Public Goods, Tax Policies, and Unemployment in LDCs.

Michael, Michael S.

Panos Hatzipanayotou [*]

Michael S. Michael [+]

We build a general equilibrium model of a small open economy characterized by unemployment and producing two privately traded goods and one nontraded public consumption good. The provision of public good is financed with an income tax or an excise tax on the manufactured good or an import tariff. Within this framework, the paper examines the effects of such policies on the country's unemployment ratio and welfare, and it derives the efficiency rules for public good provision for each policy instrument. It shows, among other things, that the private marginal cost of the public good always overstates its social marginal cost in the case of income taxes and may overstate it in the case of an excise tax on the manufactured good or a tariff even if the taxed good and the public good are substitutes in consumption.

1. Introduction

Traditionally, an analytically convenient and widely used assumption in the international trade and development economics literature has been that of lump-sum distribution of direct (e.g., income) or indirect (e.g., consumption, tariff) tax revenue when various policy implications of such instruments (e.g., terms of trade or welfare effects) were to be examined. This analytical shortcut, however, hardly ever constitutes a real-world practice either in rich developed or in poorer developing economies.

On the other hand, another extensive branch of economics, the public finance literature, has adopted a more realistic approach regarding the economic activity of a government. A government is viewed, among other things, as a provider of public (collective) consumption goods and/or of public inputs that enhance the productive capacity of the private sector. Being so, it can use revenues from nondistortionary (e.g., lump-sum) taxes or distortionary (e.g., consumption) taxes to finance the provision of such goods and services. Within this public finance context, a long-standing proposition states that when nondistortionary taxes are used to finance the provision of a public good, the first-best efficiency rule requires that the sum of the marginal rates of substitution (i.e., the social marginal benefit) equal the marginal rate of transformation (i.e., the social, marginal cost) (e.g., see Samuelson 1954). When distortionary taxes are used to finance the provision of the public good, Pigou (1947) argued that th e social marginal cost exceeds the private marginal cost because of the induced indirect cost from raising tax revenue through distortionary taxation. Stiglitz and Dasgupta (1971), Atkinson and Stern (1974), and Wildasin (1984), among others, demonstrate that in certain cases (e.g., when the taxed and the public goods are complements in consumption), Pigou's argument fails to hold and the social cost may fall short of the private marginal cost. [1]

Because of its more realistic appeal, this public finance approach to the use of tax revenue has been subsequently adopted by the relevant international trade and development economics literature. Recently, the efficiency rule for public good provision has been examined in the context of a small open economy by, among others, Feehan (1988) when tariff revenue finances the provision of the public good in an economy producing two traded goods and a nontraded public consumption good. Michael and Hatzipanayotou (1995) examine the same issue and derive the formulae for the optimal tax rates on traded or nontraded goods in an economy producing many traded and nontraded goods and where consumption tax revenue finances the provision of the public good. Michael and Hatzipanayotou (1997) demonstrate the failure of the first-best efficiency rule when lump-sum taxes are used to finance the provision of a public good in a small open economy in the presence of trade restrictions (i.e., a tariff or a VER).

Two features in the above reviewed studies of the international trade/development economics and public finance literature motivate the present paper. First, all these studies derive the efficiency rule for public good provision in the context of a small open or closed economy with full employment. Unemployment, however, to a lesser or to a larger extent remains a structural feature of many developed or developing economies. From an analytical standpoint, the existence of such a distortion may alter both the optimal tax formulae and the efficiency rule for public good provision. Second, the above reviewed literature considers the case where a government uses a single policy instrument (e.g., lump-sum taxes, income taxes, tariffs) to finance the provision of the public good. More than often, however, governments may have at their disposal several tax instruments that they can simultaneously use in order to raise revenue for financing the provision of public consumption goods.

Capitalizing on these two realizations, the present paper constructs a general equilibrium trade model of a small open developing economy characterized by Harris-Todaro (1970) (HT) type of unemployment and producing two privately traded (an exported and an imported) goods and a nontraded pure (i.e., noncongestible) public consumption good. We assume that in order to finance the provision of the public good, the government raises tax revenue through the imposition of separately an income tax, an excise tax on the manufactured good, or an import tariff. Within this context, we examine the effects of each policy regime on welfare, and we derive the efficiency rule for public good provision in each case. We show that in the presence of unemployment when income tax or lump-sum tax revenue is used to finance the provision of the public good, the private marginal cost always overstates its social marginal cost. When an excise tax on the manufactured good or a tariff is used, then the private marginal cost of public good provision may overstate its social marginal cost even if the taxed and public goods are substitutes.

2. The Model

In this section we develop a two sector (an urban and- a rural) general equilibrium trade model of a small developing economy with identical consumers characterized by HT unemployment. In the urban sector, two goods are produced: an import competing manufactured good (M) and a nontradable pure, public consumption good (g). An exported agricultural good (A) is produced in the rural sector, which is also chosen as the numeraire commodity. The exported good (A) is freely traded, while a tariff may be imposed on the imports of the manufactured good (M). All commodity markets are assumed competitive, and both goods are assumed normal in consumption. The government, in order to finance the provision of the public good, levies, independently or in combination, a tax on income from production of all goods at a rate ([rho]), an excise tax on the manufactured good at a rate ([tau]), and an import tariff at a rate (t). [2]

The Structure of Production

Labor is the intersectorally mobile factor, capital (K) is sector specific in the production of the manufactured good (M), and land (E) is sector specific in the production of the agricultural good (A). Production technologies of the two private goods exhibit constant returns to scale with positive and diminishing marginal products of factors and positive cross-partials. The production functions of the two private goods are given by

M = M([L.sup.M], K), and (1)

A = A([L.sup.A], E), (2)

where [L.sup.i], i = M, A denotes, respectively, the amounts of labor employed in the production of the two privately traded goods and K and E, respectively, are the fixed endowments of the sector-specific capital and land.

For simplicity, we assume that labor is the only factor in the production of the public good and that the labor input per unit of output is one. Thus,

g = [L.sup.g] (3)

is the amount of the public good produced and [L.sup.g] is the amount of labor used in its production. [3]

We define R(q, [lambda], K, E) to be the gross national product (GNP) function, representing the maximum attainable revenue from production of the private and public goods, given (i) the producer domestic relative price for (M) q(=[p.sup.*]) in the case of only income or excise tax and q(=[p.sup.*] + t) in the case of an import tariff, where [p.sup.*] is the constant world price for the manufactured; (ii) the urban unemployment ratio [lambda](=[L.sup.u]/([L.sup.M] + [L.sup.g])), where [L.sup.u] is the number of urban unemployed workers; and (iii) the endowments of the sector-specific capital (K) and land (E). [4] For the rest of the analysis, K and E are omitted from the GNP function since they do not affect the results of the paper. The variable [lambda](=[lambda]([rho], [tau], t); see the Appendix for derivations) enters as an argument into the GNP function to capture the loss to the economy due to unemployment, measured by the shadow wage of labor (e.g., see Beladi and Chao 1993). Since [lambda](=[L.sup.u]/([L.sup.M] + [L.sup.g])), the loss to the economy due to a one-unit increase in [lambda] is [R.sub.[lambda]] = -[w.sup.A]([L.sup.M] + [L.sup.g]), where [w.sup.A] is the rural wage. The partial derivative of the GNP function with respect to q (i.e., [R.sub.g](q, [lambda])) is the supply function of the manufactured good. Because [lambda] = [lambda]([rho], [tau], t) and p* is assumed constant, the supply function for the manufactured good can be written as [R.sub.q](q(t), [lambda](t)) = [R.sub.q](q(t)) for the case where only import tariff is used. [5] The R(q, [lambda]) function is assumed to be strictly convex in q (i.e., [R.sub.qq] [greater than] 0). For the rest of the analysis, subscripts denote partial derivatives.

The Wage-Setting and Labor Market Equilibrium

According to the HT paradigm, the rural wage ([w.sup.A]) is competitively determined ensuring full employment in that sector. In the urban sector, the existence of an institutionally fixed minimum wage (w) above the market-clearing level results in sectoral unemployment. [6] Assuming that each worker has the same chance of being hired, the probability of finding urban employment equals the ratio of employed labor (i.e., [L.sup.m] = [L.sup.M] + [L.sup.g]) to the labor force in that sector (i.e., [L.sup.m] + [L.sup.u]). Then, the expected urban wage ([w.sup.e]) equals the minimum wage (w) multiplied by the probability of finding employment (i.e., [L.sup.m]/([L.sup.m] + [L.sup.u])).

Intersectoral labor migration, which is the factor connecting the rural-urban areas, ensures the equalization of expected wages in the two sectors and labor market equilibrium. That is,

[w.sup.A] = [w.sup.e] = [[L.sup.m]/([L.sup.m] + [L.sup.u])]w. (4)

Using the definition of the urban unemployment ratio [lambda](=[L.sup.u]/[L.sup.m]), the labor market equilibrium condition in Equation 4 can be rewritten as

W = (1 + [lambda])[w.sup.A]. (5)

Labor is assumed homogeneous, and because perfect competition exists in product markets, it is paid the value of its marginal product in each sector. That is,

W = q[M.sub.L]([L.sup.M], K), and [w.sup.A] = [A.sub.L]([L.sup.A], E), (6)

where [M.sub.L](=[partial]M/[partial][L.sup.M]) and [A.sub.L](=[partial]A/[partial][L.sup.A]), respectively, are the sectoral marginal products of labor. Since labor is free to move throughout the economy, the fixed labor endowment (L) must equal the sum of employment in the urban sector (manufactured employment plus employment in the production of the public good) and agriculture plus the number of urban unemployed. Using the definition of [lambda], the economy's labor endowment constraint can be written as

(1 + [lambda])[L.sup.m] + [L.sup.A] = L. (7)

Demand Conditions, Trade, and the Government

We assume identical consumers whose utility depends positively on the consumption of the two traded goods (i.e., M and A) and the public consumption good (g). Demand conditions are described by the expenditure function E(p, g, u), denoting the minimum private spending on consumption required to achieve a level of utility u, given the consumer domestic relative price of the manufactured good p(=[p.sup.*] [tau] + t) and the level of public good provision (g). [7] The partial derivative of the expenditure function with respect to p (i.e., [E.sub.p]) denotes the compensated demand function of the manufactured good, which is assumed strictly concave in p (i.e., [E.sub.pp] [less than] 0). Moreover, [E.sub.g] is negative, denoting that an increase in the consumption of the public good reduces expenditure on the private goods required to achieve the level of utility u. In the public economics literature (i.e., King 1986), -[E.sub.g] is called the "marginal willingness to pay for the public good."

Let Z(p, g, u) be the trade expenditure function, which is defined as the difference between domestic minimum expenditure and revenue from production of the private and public goods. That is,

Z(p, g, u) = E(p, g, u) - R[q, [lambda](t)]. (8)

The trade expenditure function is assumed strictly concave in prices (i.e., [Z.sub.pp] [less than] 0), and its derivative with respect to p (i.e., [Z.sub.p] = [E.sub.p] - [R.sub.p]) is the demand for imports function. Note that for the case where the government collects only tariff revenue to finance the provisions of the public good, we have p = q(=[p.sup.*] + t).

It is assumed, as noted earlier, that the government collects revenue from (i) a tax on income from the production of the private and public consumption goods, (ii) an excise tax on the manufactured good, and (iii) an import tariff. Such tax revenue is used to finance the cost of providing the public good. The government net tax revenue (i.e., B) is written as follows:

B = [rho]R(q, [lambda]) + [tau][E.sub.p](p, g, u) + t[Z.sub.p](p, g, u) - w[L.sup.g] (9)

where [rho]R(q, [lambda]) is the income tax revenue, [tau][E.sub.p](p, g, u) is the excise tax revenue. t[Z.sub.p](p, g, u) is the tariff revenue, and w[L.sup.g] is the cost of the public good. We assume that the government maintains a balanced budget, so that B = 0.

PROPOSITION 1. Consider a small open economy characterized by HT unemployment and by local provision of a public consumption good. Then, government net tax revenue (B), ceteris paribus, increases with a decrease in the unemployment ratio and an increase in the income tax rate. Changes in the level of the public good have an ambiguous effect on (B), depending on whether the manufactured and public goods are complements or substitutes in consumption. Finally, a small excise tax or import tariff on tile manufactured good increases government net tax revenue.

PROOF. Totally differentiating Equation 9, recalling the properties of the GNP function, and rearranging terms, we obtain

dB = ([tau] + t)[E.sub.pu]du - (w - [tau][E.sub.pg] - t[E.sub.pg])d[L.sup.g] - [rho][W.sup.A][L.sup.m]d[lambda] + [[E.sub.p] + ([tau] + t)[E.sub.pp]d[tau] + ([Z.sub.p] + t[Z.sub.pp] + [rho][R.sub.q] + [tau][E.sub.pp])dt + Rd[rho], (10)

Equation 10 reveals that in the present context, ([partial]B/[partial][lambda]) = -[rho][w.sup.A][L.sup.m] [less than] 0 and ([partial]B/[partial][rho]) = R [greater than] 0. Moreover, ([partial]B/[partial][L.sup.g]) [less than] 0 when [E.sub.pg] [less than] 0 that is, when the manufactured and public goods are substitutes in consumption. When [E.sub.pg] [greater than] 0, then ([partial]B/[partial][L.sup.g]) may be positive or negative. [8] Assuming no use of other policy instrument, Equation 10 gives for the case of an excise tax on the manufactured good ([partial]B/[partial][tau]) = ([E.sub.p] + [tau][E.sub.pp]) and for the case of the import tariff ([partial]B/[partial]t) = ([Z.sub.p] + t[Z.sub.pp], from which the results of Proposition 1 follow. [9]

Some Benchmark Results

Total differentiation of Equation 11 yields

The country's income-expenditure identity (budget constraint) requires that total private spending must equal net, after tax income from production of all goods. That is,

E(p, g, u) = (1 - [rho])R(q, [lambda]). (11)

DEFINITIONS: Consider a small open economy characterized by HT unemployment and provision of a public good financed through an income tax or an excise tax on the manufactured good or an import tariff Changes in any of the three policy instruments affects welfare directly and indirectly through the, what we call, public good effect and employment effect.

du = [-[E.sup.p] - [E.sub.g][[L.sup.g].sub.[tau]] + (1 -[rho])[R.sub.[lambda]][[lambda].sub.[tau]]]d[tau] + [-[Z.sub.p] - [E.sub.g][[L.sup.g].sub.t] + (1 - [rho]) [R.sub.[lambda]][[lambda].sub.t]]dt + [-R - [E.sub.g] [[L.sup.g].sub.p] + (1 - [rho]) [R.sub.[lambda]][[lambda].sub.[rho]]]d[rho], (12)

where [E.sub.u] = 1 by choice of units, 4= [Z.sub.p] = [Z.sub.p] + [rho][R.sub.p] [greater than] 0, [[L.sup.g].sub.t], and [[lambda].sub.i], i = [rho], [tau], t are the total differentials of [L.sup.g] and [lambda] with respect to the policy parameters [rho], [tau], and t (see the Appendix for the detailed derivations). Consider, for example, the case where d[tau] [greater than] 0 and dt = d[rho] = 0. Then, from Equation 12, the right-hand-side expression for (du/d[tau]) comprises three components. The first (i.e., -[E.sub.p]) is the direct effect capturing the negative impact of a higher excise tax on welfare due to higher expenditure required to maintain a given level of consumption of the manufacturing good. The second component (i.e., -[E.sub.g][[L.sup.g].sub.[tau]]) is the so-called public good effect, capturing the impact of the higher excise tax on welfare through the provision of the public good. The last component of the (du/d[tau]) expression in Equation 12 (i.e., (1 - [rho])[R.sub.[lambda]][[lambda].sub.[tau]]) is the so-called employment effect, capturing the impact of a higher ([tau]) on welfare through changes in the unemployment ratio ([lambda]). Similarly, observing Equation 12, changes in the other two tax rates (i.e., dt [greater than] 0 when d[tau] = d[rho] = 0, or dp [greater than] 0 when d[tau] = dt = 0) affect welfare through the corresponding direct effect, public good effect, and employment effect.

PROPOSITION 2. Assume a small open economy characterized by HT unemployment and by local provision of a public consumption good. Then, an income tax or a small excise tax on the manufactured good or a small tariff unambiguously raises the provision of the public good. [10]

PROOF. Equations A3 to A5 provide the proof of this proposition. Equation A3 shows that, ceteris paribus, an income tax always raises government net tax revenue, thus the provision of the public good. Equations A4 and A5, respectively, show that this is also true for the case of a small excise tax (i.e., initially [tau] [approximate] 0) or a small import tariff (i.e., initially t [approximate] 0). Moreover, the import tariff, being a subsidy to the production of the manufactured good, raises urban employment and incomes, thus further increasing government net tax revenue and the provision of the public good. However, a larger excise tax on the manufactured good or an import tariff affects negatively the consumption of this good and thus tax revenue. If the overall effect of such a higher excise tax or of a higher import tariff on government tax revenue is negative, then production of the public good falls.

PROPOSITION 3. Assume that in a small open economy characterized by HT type of unemployment, the government provided public good is financed through an income tax, an excise tax on the manufactured good, or a tariff. An increase in the income tax rate always increases government net tax revenue and reduces the unemployment ratio. Similar effects are induced by a small excise tax on the manufactured good or a small tariff.

PROOF. Equations A6 to A8 provide the proof of this proposition. Intuitively, an income tax or a small excise tax or a small import tariff that raises government net tax revenue and public good provision also increases employment and thus reduces the unemployment ratio. If the policy of a higher excise tax or of a higher import tariff reduces government net tax revenue and the level of the public good, then it also reduces employment and raises the unemployment ratio.

When nondistortionary taxes (e.g., lump-sum taxes) are used to finance the public good, then the first-best efficiency rule for its provision requires that the social marginal benefit equal the social marginal cost. When distortionary taxes (e.g., consumption taxes) are used to finance the provision of the public good, then Pigou argued that the private marginal cost understates the social marginal cost. This, however, as subsequent authors have shown, is not always true (e.g., see Introduction). [11]

In the remainder of this paper, we examine the effects of an increase in each of the policy instruments on welfare in the presence of HT unemployment when the government uses an income tax, an excise tax on the manufactured good, or an import tariff to finance its provision. We also derive the efficiency rules for public good provision under each policy regime.

3. Income Tax Policy, Welfare, and the Efficiency Rule

Now we assume that the government's policy instrument to raise revenue and finance the provision of the public good is a tax on incomes from production of the private and public consumption goods.

Setting d[tau] = t = dt = 0, but [tau] [greater than] 0 in Equation 12, and using Equations A3 and A6 of the Appendix, after some algebraic manipulations, we obtain

([delta][R.sup.-1])(du/d[rho]) = [[delta].sub.2](w + [E.sub.g]) + [[delta].sub.1][R.sub.[lambda]] - [tau][[delta].sub.2]][E.sub.pg], (13)

where the expressions for [delta] [less than] 0, [[delta].sub.1] [greater than] 0 and [[delta].sub.2] [greater than] 0 are explicitly defined in the Appendix.

Consider the case where [tau] = 0. Then, Equation 13 indicates that the higher income tax affects welfare through the induced (i) public good effect (i.e., [[delta].sup.-1]R[[delta].sub.2](w + [E.sub.g])) and (ii) employment effect (i.e., [[delta].sup.-1]R[[delta].sub.1][R.sub.[lambda]]). [12] Through the public good effect, the higher p, which raises government net tax revenue and public good provision, affects welfare positively if the public good is undersupplied. [13] For the rest of the analysis, we assume this to be the case. Through the employment effect, the higher p exerts a positive effect on welfare since, by increasing the public good provision (i.e., [L.sup.g]), it reduces the unemployment ratio (see Eqns. A3 and A6), and thus it increases income. Thus, the higher income tax rate improves welfare since the public good is assumed undersupplied. [14]

Next we obtain the efficiency rule for the provision of the public good in the present policy regime as follows:

PROPOSITION 4. Consider an economy characterized by unemployment of the HT type and where the sole instrument of financing the provision of an undersupplied public good is an income or a lump-sum tax. Within this model, the private marginal cost of the public good always overstates its social marginal cost.

PROOF. Setting (du/d[rho]) = 0 in Equation 13, we obtain [15]

-[E.sub.g] = w + ([[delta].sub.1]/[[delta].sub.2])[R.sub.[lambda]] - [tau][E.sub.pg]. (14)

The left-hand side of Equation 14 is the social marginal benefit of public good provision, while the right-hand side is its social marginal cost. The second right-hand-side term of Equation 14 is negative. Thus, we conclude that in the present context of unemployment and public good provision, when the income tax is the sole policy instrument (i.e., [tau] = 0), the private marginal cost of public good provision (i.e., w) always overstates its true social marginal cost. [16] Intuitively, the social marginal cost of the public good is less than the private marginal cost in this case since an increase in the income tax rate to finance the provision of public good decreases the unemployment rate and increases income and welfare. When full employment exists, then the private marginal cost equals the social marginal cost. [17]

This is an important new result in terms of the relevant literature. As noted in the Introduction, contrary to Pigou's intuitive result, subsequent studies (e.g., Atkinson and Stern 1974; Wildasin 1984) concluded that when distortionary taxes are used to finance the provision of the public good, under certain conditions (e.g., when the taxed and public goods are complements in consumption) the social marginal cost of the public good falls short of the private marginal cost. In the present case of HT unemployment and public good provision solely financed through income or lump-sum taxation, the social marginal cost of the public good is always smaller than its private marginal cost regardless of the relationship between private and public goods in consumption.

4. Excise Tax on the Manufactured Good, Welfare, and the Efficiency Rule

Next we turn to the welfare effects of a higher excise tax on the manufactured good (i.e., d[tau] [greater than] 0) in the presence of HT unemployment and public good, and we derive the efficiency rule for public good provision.

Letting in Equation 12 [rho] [greater than] 0 and d[rho] = t = dt = 0 and using Equations A4 and A7 of the Appendix, after some algebraic manipulations we obtain

[delta](du/d[tau]) = [[delta].sub.2](w + [E.sub.g])[E.sub.p] + [[delta].sub.1][R.sub.[lambda]][E.sub.p] - [tau][[[delta].sub.2]([E.sub.p][[E.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - [[delta].sub.1](1 - [rho])[R.sub.[lambda]]][E.sub.pp]. (15)

Equation 15 indicates that a higher excise tax affects welfare through (i) changes in the level of public good provision (i.e., [[delta].sub.2](w + [E.sub.g])[E.sub.p]), which we call the public good effect; (ii) changes in income due to changes in the unemployment ratio (i.e., [[delta].sub.1][R.sub.[lambda]][E.sub.p] = - [[delta].sub.1][w.sup.A][L.sup.m][E.sub.p]), which we call the employment effect; and (iii) changes in government net tax revenue due to changes in consumer prices, the level of public good provision, and the unemployment ratio (i.e., - [tau][[[delta].sub.2]([E.sub.p][[E.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - [[delta].sub.1](1 - [rho])[R.sub.[lambda]]][E.sub.pp]), which we call the tax revenue effect.

Through the public good effect, the impact of the higher [tau] on welfare by and large follows that of the previous case of the income tax. Through the employment effect, the higher [tau], which raises government revenue, affects positively [L.sup.g] reduces [lambda] (see Eqns. A4 and A7), and increases incomes, thus exerting a positive impact on welfare. When such an excise tax on the manufactured good is the only source of financing the provision of the public good (i.e., [rho] = 0) and the excise tax rate is small (i.e., [tau] [approximate] 0), it is expected that the public good is undersupplied (i.e., g [approximate] 0) and -[E.sub.g] [greater than] w). In this case, an increase in [tau] raises welfare since the public good effect and the employment effect dominate the tax revenue effect. For a larger tax (i.e., [tau] [greater than] 0), a further increase in its rate may exert, through the tax revenue effect, a positive or negative impact on welfare, in part depending on whether the manufactured and pub lic consumption goods are substitutes (complements) in consumption (i.e., [E.sub.pg] [less than] 0 ([greater than] 0)). For example, if [E.sub.pg] [less than] 0, then this revenue effect of a higher [tau] on welfare is negative. In this case, if also [tau] is large, then a further increase in the excise tax reduces welfare if the tax revenue effect dominates the public good effect and employment effect.

Next, we obtain the second-best excise tax rate (i.e., [[tau].sup.*]).

PROPOSITION 5. Consider a small open economy providing an undersupplied public good. When only an excise tax on the manufactured good is chosen optimally to finance its provision, then there is a positive, second-best excise tax rate that maximizes welfare. This result holds regardless of the existence of HT unemployment or of a suboptimally chosen income tax rate.

PROOF. Setting (du/d[tau]) = 0 in Equation 15 and solving for [tau], we get

[[tau].sup.*] = [(w + [E.sub.g])[[delta].sub.2] + [[delta].sub.1][R.sub.[lambda]]][E.sub.p]/[[[delta].sub.2]([E.sub.p][ [E.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - [[delta].sub.1](1 - [rho])[R.sub.[lambda]]][E.sub.pp]. (16)

Equation 16 shows that since (w + [E.sub.g]) [less than] 0, then [[tau].sup.*] [greater than] 0 regardless of whether a suboptimal income tax rate exists (i.e., [rho] [greater than or equal to] 0). [18] If, however, [rho] [greater than] 0, then the corresponding [[tau].sup.*] is greater to that when [rho] = 0, assuming everything else is the same. With full employment (i.e., [R.sub.[lambda]] = 0), since (w + [E.sub.g]) [less than] 0, the optimal policy is again [[tau].sup.*] [greater than] 0. [19]

When [E.sub.pg] [greater than] 0, it is possible for the denominator of Equation 16 to be positive. In this case, one could conclude that the optimum excise tax is negative. This, however, is wrong. The negative excise tax is the one that minimizes welfare. When the denominator of Equation 16 is positive, that is, the third term on the right-hand side of Equation 15 is negative, it means that as the excise tax increases, welfare increases at an increasing rate, and in this case we may have a corner solution or implicit determination of the optimum tax rate. When [E.sub.pg] [less than] 0, this possibility does not exist.

PROPOSITION 6. Assume an economy with unemployment described by the HT model. When an excise tax on the manufactured good is used to finance the public good, then the private marginal cost of the public good may overstate its social marginal cost even if the public and the manufactured good are substitutes in consumption. [20]

PROOF. Setting (du/d[tau]) = 0 in Equation 15, we get

-[E.sub.g] = w + ([[delta].sub.1]/[[delta].sub.2])[R.sub.[lambda]] - [tau][([E.sub.p][[E.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - ([[lambda].sub.1]/[[lambda].sub.2])(1 - [rho])[R.sub.[lambda]]][E.sub.pp][[E.sup.-1].sub.p]. (17)

When we have full employment (i.e., [R.sub.[lambda]] = 0), we get the well-known result. That is, when the public and the taxed goods are substitutes in consumption (i.e., [E.sub.pg] [less than] 0), then the private marginal cost understates its social marginal cost. When, however, they are complements, then the private marginal cost may overstate its social marginal cost. However, in the present framework, with HT unemployment, the private marginal cost may overstate the social marginal cost even if the public and the taxed goods are substitutes in consumption.

Comparing Equations 14 and 17, we note the following point. When an income tax is chosen as a policy instrument, the existence of an excise tax on the manufactured good may alter the efficiency rule for public good provision. In case that the selected policy instrument is an excise tax, the presence of a suboptimal income tax has no bearing on the respective efficiency rule.

5. Import Tariff and Welfare

Most LDCs are frequently revenue constrained in financing government activities (e.g., the provision of public goods), for this, an import tariff, despite its known heavier deadweight losses compared to other policy instruments (e.g., income taxes), is a relatively effective and administratively low-cost policy choice for generating government revenue and financing public sector activities. In this section, assuming the absence of income taxes, we briefly note the use of only tariff revenue to finance the provision of the public good. Using Equations 12 and A5, the welfare effect of raising the tariff rate is given as follows:

[delta](du/dt) = [[delta].sub.2](w + [E.sub.g])[[Z.sub.p] - [(q[M.sub.LL]).sup.-1] [M.sub.L]w][R.sub.[lambda]] - t[[[delta].sub.2]([Z.sub.p][[Z.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - [[delta].sub.1][R.sub.[lambda]](1 + [xi])][Z.sub.pp], (18)

where [xi] = [(q[M.sub.LL][Z.sub.pp]).sup.-1] [M.sub.L][E.sub.pg] [greater than] ([less than])0, depending on whether [E.sub.pg] [greater than] ([less than])0. Equation 18 shows that the higher tariff rates affects welfare through an induced (i) public good effect (i.e., [[delta].sup.-1][[delta].sub.2](w + [E.sub.g])[Z.sub.p]), (ii) employment effect (i.e., [[delta].sup.-1][[delta].sub.1][[Z.sub.p] - [(q[M.sub.LL]).sup.-1] [M.sub.L]w][R.sub.[lambda]]), and what we call (iii) tariff revenue effect (i.e., - [[delta].sup.-1]t[[[delta].sub.2]([z.sub.p][[z.sup.-1].sub.pp][E.sub. pg] - [E.sub.g]) - [[delta].sub.1][R.sub.[lambda]](1 + [xi])][Z.sub.pp]. [21]

Through the public good effect, the higher tariff, which raises government revenue, affects welfare positively if the public good is undersupplied. Through the employment effect, the higher tariff entails a positive effect on domestic employment, thus incomes and welfare. First, as in the case of an excise or an income tax, the higher tariff raises government revenue, which affects positively [L.sup.g], reduces [lambda], and raises incomes and welfare (i.e., [[delta].sup.-1][[delta].sub.1][R.sub.[lambda]][Z.sub.p]). Second, a tariff, which acts as a subsidy to manufactured production, raises employment in that sector, thus further reducing [lambda], increasing urban incomes and overall welfare (i.e., -[[delta].sup.-1][[delta].sub.1][(q[M.sub.LL]).sup.-1] [M.sub.L]w[R.sub.[lambda]]).

Like in the case of an excise tax, when the tariff is the only policy instrument and it is small (i.e., t [approximate] 0), it is expected that the public good is undersupplied. In this case, an increase in its rate is welfare improving since the public good effect and employment effect dominate the tariff revenue effect.

Setting (du/dt) = 0 in Equation 18, we get the efficiency rule for public good provision when the government uses only tariff revenue to finance its provision as follows:

-[E.sub.g] = ([[delta].sub.1]/[[delta].sub.2])[[Z.sup.-1].sub.p][[Z.sub.p] - [(q[M.sub.LL]).sup.-1] [M.sub.L]w][R.sub.[[lambda] - t[([Z.sub.p][[Z.sup.-1].sub.pp][E.sub.pg] - [E.sub.g]) - ([[delta].sub.1]/[[delta].sub.2])[R.sub.[[lambda](1 + [xi])][Z.sub.pp][[Z.sup.-1].sub.p]. (19)

Careful examination of Equation 19 reveals that Proposition 6 also applies in this case. That is, the private marginal cost of the public good may overstate its social marginal cost even if the taxed and the public good are substitutes in consumption. When full employment exists (i.e., [R.sub.[lambda]] = 0), then we get the well-known result. That is, when the public and the taxed goods are substitutes in consumption (i.e., [E.sub.pg] [less than] 0), then the private marginal cost understates its social marginal cost.

6. Concluding Remarks

By now it is broadly accepted in the literature of international trade and economic development that governments seldom lump-sum distribute to domestic households revenues generated from the imposition of taxes (e.g., income) or tariffs. Instead, such tax revenues, by and large, are used to finance the provision of public goods and public inputs. As a result, the recent surge in this literature has evolved around this premise.

Within this existing trade literature of public good provision, the paper notes and incorporates two issues. The first is that of the existence of unemployment, an assumption particularly relevant in the context of a LDC. The second recognizes that, more than often, governments may use policies jointly (e.g., income and excise tax policies) to finance the provision of the public good or input. Either issue, when accounted for, alters nontrivially existing analytical results and provides some newer ones. For this, we construct a general equilibrium trade model of a small open economy characterized by Harris-Todaro type of unemployment, producing two privately traded goods and a nontraded public consumption good. [22] For the provision of the later commodity, the government generates the required revenue through the imposition of an income and/or an excise tax on the manufactured good or of an import tariff. The paper then examines the effect of such tax policies on the unemployment ratio and the level of welf are and derives the efficiency rules for public good provision.

Among other findings, we note the following. First, given the undersupply of the public good, with or without unemployment and the presence of a suboptimally chosen income tax, the government's second-best policy is an excise tax or an import tariff on the manufactured good when each instrument alone is optimally chosen. Under either policy regime, because of unemployment, even if the taxed and public goods are substitutes in consumption, it is possible for the private marginal cost of the public good to overstate its social marginal cost. In the case of full employment, such a possibility does not exist when the two goods are substitutes in consumption. Second, with income taxes alone, the private marginal cost of the public good always overstates its social marginal cost with unemployment, but the two are equal with full employment.

(*.) D.I.E.E.S., Athens University of Economics and Business, 76 Patission Street, Athens 104 34, Greece and CESifo; E-mail hatzip@aueb.gr.

(+.) Department of Economics, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia. Cyprus and CESifo; E-mail m.s.michael@ucy.ac.cy: corresponding author.

The authors gratefully acknowledge the insightful comments by the Editor and two referees of the Journal. Responsibility for remaining shortcomings lies entirely with the authors.

(1.) Michael and Hatzipanayotou (1995) for the case of a consumption tax and Michael (1997) for the case of an import tariff show that the social cost of the public good may understate its private marginal cost when the public good and the taxed good are general equilibrium complements.

(2.) In LDCs, by and large, imported (manufactured) goods are primarily luxury goods whose consumption is usually taxed, while the consumption of agricultural (necessity) goods, constituting a large portion of spending by the poorer segments of their population, is usually untaxed. Moreover, the use of import tariffs is historically consistent with the efforts of LDCs to raise public sector revenue. Recent trends, however, of global and regional trade liberalization have forced these countries to reduce such trade taxes and to resort to less distortionary means (e.g., income and excise taxes) of raising public sector revenue.

(3.) In part, the results depend on the assumed linear production function for the public good. For expositional purposes, however, we think that this approach is reasonable.

(4.) It can be shown that the comparative static's analysis using R(q, [lamda], k, E) as the GNP function are the same as those using a more conventional writing, for example, R(q, [L.sup.M], [L.sup.g], [L.sup.A], K, E).

(5.) Note that in the case of an excise tax, [R.sub.q[tau]] = ([partial]M/[partial][L.sup.M])([partial][L.sup.M]/[partial][tau]) 0. Similarly, in the case of an income tax, [R.sub.qp] = 0 (see the Appendix). That is, the supply of the manufactured good is unaffected by changes in the excise or the income tax.

(6.) Alternatively, the urban wage rate can be indexed in terms of consumer prices. The essence of the results, however, remains the same.

(7.) Since employed and urban unemployed households enjoy different levels of utility, equal in expectation to the rural utility level, a standard practice of the HT literature is to assume identical and homothetic demands for all (i.e., rural and urban employed or unemployed) households.

(8.) Assuming that [E.sub.pg] = 0, that is, assuming that the private and public goods are separable in consumption, then unambiguously ([partial]B/[[partial][L.sup.g]) = -w [less than] 0.

(9.) It does not add much to the results of the paper to consider the other taxes as nonzero constants.

(10.) The result that for a small (t), (d[L.sup.g]/dt) [greater than] 0, holds regardless of whether initially [rho] [greater than or equal to] 0, (see Equation A5).

(11.) For example, when the taxed and the public goods are complements in consumption or when we have a backward-bending labor supply, then the private marginal cost may overstate the social marginal cost.

(12.) Identical results emerge when [tau] = 0 and lump-sum taxes are used to finance the provision of the public good.

(13.) In the following analysis when -[E.sub.g] [greater than] w, we say that the public good is undersupplied. When -[E.sub.g] = w, we say that the public good is supplied at its first-best level. To compare our results with some standard results of the public economics literature, note that the economy-wide consumer marginal willingness to pay for the public good (i.e., -[E.sub.g]), which is the social marginal benefit, is also the sum of the marginal rates of substitution over all individuals (i.e., [sigma]MRS). Similarly, the marginal cost, which presently equals the minimum wage w, equals the marginal rate of transformation (i.e., MRT). Thus, our efficiency rule -[E.sub.g] = w is the same as the conventional efficiency rule [sigma]MRS = MRT (see Rosen 1998 for a simple analysis relating these concepts).

(14.) In the presence of an excise tax, an increase in the income tax has an additional effect on welfare through its effect on excise tax revenue. That is, through this effect, an increase in the income tax increases revenue, and the public good provision increases, causing excise tax revenue to increase (decrease) if the public good and the taxed good are complements (substitutes) in consumption. The increases (decrease) in excise tax revenue affects positively (negatively) welfare.

(15.) Setting (du/d[rho]) = 0 in Equation 13, the first-best income tax rate ([[rho].sup.*]) cannot be explicitly determined but only implicitly since p is included in g(=[L.sup.g]) [E.sub.g](p, g, u), [R.sub.[lambda]](=-[w.sup.A]([L.sup.M] + [L.sup.g])), and so on.

(16.) In the present context of unemployment, the identical efficiency rule applies when the public good is financed through lump-sum taxes (see note 12). However, this equivalency between an income and a lump-sum tax breaks down in more detailed models (e.g., one incorporating labor/leisure decision).

(17.) In the presence of an excise tax, the private marginal cost overstates its social marginal cost when the manufactured and the public goods are complements in consumption. If, however, they are substitutes, then the private marginal cost may understate its social marginal cost.

(18.) The second-best policy unambiguously is also [[tau].sup.*] [greater than] 0 in the special case where the public good is and the public and manufactured goods are neutral in consumption (i.e., [E.sub.pg] = 0).

(19.) When a suboptimal income tax rate finances the provision of the public good and w = -[E.sub.g], then the second-best policy is still an excise tax with HT unemployment, but it is a zero tax with full employment.

(20.) With distortionary taxation, the marginal cost of public funds (MCF) is usually greater than one. When, however, the private taxed good and the public good are complements in consumption, then the MCF could be less than one (Atkinson and Stern 1974). Sandmo (1998) shows that MCF could be less than one in a model with heterogeneous consumers and redistribution from high-wage to low-wage workers. In the present model with unemployment, the MCF is always less than one with income or lump-sum taxes and can be less than one with excise taxes or tariffs even if the taxed good and the public good are substitutes in consumption. For the definition of MCF, see, for example, Sandmo (1998).

(21.) The analytical interpretation of Equation 19 does not change despite the presence of additional terms when [rho] is not zero. To simplify the exposition of the results, however, we set [rho] = 0.

(22.) Similar but not identical results can be obtained when unemployment is due to a rigid minimum real wage rate in both sectors of the economy. The exact results depend on the tax instrument and on the details of the model. The rigid real wage model is frequently used in the literature (e.g., for a recent application of this model, see Hoel 1997).

References

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Beladi, Hamid, and C-C. Chao. 1993. Non-traded goods, urban unemployment and welfare in LDCs. European Journal of Political Economy 9:281-92.

Feehan, James. 1988. Efficient tariff financing of public goods. Journal of 25:155-64.

Harris, John, and Michael Todaro. 1970. Migration, unemployment and development: A two Sector analysis. American Economic Review 60:126-42.

Hoel, Michael. 1997. Coordination of environmental policy for transboundary environmental problems? Journal of Public Economics 66:199-224.

King, Michael. 1986. A pigovian rule for the optimum provision of public goods. Journal of Public Economics 30:273-91.

Michael, Michael S. 1997. The Optimal tariff for public good and public input provision. Public Finance Review 25:117-33.

Michael, Michael S., and Panos Hatzipanayotou. 1995. On public good provision with distortionary taxation. Public Finance/Finances Publiques 50:292-302.

Michael, Michael S., and Panos Hatzipanayotou, 1997. Public good production, nontraded goods, and trade restrictions. Southern Economic Journal 63:1100-7.

Pigou, A. C. 1947. A Study in Public Finance. 3rd edition. London: Macmillan.

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Sandmo, Agnar. 1998. Redistribution and the marginal cost of public funds. Journal of Public Economics 70:365-82.

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Appendix

Equations 5, 6, 7, 9, and 11 constitute a system of six equations in the endogenous variables u, [L.sup.M], [L.sup.g], [L.sup.A], [lambda], and [w.sup.A], solved as functions of the policy parameters [rho], [tau], and t. Total differentiation of these equations and rewriting Equation 12 as

du + [E.sub.g]dg - (1 - [rho])[R.sub.[lambda]]d[lambda] = - [E.sub.p]d[tau] - [Z.sub.p]dt - Rdp (A1)

produces the following matrix system:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A2)

Recall that when [rho] is nonzero, then [Z.sub.p] = [Z.sub.p] + [rho][R.sub.p] and ([partial]B/[partial]t) = [Z.sub.p] + t[Z.sub.pp]. For stability, the determinant [delta] = - [[delta].sub.1][[rho] + 1(1 - [rho])[tau][E.sub.pu]][R.sub.[lambda]] - [[delta].sub.2][w - [tau]([E.sub.pg] - [E.sub.g][E.sub.pu])] must be negative; [[delta].sub.1] = q[M.sub.LL][A.sub.LL][(1 + [lambda]).sup.2] [greater than] 0 and [[delta].sub.2] = q[M.sub.LL][(1 + [lambda])[L.sup.m][A.sub.LL] - [w.sup.A] [greater than] 0. The following results are obtained: Policy Effects on Public Good Provision

Income tax: (d[L.sup.g]/d[rho]) = [[L.sup.g].sub.p] = -[[delta].sup.-1][[delta].sub.2](1 - [tau][E.sub.pu])R [greater than] 0 (A3)

Excise tax: (d[L.sup.g]/d[tau]) = [[L.sup.g].sub.[tau]] = -[[delta].sup.-1][[delta].sub.2](1 - [tau][E.sub.pu])[E.sub.p] + [tau][E.sub.pp]] (A4)

Import tariff: (d[L.sup.g]/dt) = -[[delta].sup.-1]{[[delta].sub.2][(1 - t[E.sub.pu])[Z.sub.p] + t[Z.sub.pp]] + [[delta].sub.1][[(p[M.sub.LL])].sup.-1][M.sub.L][[rho] + (1 - [rho])t[E.sub.pu]][R.sub.[lambda]]} (A5)

Policy Effects on the Unemployment Ratio

Income tax: [delta](d[lambda]/d[rho]) = [[delta].sub.1](1 - [tau][E.sub.pu])R [less than] 0 (A6)

Excise tax: [delta](d[lambda]/d[tau]) = [[delta].sub.1][(1 - [tau][E.sub.pu])[E.sub.p] + [tau][E.sub.pp]] (A7)

Import tariff: [delta](d[lambda]/dt) = [[delta].sub.1]{(1 - t[E.sub.pu])[Z.sub.p] + t[Z.sub.pp] - [[(p[M.sub.LL])].sup.-1][M.sub.L][w - t([E.sub.pg] - [E.sub.g][E.sub.pu])]} (A8)

Note that (1 - t[E.sub.pu]) [greater than] 0 and (1 - [tau][E.sub.pu]) [greater than] 0 since both goods are normal in consumption.