Rational majoritarian taxation of the rich: with increasing returns and capital accumulation.

Yoon, Yong J.

I. Introduction

In the United States political setting of 1993, the dominant majority coalition effectively excluded high income recipients (the rich) from participation in fiscal decisions and sought to increase the differentially high taxation of members of this group under a rhetoric of "fair shares." This real-world fiscal environment motivates our analysis in this paper. We address the question: What rate of taxation should the political majority rationally impose on high-income recipients if this majority is motivated strictly in the interest of its members?

We shall use highly abstracted models of the political economy that incorporate several simplifying assumptions. We suggest, however, that the results attained are relevant for the decision calculus of the leaders of the majority coalition. And in particular, we suggest that the possible presence of generalized or economy-wide increasing returns along with saving and the accumulation of capital make such decision calculus more difficult than that which would be implied in modern normative tax analysis that may involve maximization of a specific social welfare function. More specifically, our analysis indicates that the rational fiscal exploitation of the rich may involve lower tax extraction than orthodox fiscal theory would suggest. Or, in summary terms, the middle and low income members of the dominating majority may secure both more fiscal gains as well as non-fiscal benefits from the income-producing behavior of the rich than is recognized in the traditional analyses, and these benefits should be taken into account in any comprehensive reckoning. One implication involves the strengthening of the case for expenditure based taxation, even from the perspective of members of non-saving classes.

We shall proceed as follows: we shall first, in section II, summarize the straightforward response to the question posed in a simple model that assumes all income is derived from current labor supply and that the economy operates under universalized constant returns. In section III, the constant returns assumption is replaced by one of generalized increasing returns. A central contribution in the paper is that of tracing out the effects of this change in the model. In section IV, we include income from capital, which adds complexity to the analysis of both earlier models, and introduces implications of its own that are challenging quite independently of the presence of increasing returns. In section V, we examine the prospects for an expenditure tax rather than an income tax. Finally, in section VI we discuss some extensions and qualifications on the analysis.

II. The Political Economy under Constant Returns: The Benchmark Model

Consider an economy in which production is specialized and in which exchanges of goods and services are made through an interlinked set of markets. Politically, the community has a "democratic" constitution, and government adequately meets its protective state obligations to protect property and contract against private predation. There is universal franchise and majority voting. There are no restrictions on the fiscal authority of the majority coalition, either in$imposing taxes or in allocating benefits from government spending, including direct transfers. All taxes are levied against an income base, and persons cannot be taxed on their potential rather than their observed income receipts. Leisure, as such, cannot be taxed.

For initial simplicity in exposition, we assume that all income is derived from current supplies of labor services. There are no capital goods that yield income, and labor, itself, cannot be made more productive of income by investment in either general or specific skills. The community is made up of three distinct groups of individuals, classified by value productivity. There are no non-producers in the economy. For simplicity, assume that, within each of the three groups, all persons are equivalent. We designate the groups as R (rich), M (middle), and P (poor), and individual members of these groups as r, m, and p. The economy, which we assume to be closed, is characterized by constant returns, in each industry, in each industrial category, and for the inclusive size of the network of production-exchange.

Given the parameters of the basic or benchmark model as described, we now assume that a majority coalition emerges that is made up of all members from the middle and low income classes or groups, from M and P. Members of the high income group, R, are relegated to minority status and are unable to influence political decisions. We assume that members of the dominant coalition are motivated only by their own economic interest; they are not altruistic toward members of R.

More restrictively, we also assume that members of the majority are not concerned about possible defections in the coalition membership through a series of subsequent electoral periods. We explicitly abstract from issues of potential instability in the majority coalition due to the defection of members in response to possible side-payments from non-coalition members. This assumption allows us to avoid discussion of the whole set of problems that involve rotating sequential majorities and cycles.

Since, by assumption, all members of R are identical, little could be gained by differential taxation among separate members of the exploited minority. The tax rate structure confronting each person may take many forms. Initially, consider proportional taxation. What rate will the majority coalition impose on all members of the high-income group? Note that this question may be analyzed independently of whether or not members of the majority find it advantageous to impose taxes on themselves. If revenues sufficient to meet collective purposes can be raised from the rich, no residual taxes will be accepted by members of M and P. And if revenues raised from R are more than sufficient to meet collective goods demands, as determined by members of M and P, the taxation of members of R will still be used to finance direct transfers to those persons in M and P.(1)

The rate of tax that will be imposed on all members of the high-income group, R, will depend on the predicted responses of members of this group to differing rates. If no response at all is predicted to occur, that is, if income-producing behavior of the rich is not predicted to change as a result of changes in tax rates, the majority will impose confiscatory taxes on all incomes of the group over some subsistence minimum.(2)

If any behavioral response to taxation on the part of the taxed persons is anticipated to occur, the optimal levy for the majority to impose will be that rate that maximizes total revenue extraction. Under the simplifying assumptions here, where all income is from currently supplied labor services, and further, where the coalition is not concerned about voter defections from its own ranks, there will be a uniquely determinate solution to this maximization problem. This will be attained at the extremum of the "Laffer curve" or function that relates tax rates directly with revenue totals.

More formally, and stated in terms of the taxation of a single member of R, the majority's problem is to maximize:

[V.sub.r] = t[y.sub.r] (1)

subject to

[y.sub.r] = f(t) (2)

where t denotes the tax rate and [V.sub.r] revenue extraction from a single member of R. The income of a minority member [y.sub.r] = f(t) in (2) is determined by utility maximization: given tax rate t, work effort is chosen to maximize

v(c, L)

subject to

c = (1 - t)[y.sub.r]

[y.sub.r] = F(e - L) (3)

where c is consumption, L leisure, and v is the utility function of member r; e is member r's input endowment, and F is the production function the individual member r faces. The first order condition for the majority's solution is met when

d[V.sub.r](t)/dt = 0 (4)

and the maximum tax revenue can be extracted at the tax rate at which income [y.sub.r] = f(t) attains unit elasticity.(3)

We want to call attention to one feature of this model. There is no non-fiscal interest on the part of the members of the majority in the incomes of the rich. These incomes matter to the members of the majority only as potential sources of tax revenue. The contribution to national income made by the rich in earning high incomes is totally irrelevant to the majority except through the fiscal interdependence described.

III. The Political Economy under Generalized Increasing Returns: The Effect of Non-fiscal Interdependence

We now change only one element in the basic model outlined in section II. We drop the assumption that the economy operates under constant returns and replace this with the assumption that there are increasing returns to the size of the network of market production and exchange. For our purposes it is sufficient to assume that as the size of the economy increases, the value productivity of inputs increases as measured in units of output.

This assumption of generalized mncreasing returns is not a radical departure from the central idea of economic theory. Adam Smith's widely cited principle that the division of labor is limited by the extent of the market is an early statement of the relationship. As the economy increases in size, increased specialization is made possible with consequent increases in the efficiency of resource usage. Subsequent to Smith's initial insight here, other economists have variously urged their peers to replace the constant returns postulate with that of increasing returns. Notable among these critics have been Allyn Young and Nicholas Kaldor. And one of the most interesting developments in economic theory of the 1980s and 1990s has been the return of economists' interest to increasing returns models.(4)

It is not our purpose here to mount a general criticism of orthodox usage of the constant returns postulate. A summary statement of the analytical efficacy of this postulate may, however, be helpful in understanding why economic theorists have seemed so reluctant to introduce generalized increasing returns, even for the limited objectives of examining the full implications of the change in the basic model of the economy. Under constant returns, the explicit interdependence among the separated activities of participants in the inclusive market economy is effectively minimized.

In the idealized model of general equilibrium (for instance, Debreu [14]), persons react independently and separately to the parameters they confront, and their behavior does not, in itself, affect the economic well-being of others in the nexus, except in those well-identified instances where the activities enter directly into utility or production functions of those other than the actors. In the stylized economy without the presence of these familiar externalities, there is no behavioral interdependence among participants. This sort of interdependence is eliminated be cause, under constant returns, the market distribution of payment to inputs in accordance with marginal productivity exhausts total product.

Fiscal interdependence is, of course, present, even under constant returns, once a tax system embodying an income base is in place. A person's behavior in earning or not earning income affects others in the economic-fiscal nexus through the effects on revenues (see Buchanan [4; 8]), and it is, of course, precisely these effects that are incorporated in the revenue-maximizing calculus traced out earlier. Over and beyond this fiscal linkage, however, under constant returns, the individual who chooses voluntarily to earn less income in response to the imposition of a tax suffers the full consequences of his/her action. There are no non-fiscal spillovers that affect the utilities of others in the economy.

Consider an example. The young radiologist who earns $200,000 per year and works full time when, say, the rate of tax is 20 percent, responds to an increase in the rate to 50 percent by reducing income earnings to $100,000. The revenue shortfall of $20,000 on the $100,000 of income now forgone is reckoned in the revenue maximizing calculus that dictates the imposition of the 50 percent rate on the income that is earned, on the non-foregone $100,000. The fisc gains (by $10,000); the income loss in the aggregate economy ($100,000) exerts no negative impact on the utilities of those who impose the tax increase.

The radiologist loses the value of post-tax marginal product of one-half his effort ($80,000 out of $100,000) minus the value placed on the added leisure (say $60,000) for a net loss of $20,000. The majority members gain through the enhancement of fiscal revenue ($10,000), but there are no other gains or losses, after sufficient time for adjustment takes place. All under the presumption of constant returns.

The results become quite different when we replace the constant returns postulate with generalized increasing returns. The behavior of anyone who changes the supply of input to the market affects the size of the total economy, as before. But such changes generate spillover benefits or damages to all other participants, and these effects are transmitted outside the fiscal process. The person who earns less income, whether as a result of a tax change or simply as a shift in preferences for leisure, exerts an external diseconomy on all others in the production-exchange nexus.(5)

The decrease in the size of the aggregate economy, measured in total income earned through the market process, reduces the potential for exploiting specialization. The effect is that the output price vector increases relative to the input price vector. Any input is made less productive of value than it would be had the reduction in the economy's size not occurred.

The presence of such non-fiscal interdependence among the income-earning activities of all participants in the economy modifies the decision calculus of the political majority which, in our model, seeks to determine the optimal fiscal exploitation of members of the excluded minority. By assumption, the only available instrument is the rate of tax that may be levied on incomes earned through market activity.(6) But the rate that will maximize revenues is not optimal for the majority when non-fiscal interdependence exists. The objective function of the majority is not restricted to revenues collected from the minority. Because they are also participants in the aggregate economy, members of the majority now have an independent economic interest in the total amount of income generated in the economy, and, hence, in the income earned by each individual member of the taxed minority.

In this setting, the optimal tax rate for the dominant majority to impose on the members of the minority must be lower than that rate that will maximize revenue collections. The majority's maximizing solution will describe a tax rate-total revenue position that is located on the upsloping part of the "Laffer curve" relationship rather than at the extremum.

The member of the majority coalition tries to maximize a utility function determined by own income (y) and the tax revenue:

u(y, [V.sub.r]). (5)

The income level y is determined by economy-wide productivity, which is a function of the aggregate income under generalized increasing returns. Since the tax rate affects aggregate income through the income of a minority member ([y.sub.r]), we can express y as a function of [y.sub.r],

y = g([y.sub.r]) (6)

where g is an increasing function.

The first order condition for the utility maximization (5) is met when

[u.sub.1]dy/dt + [u.sub.2]d[V.sub.r]/dt = 0,

or

d[V.sub.r]/dt = -([u.sub.1]/[u.sub.2])(dy/dt) (7)

where [u.sub.1] and [u.sub.2] are partial derivatives of the utility function with respect to income y and tax revenue [V.sub.r]. The sign of dy/dt is negative by the chain rule

dy/dt = (dy/d[y.sub.r])(d[y.sub.r]/dt) [less than] 0; (8)

where the term dy/d[t.sub.r] is positive because of the generalized increasing returns, and the next term d[y.sub.r]/dt is negative because of tax induced incentive on the behavior of the minority members. We conclude that the sign of d[V.sub.r]/dt in (7) is positive. Total tax revenue is not maximized in this solution.

IV. Capital Introduced

The models of the economy analyzed in sections II and III above are restricted by the simplifying assumption that all income is derived from currently supplied labor services. We now drop this assumption and introduce a model that allows income from both human and non-human capital to make up some share in market returns, and, further, that allows the accumulation of capital generating such income to take place by withdrawal of income from spending on current consumption. With this single change in the assumptions, we can treat the constant returns and the increasing returns cases in sequence.

Constant Returns

We continue to restrict the majority's decision makers to the single control variable, the rate of tax that may be levied proportionately on all income from market activity earned by members of the minority group, R, whether this income be from the sale of labor services or lease or sale of capital goods.

If some share of market income represents a return to capital, then any tax on income will reduce the net return on investment in capital accumulation. This reduction in rate of return may or may not reduce the proportion of income that is saved. But since the tax (or any increase in the rate of tax) reduces the net income available for consumption and saving, the effects on the amount of saving are clear. The rate of capital accumulation in the economy will be reduced as the rate of tax on income increases.

Because of this predicted effect on capital growth, the income stream in all future periods is reduced as the tax rate is increased. In this feature, the model differs from the all-labor income model analyzed earlier, in which the rate of tax imposed in one period has no effect on the income potential for subsequent periods. Does this feature make the decision calculus of the majority taxing authority different?

Consider an example in which, say, the revenue maximizing rate of tax, after full adjustment, on all market income earned by members of the minority is 50 percent, and where the fully adjusted pre-tax income under this regime is $100,000. From this income pre-tax, the fisc extracts $50,000 and the taxpayer retains $50,000. Assume that, from the retained $50,000, the taxpayer saves 22.77 percent, or $11,390. For simple exposition, we assume that the saving is the only source of future income.

Now compare this fiscal regime with an alternative one that involves only a 40 percent rate of tax, with a pre-tax adjusted income of $120,000, with revenue of $48,000 to the fisc, and taxpayer retention of $72,000. If the rate of saving out of income is invariant at 22.77 percent in the two regimes, a total of $16,390 would be saved. In a summary comparison, revenues are higher in the first regime by $2,000 ($50,000-$48,000), while savings are higher in the second by $5,000 ($16,390-$11,390).

Under what conditions would the majority be led to select the second regime rather than the revenue maximizing solution in the first? In the comparison as set up in the example, the majority should be indifferent as between these two regimes if future tax revenue is discounted at the market rate of interest. The second regime generates $2,000 less in current revenue to the fisc, but increases savings by $5,000. This measures the present value of the future income that will be generated when the savings are invested. From this income stream, the 40 percent rate of tax will yield a present value of $2,000, which is equal to the current revenue shortfall the replacement of the first regime creates.

We have, of course, rigged the arithmetical example in order to demonstrate the underlying logic of the differences in the decision makers' maximizing calculus when capital income is introduced. Nonetheless the example is helpful in suggesting several relationships. If the rate of saving from income by the rich is increased (decreased) or if the income response to taxation becomes larger (smaller), the majority's optimizing rate of tax decreases (increases) relative to the strict current revenue-maximizing rate. But this statement must be read with caution. The majority member may still try to maximize tax revenue as defined in present value terms.

On the other hand, an increase in the majority's discount rate makes strict or current-period revenue maximization more likely [3]. We have assumed that the majority coalition is not concerned about the defection of minority members to newly emergent majorities in electoral succession. Dropping this assumption would, of course, dramatically shorten the effective time horizon for the decision makers. But, even under such a restriction, there is no reason why the rate of time preference for majority decision makers need be equal to that reflected in the market.(7)

The discussion is perhaps sufficient to suggest that, once capital income is included in the tax base, the dominance of the revenue-maximizing solution in the majority's decision calculus no longer exists in the strict sense, even within the restrictive limits imposed by the constant returns postulate. There are no non-fiscal interdependencies of the sort treated in section III. But the fiscal interdependencies themselves may operate to temper somewhat the current-period exploitation of the minority, provided only that the members of the majority are rational in pursuit of their own economic interest.

Generalized Increasing Returns

The extension of the analysis to apply to an economy that operates under generalized increasing returns is straightforward. As the discussion in section III above indicated, the majority decision-makers will, in the presence of increasing returns, have a positive economic interest in the total income generated by the activity of members of the rich minority, over and beyond that interest that is effected through the fiscal process.

To the extent that the imposition of a tax on the income of the rich, or any increase in such a tax, impacts on the absolute amount of income that would have otherwise been saved, and ultimately made available for capital formation, insures that the flow of income in future periods is reduced. And this shortfall in future-period income will, in itself, forestall the potential for the exploitation of specialization that a larger market might have brought into being.

The majority decision-maker must include in the maximizing calculus both the effects of the tax on savings and capital formation and the non-fiscal effects that measure the influence of economy-wide increasing returns, directly in the current period and indirectly in present value terms for all future periods. Only if all of these effects can either be ignored altogether or be swamped in significance by a very high discount rate will the solution dictate adherence to the strict revenue-maximizing rate of tax. A formal statement of the decision-maker's maximizing calculus is indicated.

Formal Model

The fiscal interaction between majority and minority members can be formulated as a Stackelberg game in which the majority is the leader and the minority is the follower. The majority member tries to maximize intertemporal preferences

[Mathematical Expression Omitted]

subject to

[Mathematical Expression Omitted];

with

[Mathematical Expression Omitted].

Here [Beta] denotes the subjective time discount factor, r the net interest rate, and superscript f indicate next period variables; the next period income I is the sum of the earned income [Mathematical Expression Omitted] and the capital income from the saving. We express saving (s) as a function of income [y.sub.r]. But this saving function is the result of the optimal decision by the minority member in response to the given tax rate t.

Given the tax rate t, the minority member chooses current and future income levels, [y.sub.r] and [Mathematical Expression Omitted], and the saving s so as to maximize intertemporal preferences

v(c) + [[Beta].sub.r]v([c.sup.f])

subject to

c + s = (1 - t)[y.sub.r]

and

[Mathematical Expression Omitted]

where [[Beta].sub.r] is the time discount factor of the minority member, c and [c.sup.f] are current and future consumption levels; superscript f indicates future variables. The first order condition for the majority's utility maximization problem (9) is

[Mathematical Expression Omitted]

where [u.sub.1] indicates the partial derivative with respect to the current income (y), [u.sub.2] the partial derivative with respect to tax revenue [V.sub.r], and [Mathematical Expression Omitted] indicates the partial derivative with respect to future income [y.sup.f], etc.

Under constant returns, the income of the majority member is not affected by the size of the economy. In this case dy/dt = 0 and d[y.sub.f]/dt = 0, because the tax rate is the only parameter that affects the size of economy in the model. And the first order condition (11) reduces to

[Mathematical Expression Omitted].

or

[Mathematical Expression Omitted].

The first order condition above indicates that the present value of revenue is maximized according to the time discount factor [Mathematical Expression Omitted] of the majority member.

Under generalized increasing returns, however, the assumption (dy/dt = 0 and d[y.sup.f]/dt = 0) does not hold. Instead, to the majority member, his own income is a function of the size of economy and thus is a function of [y.sub.r], the income of the minority member; y = g([y.sub.r]) and [Mathematical Expression Omitted] where g is an increasing function. Then,

dy/dt = g[prime]([y.sub.r])(d[y.sub.r])/dt) [less than] 0;

and

[Mathematical Expression Omitted]

where g[prime], the derivative of g, is positive, and the derivative ds/dt is negative.

Therefore, the optimal level of present value of tax revenue is on the upsloping part of the related and appropriately defined Laffer curve. From equation (11),

[Mathematical Expression Omitted].

The tax rate on the income of the minority that is optimal for a member of the majority lies below that rate which maximizes the present value of the revenue stream, which, in return, lies below that rate which will maximize current-period revenues. This relationship holds regardless of the discount rate used by the majority, even when this rate is infinity, that is, the majority does not care about the future.

V. Expenditure Tax and Income Tax

The formal model introduced above lends itself to an examination of the question: Under what conditions might members of the majority rationally choose to allow minority members to exempt saving altogether from taxation? That is, will a spending tax be selected rather than an income tax?

Assume, first of all, that the discount rate that informs the majority member's fiscal choice is equal to the market rate of interest which, in turn, measures the return on capital investment in the economy. In this setting, as usual, a dollar's worth of saving also measures the present value of future income that can be generated by that saving, as discounted by the market rate.

Even in this restricted model, the presence of economy-wide increasing returns will tilt the balance toward the expenditure tax. Because this tax increases saving relative to that generated under the income tax, the economy's size is increased. There will be some non-fiscal benefits to the majority from the spending tax even if the two taxes are equivalent fiscally.

Under the income tax, equation (10) in section IV describes the consumption saving decision of the minority. The first order condition characterizes the saving decision

-v[prime](c) + [[Beta].sub.r](1 + r)v[prime]([c.sup.f]) = 0 (10a)

where c = (1 - t)y - s, and [c.sup.f] = [y.sup.f] + (1 + r)s; and [[Beta].sub.r](1 + r) is 1 by assumption. The relative price of saving is 1. Under the spending tax, given the tax rate [t.sup.*], the minority member chooses consumption and saving to maximize his intertemporal utility,

v(c) + [[Beta].sub.r]v([c.sup.f])

subject to

c + s= (1 - [t.sup.*])y + [t.sup.*]s

and

[c.sup.f] = [y.sup.f] + (1 + r)s. (13)

The first order condition is

-v[prime](c)(1 - [t.sup.*]) + v[prime]([y.sup.f] + (1 + r)s) = 0. (13a)

The relative price of saving is (1 - [t.sup.*]) which is less than 1. This will induce a substitution of saving for current consumption. Since the tax rates, t and [t.sup.*], are chosen so that tax revenues are the same under the two tax regimes, the outlay on consumption and saving will be the same; the tax revenues being equal, ty = [t.sup.*](y - [s.sup.*]), it follows that (1 - t)y = (1 - [t.sup.*])y + [t.sup.*][s.sup.*] where [s.sup.*] is the saving under the expenditure tax.

Under the standard assumption of concave utility function, the marginal utility of future consumption v[prime]([y.sup.f] + (1 + r)s) falls as saving increases. Thus we obtain s [less than] [s.sup.*], the minority member saves more under the spending tax, thereby increasing the size of the economy with consequent non-fiscal benefit to the majority.

If the current income-generating response to taxation is lower under the spending tax, the majority will prefer to levy the expenditure tax on the minority, even under the constant-returns postulate. The maximal present value of tax revenue is larger under the expenditure tax. This pattern of response is suggested when it is recognized that saving, itself, generates utility, to the person who saves. The spending tax, which exempts this utility-enhancing use of income, allows the prediction of a somewhat lower negative income-earning response than under the income tax [11]. If we introduce the increasing returns postulate in this setting, the relative superiority of the expenditure tax is increased.

The results sketched out above depends critically on the assumption concerning the discount rate used in the majority's calculus of choice. If this rate is higher than the market rate, then the choice is biased toward the income tax base, which will, of course, always generate higher maximum revenues in immediate periods. The simple fact that we do not observe more majoritarian support for the spending tax alternative in political discussion may itself suggest, at least indirectly, that the implicit discount rate in fiscal choice is higher than any market rate, perhaps substantially so.

VI. Qualifications, Extensions, and Conclusions

To this point, we have concentrated attention on the majority's optimizing decision in levying a proportional tax rate either on the income or the spending of the rich members of the political minority. Empiricist critics will immediately point to the irrelevance of the analysis to any real-world polity due to the fact that the tax structures are skewed to incorporate progressivity rather than proportionality in rates. Two comments are in order.

First, the analysis applies, almost without qualification, if we replace the uniform proportional rate with the effective marginal rate of tax, thereby allowing for lower rates over inframarginal ranges of tax base. Behavioral adjustments by taxpayers are made, almost exclusively, in response to effective marginal rates, rather than to average rates of tax. Secondly, the widespread existence of progressive rate structures, accompanied by a political rhetoric that seems to reflect deliberate majoritarian intent to exploit the rich fiscally, suggests that majorities are not rational in their choice behavior. Pareto-superior rearrangements may often be possible that include reductions in effective marginal rates (which may often be beyond optimal limits) along with increases in rates on inframarginal units of base. Majorities can thereby gain revenues, in current and present value terms, while at the same time securing the spillover benefits from an expanded economic nexus. At the same time, members of the class that is differentially taxed can possibly secure the benefits that emerge from a reduced distortion in relevant margins of behavioral choice [8; 2].

The thrust of our argument has been one of demonstrating that the political majority need not exploit the richer members of the polity to the extent suggested in the elementary models of revenue maximization. We suggested, in section III, that the presence of economy-wide increasing returns requires the recognition of the non-fiscal benefits, to members of the majority, that stem from the income-generating activities of the rich. This effect becomes more pronounced as the share of income received by the rich increases and as the predicted negative response to taxation increases.

In section IV, we suggested that, even in an economy with constant returns, the interdependencies produced by capital accumulation may offer rational bases for majoritarian limits on strict revenue-maximizing tax rates and, in some settings, for explicit exemption of savings from taxation altogether.

An important additional qualification on our analysis becomes necessary when we allow for particular differentiation among individuals within each income category. We explicitly assumed that members of the majority (of P and M) are not concerned with electoral sequences involving shifting coalitions. But, also, we implicitly assumed that individual members of these politically dominant groups do not expect to shift economic status over time and thus the majority coalition makes taxing decisions in each and every period. If we drop these assumptions, the analysis will, of course, be changed.

Consider a person who is, say, a member of M (middle income class) in period [t.sub.0], but who expects to be able to move to a higher income class (R) in period [t.sub.1] and beyond. Further, this person recognizes that tax rates put in place in to will tend to remain in place in [t.sub.1] and beyond. In this setting, and depending in part on the subjective rate of discount adopted, the person in question will be reluctant to levy the rate of tax on members of R in [t.sub.0] which would satisfy the conditions for optimality stated formally in our analysis. The implication is that the greater is the upward mobility expectation in the economy, the lower will be the rate of taxation of the rich.

Finally, we shall note again two critical framework assumptions of our whole analysis. First, the economy has been assumed to be closed. In effect, the inclusive production-exchange nexus has been assumed to be coincident in participation with membership in the political unit. Second, the macroeconomic stabilization instruments have been assumed to operate so as to maintain nominal aggregate demand, thereby insuring that employment remains near its natural rate.

If the economy, or parts thereof, is open to external trade, the scale efficiencies that arise from the presence of increasing returns are less pronounced. And a fully rational tax-imposing majority could, in principle, offset the scale effects that result from taxing the rich by, simultaneously, opening up the economy so as to create an expanded scope for specialization. For example, the combined Clinton program of increasing tax rates on the rich and approving NAFTA (North American Free Trade Agreement) may be mutually offsetting along some dimension of effective scale. Whether or not any political majority could be consistently rational over such disparate dimensions of policy may, of course, be open to question. And the successful political history of protectionism does not suggest extensive collective rationality, regardless of the composition of the decision making authority.

In public and media discussion, the macroeconomic impact of fiscal adjustment, whether in taxation, expenditure, or government borrowing, commands primary attention. An increase in rates of tax on the members of the high-income minority is often assessed for its effects on levels of aggregate demand, and, through these effects, on rates of employment and economic growth. The rich will, of course, generate less income, pre-tax, than before the rate increase; the return of tax revenues to the income stream is not sufficient to offset the initial income reduction.

Efficient macrostabilization policy can insure the isolation of this "excess burden" effect, keeping the reduction in aggregate demand in line with the tax-induced reduction in aggregate supply and concentrating net losses on those who are directly subject to the tax rate increases, provided that the economy is described by a constant-returns technology. Under increasing returns, however, this conceptually simple demand-supply equation is disrupted, making macroeconomic adjustment more difficult.

Whether or not the macroeconomic framework parameters operate so as to guarantee even tolerable approximation to stabilization objectives is, of course, a question that we need not address here. We should acknowledge, however, that the "taxation of the rich" that is optimal for the political majority does depend on the actual rather than the idealized operation of the macro-economy. We have basically followed conventional procedure in this respect. We have attempted to analyze the taxing calculus of the majority in isolation from any interdependence with the stabilization calculus.

1. The usage of revenues collected from persons in R may, of course, be used to finance direct transfers to members of M and P before the "efficient" level of collective goods is financed, if "efficiency" is defined to include the evaluations of members of R [16, 373-80].

2. More plausibly, although it would not emerge from the behavioral calculus postulated in the model here, we might expect that the incomes of the rich would be taxed so as to bring post-tax levels down to equality with the incomes of the members of the middle income group [5, 52-77].

3. Brennan and Buchanan have written extended treatments of the determination of the optimal rate of tax in a revenue maximizing model [1,255-73; 2]. In their analysis, they assumed that a monolithic government, separate from the taxpayers, seeks to maximize revenue collections. They did not examine the calculus of the majority in its imposition of taxes on the minority, although the same analysis can be readily applied to this case.

Buchanan and Lee examined some of the implications of temporal adjustments and differential rates of discounts in determining the rate of tax that would be imposed by government [9, 344-54; 10, 816-19]. As in the Brennan and Buchanan analysis, however, they did not extend the model to consider majority imposition of taxes on the minority.

4. We have attempted to bring together the major contributions in the increasing returns tradition in economic theory, from those of Adam Smith, through Alfred Marshall, Allyn Young, Nicholas Kaldor, and including modern contributions in several areas of application [12].

5. Buchanan, alone, and with Yoon have analyzed the economic content of the work ethic in essentially this framework [6; 7; 12].

6. Brennan and Buchanan have discussed the choice of base as well as rates [2].

7. Cohen and Noll have related work on this issue [13].

References

1. Brennan, Geoffrey and James M. Buchanan, "Toward a Tax Constitution for Leviathan." Journal of Public Economics, December 1977, 255-73.

2. ----- and -----. The Power to Tax: Analytical Foundations of a Fiscal Constitution. New York: Cambridge University Press, 1980.

3. ----- and -----. The Reason of Rules - Constitutional Political Economy. Cambridge: Cambridge University Press, 1985.

4. Buchanan, James M., "Externality in Tax Response." Southern Economic Journal, July 1966, 35-42.

5. -----. "The Political Economy of Franchise in the Welfare State," in Capitalism and Freedom: Problems and Prospects, edited by R. T. Selden. Charlottesville: University Press of Virginia, 1975, pp. 52-77. In The Economics of Legal Relationships, edited by H. B. Manne. St. Paul: West Publishing Company, 1975, pp. 78-97. As "The Political Economy of the Welfare State," in The Theory of Public Choice - II, edited with Robert D. Tollison. Ann Arbor: University of Michigan Press, 1984, pp. 174-93.

6. -----. The Economics and the Ethics of Constitutional Order. Ann Arbor: University of Michigan Press, 1991.

7. -----. Ethics and Economic Progress. Norman, Ok.: University of Oklahoma Press, 1994.

8. -----, "Pareto Superior Tax Reform: Some Simple Analytics." Eastern Economic Journal, Winter 1993, 7-9.

9. ----- and Dwight R. Lee, "Tax Rates and Tax Revenues in Political Equilibrium: Some Simple Analytics." Economic Inquiry, July 1982, 344-54. In The Theory of Public Choice - II, edited with Robert D. Tollison. Ann Arbor: University of Michigan Press, 1984, 174-93.

10. ----- and -----, "Politics, Time, and the Laffer Curve." Journal of Political Economy, August 1982, 816-19.

11. Buchanan, James M. and Yong J. Yoon. "Income Tax and Expenditure Tax." Working paper, Fairfax, Va.: Center for Study of Public Choice, George Mason University, 1993.

12. ----- and -----. The Return to Increasing Returns. Ann Arbor: University of Michigan Press, 1994.

13. Cohen, Linda and Roger Noll. The Technology Pork Barrel. Washington, D.C.: Brookings Institution, 1991.

14. Debreu, Gerard. Theory of Value. New Haven: Cowles Foundation, 1959.

15. Feldstein, Martin, "The Rate of Return, Taxation and Personal Savings." Economic Journal, September 1978, 482.-87.

16. Flowers, Marilyn and Patricia Danzon, "Separation of the Redistributive and Allocative Functions of Government: A Public Choice Perspective." Journal of Public Economics, August 1984, 373-80.

17. Kohne, Michael. "The Irrelevance of Paretian Welfare Economics with Respect to Long-term Economic Growth," 1993, manuscript.