The Power to Tax: Analytical Foundations of a Fiscal Constitution

Geoffrey Brennan.
Brennan, Geoffrey and James M. Buchanan
(1919- )
CEE
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Editor/Trans.
First Pub. Date
1980
Publisher/Edition
Indianapolis, IN: Liberty Fund, Inc.
Pub. Date
2000
Comments

Chapter 5Taxation through Time

Income Taxes, Capital Taxes, and Public Debt

9.5.0

Indeed, the abuse or misuse of the coercive power is so constant a risk that there are in pagan, Christian, and anti-Christian philosophies strong tendencies toward limitation and distrust of the state even where practice tends to exalt it.
—W. A. Orton, The Economic Role
of the State,
p. 64

9.5.1

In the analyses of Chapters 3 and 4, the activities of a revenue-maximizing government were examined in highly simplified single-period settings. In this chapter, we shall modify this single-period aspect of the model in order to introduce several interrelated issues that involve a temporal dimension.

9.5.2

One of the issues that emerges directly concerns the taxation of capital or wealth. In any multiperiod setting, individuals may save (create capital) and dissave (consume capital) in order to allocate consumption appropriately over their anticipated life cycle. They may, of course, also save in order to transmit capital values to heirs. The accumulation and maintenance of capital offers a potential source of tax revenue. We need to examine the implications of making this source available to government, and in particular we must analyze the characteristics of the capital levy as opposed to the income tax in our Leviathan model.

9.5.3

A second issue that emerges concerns public debt. Governments, as well as individuals, may have the inclination to borrow, and they may or may not be assigned the capacity to do so. How do constitutional constraints on the government's borrowing and lending powers complement—or more generally interact with—restrictions on the power to tax?

9.5.4

Questions about capital taxes and public debt must include consideration of more than just the size of the revenue source. In the single-period setting, and assuming the disposition of revenues, the a in the earlier models, to be exogenously fixed, the only criterion in the constitutional calculus is the level of public-goods supply that a particular tax base and/or rate structure is expected to generate. By assumption or analytical convention, the base-rate structure, once chosen, is presumed to generate the same level of revenue, and hence public-goods supply, in any period. In an explicit multiperiod setting, the additional problem of generating an appropriate time stream of public spending must be considered.

9.5.5

A third issue concerns the temporal characteristics of government itself. In a multiperiod setting we must allow for the possibility that governments themselves may change their identity and nature. In this connection, it is relevant to ask what happens if government assumes Leviathan characteristics only occasionally. How, for example, does this possibility influence the individual as he behaves toward the fisc within a succession of budgetary periods? How does the taxpayer adjust his plans in reaction to a threat of a revenue-maximizing Leviathan, even in the current absence of such a regime? And taking such predictions all into account, how does the shift from continuous to sporadic Leviathan—what we here term "probabilistic Leviathan"—influence the individual's constitutional calculus? The inclusive set of constitutional rules or arrangements may well include constraints on government's fiscal behavior that are not expected to be binding during "normal" periods, but which are designed to come into play only when governmental fiscal activity exceeds certain bounds. Such contingency rules become central in an analysis of a probabilistic Leviathan, and these rules may be viewed as offering protection against fiscal abuse rather than constraints on ordinary exercises of the taxing power. Restrictions on the government's power to tax capital and to borrow may take on special significance as contingency rules, even when they would have no particular status under continuous Leviathan assumptions.

9.5.6

Our aim in this chapter is to examine these interrelated issues. Before we proceed, however, it may be useful once again to review the public-finance orthodoxy briefly, for the purpose of emphasizing the distinctions between this orthodoxy and our own approach in application to the issues noted. Following this review in Section 5.1, we examine income and capital taxes in the perpetual or continuous Leviathan setting of the preceding chapters.

5.1. Income Taxes, Capital Taxes, and Public Debt in Orthodox Public Finance

9.5.7

In the traditional public-finance literature, it has long been recognized that a tax on the income from an asset is equivalent to a tax on the asset's capital value. A tax of one type can readily be converted into its equivalent as a tax of the other type. A tax of 1 percent levied on the capital value of an asset yielding 10 percent per annum is equivalent to a tax on current income from the asset of 10 percent. And as Ricardo argued, essentially the same "equivalence" logic can be applied to show that the public debt issue is identical with either of the two taxes: a specific public debt liability, implying future tax commitments to service and redeem the debt, can be converted into its equivalent as a current tax on either capital or income.*61

9.5.8

Our initial concern here is not, however, with the "equivalence" logic.*62 For the purposes of this discussion, we can assume that the taxpayer is subjectively indifferent among the various alternatives on an equivalent net liability basis. But indifference among equi-revenue present-value liabilities at a specified point in time does not imply indifference on the part of a potential taxpayer as among the several fiscal arrangements at some constitutional level. In constitutional perspective, the present values of the liabilities under the several instruments are not specified, and the tax-fiscal arrangements may vary enormously in their revenue potential and significance. Crucial for the citizen's constitutional choice are not his own predicted attitudes toward equivalent liability instruments within a single period, but rather the different possible governmental responses that emerge under access to the various revenue-raising instruments, and in particular with respect to capital taxes and debt. The distinction between the normative implications of the orthodox public-finance analysis and our own approach is critical at this point, and further discussion seems warranted. Public-finance orthodoxy includes the demonstration or proof that, within the assumptions of a rational behavior model, a tax on an income flow is equivalent to a tax on the value of the capital asset yielding the income flow. Further, by an extension of the same logic, especially if the distribution of net liabilities can be assumed away, a somewhat more extreme model of rational behavior allows for a demonstration that the tax on income or capital is also equivalent to an issue of public debt. In a single postconstitutional period, the individual taxpayer "should be," therefore, indifferent among these fiscal instruments, provided only that the rates are adjusted so as to make his net liability identical under each instrument. Given this indifference, which emerges from a postulate of rational behavior on the part of the taxpayer, the alternative fiscal instruments produce identical behavioral responses. The implication is that, on the economist's criterion of efficiency, the three alternatives are perfect substitutes.

9.5.9

We should not, however, lose sight of the implicit assumptions that underlie this familiar logic. The revenue requirements of government are presumed to be settled somehow independently of the taxing process. Here, as elsewhere, the orthodox analysis implicitly commences with: "Given any revenue requirement." Such an approach totally neglects the possible feedback effects that fiscal institutions may exert on the setting of revenue requirements in the first place. And, of course, these feedback effects become central to our whole constitutional analysis. The difference here does not depend on the Leviathan model of government at all. Whether we model government as a continuing Leviathan, as a probabilistic Leviathan, or as a median-voter-dominated majoritarian democracy, differing fiscal or revenue-raising instruments may exert differing effects on the amounts of revenue that governments will seek to raise. Once these effects are recognized, the equi-revenue or equi-liability setting for the orthodox analysis simply becomes irrelevant in any genuine choice among fiscal arrangements at the constitutional level.

9.5.10

In this chapter, we shall retain—except where otherwise stated—the central ingredients of the Leviathan model as outlined in preceding chapters. That is, we assume that government will seek to maximize revenue, but is constrained—by virtue of other elements in the fiscal constitution—to spend some proportion of that revenue on public goods genuinely desired by the citizenry. Purely electoral constraints are, however, taken to be ineffective.

5.2. The Timing of Rate Announcement

9.5.11

In the single-period or instantaneous models discussed in Chapters 3 and 4, it was not meaningful to introduce announcement effects. Implicitly, we presumed that tax rates were announced at the start of the period and that taxpayers made behavioral adjustments in full knowledge of prevailing tax arrangements. Once we introduce a multiperiod setting, however, announcement effects become important and must be explicitly discussed before we examine particular taxes.

9.5.12

Initially, let us consider a simple two-period model in which a Leviathan or revenue-maximizing government is operative in both periods, and in which the government is assigned the authority to impose a capital levy. The two-period model here is a simple extension of one version of the model outlined in Chapter 3. The behavior of only one taxpayer-citizen is examined, and Leviathan is constrained by the restriction that all tax rates are to be proportional. Characteristics of the model are specified in the following way: the individual lives for two periods only; in period 1, he expends effort to derive income from labor, income that he can either consume in that period or save; in period 2, he consumes any income "saved" from the previous period's income, plus any interest these savings have earned, but does not derive any labor income. (To counter possible objections to the "realism" of some of the corner solutions to be discussed, we can assume also that the individual can subsist without receiving either labor or interest income. We may, if we want, assume that subsistence levels are guaranteed by governmental provision of relief payments, payments computed in the a share of total revenues collected.)

9.5.13

Figure 5.1.  Click to open in new window.
Figure 5.1

The in-period behavioral adjustments in this simple intertemporal model can be depicted diagramatically in Figure 5.1. Period 1 labor income is measured along the ordinate. 0A represents the maximum level of consumption, including leisure, that is feasible or possible in period 1. If none of this income is taken in leisure, and all of it should be saved, the maximum feasible consumption of 0B could be attained in period 2; 0B is larger than 0A to the extent that the interest rate on saving is positive. The rate of interest is given by A''B/0A'', where A'' is the abscissa terminal of the 45° line drawn from A. In the absence of tax, the citizen would allocate consumption intertemporally to attain the equilibrium position shown by the point L. He would consume 0J in period 1, save AJ and consume 0K in period 2.

9.5.14

Into this extremely simplified model, we now introduce a capital levy. The effects clearly depend on the extent to which the taxpayer, at the time of his consumption-saving choice, anticipates such a tax. Initially consider the case of extreme ignorance, and suppose that the taxpayer makes his saving decision without taking any account of the possibility of tax at all. He will then behave as he would in the complete absence of tax. That is, he will save AJ in period 1 for an expected consumption of 0K in period 2. Hence, AJ would represent his capital stock at the end of period 1. In this case, and remaining within the limits of the two-period setting defined, a Leviathan government will maximize its revenue collection by appropriating all the capital. In the absence of explicit restrictions to the contrary, it will always pay Leviathan to impose a completely confiscatory capital levy. Regardless of the size of the capital stock, Leviathan does best by appropriating it all. More than this, where the taxpayer does not anticipate any capital levy, Leviathan may do even better by somehow inducing the taxpayer to increase saving in period 1 above that which would be chosen in absence of tax. In Figure 5.1, Leviathan might achieve this goal by preannouncing a tax rate on capital just sufficient to induce the taxpayer to move to the minimum of the price-consumption curve AN'L, shown by M in Figure 5.1. After the taxpayer makes the predicted behavioral adjustment, Leviathan would then levy a confiscatory tax that would acquire all of the capital as revenue. If the price-consumption curve should have its minimum beyond L to the right, beyond the no-tax equilibrium position, Leviathan might actually subsidize accumulation.

9.5.15

Especially in a model where Leviathan is perpetual, however, it is unreasonable to endow the taxpayer with such naive expectations. It is surely more reasonable to move to the opposite extreme and assume that the taxpayer will recognize Leviathan's interests in confiscating whatever capital might be accumulated. In this expectational setting, the citizen will consume all his income in period 1; he will save nothing, and a Leviathan that is limited to a capital levy will obtain no revenue at all. In this case, point A represents the highest level of utility the taxpayer can achieve.*63

9.5.16

Under these conditions, in fact, Leviathan and the taxpayer are locked into a genuine dilemma-type situation.*64 Both could be made better off than at A—the "independent adjustment equilibrium"—but only if a relevant binding agreement can be entered into. For this reason, it is rational for Leviathan to bind itself, even if no explicit constitutional restrictions are imposed by the citizenry. In choosing among all possible rules, Leviathan will select the revenue-maximizing rule—that rule which enables it to "preannounce" the revenue-maximizing tax rate on capital. In this way, Leviathan selects a rate so as to generate taxpayer equilibrium at N' in Figure 5.1, where a line parallel to AB is tangent to the price-consumption curve AN'L. This rate on capital is BY/0B and leaves the taxpayer consuming 0J' in period 1 and saving AJ' for consumption in period 2. From this saving, the tax taken is N'N'' (equal to X'B) leaving the taxpayer with a net consumption in period 2 of 0K'. However, it is quite clear that mere preannouncement of the rate BY/0B is not enough—the taxpayer must believe that this tax rate will in fact apply, and he will only have such faith if the preannouncement is genuinely binding. If it is not binding, the taxpayer may recognize it as such, and retreat to position A prior to the imposition of the tax in expectation of Leviathan's rational strategy of imposing a confiscatory capital levy.

9.5.17

In a sense, the same analysis could be applied to the income tax, and Figure 5.1 could be reinterpreted to apply to the taxpayer's choice between leisure and income-producing effort. As the analysis in Chapter 3 (particularly that illustrated in Figure 3.1) demonstrated, there will be a definitive revenue-maximizing rate of tax, given preannouncement, that enables the taxpayer to respond optimally to the tax. The preannouncement of the tax rate was, in Chapter 3, more or less assumed to be inherent in the fiscal structure. The multiperiod setting under consideration here allows us to raise the meaningful and highly relevant question as to whether the government should be granted power to set tax rates to apply to the income already earned, that is in the period just completed, as distinct from the power to set tax rates on income to be earned in the period subsequent to announcement. Would a perpetual or continuous Leviathan prefer to have the former authority? What we have succeeded in showing with our analysis of the capital levy is that, in the perpetual Leviathan case, the ability to set tax rates ex post might be desired neither by the citizen-taxpayer nor by government. And this result applies equally to all taxes, including the income tax, provided only that taxpayers in their in-period behavioral adjustments are expected to anticipate Leviathan's rational taxing strategy.

9.5.18

It should be emphasized, however, that certain aspects of the discussion on this point are restricted by the simple two-period nature of the model. For one thing, the simple "dominant strategy" character of the dilemma situation in which Leviathan and the taxpayer are placed becomes moderated as we extend the model to include many periods. Even in the absence of any binding agreement and in the presence of some positive saving by the taxpayer, a Leviathan government may refrain from imposing a confiscatory tax over some sequence of periods. It might do better over some initial sequence of periods by encouraging the taxpayer to save something, to accumulate capital, thereby enlarging the revenue base. If the "game" is finite, of course, Leviathan would impose the confiscatory levy during the final period, but with a continuing Leviathan an infinite sequence may be a more appropriate characteristic of the model than a finite one. Modeled in an infinite sequence, whether Leviathan would forbear to impose the confiscatory rate over some periods will depend on such things as its own rate of discount and its predictions of the individual taxpayer's attitude toward risk. If Leviathan's discount rate is very high, it may still be rational to appropriate all capital as soon as it appears. In the same way, if the taxpayer is highly risk averse, he will tend to prefer the certainty of a dollar's current consumption to some probability of more future consumption or confiscation. In this case, Leviathan would find it difficult to encourage the taxpayer to save by merely refraining from the capital levy over some sequence of periods. However, it seems unlikely that a zero saving-confiscatory tax solution would prevail indefinitely: scope for implicit collusion over successive "plays" of the game seems likely to secure at least some of the mutual gains. Nevertheless, a more explicit constitutional restriction relating to preannouncement with enforceability will be preferred by both parties, except in those situations where the taxpayer can be consistently fooled.

9.5.19

An important aspect of the discussion to this point has been the assumption of perpetual or continuing Leviathan. In the one-period models of Chapters 3 and 4, the assumption of a revenue-maximizing Leviathan required no direct consideration of the prospects for perpetuation of fiscal powers. As we move to a multiperiod setting, however, a new issue more or less naturally emerges. How will the constitutional calculus of the potential taxpayer-beneficiary be affected if he predicts that a true revenue-maximizing Leviathan will show up only in the occasional time period? In other periods, a government more closely modeled as a "benevolent despot" may be predicted. Alternatively, nonfiscal constitutional constraints (including electoral rules) may be expected to be operational part of the time. The possibility of Leviathan in any period will, nonetheless, imply that the potential taxpayer's constitutional decision must incorporate such possibility.

9.5.20

In this setting, which we can call that of the "probabilistic Leviathan," two departures from the previous analysis emerge. The first is that it can no longer be in Leviathan's interest to have preannouncement of tax rates. The dilemma situation between the taxpayer and Leviathan discussed earlier depends on the mutual expectation that the latter will continue in existence over some sequence of periods. The second is that, even if preannouncement of taxes is somehow required, the nature of capital is such that significant current or in-period adjustment is not feasible. A distinction arises here between capital taxation and income taxation that is not relevant in the perpetual Leviathan case.

9.5.21

The first of these differences is easily explained. The results of introducing a probabilistic Leviathan are twofold. First, the taxpayer cannot predict with certainty what the tax rate in any period will be. He cannot anticipate that revenue-maximizing tax rates will be imposed, whether these be estimated in simple one-period terms, as in Chapters 3 and 4, or in complex present values, as introduced in this chapter. Any sequence that allows for non-Leviathan government, even probabilistically, becomes less definitive. Second, the occasional Leviathan does not bear the full future period cost of current-period reductions in the tax base.

9.5.22

Consider, for example, an income tax in an environment where Leviathan is operative with probability 1 in 10 and where postbehavioral announcement of tax rates is permitted. When and if it comes into effective power, even for one period, Leviathan can collect all income earned in a single period by announcing a rate of 100 percent after the income has been earned (i.e., after the relevant leisure-effort choices have been made). In the multiperiod perpetual or continuing Leviathan setting, this fiscal behavior would not, of course, be rational because the individual would respond by supplying no tax base in all future periods. Assume that the taxpayer expects the non-Leviathan government to impose a tax rate of 10 percent, but he expects a Leviathan government to impose wholly confiscatory rates of 100 percent, announced after income-leisure choices are made. In the probabilistic setting indicated, the risk-neutral taxpayer will respond to the threat of Leviathan in accordance with his expected tax rate—which is [0.9(10) + 0.1(100)], or 19 percent. If p, the probability of a Leviathan-like fiscal authority, is one-tenth, then the taxpayer, in maximizing his expected utility, in each period will supply the amount of taxable base that he would supply if he faced a certain tax rate of 19 percent in each period. In this case, Leviathan would clearly prefer the possibility of ex post announcement. Correspondingly, the citizen-taxpayer would prefer a constitutional requirement that income-tax rates be preannounced before he makes behavioral adjustments. In the latter case, the taxpayer would always know at the start of each period whether Leviathan is operative or not, and with appropriate planning, he could presumably arrange to transfer leisure intertemporally so that he would earn relatively little income in those periods when Leviathan comes into being.

9.5.23

The advantages of preannouncement to the taxpayer are less dramatic, however, in the case of the capital levy than they are with the income tax. If he is given enough advance notice, the individual can presumably dissave drastically; he can "eat up his capital" and eventually deplete his entire stock of value. But the essence of the distinction between capital (a stock) and income (a flow) implies that whereas a strictly current tax (i.e., one not announced ex post) on income permits behavioral adjustments in leisure-effort choices to occur, a current tax on capital does not permit comparably efficacious adjustment because the capital that becomes the base of the tax is already in existence. Capital does not primarily emerge out of any decisions made currently. The size of the tax base is determined by past decisions on the accumulation of savings and what has been done is not readily undone. Hence, any tax on capital is, by the nature of capital itself, ex post, unless, of course, the tax is to be imposed only on new capital formation subsequent to the announcement. A distinction between capital and income taxation thereby emerges in the probabilistic Leviathan setting, a distinction that is much less striking when a Leviathan government exists continuously. Capital taxation has the effect of permitting the occasional revenue-maximizing government to extend its appetites so as to "enjoy" the fruits of many periods. Income taxation does not have this effect, or at least it does so only to the extent that a tax on interest income is an indirect form of a tax on capital.

9.5.24

Two implications for the individual's constitutional calculus emerge from a recognition of the points made in this section:

1. The citizen-taxpayer should insist on a constitutional requirement that all tax rates be preannounced, and that such preannouncements be binding. At least in the probabilistic Leviathan setting, one could not expect such restrictions to be self-imposed even where taxpayers take full account of the Leviathan possibility.
2. The potential taxpayer should exhibit a constitutional preference for income taxation—and a corresponding antipathy to capital taxation—based on the belief that when Leviathan is probabilistic rather than perpetual, in-period adjustment to avoid exploitative taxation is more feasible under income taxation.

5.3. Income and Capital Taxes under Perpetual Leviathan

9.5.25

We have, in the foregoing section, already indicated one major difference between income and capital taxes in the probabilistic Leviathan setting. In this section, we shall compare income and capital taxes more directly, with a consideration of both the level and timing of revenues. To do this, we return initially to the simple two-period model outlined in the beginning of Section 5.2, in which Leviathan is assumed to be operative in both periods. The essential features of this highly restricted model are:

1. All rate structures must be proportional.
2. We examine the behavior of only one (representative) taxpayer-citizen.
3. In period 1, labor income is earned and "current" consumption may occur. In period 2, no labor income is derived, but interest is earned on savings from the first period. And, of course, "future" consumption may occur.
4. All tax rates are announced in advance.

9.5.26

The capital tax.  We discussed this case in Section 5.2. Using the diagrammatics introduced in Figure 5.1, we know that the equilibrium that will emerge under these assumptions involves the maximum revenue capital levy. The position of the taxpayer is depicted by N'. Present or first-period consumption is 0J'; future or second-period consumption is 0K'. Leviathan obtains a total revenue of N'N'', all of it in period 2.

9.5.27

Figure 5.2.  Click to open in new window.
Figure 5.2

The income tax.  For the purposes of discussion, we assume that leisure-effort trade-offs are such that the revenue-maximizing rate that can be imposed on labor income is 50 percent. And for ease of analysis, we can assume that this revenue-maximizing rate depends solely on the present value of all future and current consumption. This assumption implies that whatever tax is imposed on future consumption, the revenue-maximizing rate on first-period income remains the same. With total labor income being 0A, maximum current consumption is thus given in Figure 5.2 by 0A'. The line A'Q indicates the 45° line from A'. The line A'B' traces the locus of present and future consumption opportunities, given the tax of A'A in period 1. The maximum future consumption, 0B', exceeds 0A' (0Q) by an amount QB' which represents positive interest returns.

9.5.28

An income tax of the standard type includes interest as well as labor income in the tax base.*65 An expenditure tax of the type recommended by Mill, Kaldor, Fisher, and more recently by Andrews and Feldstein does not do so. Hence, such a tax does not distort individual choices between present and future consumption. In discussing the "income" tax, therefore, it is necessary to distinguish among (1) a tax on labor income only, (2) a tax on consumption only, and (3) a tax on labor and interest incomes (i.e., consumption and saving). In this discussion, we assume initially that tax-rate changes between the two periods are not permitted.

9.5.29

Both (1) and (2) lead to a posttax equilibrium at E (Figure 5.2), at which the consumer consumes 0P in period 1 and 0F in period 2. However, the tax on labor income secures all of government revenue, A'A, in period 1; this result stems from the simple fact that no labor income is earned in the second period, by assumption of the model. This tax on labor income can be contrasted with a tax on consumption expenditures. Both these taxes are neutral intertemporally—that is, both leave the relative price of future, as against present, consumption unaffected. Both lead to equilibrium at E. But in the case of the consumption tax, tax collections are spread over the two periods in the same proportions as aggregate consumption is. For this reason, the time sequence of revenue collections is different in the consumption tax case: instead of receiving all revenue in period 1, as under the labor income tax, a proportion 0P/0A' will be received in period 1 and the remaining PA'/0A' will be received in period 2. Aggregate revenue will, however, be the same in present discounted terms.

9.5.30

Let us now consider the tax on "total income" which involves both a tax of 50 percent on labor income in period 1, and also a tax of 50 percent on interest income in period 2. This tax yields an equilibrium at E', which is determined where A'R cuts the price consumption curve from A', where R is such that it falls midway between Q and B'. At E', government revenue is E'E'' in period 2, over and above the amount AA' collected in period 1.

9.5.31

It is worth emphasizing here that, in the absence of explicit constitutional restrictions to the contrary, it would always be in Leviathan's interest to increase the income-tax rate in period 2. It would be perfectly consistent with preannouncement restrictions, for example, to apply a rate of 50 percent in period 1 along with a rate of 100 percent on interest income in period 2. Leviathan would still appropriate A'A in revenue in period 1 but could, in this manner, obtain Z'Z as revenue in period 2, as the taxpayer-citizen adjusts his savings behavior to yield equilibrium at Z, where interest returns are zero. Only if Leviathan is explicitly restricted by some requirement of intertemporal uniformity in tax rates would this prospect be precluded. It is, therefore, worth noting that intertemporal uniformity in rates of income tax does limit revenue potential, except in the special case where the revenue-maximizing rates on labor and interest income are the same.

9.5.32

If these revenue-maximizing rates are different, however, the imposition of uniformity requirements may lead Leviathan to impose an "excessive" tax on current labor income in order to approach more closely the desired rate on interest income. The effects here do not seem likely to be large. As the tax rate on labor income increases beyond the revenue-maximizing limits, first-period revenue falls. And because of the increased tax on future consumption, there is a substitution effect toward current consumption. The increased rate of tax on future consumption must generate sufficient revenue to offset both effects and seems likely to do so only over a limited range.

9.5.33

For purposes of simplifying the analysis here, we have introduced the simple two-period model in which labor income is earned exclusively in one period and interest income in the other. A possible uniformity requirement involves the elimination of intertemporal differences in rates of tax. In a more general setting, a uniformity requirement might involve the prohibition of rate differentials as among separate sources of income, even if these sources yield returns in the same period. The effects of the uniformity requirement would remain the same as those discussed for the more simplified setting.

9.5.34

Figure 5.3.  Click to open in new window.
Figure 5.3

The income tax and the capital levy.  In this subsection, we shall analyze the effects of allowing Leviathan to have access to a capital levy over and above a tax on income. For the income tax, we continue to use the assumptions adopted in the previous subsection. Leisure-effort choices are assumed to depend on the present value of income over the time sequence. From this assumption it follows that a tax on capital that is preannounced could have no influence on the revenue-maximizing rate of tax on labor income in period 1. In this context, the best that Leviathan can do is to levy the revenue-maximizing income-tax rate, in period 1, and then to select the revenue-maximizing capital levy that would generate a final equilibrium such as depicted by N in Figure 5.3. (As noted, we limit analysis to tax rates that are appropriately preannounced.) The income tax reduces maximum current consumption to 0A', and the locus of possible equilibria is shown by the price-consumption curve drawn from A'. The maximum revenue from the capital levy and/or the income tax on interest is achieved at N, where a line SS', parallel to A'B', is tangent to the price-consumption curve. Present- or first-period consumption by the individual is 0PT, future- or second-period consumption is 0FT, and total governmental revenue in present discounted value is AS. Of this intake, A'A accrues from the income tax in period 1; and S'B' accrues in period 2 from the capital levy and income tax combined. The present value of S'B' is A'S. This total revenue of A'S (or S'B') in period 2 can be raised by exclusive reliance on the capital levy, with no income tax on interest income. Or it can be raised from the tax on interest income equivalent in rate to the tax on labor income plus some capital levy. In this latter case, the share of period 2 revenue attributable to the interest income tax, given maintenance of the 50 percent income-tax rate on both labor and interest income, is E'E'', with S'B' minus E'E'' assignable to the capital levy. The revenue-maximizing capital levy will clearly involve a smaller rate in the presence of the tax on interest income than in its absence.

9.5.35

There is, of course, some tax on interest income that would obliterate the revenue potential of the capital levy entirely: the rate would be MB'/QB' (Figure 5.3) and would be well in excess of 100 percent as depicted. Generally, one might assume that rates of tax on interest in excess of 100 percent are infeasible. Taxpayers could simply substitute money balances for interest-bearing assets. In the presence of inflation, however, money is itself depreciating in value over time. Real tax rates on income from all assets in excess of 100 percent become feasible, and have indeed been operative over recent periods in many Western economies. Inflation becomes a form of capital taxation in itself, but it also makes possible rates of tax on interest-bearing assets that may approximate the maximum revenue capital levy equivalent. Of course, this result depends on the fact that the accumulation of consumption goods is costly, but the issue here involves an aspect of inflation that is worth special attention.*66

9.5.36

We can conveniently bring the discussion of this section together in Table 5.1. In this table we show, in the context of our simplified two-period model and for each of the tax arrangements discussed, (1) the revenue collected in each period, and (2) the total revenue discounted to present-value terms. Whether this total discounted revenue figure is meaningful or relevant is an issue postponed for discussion in the following section. The rubrics refer, of course, to those in Figures 5.1, 5.2, and 5.3. As Table 5.1 reveals, these various tax arrangements differ both in terms of the total value of revenue raised and in terms of the time stream of the revenue receipts. Of particular interest, in the light of equivalence theorems that inhabit orthodox analysis, is the distinction here between capital taxation and income taxation.

Table 5.1. Timing and level of revenues under alternative tax arrangements

Tax arrangements Revenue in period 1 Revenue in period 2 Total present value

Capital levy N'N''
(Fig. 5.1)
AX
(Fig. 5.1)
Income tax (labor and interest) (uniform rate) A'A
(Fig. 5.2)
E'E''
(Fig. 5.2)
AI
(Fig. 5.2)
Income tax (labor only) A'A
(Fig. 5.2)
A'A
(Fig. 5.2)
Consumption taxa 0P
(Fig. 5.2)
0F
(Fig. 5.2)
A'A
(Fig. 5.2)
Income tax plus capital levy A'A
(Fig. 5.3)
B'S'
(Fig. 5.3)
AS
(Fig. 5.3)

aOn the assumption that the revenue-maximizing rate is 50 percent, so that 0A' = A'A.

5.4 Leviathan's Time Preference

9.5.37

One interesting question that arises out of the tax comparisons summarized in Table 5.1 concerns the extent to which Leviathan's revenue-collecting strategy may depend on the timing of tax receipts, as well as on the maximum revenue in present-value terms. Initially, we restrict our attention to the two-period model with the perfect taxpayer foresight previously employed. In such a setting, the Leviathan fiscal authority will always choose that tax arrangement which maximizes the present value of its tax receipts provided it is not constrained in its ability to lend, and if it is assumed it can do so at the market rate of return.

9.5.38

Figure 5.4.  Click to open in new window.
Figure 5.4

The "best" arrangement for a revenue-maximizing Leviathan is that in which it has access to both the income tax and the capital levy. It would, of course, impose both at the maximum revenue rate, and it would obtain A'A in period 1 plus B'S' in period 2. This is the arrangement that maximizes the present value of total revenue. Because of the presumed power to lend at will, Leviathan's revenue-raising and consumption activities become completely separable. The present value of total revenue is maximized, and then by lending at the market rate of interest, the resultant surplus*67 is allocated intertemporally in accordance with Leviathan's utility function. We may depict Leviathan's consumption possibilities in Figure 5.4 by the line IK.*68

9.5.39

The assumptions of our model, in which all labor income is earned in period 1, necessarily allocate the major portion of Leviathan's consumption prospects in period 1 if no lending is attempted. (We shall examine the matter of borrowing in more detail below.) Here, we assume that Leviathan's time preference indicates a desire to postpone some consumption to period 2. We need to ask the question concerning the effect of possible restrictions on Leviathan's capacity to lend (invest) at market rates. Suppose, first, that Leviathan is not allowed to lend on the open market; government is not allowed to purchase income-earning assets. However, government might still retain a capacity to hoard; in this case, the consumption possibilities are reduced to IQ in Figure 5.4, where IQ has a slope of unity. In such a setting, will it be possible for Leviathan to allocate his desired consumption intertemporally more effectively by not maximizing present value of tax revenues? There seem to be two instruments which might facilitate this result. Leviathan may find it to his interest to reduce the rate of tax on income and to collect more revenue under the capital levy in period 2 as individuals save more in period 1. The second method would be to use the consumption-expenditure tax.

9.5.40

Consider the first of these possible adjustments. As the rate of tax on labor income is reduced, individuals will save more; this ensures that the maximum revenue capital levy will collect more. Revenue is forgone in period 1, but more revenue is collected in period 2. Whether or not Leviathan will find it advantageous to make this shift depends critically on the rate of trade-off faced. As the tax rate is reduced on first-period income, however, only some share of the extra dividend will be saved by taxpayers. Under normal conditions, the rate of return on the extra savings, along with the initial capital, could not produce a period 2 capital levy prospect for Leviathan that would exceed that which he could have available by the desired share of first-period collections simply hoarded for second-period use. In the geometry of Figure 5.4, the prospects for Leviathan that might be generated by forgoing income-tax revenue in period 1 and substituting capital-tax revenue in period 2 are shown by IN'', which lies entirely within IQ, the latter being the opportunities under hoarding.

9.5.41

Let us now consider the possible intertemporal trade-off that is offered by the consumption-expenditure tax. As the summary Table 5.1 indicates, Leviathan would never rely on this revenue-raising instrument if the objective is to maximize present value of revenue over a time sequence. However, if intertemporal adjustment in revenue use is restricted, and, specifically, if hoarding but not lending is possible, resort to less-than-optimal fiscal instruments may be considered. Since the tax on consumption expenditure wholly eliminates saving from tax, individuals would be predicted to shift more of their own consumption to period 2. In so doing, of course, they carry over, at the same time, more revenue potential for exploitation by Leviathan. If the additional saving generated by a shift to consumption taxation should be relatively great, such a prospect may be effective for a Leviathan whose utility function is weighted toward period 2 use of revenues. Under normal circumstances, however, in this as in the income-tax case, Leviathan, if given the opportunity to hoard revenues once collected, will still find it advantageous to arrange tax structures so as to maximize the present value of revenues independently of Leviathan's own time preference.*69

9.5.42

We may impose yet more restrictive conditions on Leviathan's intertemporal adjustment opportunities. If government is denied the power to hoard as well as to invest at some positive return, resort to non-present-value maximization would seem more likely to be desirable. This situation is not nearly as bizarre as it might seem at first glance. In particular, many lower-level agencies and bureaus operate on a no-carryover basis. Funds made available to such units can be neither invested nor hoarded. If the Leviathan model is interpreted, not as some centralized decision-making monolith, but instead as a useful "as if" model for the very complex set of interdependent arrangements that describe modern governments, the no investment-no hoarding model becomes much more plausible.

9.5.43

In this setting, where neither the investing nor the hoarding of revenue collections is possible, Leviathan must, of course, use revenues gathered in each period. From this perspective, access to both the income tax and the capital levy will clearly dominate reliance on either of these taxes on its own. The relevant alternative for Leviathan's consideration would be a tax on consumption expenditure. Would such a tax prove more desirable than some combination of the income tax and the capital levy? By comparison with the income tax, the consumption tax will encourage the taxpayer to save more in period 1, and to plan on consuming more in period 2. If Leviathan's intertemporal preferences, along with the taxpayer's consumption-saving behavior, fall within specific configurations, it is possible that the consumption tax will be utilized, even when the income-tax-capital-levy combination is available. Under most plausible circumstances, this sort of fiscal arrangement on the part of Leviathan is not likely to emerge. And, of course, any such possible departure from present-value maximization of revenues depends critically on an assumption that neither investment nor hoarding is possible.

9.5.44

The possible departures from present-value maximization on the part of Leviathan that we have examined in preceding paragraphs are made to seem more important than they are by the simplified two-period model we have introduced. In a more general model, of course, some taxpayers will be earning income from labor in every period. Once this point is recognized, it seems almost impossible to construct a scenario that would suggest that Leviathan's interest would dictate departure from those tax arrangements that are predicted to maximize the present value of revenues at each point in time.

9.5.45

Questions such as those discussed in this section arise only if we remain in the perpetual or continuing Leviathan model. If we consider the behavior of the revenue-maximizing government that only occasionally emerges and remains in power for only a single period, rational behavior will, of course, dictate maximum revenue extraction within that period.

5.5. The Time Preference of the Taxpayer-Citizen with Respect to Public Spending

9.5.46

We have already taken account of the taxpayer's time preferences as he adjusts between present and future consumption in the face of alternative tax arrangements. We noted that such adjustments will affect the time pattern of governmental revenue collections. Time preference will enter into the citizen's constitutional calculus in another and different fashion when he recognizes the relationship between the time pattern of revenue receipts and the time pattern of the public spending that those revenues facilitate. Throughout the analysis, we have continued to assume that a proportion of the revenue collected by Leviathan (designated by a in the initial model in Chapter 3) must be expended on public goods. Therefore, the timing of public-goods expenditure will reflect the timing of revenue receipts. Recognizing this relationship, the individual taxpayer-citizen at the constitutional stage may prefer to allocate to Leviathan greater taxing powers than otherwise might be the case, if by doing so a preferred time stream of public-goods benefits can somehow be ensured.

9.5.47

For the purpose of isolating the relevant dimensions of taxpayer choice in this regard, we may reconstruct Table 5.1 to include the taxpayer's consumption of public and private goods in each of the two periods of the simplified model. The results are shown in Table 5.2.

Table 5.2. Levels and timing of public-goods and private-goods consumption under alternative tax arrangements

Tax arrangements Private-goods consumption in period 1 Public-goods consumption in period 1 Private goods in period 2 Public goods in period 2

Capital levy 0J'
(Fig. 5.1)
0K'
(Fig. 5.1)
aN'N''
(Fig. 5.1)
Income tax (labor and interest) 0P'
(Fig. 5.2)
aA'A
(Fig. 5.2)
0F'
(Fig. 5.2)
aE'E''
(Fig. 5.2)
Income tax (labor only) 0P
(Fig. 5.2)
aA'A
(Fig. 5.2)
0F
(Fig. 5.2)
Consumption tax 0P
(Fig. 5.2)
a0P
(Fig. 5.2)
0F
(Fig. 5.2)
a0F
(Fig. 5.2)
Income tax plus capital levya 0PT
(Fig. 5.3)
aA'A
(Fig. 5.3)
0FT
(Fig. 5.3)
aB'S'
(Fig. 5.3)

aAssuming that these are used to generate maximum revenue.

9.5.48

If we assume that all public goods generate consumption benefits in the same period in which they are provided, one attribute of Table 5.2 warrants particular notice. The consumption-expenditure tax allocates public expenditures over the two periods in precisely the same proportion as the individual allocates his private expenditures. Of course, the desired intertemporal pattern of public-goods consumption may differ from the desired pattern for private goods. But there should at least be some presumption that the two desired temporal patterns will tend to be roughly the same. If this presumption is accepted, an a priori case for consumption taxation is established, by comparison with the alternatives set out in Table 5.2.

9.5.49

As previously noted, the striking intertemporal patterns of revenues associated with the income and labor income taxes is partly imposed by the simplifying assumptions of our two-period model. As we extend the analysis to many periods, and to many taxpayers, and allow labor income to be earned in all periods, the intertemporal lumpiness of income-tax revenues disappears. Nevertheless, to the extent that the time pattern of aggregate income and aggregate consumption diverge, there does seem to be something to be said for the consumption base along the lines indicated in the analysis.

9.5.50

If public goods are assumed to be durable, so that they generate benefits over both periods, there may be some preference for expenditure earlier rather than later. In order to obtain the appropriate time stream of benefits, the taxpayer may prefer larger revenues in earlier periods. There does not, however, seem to be any a priori reason for believing that public consumption goods are more durable than private goods.

5.6. The Power to Borrow

9.5.51

In the earlier section on Leviathan's time preference, we examined restrictions on government's ability to lend and hoard as a means of influencing its choice between alternative tax instruments. At that point, we deferred discussion of the power to borrow. The reason for separate treatment of government borrowing is that while this instrument may, of course, provide a means for Leviathan to allocate desired revenue use intertemporally, its major importance stems from the fact that public debt offers an additional revenue source in its own right.

9.5.52

A government's power to borrow (to issue debt) is a power to create current assets which carry an obligation for governments in future periods to pay to the holders of those assets (government bonds) designated sums, presumably to be financed from the tax revenues collected in those future periods. For purposes of meaningful analysis, we shall assume that debt obligations must be honored. A government observed, or even expected, to default could not readily market debt instruments.

9.5.53

The total amount that a government can borrow is or may be constrained in three ways: (1) by the ability of the government to service and redeem the debt—that is, the future revenue capacity assigned to government defined by its constitutionally allowable taxing powers; (2) by the relative preferences of individuals as between government bonds and other assets; and (3) by the general extent to which individuals wish to postpone current consumption (and acquire assets). These possible constraints may be separately discussed.

9.5.54

In the first place, the power to create bonds is futile unless the government also has power to tax. The power to borrow in itself assigns to government no power that is not already embodied in the assigned revenue instruments to which it has access. What the power to borrow permits government to do, within the limits imposed by the other constraints mentioned, is to appropriate now, in some current period, rather than later, the capitalized value of the future revenue streams. Under "perpetual Leviathan" the chief significance of such borrowing power is its effect on the time stream of public spending rather than the aggregate level. The situation becomes dramatically different under probabilistic Leviathan assumptions. Here, the power to borrow implies that the revenue-maximizing government, finding itself in office and not anticipating to remain, may, by means of borrowing, appropriate to itself the full value of tax revenues in all future periods, including those in which such a Leviathan is no longer operative. In other words, the power to borrow effectively transforms the "probabilistic Leviathan" into "perpetual Leviathan" from the viewpoint of the potential taxpayer at the constitutional stage—or at least does so up to the point at which the two other constraints mentioned become operative.

9.5.55

We should note, however, that the time-stream effects of borrowing—under perpetual Leviathan—may indeed be desired, under certain conditions. A recurrent theme in classical (i.e., pre-Keynesian) public finance is the idea of "extraordinary expense" (e.g., wars) and the extraordinary revenue devices that might be restricted to the financing of expenses of this type. Here, constitutional provision limiting government access to potentially large and multiperiod revenue sources might take the form of restricting the use of such sources to periods of fiscal "emergency." The precise definition of such emergency situations is, of course, highly problematic. One would hardly wish to grant Leviathan ready access to enormous fiscal powers by the simple expedient of declaring a state of emergency. Nor would one wish government to have positive incentives to create emergency situations with an eye to their revenue implications. For these reasons, borrowing may be precluded altogether: the legitimacy of its use under the "extraordinary expense" rubric may be simply too dangerous.

9.5.56

Limits to governmental power to borrow, and hence to lay claim to future revenue streams, may also be set by "supply" characteristics of assets markets. If the marginal return on investment declines over quantity, government will find it necessary to pay higher and higher rates on its bonds as it increasingly displaces private investment opportunities. Future government revenue may be exhausted before all private assets are replaced by bonds.*70

9.5.57

Figure 5.5.  Click to open in new window.
Figure 5.5

Finally, limits are set on the ability of government to sell bonds by the maximum level of the community's capital formation. In Figure 5.5, the maximal capital accumulation for the representative individual depicted is given by AM'—the level of savings when the price-consumption curve reaches its minimum at M. Whatever the level of future tax revenues, government cannot acquire more from this person than that level of savings in the current period. But can the governmental Leviathan, finding itself in power for a single period, extract this maximum from the individual as long as we continue to assume that bond purchases are voluntary?

9.5.58

The answer to this question depends critically upon the reaction of the individual concerning the future-period taxation that current-period debt issue purchase implies. If the individual fully discounts the future-period liability that any current-period debt issue embodies, he will recognize that he can escape at least some portion of this liability, in present-value terms, by consuming more in the initial period. In this setting, public debt issue becomes equivalent to the capital levy in our two-period model previously discussed. The maximum revenue that can be secured from the sale of bonds in period 1 is the amount measured by AS in Figure 5.5.

9.5.59

However, much more revenue may be secured by debt issue if the individual does not discount future tax liabilities and modify his consumption-saving behavior accordingly. If the individual whose choice calculus is depicted in Figure 5.5 acts solely in response to the apparently attractive offers of interest returns on bonds, he can be induced to purchase bonds in the maximal limit indicated by the distance AM', the limit at which saving from current-period income is maximized.

9.5.60

When we consider government borrowing, it is also necessary to distinguish between internal and external sources of funds. Such a distinction is not necessary in the treatment of alternative tax arrangements, since government's power to tax externally is prima facie implausible, at least directly.*71 But borrowing involves a voluntary exchange between government and bond purchasers (lenders), and there is no apparent constraint against the sale of bonds to foreigners. This prospect of external debt has important implications for the maximum amount of revenue that Leviathan might raise in a single period, regardless of the possible individual anticipation of future tax liability embodied in such debt. In this case, there is an important distinction between allowing government to have access to internal and external borrowing. If Leviathan can sell debt instruments externally, there is no way that the individual can make offsetting behavioral adjustments even if he fully anticipates the future-period tax liabilities. And if no such anticipation occurs, the maximal saving does not limit debt issue as in the internal debt case.

9.5.61

How much can Leviathan borrow in such circumstances? The limits here are those imposed by the full capitalized value of future-period tax revenues. The governmental Leviathan, finding itself in office, can levy revenue-maximizing current-period taxes and, in addition, can appropriate the present value of all future tax revenues. This finding suggests that the total "burden of debt" will potentially be much larger under external than under internal debt, simply because more debt will be issued in the former case. Constitutional constraints on the ability to borrow externally would, then, tend to be more restrictive than constraints on the ability to borrow internally. But in both cases, the power to borrow implies the assignment to Leviathan government of the power to gratify revenue appetites over the indefinite future, when that Leviathan government is no longer operative. One would, therefore, expect that restrictions on the power to borrow would be particularly severe.

5.7. Conclusions

9.5.62

The highly abstract and simplified analytical models introduced in Chapters 3 and 4 as well as in this chapter have been constructed to demonstrate the dramatic differences in the normative implications for taxation that emerge as between the orthodox model of the benevolent despot and our model of government as a revenue-maximizing Leviathan. The analysis in Chapters 3 and 4 was limited to a single-period or instantaneous model. Under the assumption that a designated proportion of all revenue collections is expended on public goods and services desired by citizens-taxpayers, the analysis demonstrated that Leviathan's revenue-raising proclivities might be efficiently constrained by some appropriate selection of tax bases and tax rates. The analysis of this chapter has extended essentially the same model to a multiperiod sequence.

9.5.63

The distinction between the taxation of income or expenditure on the one hand and the taxation of capital (along with the issue of public debt) on the other becomes especially important in such an intertemporal fiscal structure. If a revenue-maximizing government, whether such an entity be envisaged permanently or only probabilistically, is predicted, the constitutional calculus of the potential taxpayer-beneficiary would probably incorporate severe restrictions on both capital levies and on public debt, except in times of dire fiscal emergencies as described by forces exogenous to the political process. To allow unrestricted access to either capital taxation or to public-debt issue ensures that a revenue-maximizing government may appropriate future revenue potential for current-period usage, a result that the potential taxpayer could hardly be expected to prefer.

9.5.64

The analysis does not necessarily suggest that the consumption tax will dominate the income tax in the rational constitutional calculus of the potential taxpayer. As we have noted, under some conditions, the consumption tax will tend to ensure a more even supply of public goods over time. Further, restriction of the tax base to consumption outlays will reduce the revenue potential of Leviathan, an objective that may in itself be desirable if the income tax is predicted to generate an overly large sum under revenue maximization. That is, saving becomes one possible nontaxable option that may be allowed to taxpayers. A by-product advantage of the consumption base, of course, lies in the additional saving, and additional economic growth, that is generated. Our analysis does not, however, bear directly on this aspect of fiscal choice.

9.5.65

As in the more simplified analysis of Chapters 3 and 4, the results here reinforce what appear to be widely held taxpayer attitudes concerning governmental fiscal powers. Capital levies are viewed with alarm by the ordinary citizen-taxpayer, and we observe debt limitation on the fiscal powers of many modern states. Our analysis here offers the theoretical basis for what may have often been interpreted to be such "gut" reactions to alternative fiscal arrangements.

9.5.66

An important conclusion that emerges directly from the analysis of this chapter concerns the effects of preannouncement of taxes. At the constitutional stage of decision, the potential taxpayer will prefer that governments be required to announce tax rates before the appropriate behavioral adjustments take place. This generalization of the legal precept against ex post facto legislation becomes especially significant under capital taxation, although it is by no means absent from income-tax considerations.

9.5.67

As regards public borrowing, the analysis tends to reinforce classical precepts that limit governmental resort to this revenue-raising instrument to periods of demonstrable fiscal emergency, when extraordinary expenses must somehow be financed. Even in such emergencies, however, constitutional restrictions against external as opposed to internal borrowing may remain in force. As the analysis has demonstrated, resort to external borrowing allows government to appropriate the full value of future revenues. Even if the citizen-taxpayer, at the constitutional stage of decision, projects only the possibility that a revenue-maximizing Leviathan may emerge, rational choice should dictate a preference for quite severe constraints on governmental power either to levy taxes on capital or to create public debt.


Notes for this chapter


61.
It can, of course, be argued that the full discounting of future tax liabilities that is required for full Ricardian equivalence is psychologically and empirically unrealistic, and hence that policy analysis should not be based on it. See James M. Buchanan, "Barro on the Ricardian Equivalence Theorem," Journal of Political Economy, 83 (April 1976), 337-42.

62.
For our criticism of this basic theorem, see Geoffrey Brennan and James M. Buchanan, "The Logic of the Ricardian Equivalence Theorem," Finanzarchiv, Heft 38/1 (1980), 4-16.

63.
We set aside at this stage any limits on taxpayer behavior caused by the recognition that some proportion of revenue is spent on public goods which would otherwise not be provided. This is entirely reasonable if we bear in mind that the taxpayer in question is one among many, each of whom will rationally "free-ride" by avoiding taxes.

64.
The game may be depicted as follows:

Leviathan's strategy
Taxpayer's strategy Confiscatory levy Nonconfiscatory levy

Save something [5,20] [15,10]
Consume everything [10,0] [10,0]

where the taxpayer's payoff is the first-mentioned in the pair and Leviathan's payoff is the second-mentioned. Since the confiscatory levy is dominant for Leviathan, the taxpayer consumes everything.

65.
So, too, would a tax on income measured in the Haig-Simons manner, sometimes referred to as the "net-accretions" conception or definition of income.

66.
It is also an aspect that most conventional "indexing" schemes for income-tax rates ignore. The simple rate-adjustment process as practiced in Canada and Australia cannot handle this problem.

67.
Surplus is a proportion (1 - a) of (maximum) revenue, where a is the proportion of revenues collected that must be spent on public goods.

68.
Both axes reflect maximum revenue in each period scaled down by the factor 1 - a.

69.
Under the consumption-tax arrangement, the locus of potential equilibria in Figure 5.2 is A'B', so that the locus of potential revenue receipts is AB minus A'B', or A'B' (since the maximum revenue consumption rate is 50 percent). Thus, the consumption-tax revenue combination lies somewhere along the line AV in Figure 5.4, and this will lie inside IQ, unless the maximum revenue under the capital tax (B'S' in Figure 5.3) is less than interest on A'A, depicted as QK in Figure 5.4. It is conceivable that B'Q in Figure 5.2 exceeds B'S' in Figure 5.3, but it is not by any means necessary and indeed seems somewhat unlikely. We have drawn it this way in Figure 5.3. In any case, it is clear that for this to be a utility-maximizing possibility for Leviathan, the taxpayer must save a great deal, so that the superior efficiency of the individual as a saver offsets the revenue loss due to the removal of the income-capital tax combination.

70.
Leviathan may be able to compel individuals to buy bonds, or by use of tax or other concessions induce them to do so. We do not examine coerced purchase here.

71.
See the discussion in Chapter 9 on possible tax exportation within a constitutional choice perspective.

End of Notes


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