Front Page Titles (by Subject) 5.3.: Income and Capital Taxes under Perpetual Leviathan - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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5.3.: Income and Capital Taxes under Perpetual Leviathan - James M. Buchanan, The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution) 
The Collected Works of James M. Buchanan, Vol. 9 The Power to Tax: Analytical Foundations of a Fiscal Constitution, Foreword by Geoffrey Brennan (Indianapolis: Liberty Fund, 2000).
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Income and Capital Taxes under Perpetual Leviathan
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:
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.
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.
An income tax of the standard type includes interest as well as labor income in the tax base.5 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.
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.
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.
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.
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.
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.
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.
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.6
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.
[5. ] 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.
[6. ] 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.