Public Finance in Democratic Process: Fiscal Institutions and Individual Choice
Specific Excise Taxation†
How should taxes be paid? This question has been discussed for centuries, and will continue to be discussed for centuries more. It has not been resolved, either in the formal theory of public finance or in the practical structure of modern fiscal systems. In this chapter, as in the one preceding, this old and familiar question is asked in what is essentially a novel setting. How would the individual prefer to meet his tax obligations over time if he must choose among fiscal alternatives as quasi-permanent institutions? The earlier chapter examined the standard direct tax alternatives. Here the direct tax-indirect tax problem will be analyzed, a problem that continues to occupy an important position in the literature of fiscal theory.
In recent decades, the choice between direct and indirect taxes has been discussed in terms of the now-famous excess-burden theorem, initially stated by Barone,*84 later elaborated many times, and, more recently, subjected to several criticisms. Broadly speaking, it seems correct to say, despite the acknowledged relevance of second-best arguments, most modern scholars would accept the view that, other things equal, direct and general taxes are to be recommended over indirect and specific taxes on both equity and efficiency grounds. Employing the methodology previously applied, I shall demonstrate that this widespread conclusion cannot be supported. As was the case with income-tax progression, the purpose of the analysis is not to defend specific commodity taxation, per se, but to use the traditional direct tax-indirect tax comparison to illustrate the efficacy of the general institutional approach to fiscal choice.
The One-Period Argument Summarized
Almost without exception, the direct-indirect tax comparison has proceeded on the assumption that a choice between tax instruments must be made only in a one-period setting. To my knowledge, no attempt has been made to extend the comparison to a multiperiod or long-run setting; no one has assumed, for analytical purposes, that the tax instrument chosen shall remain in effect over several income- or fiscal-accounting periods. The introduction of such a temporal sequence, along with the concentration on individual choice behavior, is central to the analysis that will be developed. Initially, however, it will be useful to examine briefly the standard one-period model.
Barone demonstrated that, for the individual taxpayer, a direct tax should rationally be preferred to an indirect tax of equal yield. His argument has become one of the textbook examples of indifference curve economics, and it need not be repeated here. Little showed that, strictly speaking, the Barone conclusions follow only when a lump-sum tax is compared with a specific commodity tax.*85 Friedman*86 and Rolph and Break*87 showed that the Barone theorem could be extended from the single individual to the whole community only if all of the remaining conditions necessary for Pareto optimality should be satisfied. These criticisms, which may be summarized as those deriving from second-best arguments, need not affect the analysis to be developed here, since, initially at least, the latter does not go beyond individual choice. In the restricted one-period model, the rational person will always prefer the direct tax over the indirect tax of equal yield for the simple reason that he can in this manner enjoy the widest range of choice.
In order to relate it to the subsequent discussion, the one-period question may be put as follows: Should the utility-maximizing individual, confronted with a determined tax liability, choose to pay this liability through a lump-sum payment, a proportional tax on income, a progressive tax on income, a general tax on consumption expenditure, or a specific tax on the consumption of one commodity? In such a model, the first alternative provides the widest area of choice. The lump-sum tax will be preferred over the proportional income tax which will, in its turn, be preferred over the progressive tax which introduces an additional element of discrimination. The latter tax will, in its own turn, be preferred over the general expenditure tax. And, finally, the tax on a specific commodity becomes the least desired of the lot; it produces the largest distortion in the pattern of earning-spending behavior. These familiar conclusions hold, however, only if the individual is allowed to select among fiscal alternatives separately in each discrete period of time or if the results can somehow be generalized to apply to a sequence of time periods.
Choice Through Time
Let the same question be posed, only assume now that the fiscal alternative, once selected, must remain in force over a whole series of periods, t0, t1, ... , tn. As was the case with the analysis of progression, it will be useful to develop initially a certainty model. Hence the individual is assumed able to predict with certainty, at t0, what his income receipts will be in each of the periods, t1, t2, ... , tn. We shall also assume that his decision, at t0, reflects consideration of anticipated fluctuations in spending plans over time. Viewed from t0, his preferred spending pattern over the whole time sequence is known with certainty; this pattern need not, of course, exhibit uniformity in time.
The choice calculus to be analyzed here is somewhat more complex than that required for the preceding chapter. It is useful, therefore, to establish some general principles of rational behavior for the individual before posing the fiscal decision issue specifically. For convenience, we may assume that the individual saves only in order to retire debt or to accumulate funds for future consumption spending. This is a life-cycle model of saving behavior that is similar to those suggested by several economists in recent years.*88 In such a model, the present value of the income stream, at t0, is equal to the present value of the planned outlay or spending stream.
To avoid confusion, it is first necessary to distinguish between spending on items of consumption and actual consumption of these items. For simplicity here, assume that these acts are simultaneous. This implies that the services of all durable consumption goods are purchased or leased as consumption actually takes place. We now break down consumption spending into two provisional categories, the dividing line between which cannot be rigorously defined. The first includes those consumption services designed to meet what may be called "basic needs." The second category includes those services that are purchased with a view toward meeting "residual needs," which are, in some sense, less urgent than those in the first category. Despite the admitted arbitrariness of any dividing line here, some such order of priorities must exist for almost any individual or family unit. Some needs must be met in the normal order of affairs; others may be met only if the opportunity (in part determined by income) arises.
Orthodox rationality criteria suggest that the individual should equalize the utility per dollar spent on each consumption service in each period. This may suggest that any attempt to distinguish between "basic" and "residual" items is misleading. If income fluctuates over time, however, casual observation indicates that residual items are, in fact, purchased and consumed only in periods of relative affluence. Such behavior would, nonetheless, be irrational in a world of perfect certainty. Here the individual would, through his saving activity, attain results that would be closely similar to those attained under a stable income flow. He should, in other terms, equalize the marginal rates of substitution between any two items of consumption for all time periods, viewed from the planning moment, t0, independently of predicted fluctuations in income receipts or in spending needs, on the assumption that price ratios remain invariant over time. If needs vary as among separate periods, this equalization need not, of course, imply equal consumption flows of either service in separate periods of time.*89
Viewed from the moment, t0, the individual will set out a pattern of saving and spending over the several periods such that, in each period, the marginal rate of substitution between any two goods, say, bread and coal, is equal to the ratio of their prices. If, as an example, we consider the two-season year as a sequence, the rational individual will plan his spending over the whole year to insure that his needs for bread and coal will be equally satisfied, in a relative sense, in each season. He will not skimp on bread during the winter merely because his needs for coal are great. Nor will he gorge himself in the summer because he need make no outlay on coal for current usage. He will, of course, save some share of his income during the summer to meet his varying need for coal over the whole sequence. The example suggests that either income or needs or both can fluctuate over a temporal sequence and that the individual must take such variations into account as he attempts to maximize the present value of expected utility.
After this digression, let us return to the problem of individual choice among fiscal alternatives. Examine now the same alternatives listed above for the one-period model, but assume a multiperiod setting. How will the individual choose to pay his taxes? Or, more correctly stated, how will he "vote" in a collective decision process, elements of interdependence being temporarily neglected? As in Chapter 15, assume either that the pattern of public spending is wholly unpredictable as to benefit incidence or that such spending is committed quite independently from the individual's choice calculus.
Exchange Through Time
The individual will consider his possible resort to the capital market. If this market works in such a manner as to allow the individual both to borrow and to lend at the governmental borrowing rate, the specific commodity tax remains the least desired among the fiscal alternatives listed. If the individual confronts this kind of market opportunity, no temporal distortion need be introduced in his spending stream under any of the tax institutions. Hence, he can simply array the various institutions in order of preference based on minimizing pattern distortion within each period, the setting for the one-period model. Here the one-period results are general; the lump-sum tax becomes the optimal fiscal device.
If, however, the individual cannot borrow at public rates, temporal distortion does become relevant. The objective of the individual is not modified. He will try, as best he can after the imposition of the tax, to maintain the desired equalities in marginal rates of substitution. Assume, now, that prior to his confrontation with tax choice, the individual attains a position of planning "equilibrium." That is to say, he has formulated a pattern of saving and spending over time that will equalize the relevant marginal rates of substitution in the different periods, always viewed only from the moment, t0.*90 He now confronts the tax obligation, which we assume he is able to quantify in present-value terms. He will try to choose that tax instrument which introduces, on balance, the least disturbance in his planned pattern of consumption spending over time. If both income receipts and spending needs are expected to be stable, the orthodox conclusions hold. If, however, we allow for some temporal fluctuations in either income receipts or in spending, these conclusions are modified. Temporal distortion must be considered, and the one-period results no longer are general.
If spending patterns are expected to be more uniform over time than income receipts, the progressive income tax will tend to be optimal as the analysis of Chapter 15 has shown. The question to be asked at this point is whether or not the general sales tax or the specific excise tax might not be preferred, even to the progressive income tax, on similar grounds. The answer seems clearly to be negative under the conditions outlined. Either of these taxes on spending would, in the model where spending needs are more uniform in time than income receipts, introduce familiar in-period distortion that is greater than that under any of the direct-tax alternatives. At the same time, these taxes would represent no improvement over the progressive tax on income in minimizing temporal distortion.
If, however, we modify the conditions and now assume that anticipated spending desires fluctuate more than anticipated income receipts, different results may emerge. For simplicity, assume that income is expected to be stable, but that spending is expected to fluctuate sharply from one period of time to the next. This suggests that, without some recourse to the capital market, the marginal utility of the individual's spending dollar will be expected to vary over time. If "imperfections" in the investing-borrowing market involve sizable costs, the final adjustment attainable by the individual may involve a consumption-spending sequence that allows for rather significant variation in the per-period outlay on certain residual consumption items. Under this set of conditions, a specific commodity tax, levied on a single item or set of items of residual consumption, may well minimize over-all distortion, and hence be preferred, even to the progressive income tax.
Rational behavior on the part of the individual who expects his income and his spending to fluctuate over time dictates that he adjust his consumption in time so as to "bunch" his usage of residual items during periods when the marginal utility of his spending dollar is low. He will plan to satisfy certain residual consumption requirements only during those periods when his level of spending is relatively low, or when his level of income is relatively high. This pattern of behavior need not violate any norms of rationality when it is recognized that temporal substitution among consumption services is clearly possible. Certain items of consumption are postponable, necessarily so. For example, the individual may "need" only one holiday each year. It is sensible for him to plan his holiday for a period when either income receipts are higher than usual or when his desires for remaining consumption items are lower than usual.*91
If the individual does, in fact, tend to bunch spending on residual consumption items, an activity that is surely descriptive of real-world behavior, it seems evident that a tax on a specific commodity or service may, under the proper combination of circumstances, be the most desirable of all the fiscal alternatives posed. The familiar in-period distortion in consumption patterns may be more than offset by the advantages that this tax possesses in allowing the individual to concentrate his tax payments during those periods when the marginal utility of his spending dollar is expected to be low, and, conversely, to escape altogether tax payment during periods when the marginal utility of his spending dollar is expected to be high. The minimization of temporal distortion in the individual's spending plans which this tax instrument allows may more than offset the maximization of the in-period distortion that it also embodies.
As compared with the progressive tax levied on income receipts in each period, the tax on a single item of postponable residual consumption can allow for adjustment in tax liability for fluctuating levels of spending in addition to fluctuating levels of income receipts. To demonstrate this point by a simple example, assume that income receipts are expected to be uniform over time; a family anticipates that, over the next decade, t1, t2, ... , t10, it will receive an annual income of $10,000. The decade is taken to be the relevant planning horizon. During these years, a son is expected to be attending college during t3, t4, t5, and t6. Without any adjustment in the capital market, the marginal utility of this family's spending dollar will be higher during these four years than in other years of the decade. The progressive tax would, in this example with uniform income, require the payment of the same net tax during each year. But this family, if allowed to choose, might prefer to bunch its tax payments for the whole decade in the noncollege years, t1, t2, t7, ... , t10. It may do so, without recourse to the capital market either as net lender or borrower, if the tax should be imposed on some item or set of items of genuinely residual consumption spending, items that the family plans to purchase only during the noncollege years. For example, holidays in Europe may be projected for such relatively affluent periods. Despite the in-period or pattern distortion that a tax on European holiday spending would surely involve, such a tax might, over time, actually expand the range of choice open to the family in question, relative to the situation under any other tax alternative considered.
It is interesting to note that when the whole set of tax instruments considered are arrayed in some order of distortion, the general tax on all spending becomes the least desirable fiscal alternative. The specific tax on a single item, or set of items, of residual consumption spending allows tax liability to be bunched in periods when the predicted marginal utility of spending is low. The income tax, whether proportional or progressive, allows the liability to be spread equally over time in this example where income does not fluctuate. The general tax on spending, by comparison, would require that the family pay a higher total tax precisely during those periods when the "needs" for basic consumption items are greatest. This conclusion is perhaps noteworthy since it runs counter to the familiar argument that the general expenditure tax may be more "efficient," in some sense, than the income tax because of the removal of discrimination against saving. The contrast in results here stems from the fundamental difference in approach to fiscal choice.*92
Many other examples could be constructed by using differing assumptions about predicted fluctuations in income receipts and in spending plans over time. These need not be elaborated here since the main purpose of the analysis is showing that under some conditions the rational person may prefer to meet a fiscal obligation through the specific commodity tax.
The results of the analysis are strongly reinforced when we relax somewhat the rationality assumption. If moral scruples, the "Puritan ethic," influence behavior in the direction of making individuals "live within their incomes" and cause them to consider "eating up capital" or "going in debt" to be repugnant or, at best, imprudent, the marginal adjustments necessary for achieving any planned "equilibrium" pattern of spending may not take place. The marginal rates of substitution among items of spending will not be equated in separate time periods, even when viewed from a single moment. As such departures from any rationally planned equilibrium become more significant, the possible advantages of the specific commodity tax become larger.
The rationally planned pattern of spending is, of course, one normative version of the permanent-income hypothesis, either in the limited horizon, life-cycle sense, or in the unlimited Ricardian sense. To the extent that empirical findings lend support to this hypothesis, in either form, the possible advantages of the specific commodity tax in minimizing temporal distortion in spending are reduced. To the extent that the findings suggest that individuals plan spending largely on the basis of current income receipts and not on permanent income, the relative advantages of the indirect tax instrument are increased.
To this point the individual, whose decision calculus has been analyzed, has been assumed certain as to his future income prospects, future spending needs, and the life of the fiscal alternatives considered. In any real-world setting, of course, uncertainty rather than certainty prevails. As compared with the analysis of the preceding chapter, the distinction between the certainty and the uncertainty models is less marked here, although much of the discussion there can be applied again and need not be repeated. The central point is that distributional considerations which might influence the selection among tax instruments tend to be reduced in importance as genuine uncertainty increases at the moment of fiscal choice. If the individual is uncertain as to his own income prospects over time, and also as to his own basic expenditure desires, he may accept that there are certain criteria which will, roughly and approximately, measure his unadjusted marginal utility of spending in future time periods. He may say something like the following: "If either my income is high enough or my essential spending desires low enough, I shall probably find myself purchasing a boat or a custom-tailored suit and my wife a mink cape. Such items seem now to me to be reasonably good independent measures of the marginal utility of income. Hence, if a tax is laid on the purchase of such items, I can maintain some insurance against being subjected to burdensome tax pressure when my needs for basic goods and services are unexpectedly high or my income is unexpectedly low." In one sense, the choice of the excise on residual and postponable items of consumption spending reflects the same sort of mental calculus that might support a decision to exempt certain basic consumption spending from income tax (more on this below).
In the uncertainty model, we need make no particular assumption about the workings of the capital market. With future income receipts as well as spending plans uncertain, the whole conception of an "optimal" or "equilibrium" pattern of spending over time loses much of its meaning. The individual will, more or less as a natural order of events, expect the marginal utility of his expenditure dollar to vary as among periods. If he could, with some certainty, map out a preferred stream of spending, he might find that attainable resort to the capital market would eliminate any possible differential advantage of the specific excise tax. If uncertainty exists beyond some degree, however, he may find such resort to the capital market impossible.
The individual has been assumed to be motivated by straightforward utility-maximizing considerations. A somewhat broader conception of choice allows for a more complex preference function. The first additional element involves the subjective or "felt" burden of tax payments in future time periods. At the moment of constitutional-institutional choice among tax instruments, the individual may be influenced by his predictions about his own reactions, in later periods, to the institution that is selected. He may realize, for example, that on each tax payment date, the income tax will impose on him a genuine "felt" burden. On the other hand, he may also recognize that, since he pays the tax along with the price of a specific commodity, such a burden may be absent under the commodity tax. This is a fiscal illusion, and the individual in his more rational moments may recognize that he will be subject to it. But he may, deliberately, choose to impose the future taxes upon himself in such a way as to minimize subsequent subjective burdens of payment. Or, conversely, he may recognize that the presence of illusion will cause him to act unwisely in operational fiscal choices concerned with the extension of public activities. And, for this reason, he may choose to reject the excise-tax alternative.
A second possible complexity in the individual's preference function involves his attitude toward his consumption of the residual items. He may recognize that, on occasion, he is the slave of his passions, and because of this, he may choose to place obstacles on his own behavior. Sumptuary taxation can be derived from an individual calculus of choice. Nevertheless, care must be taken to distinguish this attitude from the paternalist or dirigiste one, through which the individual attempts to lay down standards of conduct, not for himself, but for others in the social group (more on this point below).
Problems of Aggregation
Individuals are not, of course, allowed to choose separately and independently the fiscal instruments through which their financial obligations will be met. As in the earlier analysis of the progressive tax, it is necessary to shift from isolated individual choice to individual participation in group choice. The collectivity must select the tax instrument which will, when chosen, be imposed on all members of the community.
The consistency of individual decisions or preferences, one with the other, must be examined. While it may be rational for the isolated person to prefer a privately levied tax on a specific commodity, he may not want the collectivity to impose such an indirect tax. There may exist no substantial agreement on a single commodity or service to be taxed. What one man may think of as a "luxury" good, and its purchase a reasonably good independent criterion for the marginal utility of his own spending, a second man may consider to be a basic and essential item, necessary to life, happiness, and well-being. If wide divergencies of this sort exist, the individual participant in group choice may well abandon any support for excise taxation. On the other hand, members of most political communities are culturally homogeneous to some degree. This suggests that substantial, if not total, agreement may be attainable on a relatively small set of specific commodities that might be subjected to excise levies. To the extent that the required homogeneity holds, indirect taxation may emerge from the group decision process, in which individual attitudes and choices are based, at least in part, on the sort of considerations that have been discussed here. One person, participating in group choice, may estimate his own future consumption purchases of champagne to be a good measure of his relative "welfare" in future periods of time. A second may consider his wife's purchases of perfume a somewhat better indicator. After discussion, argument, and compromise the whole group may agree that a relatively small bundle of commodities, including champagne and perfume, provides a reasonably good index for the marginal utility of future spending for each man.
Elements of paternalism cannot, of course, be eliminated from a collective choice among tax instruments. Each participant in a collective decision, be he voter, political leader, or bureaucrat, has a set of preferences, of "values" not only for himself but also regarding the behavior of others in the community. And since the outcome to be chosen must apply to all members of the group, there is no way that the individual participant can be limited to basing his choices on the considerations of his own future behavior pattern. The point to be stressed here is not the absence of parternalist elements in choice; instead, the emphasis should be on the fact that such elements need not be present to derive individual, and through these, group preferences for specific commodity taxation. Alcohol may be taxed heavily in most jurisdictions because voters and political leaders think that their fellow citizens "should" be discouraged from drinking. But, also, alcohol taxes may be accepted because the potential taxpayer, himself, knows that he can escape taxation by refraining from drink. In some basic, philosophical sense, indirect taxation of specific commodities allows the potential taxpayer more ultimate choice than direct taxation precisely because it is specific. He retains an additional faculty of choice over time, so to speak, because he has available a wider range of alternatives than he would retain under direct taxation. This faculty may never be exploited; indeed, the individual will hope that he will never find it necessary to reduce his net tax payment to zero in any period. But the existence of this wider range of potential choice may be decisive in certain circumstances.
This chapter has not been aimed at providing a normative "defense" of specific excise taxation. The analysis has shown that there exist certain conditions under which such taxation becomes "efficient" for the rational individual taxpayer. The results may be generalized to a community of individuals only if there exists reasonable consensus on a set of commodities or services, the purchases of which provide a criterion for the marginal utility of spending in different periods of time.
At one point the similarity between the imposition of specific levies on items of residual consumption and the exemption of certain items of basic expenditure from the income-tax base was noted. It will be useful to examine these two fiscal devices more carefully, since both are to be found in modern fiscal structures. Both schemes may have been introduced, and supported, at least in part, to include some recognition of fluctuating needs for basic consumption over time, and the relevance of this for defining the tax base. The exemption or deduction of such items as medical care and education from the tax base involves the acknowledgment that, during periods when expenses on these are high, income alone does not provide an adequate criterion for computing tax liabilities. Outlays for residual consumption items provide another set of independent criteria, at the "other end" of the consumption spectrum, so to speak. In either case, the taxpayer retains a somewhat greater freedom of action than he would retain under the general income tax without exemptions. The freedom of the taxpayer to adjust his own liability through a modified pattern of consumption spending is present in both cases, but there is a difference. Under the deduction scheme, the taxpayer can reduce his liability for income tax only by purchasing the specific items, say, medical services or education. Under the specific excise tax, he can reduce his fiscal liability by reducing his purchases of one or a few items, leaving him a broader range of alternatives on which to spend.
One of the interesting by-products of the analysis is the relatively low ranking that emerges for the general consumption or expenditure tax, which adjusts individual tax liabilities to total spending in each period.*93 The case that has been made out for specific excise taxation depends, strictly, on the specificity of the objects taxed. On the basis of an individual choice calculus, it is difficult to see how an argument for general spendings taxation could be derived. The familiar distortion in static spending patterns is, of course, smaller under the general tax than under the specific levies. However, static or in-period distortion can always be minimized with direct taxes on income which are also preferred on the temporal distortion scale.
Notes for this chapter
"ndag"> † The analysis contained in this chapter was developed jointly with Professor Francesco Forte of Turin, Italy, in the spring of 1962, and the argument was first presented that year in a seminar at the University of Exeter, England. The analysis, in a somewhat different form, provides the basis for the paper, written jointly with Forte, "Fiscal Choice Through Time: A Case for Indirect Taxation?" National Tax Journal, XVII (September, 1964), 144-57, and circulated as No. 81, Studies of Government Finance Reprints, Brookings Institution, 1964. I am, of course, indebted to Professor Forte for his assistance in developing the argument, along with any other spillover effects this assistance might have had on other parts of this study.
E. Barone, "Studi di economia finanziaria," Giornale degli economisti (1912), II, 329-30, in notes.
I. M. D. Little, "Direct Versus Indirect Taxes," Economic Journal, LXI (1951), 577-84.
Milton Friedman, "The 'Welfare' Aspects of an Income Tax and an Excise Tax," Journal of Political Economy, LX (1952), 25-33, reprinted in Essays in Positive Economics (Chicago: University of Chicago Press, 1953), pp. 100-16.
Earl R. Rolph and George Break, "The Welfare Aspects of Excise Taxes," Journal of Political Economy, LVII (1949), 46-54.
For a summary discussion that contains references to the other works, see M. J. Farrell, "New Theories of the Consumption Function," Economic Journal, LXIX (1959), 678-96.
For each time period, the standard necessary conditions hold. One of these is,
If we assume that the individual has no control over the income that he earns, and, further, that income payments are lagged by one period, the over-all income constraint becomes,
We are concerned here only with the individual's calculus at t0. The fact that, when t1 arrives, he may have a different set of "optimal" plans need not concern us. On this latter point, see Robert H. Strotz, "Myopia and Inconsistency in Dynamic Utility Maximization," Review of Economic Studies, XXIII (1956), 165-80.
Care should be taken to distinguish postponable items of residual consumption from durable consumer goods. The durable goods-nondurable goods distinction need not concern us here, and we have assumed that all services are purchased as they are actually used. A postponable service is characterized by some nonrecurrence of "need" over time.
The relationship between the analysis here and the traditional "double taxation of saving" argument should be explained. This latter argument, as developed by J. S. Mill, Irving Fisher, Luigi Einaudi, and others, supports the imposition of a general expenditure tax in lieu of a general income tax on efficiency criteria, holding that any income tax tends to discriminate against income that is saved. This argument assumes meaning, however, only when the distribution of the tax load among separate persons is introduced. It is not relevant here since the analysis is limited, specifically, to the calculus of a single potential taxpayer who is placed in the position of choosing among several instruments of payment. In the life-cycle pattern of saving behavior postulated, the present value of future spending must equal the present value of income receipts. If the individual is taxed on income received in each period, including income earned as a return on saving from previous periods, the rate of tax would tend to be somewhat lower than that rate which would be required to produce an equivalent present-value tax liability under some general expenditure tax.
The general expenditure tax is assumed here to impose a pattern of final incidence among individuals in relation to spending. This is not the place to introduce complex issues of incidence theory. However, it may be noted that, even should the final incidence of the tax not be in this pattern, the analysis traced above will hold so long as, when he considers the alternatives, the individual thinks that the incidence will be proportionate to spending.
End of Notes
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