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Political economy and the social marginal cost of public funds: the case of the Meltzer-Richard economy.

Article Excerpt
I. INTRODUCTION

The marginal cost of public funds (MCF) is defined as the full cost to the private sector of raising an additional dollar of tax revenue, including deadweight loss or excess burden of taxation imposed on taxpayers. Much of the theoretical literature on the MCF is cast in the framework of a one-consumer economy. However, the main reason why we have distortionary taxes in the first place is precisely because of the need for redistribution or the existence of consumers with heterogeneity. In view of this inconsistency, several papers, including Dahlby (1998) and Sandmo (1998), have recently started addressing the so-called "social marginal cost of public funds" (SMCF) in models with heterogenous consumers. (1) These papers highlight how the redistributive concern may alter the calculation of the SMCF. (2)

In previous studies on the MCF or SMCF, the existing of status quo tax system has been assumed to be either arbitrary or optimal. (3) It is arguable, however, that the existing tax system is neither arbitrary nor optimal but rather represents a political equilibrium. The approach adopted by Hettich and Winer (1999) and Persson and Tabellini (2000) corroborates this argument. In surveying the political economy of public finance, the authors of these two books explicitly portrayed public policy as the equilibrium outcome of some specified political process.

In this note, we study the SMCF issue on the basis of the plausible premise that the existing tax system itself represents a political equilibrium. The calculation of the SMCF is basically a normative exercise. The premise that the existing tax system is a policy outcome in political equilibrium will enable us to exploit the positive property of political equilibrium in this normative exercise.

As an illustration of our approach, we revisit the political economy of redistributive taxation as set out in Meltzer and Richard (1981) (hereafter, M-R). The M-R model holds a prominent position in the redistribution literature and has been elaborated and extended in many directions (Persson and Tabellini 2000, Part II). (4) Section II overviews the M-R model. Sections III and IV derive and discuss the SMCF in the M-R economy. An interesting feature of our finding is that the degree of income inequality as measured by the ratio of mean to median income can play an important role in estimating the SMCF and judging whether the level of redistribution is excessive or inadequate.

II. THE M-R MODEL

A. Economy

Consideran economy in which there are n < [infinity] individuals. Each individual is characterized by a wage rate [w.sup.i] (i = 1, ..., n). There are two commodities in the economy: a consumption good c and leisure l. The consumption good is taken as the numeraire. The preferences of individuals qua consumers are represented by a common utility function:

(1) [u.sup.i] = u([c.sup.i],[l.sup.i]), i = 1, ..., n.

This utility function is assumed to be smooth and possess the usual properties.

The income tax system consists of two parameters: a marginal tax rate t and a lump-sum grant a. The tax system pays the lump-sum grant or "demogrant" a to each individual and finances the payment by imposing the marginal tax rate t on all earned income. (5)

The budget constraint facing individual i is:

(2) [c.sup.i] = (1 - t)[w.sup.i][L.sup.i] + a, i = 1, ..., n.

where [L.sup.i] denotes the labor supply with [L.sup.i] + [l.sup.i] = 1. From Equations (1) and (2), we can derive the indirect utility function:

(3) [v.sup.i] = v((1 - t)[w.sup.i], a) = u((1 - t)[w.sup.i][L.sup.i] + a, 1 - [L.sup.i]), i = 1, ..., n.

It is assumed that the government budget is balanced. Denoting per capita pretax income by y, we then have:

(4) ty = a

where y = [summation][y.sup.i]/n with [y.sup.i] = [w.sup.i][L.sup.i].

B. Political Economy

The preferences of individuals qua voters over income tax policy are represented by the indirect utility function (3). Applying the envelope theorem to Equation (3), we obtain the marginal rate of substitution between t and a for individual i: (6)

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

From Equation (4), we also have the marginal rate of transformation between t and a:

(6) da/dt = y + t(dy/dt),

where the second right-hand-side (RHS) term has to do with the change in the tax base. Note that if dy/dt = 0, then da/dt = y, which indicates that an increase in the tax rate can accommodate an increase in the demogrant of the same proportion.

The individually preferred tax rate is implicitly determined by equating Equation (5) with Equation (6), that is:

(7) [y.sup.i] - y = t(dy/dt).

Imposing the minor assumption that both consumption and leisure are normal goods, M-R were able to show that the voter with median income is decisive under simple majority voting. Thus, the political equilibrium is characterized by (M-R's Equation 13):

(8) [y.sup.m] - y = t(dy/dt),

where [y.sup.m] denotes the median income of the economy. The value of [y.sup.m] - y is negative for most societies since positively skewed income distributions are most of ten observed in the real world. (7)

In Equation (7), each voter trades off the marginal redistributive benefit from taxation (in the form of the deviation between his own income and the economy's mean income, the left hand side) against the marginal distortionary cost of taxation (in the form of a smaller tax base, the RHS). The political equilibrium (Equation 8) results from the balancing of this trade-off by the decisive median income voter. We exploit the property of this equilibrium in our calculation of the SMCF in the next section.

III. SMCF FOR REDISTRIBUTION

The previous section has characterized the political equilibrium in the M-R model. How well or badly does this equilibrium perform? To answer this question, we clearly need some criterion to evaluate the performance. Our criterion is assumed to follow the Benthamite social welfare function:

(9) W = [summation] [v.sup.i].

Adopting this criterion raises the question as to the compatibility of evaluating outcomes using a social welfare function when the median voter is decisive. Before proceeding to the SMCF calculation,...

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