Public Finance in Democratic Process: Fiscal Institutions and Individual Choice
In this chapter income-tax progression will be examined in the constitutional-institutional framework introduced in Chapter 14. Under what conditions, if at all, will the individual choose a tax structure that embodies rate progression on an income base?
This analysis may be clarified by its contrast with the traditional approach to income taxation. In the latter, progression in a rate structure is explicitly discussed in terms of externally selected ethical norms. That is to say, progression is either justified or attacked on grounds of its agreement or contradiction with a set of norms for fiscal organization that are chosen by the observer, who conceptually stands outside the whole system. Modern economists have advanced in sophistication over the English utilitarians in that they have recognized the necessity of introducing such norms. Henry Simons, who followed Adolf Wagner in this respect, openly and avowedly based his own argument for progressive income taxation on the desirability for greater income equality among persons and families, a social objective that the fiscal structure "should" be organized to promote.*81 More recently, such scholars as Paul Samuelson*82 and Richard A. Musgrave*83 have distinguished the redistributive function of the fiscal mechanism sharply from the allocative function, and, for the former, they have suggested the necessity of introducing external ethical norms.
Progressive income taxation can be fruitfully discussed in such terms. Nevertheless, it is also true that, to the extent that value judgments enter the discussion, genuine "scientific" analysis comes to an end. It follows that if progression, or any other institution, can be discussed meaningfully without the introduction of external norms there are net methodological gains. This is not, of course, to suggest that normative discussions cannot be helpful. I suggest only that such discussions can best be postponed until analysis on a prevalue basis is fully exhausted.
What the institutional-choice approach does is to allow progression to be examined in an individualistic reference system. That is to say, we are enabled to analyze the choice calculus of the individual as he evaluates alternative tax structures, one of which is a progressive tax on income. It is not necessary to assume a position as external observer, and progression need not be discussed only in terms of its impact on a set of separate persons at different income levels. One way of putting this point is to say that, whereas orthodox analysis has considered progression largely, if not exclusively, in terms of redistribution among persons, the analysis here allows progression to be treated as one among several alternatives of individual choice. Both the proponents and the opponents of the neoclassical utilitarian argument in support of progression, including its modern counterparts, have overlooked the fact that interpersonal comparisons of utility need not be introduced. Progression has been discussed almost exclusively in terms of the relative tax loads imposed on Tizio and Caio. The analysis here transforms the problem into one of choice among institutions faced by Tizio alone.
What makes this difference possible? The orthodox model requires that attention be devoted to single, isolated events located precisely in time rather than to a series or sequence of events extending over time. Implicitly the standard analytical model assumes that relevant choices are among uniquely timed events. The traditional posing of the tax problem is: If the government must raise X dollars of revenue in Period t0, how much of this sum shall be raised from Tizio and how much from Caio? Progression, proportion, regression, and other terms descriptive of a rate structure are taken to refer to comparative rates imposed on the separate persons, these being, in turn, arrayed with respect to some income or wealth characteristic.
A cursory examination of real-world political process suggests that tax issues are rarely, if ever, presented in so simple a manner as the traditional discussion suggests. Tax institutions are selected independently of spending programs, but, also, choices are made among instruments that are expected to remain in being over an extended and usually intermediate number of fiscal-accounting periods. When this fact is acknowledged and when its implications are incorporated into the analysis, the question of rate structure can be treated as a problem of individual choice, and the utilitarian dilemma of interpersonal incomparability at least partially resolved. There can exist an individual choice among tax instruments, all of which may, in any one specific period, subject the taxpayer to the same charge.
Before comparison can be meaningful, however, alternatives for choice must be made roughly equivalent in quantitative impact. Familiarly, economists have employed the equal-yield assumption as a means of evaluating various taxes. Since the model to be used here implies a whole series of time periods, we may adopt the constraining assumption that the tax alternatives to the individual embody equal present values of future tax obligations. This provides a substitute for the equal-yield-per-period model of orthodox analysis. With this assumption of equal present values we can proceed directly to discuss the individual's choice among various tax instruments, independently of the positions of other individuals, at least initially. The following section develops the analysis under conditions of certainty. In a later section, uncertainty is introduced, with interesting consequences for the results.
Institutional Choice Under Certainty
Consider now a political community faced with the problem of choosing a tax institution independently of public expenditure programs. To simplify the analysis, we shall introduce an assumption with regard to the spending side that will enable us to limit discussion to the tax side. The community is faced with the necessity of meeting an annual interest charge of X dollars on a deadweight public debt. We assume further that, through some collective decision rule, the distribution for the liability of meeting this debt service obligation has been determined, not for any specific period, but rather in terms of some specific assignment of present-value liabilities. Each person has assigned to him a defined share in the total community liability that the necessity of servicing the debt represents. This rather unusual assumption allows us to neglect initially the whole question of distribution of tax shares among separate persons.
In the private economy, when an individual is confronted with a fixed present-value liability, we do not normally think about his selecting or choosing an institution of payment, although we recognize, of course, that different individuals will meet such obligations differently. Some will act to discharge the obligation immediately; others will schedule regular payments over time; still others will only service the outstanding debt, leaving the principal sum unchanged. The private economy is organized so as to allow each person wide degrees of freedom in choosing privately the most preferred means of meeting an obligation of this nature. Conceptually, we could think of separate individuals meeting their own shares in a public or aggregate liability individualistically and voluntarily. Each person in our model, assigned a specific share in the liability represented in the public debt, could select his own means of payment, and different persons could be allowed to select different instruments.
We move somewhat closer to fiscal reality, however, if we require that all members of the group meet their obligation under the same institution of payment. Let us limit consideration to three fiscal alternatives: an annual tax of equal amount each year, a proportional tax on income, and a single progressive tax on income. We define these three alternatives in such a way that the reference individual, any member of the group, is presented with the same present value, this representing his own assigned share in the total community liability. These present-value liabilities must be defined with respect to an objectively determined discount rate, which we postulate to be that rate at which the collectivity, the government, can borrow funds in the market. If, instead of this, some subjective or personal rate of discount should be used, equality in present values would simply be another way of defining the three alternatives to be equally preferred by the individual. Choice would be eliminated, which is precisely what we want to examine. In addition, the total of individual liabilities need not add to the total community liability under this sort of computation. If, however, present values are computed by some objective discount rate, equal for all persons, then equality in these values for the three separate fiscal alternatives need not imply that the individual will be indifferent among them.
Faced with the choice posed in this model, the individual will first consider possible resort to the capital market, either as a lender or as a borrower of funds. If this market works in such a way that allows the individual to lend funds or to borrow funds at the same rate at which the government borrows, the individual's own subjective discount rate will be brought into line with that rate which is employed in defining the liability. In such a case, he will remain wholly indifferent as among the three tax alternatives, regardless of his anticipations as to income and spending needs, because he can, at no net cost, convert any one time stream into any other. His own most preferred time stream of spending will not, in this case, be affected at all by the choice of the tax instrument that is imposed on all members of the group. If, however, the capital market does not operate so as to produce these results, the individual may be led, by ordinary utility-maximizing considerations, to prefer one of the three taxes to the others. If he cannot lend funds or borrow funds at the objective discount rate that is used to define the liability with which he is confronted, but must, instead, lend or borrow at different rates, he will prefer that fiscal alternative that will minimize the distortion from his own optimal time stream of spending.
It is reasonable to assume that the individual can always lend funds at the government borrowing rate; he may do so by purchasing government securities. However, private individuals cannot normally borrow at rates equal to those at which governments can borrow, for obvious reasons. Some differential over and above this rate must be paid. If this direction of difference is accepted, and if the individual expects his income to rise over time, rational choice will dictate that he "vote for" meeting his obligation through the progressive income tax, provided only that his planned or preferred stream of private spending is more uniform than that of anticipated income receipts.
A Numerical Example
Assume that the reference individual knows with certainty that he will receive $1000 in the current time period t0, and that he will receive $2000 in the following period t1. We limit the analysis to two periods. Assume now that a total fiscal liability, defined at the beginning of t0, amounting to $976.19 is assigned to this individual. The discount rate is 5 per cent.
This obligation may be met by a tax of $500 in each of the two periods; by a proportional tax levied at 33.6 per cent of income received in each period; or by a single-step progressive tax on income in each period, with a rate of 50.6 per cent on all income above a $500 exemption. This third alternative is, of course, only one among many possible progressive rate structures. It is chosen here because of its numerical simplicity. The details of the situation are set out in Table 15.1.
This numerical example makes it clear that if the individual's preferred time stream of private spending is more stable than his anticipated income stream, the tax obligation can best be met through the progressive levy. This allows him to meet a disproportionate share of his liability during the period when his income receipts are high, thereby eliminating or reducing the necessity of his entering the loanable funds market to borrow at private rates of interest. In effect, the progressive tax scheme allows the individual to "borrow" from the government, at the public borrowing rate, by postponing his tax liability through time.
This model need not be nearly so restrictive or rarified as the various assumptions make it seem. The essential requirements are that desired or planned private spending be related in some way to permanent income rather than to annually measured income and that the latter be expected to increase over time. Both of these seem plausible enough, and both have been supported by empirical evidence.
As presented in this model, we have assumed that public spending in each period is limited to servicing a deadweight public debt. It is easy to see that this assumption can be replaced by one that allows public spending on almost any mix of collective goods, provided that the individual does not expect, on the average, to be benefited differentially. In other words, the analysis holds without change if the distribution of benefits from whatever public services that may be provided is expected to be determined on some essentially random basis.
From Individual to Group Choice
The whole analysis remains highly restricted, however, in that it is applicable to the choice problem as this might be faced by the single, isolated individual. To be relevant for policy discussion, the analysis must be extended to the collective outcome for the whole community of persons.
A difficult adding-up problem arises when we shift from the isolated individual decision calculus to that of a group of individuals. Assume, now, that the collectivity, as a unit, must reach agreement as to one of the three fiscal alternatives. This outcome, once selected, will be then imposed on all individual citizens. We want to examine the process through which agreement might be attained.
If we continue to assume that each person has assigned to him a fixed share in some total community liability, or else a fixed proportion of variable aggregate liability, general agreement among large numbers of people seems possible. This is because, for the majority of taxpayers, incomes will be expected to grow over time, and private spending patterns are, ideally, more stable than income receipts. However, it becomes clear that by continuing to assume away the basic distributional issue at this stage, we are neglecting the central and indeed the critical problem in tax choice.
Assume, therefore, that there exists no such pre-choice assignment of personal fiscal liabilities, even in present-value terms. Instead, we now assume that the whole group, as a collectivity, must reach some decision on assigning the appropriate shares as well as some decision on the tax institution through which the individual tax bills are to be paid.
Regardless of the prevailing set of rules for reaching collective decisions, whether this be Wicksellian unanimity, simple majority voting, or something different, the problem quickly becomes one that is dominated by pure bargaining and the results are, of course, unpredictable. Presumably, some allocation of shares among persons will be chosen, but a great amount of investment in strategic bargaining effort may be observed to take place. Once a bargain is struck, once a "solution" as to the proportionate shares is reached, the individual calculus discussed above might come into play. Here the individual, whatever his final lot in the bargain, should rationally prefer to pay his share through the institution of progressive income taxation, given the suggested side conditions. In the process of bargaining on the assignment of shares, however, the institutions for collecting revenue take on wholly different characteristics from those that these same institutions possess in the individual calculus. It is this interdependence between the bargaining on shares in the tax bill, the distributional problem, and the efficiency problem that confounds both choices, and the analysis of choice, here. Because of this interdependence, tax institutions become means of assigning shares.
If it were possible to conceive of a separate bargaining process in which liability shares are assigned, but where the choice among institutions of payment is not settled, the distributional and the efficiency aspects could be distinguished. Interdependence almost necessarily arises, however, especially when additional constraints and side conditions are placed on the structure of the bargains or the workings of the institutions of payment. The individual who should, rationally, prefer the progressive income tax as the efficient means of meeting his own share of community liability may, also rationally, oppose this tax if a side condition is imposed to the effect that rates of tax must be uniform over separate persons. Through such conditions as these, the tax alternatives necessarily become counters in the bargaining game.
A Numerical Example
An extension of the earlier numerical example, summarized in Table 15.1, will clarify this somewhat complex point. Assume now a two-man community, and, as before, a two-period sequence. The first man, whom we may call A, is the one whose income prospects have been set out in Table 15.1. The second man, whom we shall call B, anticipates a somewhat lower income stream than his fellow citizen; B's income prospects, again assumed to be known with certainty, are set out in Table 15.2.
Let us, for now, assume that the distributional or share-assignment problem has been resolved and that B has a present-value liability of $748.80 as compared with A's, $976.19. Note that this figure for B is computed by imposing the same proportional rate on measured in-period income as that imposed on A under this alternative, or a rate of 33.6 per cent. As with A, B should also "prefer" to meet this obligation through the payment of a progressive tax, as Table 15.2 shows, with the suggested side conditions. If we choose the same form of this tax as that discussed with reference to A's choice, a single-step progressive structure, with a flat rate above the $500 exemption, B must pay a rate of 59.7 per cent. Note that this exceeds the comparable rate for A, which was 50.6 per cent.
The interdependence between the share-assignment problem and the institutional efficiency problem is evident in the example. It is not possible that both uniformity in rates among separate persons and predetermined liability shares can be maintained over more than one tax alternative. In the example, an equalization of proportional rates, as between the two persons, implies discrimination in progressive rates that would generate the same present-value revenues. The converse also holds, of course. An equalization of progressive rates would imply some discrimination in proportional rates.
The individual or group with the higher-income anticipations, A in the example, will bargain for a distributional solution that reduces his own liability. In so doing, he will find that distributional advantages can be secured through the selection of tax institutions themselves under the side condition of rate uniformity. Recognizing this, A will argue in favor of the imposition of uniform annual taxes, or the institutions nearest to this alternative that seems practicable. Individual B, in the example, the person with the relatively low income prospects, will behave in the opposing fashion. He will argue for the progressive tax, under the most extreme rate structure possible. Individual A, the high-income receiver, finds that distributional and efficiency objectives come into conflict, and, in the normal case, the distributional elements assume considerably more importance. Hence, we should expect the traditional intergroup conflicts over tax institutions. The individual who expects to receive the relatively higher income is led to support the selection of fiscal institutions that are inefficient because of the nature of the political bargaining process in which he must engage.
At this point, our whole analysis seems to be back where it started. If a "social compromise" or "agreement" on tax institutions cannot be worked out without the introduction of purely distributional considerations, the tedium of analyzing the decision calculus of the single, isolated individual may appear to have been useless. To say that, if he could separate the efficiency considerations out, the individual should rationally prefer the progressive tax, really says nothing at all if such a separation is shown to be impossible when participation in group choice is introduced.
Fiscal Choice Under Uncertainty
To this point in the analysis, however, the individual has been assumed to be able to predict future income receipts with certainty. The analysis is interesting here in that, when uncertainties are introduced, some of the complex interdependencies tend to disappear. In a certain world, where separate individuals and groups expect particular patterns of income over a series of time periods, the distributional elements of a choice among tax institutions can rarely be put aside. This feature is, however, modified dramatically when individual choice is assumed to take place under uncertainty in regard to future income prospects.
Again it is useful to consider a simplified example. And for present purposes, we need not consider a time sequence at all. Take an individual who faces what he estimates to be an equal probability that he will receive an income of $1000 or $2000 in the current period; he assigns a subjective probability of one-half to each of these prospects. We need now only to assume that his most preferred pattern of private spending is more predictable than his income receipts in order for the analysis developed to hold without qualification. Suppose that we postulate that the individual is to be subjected to a tax which carries a certainty equivalent of $100 and that he desires to maintain a private spending rate of $1400 per period. If he selects an invariant tax, unrelated to actual income receipts, he agrees to pay the flat sum of $100 regardless of his income event. If he selects a proportional tax on measured in-period income, he has a probability of one-half of paying $132 and a probability of one-half of paying only $66. On the other hand, suppose that he chooses a single-step progressive levy, with all income above $1000 exempted from tax. Under this fiscal alternative, he has an equal chance of paying $200 and of paying nothing at all. In the case of low-income realization in the period, his resort to the capital market is minimized under the third alternative. It seems clear that he should, rationally, opt for this scheme.
This single-period model is, of course, highly unrealistic in all respects. If we incorporate uncertainty as to income prospects into a multiperiod model, a more relevant choice situation emerges. In this case, the individual will tend to choose among tax alternatives on the basis of efficiency criteria. Distributional aspects are eliminated to the extent that the individual cannot predict the shape of the bargain that will, in fact, yield him maximum gain.
It is not reasonable to assume that the individual is uncertain as to income prospects in the near future except, of course, to a limited degree. He will tend to know with some accuracy what his income prospects are over a succession of periods subsequent to choice. But it is surely reasonable also to assume that income uncertainty increases as plans are projected forward in time. This implies that the efficiency elements in fiscal choice become relatively more important as longer and longer time horizons are introduced. It becomes possible, in this manner, to conceive of situations in which distributional considerations come to be effectively swamped by efficiency considerations in the individual's own calculus of choice among the tax alternatives. If, for example, we think of a group confronted with an aggregate fiscal liability over time (the benefits from public expenditure programs being distributed in some unpredictable fashion), with each member of the group wholly uncertain as to his own income prospects beyond some intermediate period, each individual may, quite rationally, prefer that the collectivity adopt the institution of progression with specific rates to be levied on all who may qualify as taxpayers by the designated income criteria. This agreement on the choice of a tax institution may take place despite the fact that each individual recognizes that, should he happen to receive the relatively high income, he will bear a major share of the aggregate tax load through time. In such a decision model as this, the problem of assigning shares among persons whose future income prospects are clearly identifiable cannot arise, and each person is led by utility-maximizing considerations to opt for that institution of payment that he thinks will be most "efficient" given some probability distribution of his income expectations in future periods.
Institutional Choice in the Real World
As we have noted, choices in the real world are not made for each period separately. Institutions are selected as if they were semipermanent. This suggests that elements of both the certainty and the uncertainty models may be present in the normal individual calculus. It is reasonable to suggest that at least some measure of the popular support for progressive income taxation in Western democratic societies has been based intuitively on some such "efficiency" calculus as that outlined in this chapter, in contrast to purely distributional motivations.
There are several features of the prevailing institutional structure that confirm this suggestion. For one thing, explicit redistribution of incomes, as such, is not normally introduced into the political commentaries on rate progression, nor, indeed, is this present to any large extent in the fiscal system as it actually operates. Instead of being employed directly as a means of transferring general purchasing power from the rich to the poor, the progressive income tax produces revenues for the financing of "general" or "collective" purposes. The result is, in many cases, net redistribution, but this remains a result, rather than an openly avowed aim except in relatively special circumstances. The sequential model of choice is confirmed by the fact that tax proposals are usually discussed, not as unique annual allocations of fiscal charges, but as quasi-permanent features of a continuing institutional structure. Temporary taxes are explicitly designated as such in the discussion.
All this is not to suggest, of course, that redistributionist arguments or objectives have been absent from the practical political discussion of tax alternatives, on the side of either the supporters or the attackers of progression. The point is rather that there may have been an undue emphasis on the redistributional elements in the choice among fiscal institutions, and perhaps especially by public finance scholars. When models that reflect the actual choice situations more carefully are used, nonredistributional aspects assume considerable importance, and progressive income taxation emerges in a somewhat different light. Egalitarian aims, explicitly avowed as ethical norms, need not be introduced to "defend" the institution of progression, or to "explain" its acceptance in modern fiscal structures.
Again it must be noted that the analysis in this chapter is not intended to be an exhaustive treatment of income-tax progression, even in the reference system of individual institutional choice. The purpose has been that of demonstrating the efficacy, or potential efficacy, of approaching some of the familiar institutions of the fiscal system in terms of the choices that must ultimately confront the individual taxpayer as he participates in some quasi-constitutional collective choice among several fiscal alternatives. The analysis has shown that under certain conditions progressive income taxation may be rationally preferred by the individual, and, at least to some extent, these conditions embody features of real-world institutional choice.
The required conditions may not be present in many circumstances, and the choice behavior of the individual may be predictably different from that suggested above. In the following chapter, we shall outline a set of conditions only slightly different from that postulated here and demonstrate that the individual may choose to pay his fiscal obligations through specific excise levies. Exhaustive treatment would require that many sets of possible situations of choice be examined. As an example, in the models of this chapter, income receipts have been assumed to be determined more or less externally to the individual's own decisions about earning income. This means, of course, that the models have ignored the whole issue concerning the possible effects of progression on incentives to earn taxable income, an issue that has been central to much of the traditional discussion. Alternative models could be introduced in which the individual is assumed to be able to vary the amount of taxable income earned in each period. An extreme model of this variety might allow the individual to adjust income precisely to spending plans in each period. In this case the efficiency argument in support of progression would not hold. If, however, the individual is allowed to vary his income receipts only within relatively narrow limits, and if his preferred stream of private spending is somehow independent of his measured in-period income receipts, the efficiency argument must enter his evaluation. To the extent that the individual, when confronted with institutional choice, does recognize that his own income-earning choices during future periods will be influenced by the tax alternative in existence, and that the progressive tax will introduce differential effects in this respect, the efficiency argument in support of progression is reduced in weight. Even here, however, there may be situations in which the individual will prefer the progressive tax to its alternatives. The distortions in the individual's intertemporal income-earning pattern may be more than offset by the relative improvements in his intertemporal income-spending pattern that progression may allow.
If the basic analysis of this and the following chapters is accepted, certain normative implications follow with respect to fiscal reforms. First of all, the advantages that may be secured from having fundamental decisions on the fiscal structure discussed, enacted, and implemented as quasi-permanent changes, whose effects are expected to endure over a long series of fiscal-accounting periods, become clear. To the extent that the individual as a potential taxpayer and as a participant in collective decisions considers the long-run implications of his choices, the purely distributional influences in these choices tend to be damped. A second, and perhaps more important, general implication that emerges from the analysis is the possible significance of social-economic mobility in affecting individual choice behavior. In a society that is descriptively characterized by the pervasiveness of the "log-cabin myth"; that is, one in which expectations of future income prospects among the young, generally, are buoyant over large subgroups, the distributional aspects of fiscal decisions tend to become secondary. By contrast, in a society that is characterized by a hierarchy of class distinctions which imply corollary income expectations, even relatively permanent decisions among fiscal alternatives may primarily involve issues of interclass or intergroup equity.
There are also important philosophical implications to be drawn from this exploratory discussion of progressive income taxation. If the efficiency-under-uncertainty argument is wholly rejected, as might appear to be the case in some scholarly discussions of progression, the nature of democratic political society itself is called into question. This is a subject about which social scientists, and especially economists, have remained strangely silent. Implicitly, as Wicksell suggested, they have been content to assume a benevolent despotism, a central decision-making authority, the "men in Washington or Whitehall," who, somehow, know what is "best" for other members of the community. This dirigiste vision or model of political order is useful in certain contexts, as we have suggested, but it is at odds with effective democratic process, as this latter has been traditionally interpreted. Once this simple point is recognized many of the policy aspects of modern economic analysis cease to have relevance.
In this book the collectivity is viewed as a set of individuals who seek to arrive at joint decisions for the achievement of mutually beneficial objectives. In this model or vision of political order, the whole manner of looking at most matters of economic policy must be significantly changed. Here we simply are not allowed to introduce external ethical norms to resolve issues of conflict that arise. We cannot rely on an externally imposed objective of "equality," or upon a "social welfare function" to inform decisions about the basic fiscal structure. Somehow, and in some fashion, we must try to evolve collective agreements out of the rational calculus of men as they participate in governmental choice processes. If, in these, men are considered, and consider themselves, purely in terms of immediate and identifiable economic position or status, analysis reduces, simply and quickly, to that of coalition formation. Social and collective decisions represent solutions to zero-sum games, and, as is the case with all such games, one is prompted to ask why the losers continue to play. The answer is, of course, that they enjoy playing and that the game is held to be reasonably "fair" in that losers continually expect to win in subsequent rounds of play. But purely redistributional outcomes are difficult to think about in these terms; the collectivity becomes, all too readily, a means through which the politically strong can exploit the politically weak.
A more encouraging, and in some respects a more realistic, vision of social process emerges from the analysis developed here. The political game is not zero sum; it is, like the economic game, positive sum. Individuals, in their capacities as participants in basic fiscal decisions, are acting without full knowledge of their own shares in the financing of general public services over time. The game has not really been played at the time the rules are chosen, and the levy of progressive income taxation may be somewhat analogous to the familiar "big winner buys the drinks" comment heard at the onset of many a parlor poker game.
Notes for this chapter
The central argument of this chapter was first presented in early 1964 in seminars and lectures at the University of Florida, University of California (Davis and Los Angeles), and Oklahoma State University.
Henry Simons, Personal Income Taxation (Chicago: University of Chicago Press, 1938).
Paul A. Samuelson, "The Pure Theory of Public Expenditure," Review of Economics and Statistics, XXXVI (November, 1954), 387-89.
Richard A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill, 1959).
End of Notes
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