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International capital competition and environmental standards.

1. Introduction

Over the last decade, increasingly strong advocacy for environmental preservation in the U.S. has led to the passage of environmental regulations and laws that have resulted in the relocation of many U.S. firms and plants to other less environmentally conscious countries. Similarly, the tougher environmental regulations recently adopted by the newly industrialized economies, for example, the Asian Four Little Dragons - Korea, Taiwan, Hong Kong, and Singapore - have also resulted in the relocation of theft polluting industries into neighboring mainland China and several Southeast Asian nations. Raising environmental standards apparently can have the effect of triggering outflows of capital and the loss of domestic jobs.

Another major factor affecting international capital movement is the tax-rate differential on capital. For example, Hong Kong has perhaps the lowest corporate tax rate in the world, and the city-state has attracted foreign capital inflows from all over the world. A ceteris paribus increase in the capital tax rate means a diminishing competitive edge for keeping capital at home and, subsequently, capital outflow. Capital outflows can result in a fall in capital-tax revenue for the home country. If the country relies on revenue from capital tax to finance public expenditures, the fall in capital-tax revenue would jeopardize the provision of public services and the implementation of worthy noneconomic activities.

Apparently, intricate links exist among environmental standards, capital tax rates, private income, and social welfare. Recently, there has been an upsurge of academic interest in the effects of environmental policies in conjunction with international trade and investment. For example, Krutilla (1991) and Copeland (1994) study the effects of tariffs and pollution taxes under perfect competition. Nevertheless, to the best of our knowledge, no studies have been undertaken to explore the relationship between environmental and tax competition for capital from an international perspective. Our analysis appears to tie in with the literature on interregional tax competition (Wilson 1986; Oates and Schwab 1988; Wildasin 1988; Wellisch 1995)(1) as well as the literature on international investment (Kemp 1966; Jones 1967, 1987; Batra 1986; Batra and Ramachandran 1980; Beladi and Marjit 1992; Neary 1993). This paper provides a synthesis of these areas by analyzing a host of tax and pollution issues in a world with mobile capital.

The organization of the paper is as follows. Section 2 presents a basic setup of the model with a Niskanen (1977) government in which government welfare depends on private utility and governmental objectives. Section 3 examines the welfare effects of environmental regulation and capital taxation. In sections 4 and 5, we reexamine the welfare issues by considering two cases: (i) a fixed level of governmental spending and (ii) provision of investment tax credits, respectively. In addition, we compare the optimal environmental regulations under various scenarios. Section 6 contains a summary and conclusions.

2. The Basic Model with a Niskanen Government

In this section, we set forth a simple model to depict an economy that produces two goods, x and y, by using labor, capital, or land. While capital is assumed to be mobile internationally, labor is mobile only intersectorally within the economy. It is also assumed that capital is specific to sector x and land is specific to sector y, and pollution is generated only in the production of good x. That is, sector x (y) is the polluting (nonpolluting) industry. The home country adopts an environmental policy by setting a standard for pollution emissions, which should not exceed a certain threshold level in terms of a physical quantity [Mathematical Expression Omitted]. Following Yohe (1979), Yu and Ingene (1982), and Oates and Schwab (1988), we consider pollution as an input, i.e., pollution is interpreted as the use of quality environment, in the production of good x. Thus, the production functions for the two industries are

x = x([l.sub.x], k, z),

y = y([l.sub.y], v),

where [l.sub.i], i = x, y, is the amount of labor employed in sector i, k (v) is the amount of capital (land) used specifically for the production of x (y), and z is the emission quantity. Note that the partial derivatives of x and y with respect to all the inputs are positive. In particular, [Delta]x/[Delta]z [greater than] 0, indicating that pollution, that is, use of quality environment, contributes to the production of x. As usual, both x([center dot]) and y([center dot]) are continuous and twice differentiable with diminishing returns to inputs. Note that labor is the only input that is perfectly mobile between sectors. Our model is similar to the Ricardian-Viner sector-specific factors model. It is reasonable to assume that the polluting sector will use the environment by emission z up to the allowable limit [Mathematical Expression Omitted]. So a change in the environmental standard amounts to a corresponding change in the use of quality environment by the x sector.

Let p be the relative price of good x and assume for tractability that p is given in the world market. Endogenizing p would not add insight to the subsequent analysis. We use the now-popular duality approach for this analysis. The national revenue from production is

G(p, z, k) = maximum {y + px : (y, x) [element of] F(l, v, k, z)},

where l = [l.sub.x] + [l.sub.y] denotes the labor endowment in the home country and F(.) is the technology set. Here the labor and land endowments are fixed, so both l and v can be suppressed in the above revenue function. When the home country exports (imports) capital, the domestic use of capital k is smaller (larger) than the domestic capital endowment [Mathematical Expression Omitted]. By applying the envelope theorem, we obtain [G.sub.k] = [Delta]G/[Delta]k, which is the before-tax rate of return to capital in the home country, and [G.sub.z] = [Delta]G/[Delta]z, which is the marginal gain in revenue as a result of an increase in the allowable emission level. Diminishing returns to inputs imply [G.sub.kk] = [Delta][G.sub.k]/[Delta]k [less than] 0 and [G.sub.zz] = [Delta][G.sub.z]/[Delta]z [less than] 0.

Let asterisks indicate the corresponding variables for the foreign country. It is assumed that foreign pollution is passive and foreign pollution is treated as given. Given internationally mobile capital, arbitrage in the capital market leads to, at equilibrium, equalization in the net-of-tax returns on capital between the two countries. Thus, the capital equilibrium condition is

[Mathematical Expression Omitted], (2.1)

where [Tau] ([[Tau].sup.*]) denotes the domestic (foreign) capital tax rate, [Mathematical Expression Omitted] is the foreign capital endowment, and [Mathematical Expression Omitted] is the before-tax return on capital in the foreign country. Note that the tax on capital does not introduce a domestic production distortion and [G.sub.k] is not fixed but is determined by the environmental standards and the capital employed in the home country. In the setting of international competition for capital, the capital returns of both countries are endogenously determined. For concreteness, we assume hereafter that the home country exports capital, [Mathematical Expression Omitted]. (The case that the home country imports capital, i.e., [Mathematical Expression Omitted], can be similarly analyzed.) We abstract from transboundary pollution; therefore, the foreign pollution level [z.sup.*] is exogenously fixed by foreign authority and [z.sup.*] thus can be suppressed for the sake of simplicity in the foreign revenue function.

Let us now turn to the demand side of this economy. The demand for both goods by the private sector for a given level of pollution is represented by the following expenditure function:

E(p, z, u) = minimum{[c.sub.y] + p[c.sub.x]: U([c.sub.y], [c.sub.x], z) [greater than or equal to] u},

with respect to the consumption of goods, [c.sub.i], i = x, y, where u is the utility of the private sector. Note that pollution, a public "bad," harms the consumer. The utility function is decreasing in z and, hence, E is increasing in z, that is, [Delta]E/[Delta]z = [E.sub.z] [greater than] 0. [E.sub.z] denotes the consumers' marginal willingness to pay for pollution reduction (for maintaining the same level of utility).

The domestic private sector owns initial capital endowment [Mathematical Expression Omitted]. The budget constraint of the private sector stipulates that expenditure equals total revenue derived from (i) domestic production net of tax payments and (ii) net income from capital invested abroad, that is,

[Mathematical Expression Omitted], (2.2)

where [Mathematical Expression Omitted], given that the economy exports capital.

The economy consists of a public sector in addition to the private sector. The public sector in the home country is depicted by a governmental budget constraint. Assume in this analysis that the government imposes only a capital-income tax to finance its various public services and/or noneconomic programs, for example, foreign aid. The government budget constraint is simply

[Tau][G.sub.k](p, z, k)k = T, (2.3)

where T denotes governmental spending.

Government, like an individual consumer, is an organic unit that has its own utility. Niskanen (1977) postulates that government agencies have their own set of concerns in public consumption and noneconomic objectives that are, to varying degrees, independent of the interests of private citizens. The Niskanen government utility used by Oates and Schwab (1988) specifies that social welfare is dependent upon public-project spending T and private household utility u.(2) So, we may write

w = w(T, u). (2.4)

Changes in government utility are given by

dw = [w.sub.T]dT + [w.sub.u]du, (2.5)

where the two parameters [w.sub.T] and [w.sub.u] are both positive ([w.sub.T] + [w.sub.u] = 1) and represent, respectively, the relative weights of government spending and private utility in forming government welfare. For simplicity, it is assumed that government spending contributes nothing to private utility. In general, we expect [w.sub.T] [not equal to] [w.sub.u], and [w.sub.T] = [w.sub.u] can be simply treated as a special benchmark case.(3)

Essentially, the government has three targets: (i) regulating pollution, (ii) extracting revenue from domestic consumers, and (iii) affecting world capital rental rate. Nevertheless, the government has only two instruments: a tax on capital and a quota on pollution. The first-best policy, which is not available, would involve a lump-sum consumption tax to raise revenue, a pollution tax to internalize externality, and a capital tax to influence the capital rental. In the present model, lump-sum taxes are not available. So we focus on the second-best capital tax and pollution policies.

3. Welfare Effects of Capital Taxation and Environmental Regulation

In this section, we present an analysis of the welfare effects of the two policy instruments, that is, capital tax rate and environmental standards, which affect the two arguments in the government utility function, T and u. To solve for the impacts of [Tau] and z on T and u, and hence w in Equation 2.4, we need to use the capital-equilibrium condition in Equation 2.1 and the private, as well as the governmental, budget constraints in Equations 2.2 and 2.3. Totally differentiating Equation 2.1 with respect to k, z, and [Tau] yields

[Mathematical Expression Omitted], (3.1)

where [G.sub.kz] = [Delta][G.sub.k]/[Delta]z [greater than] 0. Loosening environmental controls by allowing increases in pollution emissions leads to a higher domestic rate of return on capital, resulting in a fall in the capital export, that is, [Delta]k/[Delta]z [greater than] 0. Meanwhile, an increase in domestic capital tax, d[Tau] [greater than] 0, leads to a higher capital cost and a corresponding decrease in the net returns to capital in the home country, thereby increasing the outflows of capital.

The impact of environmental policy on private utility can be seen by totally differentiating Equation 2.2:

[Mathematical Expression Omitted], (3.2)

where, without loss of generality, we may set [E.sub.u] = 1. An inspection of Equation 3.2 reveals the effects of changes in pollution standards and the capital tax rate on private utility as well as on the use of capital by the polluting industry. The direct effect of relaxing the emission control, dz [greater than] 0, on private utility consists of three components as follows. Allowing more emissions leads to an expansion of the polluting sector and thus an increase in revenue gain [G.sub.z]. More pollution, however, causes more harm to the private citizens, as shown by -[E.sub.z]. The use of more capital by the polluting sector entails a greater tax payment [Tau]k[G.sub.kz]. Furthermore, the tax-rate hike on capital, d[Tau] [greater than] 0, means an additional increase in tax payment by the private sector, as denoted by the last term, k[G.sub.k], in Equation 3.2.

The effects of environmental standards and the capital tax rate on tax revenue can be obtained by totally differentiating Equation 2.3:

[Tau]([G.sub.k] + k[G.sub.kk])dk - dT = -[Tau]k[G.sub.kz]dz - k[G.sub.k]d[Tau]. (3.3)

Loosening of environmental policy (dz [greater than] 0) leads to an expansion of the production of good x, resulting in more tax revenue ([Delta]T/[Delta]z [greater than] 0). Similarly, a rise in [Tau] increases T ([Delta]T/[Delta][Tau] [greater than] 0).

By using Equations 2.5-3.3, we can derive the effect of changes in the domestic capital tax rate on government welfare, that is,

[Mathematical Expression Omitted], (3.4)

where [Mathematical Expression Omitted].

Equation 3.4 reveals the various direct and indirect effects of a change in domestic capital tax rate. A rise in [Tau] triggers capital to flow from the home country to the foreign country. The outflow of capital generates two direct effects: (i) Less capital will be available in the home country, thereby resulting in a lower output and a smaller government revenue, as shown by the first term in the bracket in Equation 3.4; (ii) More capital will be available in the foreign country, thereby lowering the foreign rate of return on capital and possibly reducing capital income from investing abroad, as denoted by the second term in Equation 3.4. In addition, domestic capital outflows lead to a rise in the domestic rate of return on capital, thereby resulting in a lower or higher tax payment by the private sector and hence a tax loss or gain to home government. This indirect effect of capital outflows is captured by the last terms in Equation 3.4.

In view of the presence of both negative direct effects and one positive indirect effect, the impact on government welfare of a capital tax is ambiguous. Apparently, the net effect of a higher domestic capital tax rate depends upon the relative magnitudes between the contrasting effects. We can thus proceed to determine, for any given z, the optimal domestic capital tax [[Tau].sup.o] by setting Equation 3.4 to zero:

[Mathematical Expression Omitted]. (3.5)

Several interesting results are immediate. First, for the special case in which [w.sub.T] = [w.sub.u] and the foreign capital rate is constant [Mathematical Expression Omitted], the optimal domestic capital tax rate is zero ([[Tau].sup.o] = 0). We thus confirm a well-known result in the literature on regional capital-tax competition (see Wildasin 1988). Second, if [w.sub.T] = [w.sub.u] but [Mathematical Expression Omitted], then the optimal policy involves a subsidy on domestic capital, [[Tau].sup.o] [less than] 0, a result recently obtained by DePater and Myers (1994). Third, if [w.sub.u] [greater than] [w.sub.T] and [Mathematical Expression Omitted], then the DePater and Myers result is reinforced, [[Tau].sup.o] [less than] 0. A greater subsidy on domestic capital is warranted. A capital subsidy, by the budget constraint of Equation 2.3, implies that T [less than] 0. T can be interpreted as a head tax rather than government services. Finally, if [w.sub.T] [greater than] [w.sub.u], then a tax in lieu of a subsidy on domestic capital may be warranted, and the optimal rate can be determined from Equation 3.5.

The economic rationale for Equation 3.5 is simple. Given the two-agent formulation of the Niskanen welfare function, the government is forced to use a capital tax or subsidy as a lumpsum consumption tax is ruled out. The capital tax policy is an inefficient way of income redistribution. Thus, the government will also use environmental policy, which can affect the returns to capital, to minimize the distorting effects of the capital taxes.

Having analyzed the effects of a domestic capital tax-cum-subsidy on government welfare, we can now proceed to examine the impact of environmental policy on government welfare. By solving Equations 2.5-3.3, we obtain

[Mathematical Expression Omitted]. (3.6)

Equation 3.6 reveals the direct, as well as the indirect, effects of a change in emission standards on government welfare. The first term in Equation 3.5 shows the marginal social benefit [G.sub.z] relative to the marginal social cost [E.sub.z], and this comparison captures the direct impact of emission controls. There are nevertheless three additional indirect effects of environmental policy, all related to the mobility and use of capital in the home country. The indirect effects are denoted by the three-braced consecutive terms in Equation 3.6. A relaxation in pollution standard (dz [greater than] 0) leads to an expansion in the polluting sector and hence an increased employment of capital. As a result, the home country experiences (i) larger government revenue, (ii) higher returns from investment abroad, and (iii) higher foreign return (through a greater tax burden on the private sector), yielding a tax gain to the government. In short, the overall effects are a priori ambiguous; dw/dz in Equation 3.6 can take any sign.

What would be the jointly optimal environmental policy when the capital tax rate is at optimum (i.e., [Tau] = [[Tau].sup.o])?(4) Substituting Equation 3.5 into Equation 3.6 and setting dw/dz = 0, we obtain

[E.sub.z] = [G.sub.z] - [([w.sub.u] - [w.sub.T])/[w.sub.u]][G.sub.kz]k. (3.7)

The policy implications are readily clear. Under the optimal capital tax rate, the environmental standard should be set according to the traditional wisdom that the marginal social benefit [G.sub.z] equals the marginal social cost of emissions [E.sub.z] if [w.sub.u] = [w.sub.T]. This is the case where the objective function is equivalent to one that allows lump-sum transfer. Thus, capital tax can be used solely for influencing capital rental rate, and pollution policy is available mainly for dealing with pollution. The traditional result holds here. Furthermore, when [w.sub.u] [greater than] ([less than]) [w.sub.T], the capital tax (subsidy) is inefficient to transfer income from the consumer to the government, and the implicit pollution tax in the presence of international capital mobility will not simply internalize the externality. Thus, environmental policy is invoked to supplement the capital tax for improving efficiency in income transfer. Specifically, we have [E.sub.z] [less than] ([greater than]) [G.sub.z], implying that a more (less) stringent environmental standard is socially optimal. Thus, the following proposition is immediate.

PROPOSITION 1. Under the optimal capital tax rate, the ranking between the relative weights of government revenue and private utility determines the optimal environmental policy. When [w.sub.u] = [w.sub.T], the optimal environmental standard is determined by equating the marginal social benefit and marginal social cost of emission. When [w.sub.u] [greater than] ([less than]) [w.sub.T], the optimal environmental standard for a capital-exporting economy should be more (less) stringent relative to the optimal standard with [w.sub.u] = [w.sub.T].

4. An Economy with Fixed Governmental Spending

In this section, we consider a simple but realistic case where governmental agencies are constrained to a fixed level of spending on various public projects and noneconomic activities. Under such a fixed spending mandate, T in Equation 2.3 is predetermined. To maintain a balanced budget with a binding spending level,(5) the capital tax rate will be endogenously determined. It turns out that from Equation 3.2, the capital tax rate now has to be positive and, unlike the earlier analysis, subsidies on capital are incompatible with an optimal pollution policy. The implications of a fixed level of governmental spending are briefly analyzed in this section.

In view of the revenue constraint, the tax rate is constrained. Thus, the pollution policy plays a major role in influencing the capital rental rate and hence welfare. Analytically, by using Equations 2.5-3.3 and setting dT = 0, we obtain the welfare effect of changes in environmental policies in the presence of a fixed level of government spending as

[Mathematical Expression Omitted], (4.1)

where [Mathematical Expression Omitted] by the stability condition, shown in the Appendix. Since T is fixed, [w.sub.T] does not appear in Equation 4.1, and hence the impact of environmental policy on government welfare collapses and is identical to that on private utility.

With a tax on capital in place, a loosening of pollution controls unambiguously improves welfare when [G.sub.z] [greater than] [E.sub.z], whereas the policy change may lower welfare when [G.sub.z] [less than] [E.sub.z]. The optimal allowable pollution level is obtained by setting, in Equation 4.1, dw/dz = 0:

[Mathematical Expression Omitted]. (4.2)

Noting that the second term on the right-hand side of Equation 4.2 is positive, we have [E.sub.z] [greater than] [G.sub.z]. The policy implication, from Equation 4.2, is straightforward. For maintaining a mandatory fixed level of fiscal spending, an optimal environmental policy will require the government to select a less stringent pollution standard, coupled with a positive tax rate on capital. With a capital tax in place, the home country loses its competitive edge in the capital market and hence experiences an outflow of capital. To mitigate the capital outflow, the home country may choose to relax environmental standards imposed upon the polluting industries. This result bears testimony to the formulation of environmental policies in many countries.

5. An Economy with a Tax Credit System

The foregoing analysis on international capital competition and environmental standards was carried out under the assumption that foreign investors pay capital taxes to the home country, and the amount of taxes paid cannot be deducted from the tax liability in the source foreign country. Nevertheless, tax-credit systems have been implemented in the United States, OECD countries, and newly industrialized economies in which investment taxes paid to foreign countries can be deducted at home if the home tax rate exceeds the foreign tax rate. In this section, we briefly examine the environmental policies when international tax credits are available.(6)

When tax payments to foreign countries can be deducted under the tax-credit system, the capital arbitrage condition in Equation 2.1 is modified to

[Mathematical Expression Omitted]. (5.1)

Utilizing Equation 5.1, we can rewrite the private-sector budget constraint in Equation 2.2 as

[Mathematical Expression Omitted] (5.2)

and the government budget constraint in Equation 2.3 as

[Mathematical Expression Omitted], (5.3)

where the second term in Equation 5.3 denotes the tax revenue from foreign-source income under tax credit.

Note that if the domestic-capital tax rate falls short of the foreign-capital tax rate ([Tau] [less than] [[Tau].sup.*]), Equations 5.1-5.3 reduce to Equations 2.1-2.3, and the analysis and results in section 3 apply. So we need to consider only the case that [Tau] [greater than] [[Tau].sup.*]. The arbitrage condition in Equation 5.1 can then be simplified to

[Mathematical Expression Omitted]. (5.4)

Differentiating Equation 5.4 reveals a neat linkage from pollution emission z to domestic use of capital k:

[Mathematical Expression Omitted]. (5.5)

The reason for the link between k and z in Equation 5.5 is simple: The effective home-capital tax rate is [Tau] under the tax-credit scheme. Regardless of where the home capital locates in the world, the change in [Tau] has no bearing on the location of domestic capital. It follows that cannot affect capital rental rate so that pollution policy becomes the only instrument that can affect the capital rental.

Similarly, the changes of the variables and parameters in Equations 5.2 and 5.3 are as follows:

[Mathematical Expression Omitted], (5.6)

and

[Mathematical Expression Omitted]. (5.7)

Solving Equations 2.4 and 5.5-5.7 yields the effect of changes in the home capital tax rate on governmental welfare, and the effect is given by

[Mathematical Expression Omitted]. (5.8)

Given that the same effective capital tax rate ([Tau]) prevails regardless of where the home capital is located, a change in [Tau] can only cause redistribution of income between households and government. Consequently, the change in governmental welfare depends upon the relative weights of government spending and private utility, [w.sub.T] - [w.sub.u].

If [w.sub.T] [greater than] [w.sub.u], it is obvious that dw/d[Tau] in Equation 5.8 is positive. This implies that the optimal tax rate on capital is 100%, and thus the tax-credit system would not be feasible. Furthermore, recall that the tax on capital is nondistortionary in the present case. When a higher weight is assigned to government spending than to consumer, all the revenue goes to the government. This appears not to be sustainable either. Subsequently, the weights would adjust endogenously until [w.sub.[Tau]] = [w.sub.u]. On the other hand, if [w.sub.T] [less than] [w.sub.u], Equation 5.8 states that dw/d[Tau] [less than] 0 and, therefore, [Tau] falls to or below the rate [[Tau].sup.*]. This implies the tax credit system with [w.sub.T] [less than] [w.sub.u] would also not be sustainable. Hence, the only case in which the tax-credit system will work is [w.sub.T] = [w.sub.u]. And consequently, dw/d[Tau] = 0. That is, the optimal capital tax rate is nonunique; it is whatever rate that is currently in place, that is, [[Tau].sup.o] = [Tau], if [Tau] [greater than] [[Tau].sup.*].

It may be noted that for simplicity the foreign government is treated as passive. If the foreign government is allowed to make best responses in a game-theoretic context, the results would be affected.

We turn to the effect of environmental policies on government welfare under the tax-credit system with [Tau] [greater than] [[Tau].sup.*]. Solving Equations 2.4 and 5.5-5.7 and imposing [w.sub.T] = [w.sub.u], we obtain

[Mathematical Expression Omitted]. (5.9)

Since the second term in Equation 5.9 is positive, a loosening of environmental controls unambiguously improves welfare when [G.sub.z] [greater than] [E.sub.z], whereas the policy may lower welfare when [G.sub.z] [less than] [E.sub.z]. The optimal pollution level is obtained by setting dwldz = 0 in Equation 5.9:

[Mathematical Expression Omitted], (5.10)

where the right-hand side of Equation 5.10 is positive, implying [E.sub.z] [greater than] [G.sub.z]. When [Tau] [greater than] [[Tau].sup.*], the optimal pollution level is set such that marginal social willingness to pay for abating pollution is greater than marginal gain in government revenue. The reasoning underlying this result is as follows. As shown earlier, a positive tax rate on capital is warranted under the tax-credit system. To correct for the tax distortion, more lax environmental policy would be set to entice capital to stay and be used by the home polluting sector.

Finally, we compare the optimal environmental standard under the system of a fixed level of governmental spending to that when the system of international tax credits is employed. Let [Mathematical Expression Omitted] and [Mathematical Expression Omitted] denote the marginal social benefit under the fixed government-spending system and the tax-credit system. By subtracting Equation 5.10 from Equation 4.2, we have

[Mathematical Expression Omitted], (5.11)

which is negative. The following proposition is immediate,

PROPOSITION 2. For a capital-exporting economy, the optimal environmental standard would be less stringent under the system of a fixed level of government spending than that under the system of tax credits. Moreover, the optimal environmental standard in the tax-credit system is more lax than that of a Niskanen government with equal welfare weights of fiscal spending and private utility.

6. Concluding Remarks

This paper has examined the welfare effects of the policies of capital taxation and environmental standards with and without governmental spending constraint or international tax credits. This analysis delineates the intricate linkages between the two policy measures and both private income and governmental welfare. Several results were derived. Loosening environmental control leads to more capital tax revenue for the government. The optimal capital tax rate may be of any sign, depending upon the ranking of the weights of government objectives and private utility. The same criterion also applies in determining how stringent the optimal environmental standards should be set.

In addition, it was shown that when the government faces a fixed level of spending, a positive tax rate on capital is warranted. As a result, an optimal environmental policy consists of a less stringent standard in order to mitigate capital outflow. Furthermore, when international tax credits are available, an optimal pollution policy in the meaningful cases also consists of a relatively lax standard. However, the standard under tax credits is still more stringent than that of a fixed level of government spending.

An earlier version of this paper was presented at the Western Economic Association International meeting in San Diego, July 1995, and the City University of Hong Kong. The authors are indebted to Pasquale Sgro, seminar participants, and an anonymous referee for insightful comments. E.S.H.Y. was supported by a grant funded by the Center for Environmental Studies of the Chinese University of Hong Kong. The authors, however, are responsible for any remaining shortcomings.

Appendix

We assume the following adjustment process for capital movement between the two countries:

[Mathematical Expression Omitted],

where [Alpha] is a positive coefficient and [Mathematical Expression Omitted] is the international capital rental-rate differential. By Equation 3.3, [Tau] is a function of k and hence p is a function of k for a given z. Linearly approximating the adjustment equation yields

[Mathematical Expression Omitted],

where [k.sup.e] denotes the equilibrium k. The necessary and sufficient condition for stability requires d[Rho]/dk [less than] 0. From Equations 3.1 and 3.3, we can obtain

d[Rho]/dk = k/D,

where [Mathematical Expression Omitted]. Hence, for obtaining stability, we need D [less than] 0.

1 There are several key differences between interjurisdictional tax competition in the public finance literature and international tax competition in this study, as follows: (i) interregional capital flows within a national market would not affect the country's capital return since total capital stock in the country is fixed. That is a valid assumption usually made in the local tax-competition literature. However, international capital flows affect a country's capital availability, which in turn affects domestic as well as foreign capital returns; (ii) noneconomic objectives, such as foreign aid, are important activities considered by central government but not by local governments; and (iii) tax credits for foreign-source income are usually available these days from central government, and such tax credits are not available at the regional level.

2 An alternative, but more traditional, interpretation of the welfare function w(T, u) is that it is the utility function for a representative citizen where u is consumption of private goods and T is a publicly provided good. Chao and Yu (1993) examine the income effect of fiscal spending in a model where the private and government sectors have different utility functions.

3 If w is interpreted as the utility function, then with [w.sub.T] = [w.sub.u], T becomes a lump-sum head subsidy (tax).

4 From Equation 3.6, the individually optimal z for a given [Tau] is [Mathematical Expression Omitted].

5 See Michael, Hatzipanayotou, and Miller (1993) for a study of tariffs and consumption taxes under a fixed government budget.

6 See Bond (1991) for a perceptive study on the issue of international tax credits.

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Author:Yu, Eden S.H.
Publication:Southern Economic Journal
Date:Oct 1, 1997
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