactly offset. Inefficiency is thus limited to public input underprovision. In the short-run case, a rise in the public input supply creates a positive externality regardless of the method of financing Žthe profits tax or the capital tax.. 12 In the tax competition literature, welfare-improving policy changes are analyzed to identify how local public policies are distorted. See, for example, Bucovetsky and Wilson w3x, Keen and Marchand w6x, and Wilson w17, 18x.
CONGESTIBLE PUBLIC INPUTS
253
variables are given by the following system of equations:
M q tK * s C Ž M, b .
Ž 27 .
bFB Ž Q, K *, Mb . s S q .
Ž 28 .
and
The net return on capital is also altered according to FK Ž Q, K *, Mb. s r q t, but this equation is irrelevant to the analysis because ⌽ does not depend on r. Using Ž26. ᎐ Ž28., the direction of welfare-improving policy changes is considered. PROPOSITION 2. Starting from a symmetric equilibrium, Ža. A marginal decrease in all jurisdictions’ is welfare-impro¨ ing if t is adjusted to maintain the public budget constraint, and Žb. A marginal increase in all jurisdictions’ b is welfare-impro¨ ing under capital-tax financing, but profit-tax financing has no welfare impact. Proof. Ža. From Ž26. and Ž28., a coordinated change in the tax mix alters ⌽ by
␦ ⌽r␦ < b , constant s yK * Ž ␦ tr␦ . y M,
Ž 29 .
where ␦ is the symbol of differentiation in the case of coordinated policy changes made by all jurisdictions. Differentiating Eq. Ž27. and inserting the result into Ž29. yields
␦ ⌽r␦ < b , constant s Ž y CM . Ž ␦ Mr␦ . .
Ž 30 .
Equation Ž28. shows that ␦ Mr␦ - 0 at a given b. Since ) CM in equilibrium, the policy change stated in Ža. is welfare-improving. Žb. Suppose that all jurisdictions uniformly increase b by capital-tax financing. From Ž26. and Ž28., the resultant change in ⌽ equals
␦ ⌽r␦ b < , constant s MFB y K * Ž ␦ tr␦ b . .
Ž 31 .
The term, ␦ tr␦ b, can be derived by differentiating Eqs. Ž27. and Ž28. with respect to M, t, and b:
y CM ; 2
b FB B ;
K *; ␦ M Cb s ␦ b. ␦t y Ž FB q MbFB B . 0;
Ž 32 .
Solving Ž32. and substituting y CM s Ž brM .Ž MFB y Cb . from Eq. Ž19. yields
␦ tr␦ b s MFBrK * q FB Ž MFB y Cb . r Ž MbK*FB B . .
Ž 33 .
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MUTSUMI MATSUMOTO
Inserting Ž33. into Ž31. shows that the welfare impact of capital-tax financing is
␦ ⌽r␦ b < , constant s yFB Ž MFB y Cb . r Ž MbFB B . .
Ž 34 .
Since MFB ) Cb in equilibrium, Ž34. is positive. Profit-tax financing can be examined in a similar manner. The change in ⌽ is
␦ ⌽r␦ b < t , constant s MFB y M Ž ␦r␦ b . .
Ž 35 .
Differentiating Eqs. Ž27. and Ž28. with respect to M, , and b gives
y CM ; 2
b FB B ;
M;
Cb ␦M s ␦ b. ␦ y Ž FB q MbFB B . y1;
Ž 36 .
This equation, together with Eq. Ž19., yields ␦r␦ b s FB . Thus, ␦ ⌽r␦ b < t, constant s 0. Q.E.D. One can confirm from Eqs. Ž27. and Ž28. that ␦ tr␦ - 0 and ␦ tr␦ b ) 0 when a rise in in all jurisdictions increases fiscal surplus at a given t and b. Under this reasonable condition, Proposition 2 makes it clear that undertaxation of capital is responsible for inefficient tax and expenditure policies. A welfare improvement can be achieved by increasing all jurisdictions’ capital taxes and using the revenue to reduce their profits taxes and raise their expenditures. In particular, Part Žb. of Proposition 2 shows that no coordinated decrease in public expenditure can ever improve welfare. The equilibrium level of public input provision is thus too low. Note also that although profits-tax financing of expenditure has no welfare impact under market entry,13 there is a close relation between this tax and expenditure inefficiency. In Eq. Ž34., the welfare impact of capital-tax financing is positive if and only if ) CM . This reflects the fact that the marginal excess burdens of both financing measures are equalized Žsee Sect. 3.. From the viewpoint of the entire economy, overpricing of congestion costs is closely related to fiscal externalities due to capital mobility. 5. COMPARISON BETWEEN PUBLIC GOODS AND PUBLIC INPUTS This section compares my study of congestible public inputs and Wilson’s w18x study of congestible public goods. These studies outwardly yield different conclusions regarding expenditure inefficiency. Still, they can be reconciled under an appropriate comparison. 13 If, as in the short-run case stated in Footnote 11, the total number of firms is exogenous, a coordinated rise in the public input supply financed by the profits-tax is welfare-improving, as it is with capital-tax financing.
CONGESTIBLE PUBLIC INPUTS
255
In the Wilson w18x model with three factors of production Žmobile labor, mobile capital, and immobile land., a property tax is imposed on capital and land when public good provision exhibits scale economies, which are defined as declining per capita cost of the provision. Two cases are examined according to the specification of congestion taxation: a head tax and a labor tax. While each resident supplies a fixed amount of labor in the case of head taxation, the case of labor taxation allows for endogenous labor᎐leisure choice. In both cases, there is no tendency toward public good underprovision. Yet this section argues that if labor᎐leisure distortions are incorporated into Wilson’s w18x case of head taxation, a similarity between his analysis and this paper is obtained in terms of expenditure inefficiency. To make the similarity complete, the use of capital taxation instead of property taxation must be assumed under scale economies. This replacement of taxation is necessary to derive underprovision. On the other hand, this paper does not parallel Wilson’s w18x case of labor taxation, because there may not be underprovision in the presence of this distortionary congestion tax, regardless of whether property taxation or capital taxation is used under scale economies. In what follows, these discussions are summarized. ŽThe derivations are available from the author upon request.. It is useful, for my comparison, to describe the impact of a single jurisdiction’s head-tax financing of public goods. With mobile residents, an important characteristic of this financing is that it does not affect the local supply of labor and capital. It turns out that if each resident’s labor supply is endogenous, local population Žthe head tax base. alters to offset labor᎐leisure distortions. ŽA jurisdiction’s labor supply equals its population times the labor supplied per capita.. As long as the head tax rate does not equal the marginal cost of congestion, the change in local population affects the fiscal surplus associated with the head tax base, creating a distortionary cost of public good provision. In contrast, the fact that the local supply of labor and capital remains unchanged implies that head-tax financing has no impact on mobile tax bases without labor᎐leisure distortions. For this reason, public good provision follows the first-best rule in Wilson’s w18x case of head taxation, even if congestion pricing is distorting in the presence of scale economies Žsee his Proposition 1..14 This argument is related to Richter and Wellisch w12, Proposition 4.1x. In their model with a land tax and a head tax, the provision of congestible public goods under labor mobility follows the first-best rule, even if the land tax is fixed at a suboptimal level. Their result is due to the absence of a labor᎐leisure choice. Note also that, in Wilson w18x, a single jurisdiction’s labor-tax financing of public goods has no impact on the local supply of labor and capital, as in the case of head taxation. The neutrality to the labor tax base implies that the provision rule for public goods does not depend on congestion pricing Žsee Proposition 2 in Wilson w18x.. 14
256
MUTSUMI MATSUMOTO
The impact of head-tax financing under labor᎐leisure distortions resembles that of profits-tax financing in this paper. The profits-tax financing rule for public inputs, Eq. Ž23., shows that the policy-induced decline in the number of local firms represents a distortionary cost of public expenditure. Similarly, head-tax financing of public goods reduces local population if leisure is a normal good and if the utility function is separable between private commodities and public goods. Under these assumptions, a coordinated increase in the public good supply improves welfare if and only if the head tax rate exceeds the marginal cost of congestion Žoverpricing of congestion costs., in which case the marginal benefit of expenditure exceeds its marginal cost because of the policy-induced population outflows. This necessary and sufficient condition for underprovision is satisfied when a capital tax is used under scale economies. As in this paper’s analysis of public inputs, the resultant inefficiency can be explained in terms of fiscal externalities due to capital mobility. A single jurisdiction’s capital-tax financing of public goods reduces its capital stock and generates a positive externality on other jurisdictions.15 On the other hand, underprovision may not occur when, as in Wilson w18x, the capital tax is replaced with a property tax on capital and land, because the impact of this tax on local capital stock is obscure. The same qualification applies to this paper. The impact of the tax mix and public inputs on business investment is obscure under property taxation, so that my results regarding the sign of externalities may be reversed. However, given that most of the studies in the tax competition literature have examined capital taxation, this argument is not surprising. In Matsumoto w7x, underprovision of pure public inputs depends on the assumption of capital taxation. ŽThis should not be confused with potential overprovision in Bayindir-Upmann w1x, Noiset w9x, and Noiset and Oakland w10x referred to in Sect. 1, since they assume the use of capital taxation.. Under labor mobility, a similar argument carries over to pure public goods if the sole source of local tax revenue is either a capital tax or a property tax. While capital-tax financing of public expenditure causes capital outflows and
15 Strictly speaking, the case of head taxation under labor᎐leisure distortions yields a result similar to the short-run case argued in Footnote 11. With the total number of residents being constant, labor mobility is also a source of fiscal externalities. As a result, the equilibrium tax mix is efficient while public good provision is inefficient. Local tax policy creates externalities through mobility of residents and capital, but these externalities are offset in equilibrium. This result regarding the mix of taxes holds regardless of whether capital taxation or property taxation is used. ŽA similar result applies to the short-run case in this paper..
CONGESTIBLE PUBLIC INPUTS
257
leads to underprovision, property-tax financing may increase local capital stock. ŽThe sign of fiscal externalities is obscure..16 Lastly, Wilson’s w18x case of labor taxation is discussed. In this case, inefficient public policies are due to policy-induced labor᎐leisure distortions. Unlike the case of head taxation with a labor᎐leisure choice, however, these distortions are not related to fiscal externalities due to capital mobility, even if business investment is subject to taxation. As a result, the case of labor taxation differs in its implications from those in this paper. A close look at the welfare impact of coordinated policy changes makes this clear Žsee Propositions 3 and 4 in Wilson w18x.. Although welfare is improved under plausible conditions if all jurisdictions’ public goods are increased by property-tax financing, labor-tax financing may not be welfare-improving because labor-leisure distortions increase.17 Due to the ambiguity of the welfare impact of labor-tax financing, the direction of welfare-improving changes in expenditure cannot be easily identified. Interestingly, these results hold even if capital taxation is used instead of property taxation. Despite the negative impact of capital-tax financing of public goods on business investment, this tax does not necessarily lead to underprovision in the case of labor taxation. 6. CONCLUDING REMARKS In the tax competition literature, a large number of studies have been made on the impact of competition for mobile capital on local public expenditure. While that literature has mostly clarified public good provision, several papers have recently been devoted to the study of public input provision. This paper has extended the study of public input provision by introducing the congestion costs involved in the use of public inputs. Local public expenditure is financed with the revenue raised by a profits tax on firms and by a capital tax. In addition to the profits tax as a congestion tax, the capital tax is used when the congestibility of public inputs is incomplete because of scale economies. The dependence on the capital tax causes inefficient local tax and expenditure policies. As the standard tax competition argument shows, fiscal externalities due to capital mobility are 16
If residents cannot migrate, both property taxation and capital taxation cause public good underprovision Žsee Braid w2x.. Wilson w18, Appendixx shows that even if residents are mobile, underprovision results from property taxation in the absence of scale economies. In the Wilson model, property-tax financing of public goods may increase local capital stock, but a labor inflow occurs so that the property tax base per capita declines. 17 Wilson w18x shows that the direction of welfare-improving changes in public expenditure is clearly determined under labor-tax financing if public goods are either pure public or pure private. Without this assumption, however, the welfare impact of labor-tax financing of public goods is obscure. In contrast, regardless of the degree of scale economies in public good provision, property-tax financing improves welfare.
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MUTSUMI MATSUMOTO
ignored in decentralized decision making. With hopes of gaining an advantage over other jurisdictions in competition for mobile capital, local governments attempt to keep their capital tax rates low. Consequently, they rely too heavily on the profits tax and choose inefficiently low levels of public inputs. In comparing Wilson’s w18x analysis of congestible public goods and this paper, their different assumptions of local tax bases should be taken into account. In principle, this paper is the counterpart of his case of head taxation when labor᎐leisure distortions are incorporated. Once his property tax is replaced with a capital tax, the familiar underprovision result applies to congestible public goods if a head tax serves as a congestion tax. The intuition underlying expenditure inefficiency is similar to that in this paper Žwith the proviso stated in Footnote 15.. On the other hand, Wilson’s w18x case of labor taxation does not parallel my analysis of public inputs. Under this distortionary congestion tax and labor mobility, there may not be underprovision even if capital taxation is used, because inefficient public polices are no longer related to policy-induced capital movements.
REFERENCES 1. T. Bayindir-Upmann, Two games of interjurisdictional competition when local governments provide industrial public good, International Tax and Public Finance, 5, 471᎐487 Ž1998.. 2. R. M. Braid, Symmetric tax competition with multiple jurisdictions in each metropolitan area, American Economic Re¨ iew, 86, 1279᎐1290 Ž1996.. 3. S. Bucovetsky and J. D. Wilson, Tax competition with two tax instruments, Regional Science and Urban Economics, 21, 333᎐350 Ž1991.. 4. J. P. Feehan, Pareto-efficiency with three varieties of public input, Public Finance, 44, 237᎐248 Ž1989.. 5. W. H. Hoyt, Property taxation, Nash equilibrium, and market power, Journal of Urban Economics, 30, 123᎐131 Ž1991.. 6. M. Keen and M. Marchand, Fiscal competition and the pattern of public spending, Journal of Public Economics, 66, 33᎐53 Ž1997.. 7. M. Matsumoto, A note on tax competition and public input provision, Regional Science and Urban Economics, 28, 465᎐473 Ž1998.. 8. P. Mieszkowski and G. R. Zodrow, Taxation and the Tiebout Model: The differential effects of head taxes, taxes on land rents, and property taxes, Journal of Economic Literature, 27, 1098᎐1146 Ž1989.. 9. L. Noiset, Pigou, Tiebout, property taxation, and the underprovision of local public goods: A comment, Journal of Urban Economics, 38, 312᎐316 Ž1995.. 10. L. Noiset and W. Oakland, The taxation of mobile capital by central cities, Journal of Public Economics, 57, 296᎐316 Ž1995.. 11. W. F. Richter, The efficient allocation of local public factors in Tiebout’s tradition, Regional Science and Urban Economics, 24, 323᎐340 Ž1994..
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12. W. F. Richter and D. Wellisch, The provision of local public goods and factors in the presence of firm and household mobility, Journal of Public Economics, 60, 73᎐93 Ž1996.. 13. D. E. Wildasin, ‘‘Urban Public Finance,’’ Harwood Academic Publishers, New York Ž1986.. 14. D. E. Wildasin, Theoretical analysis of local public economics, in ‘‘Handbook of Regional and Urban Economics Vol. 2’’ ŽE. S. Mills, Ed.., North-Holland, Amsterdam Ž1987.. 15. D. E. Wildasin, Nash equilibria in models of fiscal competition, Journal of Public Economics, 35, 241᎐249 Ž1988.. 16. D. E. Wildasin, Interjurisdictional capital mobility: Fiscal externality and a corrective subsidy, Journal of Urban Economics, 25, 193᎐212 Ž1989.. 17. J. D. Wilson, A theory of interregional tax competition, Journal of Urban Economics, 19, 296᎐315 Ž1986.. 18. J. D. Wilson, Mobile labor, multiple tax instruments, and tax competition, Journal of Urban Economics, 38, 333᎐356 Ž1995.. 19. M. Wrede, Tax competition and federalism: The underprovision of public goods, Finanzar¨ hi¨ , 54, 494᎐515 Ž1997.. 20. G. R. Zodrow and P. Mieszkowski, Pigou, Tiebout, property taxation, and the underprovision of local public goods, Journal of Urban Economics, 19, 356᎐370 Ž1986..