- Email: [email protected]

Capital mobility, tax competition, and lobbying for redistributive capital taxation Oliver Lorz

)

UniÕersity of Kiel, Kiel, Germany

Abstract This paper analyses the effects of international capital mobility on redistributive capital taxation and on lobbying activities by interest groups. A model is set up where unequally distributed endowments lead to a conflict between households concerning their most preferred capital tax rate. In a symmetric equilibrium, lobbying activities of all interest groups decline with the introduction of international capital mobility, and the welfare of all households increases. q 1998 Elsevier Science B.V. All rights reserved. JEL classification: D 72; F 42; H 77 Keywords: Tax competition; Interest groups; Redistribution

1. Introduction This paper analyses capital tax competition in a model with endogenous policy formation and interest groups. In an open economy with internationally mobile capital, investors have the possibility to transfer their capital to the country with the most favourable investment conditions. This opportunity changes the environment for national tax policy: 1 capital that is taxed heavily in the country where it ) Corresponding author. Institut fur Weg 120, 24105 Kiel, Germany. ¨ Weltwirtschaft, Dusternbrooker ¨ Tel.: q49-431-8814-483, fax: q49-431-8814-500; e-mail: [email protected] 1 Competition between governments or other national institutions may also arise in other fields than capital taxation. For a general description of institutional competition caused by capital mobility, see, e.g., Siebert and Koop Ž1990..

0176-2680r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 7 6 - 2 6 8 0 Ž 9 8 . 0 0 0 0 7 - X

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O. Lorz r European Journal of Political Economy 14 (1998) 265–279

is invested may escape to other countries with a lower tax burden. Governments then have to compete for this internationally mobile capital as a tax base. An extensive theoretical literature on interjurisdictional tax competition has emerged in the last years. The majority of this literature deals with capital taxes raised entirely for allocative reasons. 2 In these models, governments have to rely on source-based capital taxes to finance public goods or public infrastructure. Tax competition between symmetric countries leads to declining capital taxes in such a setting. 3 Since governments are predominantly assumed to maximise the welfare of their respective representative citizen, tax competition is viewed as inefficient: governments could increase the welfare of the representative citizen in their countries, if they raised the capital tax rate cooperatively. 4 In contrast to the literature on tax competition with allocative capital taxes, this paper focuses on capital taxes raised to redistribute income. The better a household is endowed with capital, the more the household is hit by a rising capital tax rate. Different capital endowments therefore cause a conflict between households concerning the desired tax rate: households with a low capital endowment prefer a high capital tax rate compared to households with a higher capital endowment who prefer a lower capital tax rate or even a capital subsidy. The effects of capital taxes on the distribution of incomes give households an incentive to influence policy through lobbying of interest groups. Two normative issues arise concerning the influence of interest groups on political decision-making. First, lobbying might influence tax policy. Governments then might raise a capital tax or subsidy where they would have raised none without lobbying. This kind of lobbying influence is not necessarily desirable from a normative viewpoint as the political power of interest groups determines which group of households benefits and which group suffers from a redistribution of incomes. Second, resources are dissipated in the process of lobbying and are then lost for production or consumption ŽTullock, 1967, 1971.. This dissipation of rents in the political process might depress the welfare of all households. To the degree to which tax competition affects redistributive capital taxation and lobbying of interest groups, it has welfare consequences which have not been treated so far in the existing literature. This paper explicitly considers lobbying as a determinant of equilibrium tax policy. It derives the lobbying equilibrium for a closed and for an open economy. It is shown that lobbying of all interest groups declines with the introduction of

2 Examples are the works of Zodrow and Mieszkowski Ž1986., Wilson Ž1986., Bucovetsky and Wilson Ž1991., Wildasin Ž1989., Oates and Schwab Ž1988, 1991. and Razin and Sadka Ž1991a,b.. 3 As Bucovetsky and Wilson Ž1991. and Razin and Sadka Ž1991a. show, this result holds as long as residence-based capital taxes cannot be raised adequately in addition to source-based capital taxes. 4 In contrast to the assumption of purely welfare maximising governments, Edwards and Keen Ž1996. and Rauscher Ž1996. treat tax competition in a ‘Leviathan’ model of the government Žsee also Sinn, 1992.. They reach ambiguous conclusions concerning the welfare effects of tax competition.

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international capital mobility in a symmetric equilibrium. Because of this effect, the welfare of all households increases. Persson and Tabellini Ž1992. also set up a political economy model of tax competition with redistributive capital taxes. 5 As in this paper, a proportional capital tax is used to redistribute between capital-abundant and capital-poor households. In Persson and Tabellini Ž1992., the policy-makers receive income from capital and from distributed tax revenues as like any other household. The equilibrium capital tax rate maximises the income of the elected policy-maker. In this setting, tax competition between symmetric countries leads to a declining redistributive capital tax. Lobbying of interest groups is not considered by Persson and Tabellini Ž1992.. 6 Section 2 of this paper derives the effects of capital taxes on income distribution with unequally distributed capital endowments. Section 3 investigates the properties of the equilibrium capital tax rate for a given lobbying influence of interest groups. Section 4 then endogenises lobbying and derives the lobbying equilibrium for a closed and for an open economy.

2. Capital taxes and income distribution This section sets up a simple neoclassical model of the international capital market equilibrium. It shows how source-based capital taxes influence the allocation of internationally mobile capital and how they affect the capital price and the price of the immobile factor. The effects of capital taxes on the distribution of incomes are then derived for the case of unequally distributed capital endowments. According to the model, the world consists of N identical countries. A representative, price-taking firm has the possibility to produce in each of these countries the same internationally tradable composite commodity. Production factors are internationally perfectly mobile capital and internationally immobile labour. In each country i, the firm has to pay a capital tax with a constant rate t i for the amount of capital invested there. This tax rate represents an aggregate measure of the burden of source-based capital taxes. 7 A negative t i corresponds to a net capital subsidy in country i. The positive or negative tax revenue is 5

Redistribution aspects of tax competition with capital mobility are also treated in Gerber and Hewitt Ž1987. and Ghosh Ž1991., albeit in different settings. 6 In Persson and Tabellini Ž1992., households influence policy only through their vote decision. As voters anticipate the influence of tax competition on the equilibrium tax rate, they vote for a politician with a capital endowment differing from their own endowment. 7 Since this model does not differentiate between international capital movements on the firm level and on the household level, a source-based savings tax raised from the households would influence the capital market equilibrium in the same way as the investment tax considered here.

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distributed as an equal lump sum transfer between the households. 8 The firm produces with constant returns to scale. It chooses its capital input K i and its labour input Li to maximise its profit. With w i as the wage rate in country i, r as the world interest rate, and the price of the consumption good set to 1, the profit of the firm is defined as follows: N

p s Ý F Ž K i , Li . y t i K i y w i Li y w 1 q r x K i .

Ž 1.

is1

In each country, there exist n households. Each household supplies l units of labour inelastically. The households save to maximise utility from present and future consumption. Present consumption of a household k is given by the difference between its exogenous endowment n k and its savings sk . Future consumption equals the sum of factor income from capital and labour and each household’s share of the tax income. For simplicity, the utility of each household is assumed to be linear with respect to future consumption: 9 U Ž Õki y ski . q b ski w 1 q r x q w i l q

t iK i n

.

Ž 2.

In equilibrium, all households maximise their utility and the representative firm maximises its profit. Worldwide aggregate capital supply through savings equals capital demand of the representative firm. Moreover, in each country, aggregate labour supply equals labour demand. Thus, the following set of equations describes the equilibrium on the world capital market Ž i s 1 . . . N, k s 1 . . . n.: F1 Ž K i ,nl . y t i s 1 q r , i

i

F2 Ž K ,nl . s w ,

Ž 3. Ž 4.

X

U Ž Õ ki y ski .

b N

n

s1qr, N

Ý Ý ski s Ý K i . is1ks1

Ž 5. Ž 6.

is1

Starting from a symmetric equilibrium where all countries choose the same capital tax rate, a marginal increase of the domestic capital tax rate affects the 8

This assumption allows me to focus on the redistribution conflict arising from the different tax burden for the households and to separate it from conflicts that might arise from the distribution of tax revenues. 9 This quite restrictive utility function is employed for three reasons in this paper: first, it facilitates the comparative static analysis of the capital market equilibrium; second, it helps to focus on redistribution caused by lobbying activities as it neglects redistribution motives caused by a declining marginal utility of income; third, it is a precondition for the symmetry of the lobbying equilibrium in Section 4.

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domestic and foreign capital stock according to the following equations Žsee Appendix A.: 10 dK1 dt

1q

F11

d Ky1 dt

c

1 s

1

- 0,

Ž 7.

c s

1

N

NF11

with y1 - c - 0.

) 0,

Ž 8.

The term c denotes the marginal influence of a rising capital tax rate on the interest rate in a closed economy. A rising capital tax lowers aggregate savings in a closed economy, given the linear specification of the utility function. This is the reason for c ) y1. 11 The degree to which the capital stock reacts on a changing tax rate determines the incidence of the capital tax for the income of both factors, capital and labour. With international capital mobility, a changing capital tax rate affects the income of the mobile factor capital less than in a closed economy; the converse is true for the immobile factor. With a rising number of competing countries, the burden of the capital tax shifts more and more from mobile capital to immobile labour. 12 These results follow from Eq. Ž3., Eq. Ž4., and Eq. Ž7.: dr dt

1

c s N

dw 1 d t1

s

,

F21 F11

Ž 9. c 1q

N

.

Ž 10 .

Given this influence on factor incomes, the redistribution effects of a capital tax or subsidy can now be derived. According to its capital endowment in the first period, each household belongs to one of the household groups j s 1 . . . m, m F n. The better a household is endowed with n in the first period, the higher are its savings. 13 An increasing domestic capital tax rate affects the indirect utility Vq1 10

The adjuncts 1 and y1 denote the domestic country and a representative foreign country, respectively. 11 In general, a rising capital tax rate causes both an income and a substitution effect on domestic savings. The income effect of the capital tax vanishes for a linear utility of future consumption. 12 In the limit case where the number of countries approaches infinity, the model resembles that of a small open economy with a fixed interest rate. In this case the burden of the capital tax lies entirely on the wage rate ŽMcLure, 1969.. 13 A higher n will lead to higher savings, if future consumption is a normal good with respect to an increasing lifetime income. This condition is satisfied in this paper as the utility function is time-separable.

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270

Ž t 1, ty1 . of a household in group q according to the following equation: dVq1 dt

1

sb

½

s 1q y

K1 c

t1 q

n

N

nF11

c 1q

N

5

.

14

Ž 11 .

In a closed economy and in an open country where all countries choose the same capital tax rate, average domestic savings are equal to the capital stock invested per head. The first term in Eq. Ž11. then measures the redistribution effect of a capital tax. This term is positive for all households saving less than the average. These households prefer a positive tax rate, whereas households who save more than the average prefer a capital subsidy. With a rising number of countries, the redistribution effect of the capital tax declines and it converges to zero for N approaching infinity. In an open economy, not only the domestic tax rate affects the individual’s welfare, but also the tax rate abroad. The effect of an increasing tax rate in any foreign country is given by the following equation: dVq1 y1

dt

sb

½

s 1q y

K1 c

t1

c

q n

N

nF11 N

5

.

Ž 12 .

3. Tax competition and redistributive capital taxation In this section, the equilibrium tax rate is derived for a closed and for an open economy. This section thus shows how international capital mobility and tax competition affect redistributive capital taxation. A comparative static analysis demonstrates the influence of lobbying on redistributive capital taxation in a closed and in an open economy. This paper incorporates lobbying in the process of political decision-making in a simple and straightforward way. The political representatives are assumed to maximise the weighted sum of the indirect utilities of all households. 15 The welfare weight v j of a household of group j depends positively on the lobbying expenditures of its interest group. It is assumed that v j is given by the same differentiable, monotonically increasing function v j s v Ž f j . for all households. 14 Eq. Ž11. is obtained from differentiating Eq. Ž2. with respect to t 1 , inserting Eqs. Ž5., Ž7., Ž9. and Ž10. and using the property nlF21 sy KF11 of the linear–homogenous production function. 15 Coughlin et al. Ž1990a,b. provide a theoretical foundation of this approach. In their probabilistic voting model, parties choose a political platform which maximises the weighted welfare sum of all household groups. The weights in this implicit objective function depend on the degree of the parties’ uncertainty concerning the political preferences of the different household groups. Lobbying can be incorporated in their model as an attempt to reduce this uncertainty ŽMueller, 1989: 205..

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The objective function of the tax authority in country 1 thus can be represented as follows, with n j as the size of interest group j: m

Z 1 Ž t 1 ,ty1 . s Ý n j P v 1 Ž f j1 . P Vj 1 Ž t 1 ,ty1 . .

Ž 13 .

js1

The sequencing of the tax competition model with lobbying is the following. First, all interest groups in all countries simultaneously choose a f in w0,`.. This first step determines the welfare weights v j . Second, the tax authorities in all countries simultaneously choose a capital tax rate t. Third, the households and the representative firm determine the capital allocation as described in Section 2. The subgame perfect equilibrium of the model may be derived by backward induction. The solution of the third step of the game is given by the results of Section 2. This section characterises the pure strategy equilibrium of the second step of the game, the equilibrium tax rates for given welfare weights v j . Section 4 then derives the pure strategy equilibrium of the lobbying stage of the game. This paper only considers a symmetric equilibrium where the welfare weights of the respective interest groups and the tax rates are identical in all countries. It is assumed that such an interior, symmetric equilibrium of the tax competition subgame exists. The equilibrium tax rate has to satisfy the following first order condition, with x ' Žd Z 1 ŽP..rŽd t 1 .: 16 m

x s Ý n j vj js1

½

sj y

K c

t q

n

N

F11 n

c 1q

N

5

s 0.

Ž 14 .

The objective function Ž13. is assumed to be strictly concave in t 1 wherever condition Ž14. is satisfied so that condition Ž14. is also sufficient for an interior symmetric equilibrium. The equilibrium is also assumed to be stable. 17 Rearranging Eq. Ž14. leads to the following explicit expression for the capital tax rate in equilibrium: t s Ýv˜ j j

K n

c y s j F11 n

Nqc

,

with v˜ j '

n j vj

Ýn j v j

.

Ž 15 .

j

The relative welfare weights v˜ j of the household groups determine whether capital is taxed or subsidised in equilibrium. For example, suppose there are only two household groups. Capital will then be taxed, if the lobbying expenditures of the capital-poor households exceed the lobbying expenditures of the capital-abundant households. In this case, the households with low savings are represented more than proportionally to their size in the political objective function. A less 16

Wherever tax rates are identical in all countries, the country index is dropped. The assumption of stability is necessary to obtain plausible comparative static results in the following analysis. It also ensures that only one symmetric equilibrium exists. 17

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272

than proportional political representation of capital-poor households leads to a capital subsidy. Implicit derivation of Eq. Ž14. shows how the number of competing countries influences the capital tax rate: dt xN sy . Ž 16 . dN xt The term x t measures the effects on x of a marginal increase of the capital tax rate carried out in all countries symmetrically: x t s a q w N y 1 x b, with a '

d 2 Z 1 Ž t 1 ,ty1 .

wd t 1 x

2

- 0 and b '

d 2 Z 1 Ž t 1 ,ty1 . d t 1 d ty1

.

Ž 17 . Stability of the equilibrium implies a " w N y 1x b - 0 Žsee Dixit, 1986.. The term x t is therefore negative. The following equation gives the value of X N : 18 t 1 x N s Ýn j v j . Ž 18 . F11 n N j With a rising number of countries, a positive capital tax rate declines and a negative tax rate increases. Capital mobility thus limits redistribution between households differing with respect to their capital endowment. This result confirms the findings of Persson and Tabellini Ž1992. in a slightly different setting with more than two countries and a more general production function. 19 Eq. Ž15. not only shows how capital mobility and tax competition affect the degree of redistributive capital taxation, it also determines the influence of lobbying on the capital tax rate in equilibrium. Lobbying affects equilibrium tax policy in this model through its effects on the welfare weights v . Proceeding from symmetric tax rates, an increasing weight of household group q in one country has the following effects on equilibrium capital taxes Žsee Appendix B.: d t1 d v q1

a q w N y 2x b sy

d ty1 d v q1

a q w N y 1x b w a y b x b

s

a q w N y 1x b w a y b x

xv q ,

xv q .

Ž 19 . Ž 20 .

The stability condition a " w N y 1x b - 0 and the condition a - 0 together imply a q w N y 1x b - 0, a y b - 0 and a q w N y 2x b - 0. The domestic tax rate 18

This equation is obtained from differentiating Eq. Ž14. with respect to N and then inserting from Eq. Ž14.. 19 This result also parallels the findings of Hoyt Ž1991. and Bucovetsky and Wilson Ž1991. where capital taxes raised for allocative reasons decline with a rising number of countries.

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will rise with an increasing weight of household group q, if and only if x increases in v q . The sign of b determines the foreign reaction on a changing domestic tax rate. For a positive b, domestic and foreign tax rates are strategic complements. The influence of a marginally rising v q on x may be obtained from deriving Eq. Ž14. and inserting Eq. Ž15.:

c x v q s n qÝv˜ j w s q y s j x j

N

.

Ž 21 .

For an interpretation of this result, assume that initially all households in all countries are weighted equally in the respective political objective functions. The capital tax rate then takes the value of zero in all countries. 20 In this case, the domestic tax rate rises with an increasing weight of a household who saves less than the average. The rising political influence of a capital-poor interest group then leads to capital outflows through its effect on capital taxes.

4. Endogenous lobbying and tax competition International capital mobility not only affects the capital tax rate for a given lobbying influence, it also has consequences for the lobbying process itself. In this section, the equilibrium lobbying expenditures are derived. In a lobbying equilibrium that shows certain symmetry properties, lobbying expenditures decline with the introduction of capital mobility and with a rising number of countries. An interest group q can raise the political weight v q of its members by increasing its lobbying expenditures f q . These lobbying expenditures are measured in terms of future consumption. 21 They are financed with contributions raised from all members of the interest group equally. The first order conditions for an interior lobbying equilibrium in country 1 can be represented as follows, with V q1 as objective function of interest group q Ž q s 1 . . . m.: d V q1 d f q1

s

dVq1 d t 1 dt

1

d v q1

q w N y 1x

dVq1 d ty1 d v q1 y1

dt

d v q1

d f q1

b y nq

s 0.

Ž 22 .

The second order condition is assumed to be satisfied. The effects of an increasing political weight on the capital tax rate at home and abroad are given by 20 It can be shown that the second order condition and the stability conditions are satisfied and domestic and foreign tax rates are strategic complements in this case. 21 Together with the linear utility of future consumption, this assumption guarantees that lobbying expenditures do not influence the savings decision of the households. Therefore, lobbying expenditures do not have to be incorporated in Eq. Ž2..

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274

Eqs. Ž19. and Ž20. of the preceding section. The marginal welfare effects of domestic and foreign taxes are given by Eqs. Ž11. and Ž12.. Inserting these equations and using Eq. Ž14. gives the following condition: y

a q w N y 2x b w xv q x

2

a q w N y 1x b w a y b x n q 1 y

X

n q v Ž fq .

q

w N y 1 x b P xv q xv q rn q y trnF11 a q w N y 1x b w a y b x

s 0.

Ž 23 .

Using Eqs. Ž15. and Ž21., Eq. Ž23. can be rewritten as follows: 2

c 2 s q y Ýv˜ j s j y

j 2

N a q w N y 1x b 1 s

X

n q v Ž fq .

s q y Ýv˜ j s j

nq y

.

j

Krn y Ýv˜ j s j w N y 1 x bc 2 n q j

a q w N y 1 x b w a y b xw N q c x N

Ž 24 .

The influence of the number of countries on equilibrium lobbying activities can be derived by comparative statics from this condition. To reduce the complexity of this problem however, only the case is analysed where both the capital endowment and the lobbying activities are distributed symmetrically between all household groups in all countries. Symmetrical distribution of the capital endowments means that for each household group with a capital endowment above the average endowment, there exists another household group of the same size with a capital endowment below the average. The distance from the average endowment is the same for both interest groups. Because of the linear utility of future consumption, savings are distributed exactly in the same way between the households as exogenous capital endowments. Lobbying is assumed to have positive, declining marginal returns; these marginal returns are infinitely high starting from zero lobbying and decline continuously to approach zero for very high levels of lobbying— v X Ž f q . ) 0, v Y Ž f q . - 0, lim f q ™ 0 v X Ž f q . s ` and lim f q ™` v X Ž f q . s 0. Then a symmetric lobbying equilibrium exists for symmetrically distributed capital endowments. In this symmetric lobbying equilibrium, interest groups with the same distance from average savings exert the same lobbying pressure. This can be shown as follows: all symmetric lobbying vectors imply Ý j v˜ j s j s Krn. Then the first order condition Ž24. is given by the following equation, with D q as the distance between savings of interest group q and average savings: y

c 2 n q Dq

2

v X Ž fq .

N 2 a q w N y 1x b

s 1.

Ž 25 .

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275

With symmetrically distributed savings, there are always two interest groups with the same w n q D q x 2 . Thus, the lobbying vector which solves Eq. Ž25. for all q s 1 . . . m is symmetric. This lobbying vector also solves Eq. Ž24., the first order condition for a lobbying equilibrium. Such a symmetric lobbying equilibrium induces t s 0 in the tax competition subgame Žsee Eq. Ž15... Inserting for a q w N y 1x b Žsee Appendix C. gives the following simplified first order condition for the symmetric lobbying equilibrium:

y

n q Dq

2

F11 n v X Ž f q .

c2 N 2qc N

Ýv j n j

s 1.

Ž 26 .

j

The left hand side of Eq. Ž26. gives the marginal benefit of lobbying for interest group q. Denote this function with y. The influence of a rising number of countries on the marginal benefit of lobbying is given by the following equation:

E y Ž f 1 , f 2 , . . . fm , N . EN

s

n q Dq

2

F11 n v X Ž f q . c 2

Ýv j n j

2 Nqc N 2qc N

2

- 0.

j

Ž 27 . The marginal benefit of lobbying declines with a rising number of countries. If the lobbying equilibrium is stable in the sense that a declining marginal benefit of lobbying for all interest groups lowers the lobbying expenditures in the symmetric equilibrium, then lobbying expenditures will continuously decline with a rising number of countries. The following proposition summarises this result.

Proposition: Assume that all countries are symmetric and that capital endowments are distributed symmetrically between all households. Then there exists a symmetric lobbying equilibrium which induces a capital tax rate of zero irrespective of the number of countries. With a rising number of countries, the lobbying activities of all interest groups will decline, if the lobbying equilibrium is stable. Welfare of all households then increases.

With redistributive capital taxation and lobbying activities of interest groups, the welfare effects of tax competition differ from those derived for allocative capital taxes. As Section 2 has shown, for given welfare weights of the households, tax competition leads to a declining capital tax or subsidy rate. Some households lose from this declining redistribution activity of governments whereas others gain. An explicit social welfare function is therefore necessary to compare

276

O. Lorz r European Journal of Political Economy 14 (1998) 265–279

these individual welfare gains and losses. The political objective function Ž13. is not necessarily identical to this social welfare function, as it has been introduced to describe the objectives of the tax authorities and not to represent social welfare. Given the symmetry properties introduced in this section, the tax rate is not affected by international capital mobility. In this case, the welfare consequences of tax competition entirely come from its effects on lobbying activities. As these lobbying activities decline, the welfare of all households increases with the introduction of tax competition. Tax competition limits the ability of governments to redistribute between the household groups; it thus keeps the interest groups from investing resources in the prisoner’s dilemma game of lobbying. 22

5. Conclusions The consequences of capital mobility for lobbying have been derived under the special assumptions of a linear utility of future consumption, a symmetrically distributed capital endowment, and identical lobbying influence functions for all interest groups in this paper. Without these assumptions, the lobbying equilibrium is not symmetric and the equilibrium tax rate differs from zero. Capital taxes then decline with capital mobility and a rising number of countries. It is not clear ex ante how this effect influences lobbying in an asymmetric equilibrium. However, at least for a sufficiently large number of countries, the results of this paper can be generalised to the case of asymmetric lobbying. As Section 2 has shown, the redistribution effects of the capital tax converge to zero for a large number of countries. Both, the equilibrium rate of the capital tax and the lobbying expenditures of all interest groups, then also converge to zero in this case. In this paper the redistribution conflict between households results exclusively from an unequal distribution of capital endowments. Redistribution conflicts with respect to capital taxation may also arise from other reasons. For example, tax revenues may be used to finance public goods which are beneficial only for some household groups. It may also be possible that the immobile factor labour is distributed unequally between households; redistribution conflicts then result from the incidence of the capital tax for the income of labour. These forms of redistribution conflicts are not treated in this paper. Therefore, this paper should be interpreted as an example, showing how capital mobility can dissolve a specific type of redistribution conflict and not as a general treatment of redistribution

22 Lobbying is a prisoner’s dilemma game for all interest groups as they all would benefit from a co-operative reduction of their lobbying activities. See Becker Ž1983. for a general description of the welfare effects of lobbying for the interest groups.

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policies and lobbying with capital mobility. The welfare implications derived here should also be interpreted in the light of these qualifications.

Acknowledgements The paper draws on some results of my doctoral thesis ‘Standortwettbewerb bei internationaler Kapitalmobilitat—Eine modelltheoretische Untersuchung’. Finan¨ cial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. I am indebted to Horst Siebert for his encouragement and support and to Sven Arndt and other participants of the 6th Silvaplana Workshop on Political Economy and two anonymous referees for their helpful comments and suggestions.

Appendix A Eqs. Ž3., Ž5. and Ž6. are totally differentiated and written in matrix form Žd ty1 s 0.: 23 F11 0

0 F11

0

0 0 UY

0

y

0 0 0

b

0

0

0

y1

y w N y 1x

1

y1 y1

dK1 d Ky1

yn

sk1

dÝ k

UY y

yn

b

w N y 1x

dÝsy1 k k

0

d t1 0 s 0 . 0 0

dr

Ž A.1 . Using Cramer’s rule, the following equations can be derived: dK1 d t1

q F11

d t1

,

UY

d Ky1 d t1

d Ky1

1 s

sy

NF11 w U Y q b nF11 x

Ž A.2 . .

Ž A.3 .

These equations lead to Eqs. Ž7. and Ž8., with c ' yŽU Y .rŽU Y q b nF11 .. 23

In a symmetric equilibrium all countries choose the same tax rate. Therefore, all savings, the invested capital stock, and the term F11ŽP. are the same in all countries; the index i can be dropped in these terms. Because of the linear utility of future consumption, all households in all countries choose Y the same consumption level in the first period and therefore all have the same U .

O. Lorz r European Journal of Political Economy 14 (1998) 265–279

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Appendix B The following comparative static analysis of the tax competition equilibrium is based on Dixit Ž1986.. The first order condition for the equilibrium tax rate in country i can be represented as follows: x i Ž t i ,tyi , v 1i , . . . , v mi . s 0.

Ž A.4 .

i Total differentiation of this equation leads to the following expression Žd vyk s

0.: ad t i q w N y 1 x bd tyi s yxvi ki d v ki . i

Ž A.5 .

yi

With t defined as t q w N y 1x t , Eq. ŽA.5. can be transformed as follows:

w a y b x d t i q bd t s yxvi ki d v ki .

Ž A.6 .

Summing up Eq. ŽA.6. over all countries gives the following equation Žd vyi k s 0: dtsy

x vi ki d v ki a q w N y 1x b

.

Ž A.7 .

Inserting this equation into Eq. ŽA.6. and setting i s 1 leads to Eq. Ž19.. Inserting Eq. Ž19. into Eq. ŽA.5. then gives Eq. Ž20..

Appendix C Eq. Ž5. and Eq. Ž9. imply the following marginal tax effect on savings: d s 1j

d s 1j

bc

. Ž A.8 . UYN dt dt The following equation can be derived for Ý j v˜ j s j s Krn, with D z ' Žd z .rŽd t 1 . q w N y 1xŽd z .rŽd ty1 ., z s s 1j K 1 : 1

s

y1

sy

a q w N y 1 x b s Ýn j v j j

½

D s 1j y

DK1 c

Nqc q

n

N

NF11 n

5

.

Inserting Eqs. ŽA.2., ŽA.3. and ŽA.8. gives the following equation: Nqc a q w N y 1 x b s Ýn j v j . NF11 n j

Ž A.9 .

Ž A.10 .

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