Front Page Titles (by Subject) 3.3.: One among Many - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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3.3.: One among Many - 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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One among Many
In the simple model analyzed in the preceding section, attention was focused on the single individual’s choice calculus. This model need not be nearly so restrictive as it might appear, since we have examined choice in a constitutional setting, where the chooser is not expected to know just what his own position will be in subsequent postconstitutional periods. Nonetheless, we have neglected the problems that arise when the individual recognizes that, regardless of what his own position might be, he will be one among many taxpayers, with differences in public-goods preferences and in tax-base characteristics.
We may first consider whether or not our earlier results concerning tax-base limitations will hold in this setting. We may look at a highly simplified two-person illustration. In Figure 3.3, we assume that two persons, A and B, will earn identical amounts of money income in some pretax or no-tax equilibrium, in the amount Y0. (Recall that, under our constitutional-stage assumptions, the individual will know only that the two persons will have the characteristics depicted; he will not know which of the two positions he will personally occupy.) The two persons are predicted to differ substantially in their response to the imposition of a tax on the limited or money-income base, with leisure (and/or other valued end products) exempted from tax. This differential responsiveness is indicated by the slopes of the “demand curves” for money income, as shown by Da and Db.
The first point to be noted here is that so long as any responsiveness at all is predicted, the argument for the noncomprehensive base developed earlier holds without qualification. Each of the two persons whose preferences are depicted in Figure 3.3 will be protected against the exploitation potential of government that would be present under the full income as opposed to the money-income tax scheme.
Let us now examine the revenue-maximizing government’s predicted taxing behavior in this two-person situation. If the government could treat A and B differently, and separately, and if it could levy a proportional tax on the money income of each person (we assume that a regressive schedule is not allowed), it would impose a tax rate of ta on A and a rate of tb on B. This sort of differential treatment would, under almost all circumstances, allow scope for the extraction of more revenue from the community than would be possible if the government were constitutionally required to levy the same proportional rate on each person, or, stated more generally, to confront each person with the same rate structure or schedule.
On the assumption that positive revenue is extracted from both persons in the uniform-rate case, that uniform rate will lie strictly between ta and tb (tb > t > ta). The revenue-maximizing uniform proportional rate, t, is determined in Figure 3.3, where the “market” marginal revenue curve, MRm, cuts the dollar-price line, with “price” set at the intercept of the vertical drawn from this intersection and the aggregate “demand curve,” Dab.
As suggested in the introduction to this chapter, the requirement that all persons in the community be confronted with the same tax-rate schedule, or, in other words, that persons be treated uniformly, becomes an institutional means of reining the revenue-seeking proclivities of Leviathan. Such an argument for uniformity, which is related to but different from the more familiar “horizontal equity” norm, has not, to our knowledge, been developed in normative tax theory. With respect to horizontal equity, it is perhaps interesting to note that no constitutional rationalization for this principle, per se, emerges from our analysis.
The construction in Figure 3.3 can also be used to illustrate a proposition that seems at variance with that reached in models that assume institutional fixity. In the latter conventional framework, the behavior of individuals within the structure of given tax institutions is analyzed, and any attempt on the part of one person or group of persons to avoid or to reduce tax payments, through recourse to nontaxable sources or uses of income, is interpreted as imposing an external cost or diseconomy on less responsive taxpayers and/or on public-goods beneficiaries.12 Behavior in reducing tax liability generates costs for others in the community by making higher rates of tax and/or lower rates of public spending necessary than would otherwise be required.
But now consider the same issue in our constitutional framework. An individual seeks to limit the revenue potential of Leviathan, while remaining uncertain as to his own position. In such a case, he is benefited by the fact that at least some taxpayers in the community will be able to reduce tax liabilities by shifting into nontaxable options because this will lead to a lower revenue-maximizing uniform tax rate. This result may be shown easily, as in Figure 3.3. Compare the revenue-maximizing uniform rate, t, with that rate which would be revenue-maximizing if the two taxpayers were predicted to be equally responsive in the manner indicated by Db. The uniform rate would rise to tb, with higher revenue collections by government. Therefore, B benefits by virtue of the fact that A responds along Da rather than Db, thereby ensuring that the tax rate is t, not tb. To the extent, therefore, that a person in constitutional choice predicts that some members of the whole set of taxpayers will be able to shift to nontaxable sources or uses of income in postconstitutional periods, his own concern about the fiscal exploitation of Leviathan is correspondingly reduced.
As a final point in this section, we want to consider whether or not our earlier result concerning the relationship among progression, proportionality, and maximum revenue holds in the many-person setting. Recall that, in the one-person setting, the introduction of any progressive features into the tax-rate schedule would tend to reduce the potential maximum revenue that government might extract from the single taxpayer. The problem in the many-person setting becomes much more complex because both the differing behavioral responses and the differing pretax levels of income must be taken into account, within the requirement that uniformity in tax treatment be preserved. Recall that, in the simple two-person setting depicted in Figure 3.3, tb > t > ta, where ta and tb were revenue-maximizing proportional rates upon the two persons treated in isolation from each other, and where t was the revenue-maximizing proportional rate uniformly imposed on both persons. Can total revenues be increased above those raised by rate t if government is allowed to or required to introduce progression? By lowering the rate over some initial ranges of income, revenue collections from A, the most responsive person, will increase. But offsetting this increase in collections from A, there must be, over this range of incomes, a reduction in collections from B, who must be treated uniformly. Beyond this limit, however, collections from B may be increased by setting some rate above t. Whether or not the increase in revenue collections exceeds or falls short of the decrease clearly depends on the relative elasticities of the two persons’ “demand curves” where they cut the horizontal at s + t, the revenue-maximizing proportional rate of tax. If the person designated as A in Figure 3.3 is much more responsive to the reduction in tax below t than B is to the increase in tax above t over the higher income ranges, progression may increase revenues above those raised by uniform proportionality. In other cases, this increase may not be possible.13 The limitations imposed by dealing with a two-person model should be stressed here. What is of importance is the tax-adjustment elasticities of different groups of taxpayers. In terms of the representation in Figure 3.3, the addition of a third person equivalent to A would increase the likelihood that progression would be revenue-enhancing. On the other hand, adding a third person equivalent to B would reduce such a prospect. This result suggests that the relative revenue-generating properties of revenue-maximizing proportional and progressive rate structures depend critically on the distribution of taxpayers among the separate response groups, with separate levels of taxable income.
[12. ] For an explicit discussion in such an externality setting, see James M. Buchanan, “Externality in Tax Response,” Southern Economic Journal, 33 (July 1966), 35-42.
[13. ] Algebraic derivation of the conditions under which different results apply is presented in the appendix to this chapter.