Front Page Titles (by Subject) V.: Tax Rules and Distribution under Majority Rule - The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy)
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V.: Tax Rules and Distribution under Majority Rule - Geoffrey Brennan, The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy) 
The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy) Foreword by Robert D. Tollison (Indianapolis: Liberty Fund, 1999).
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Tax Rules and Distribution under Majority Rule
Retaining the basic model of majority rule set out in the previous section, we shall proceed to examine the nature of distributional outcomes that emerge from political process in the presence of fiscal restrictions of various types, assuming that tax-transfer operations generate “excess burdens” and generalized efficiency losses for the community. We shall consider, in turn, restrictions imposed on the taxing process and the transfer process, adding an additional restriction at each turn. First, we shall suppose that the constitution restricts the taxing authorities to a single-rate income tax, no other restrictions being applied. Then we shall add the requirement that the income tax be levied at a uniform proportional rate on all individuals. We shall add the further restriction that transfers be paid in equal per capita amounts, in the form of a “demogrant.” Finally, we shall consider a direct constitutional selection of the tax-rate-transfer level.
Flat-rate income tax
Suppose that the majority is restricted to the use of a flat-rate tax on money income in imposing taxes on the minority. That is, although only minority members pay the tax, there is a well-defined tax base, money income, and a single rate applied equally to all minority group members. The significance of this restriction is twofold. First, the single-rate restriction is important because it prevents the majority from levying a tax that discriminates over inframarginal units of the minority members’ money income. Just as a discriminating monopolist can charge higher prices on inframarginal units of product and thereby secure some of the value of the consumer surplus otherwise accruing to the purchaser, so a taxing authority can appropriate some (and in the limit all) of the citizens’ consumer surplus by means of an appropriately regressive tax.9 The requirement of a uniform tax rate across all units of an individual’s income rules out any such prospects.
Second, the requirement that taxes be levied on money income explicitly rules out the power of the majority to confiscate the minority’s asset holdings—something that would be feasible under a wealth tax, for example. Income from assets can be taxed at the same rate as income from other sources, but the assets themselves remain more or less inviolable.10
Several things follow from these restrictions on the tax side. First, there will be, for each individual, a maximum amount of revenue, R*i, that can be obtained from him through the flat-rate income tax. Second, there will be for each individual an associated minimal income level, ni, which he secures, posttax, when faced with the maximum revenue tax rate. Third, we know that the taxing process will inflict net losses on taxpayers, over and above the revenue collected, as individuals are induced by the tax to substitute tax-free leisure for income.
These claims can be readily justified analytically,11 but it is perhaps necessary here only to provide an analogy. We can think of the majority as owning a monopoly right in the sale of the minority’s factor services. The maximum tax revenue obtainable corresponds to the maximum monopoly profit from the sale of those services, and the minority’s minimal income can be thought of as the cost borne by the monopolist of providing those services and accruing to the basic productive factors (in this case, the minority). The excess burden is then analogous to the efficiency losses associated with monopoly.
On this basis, it is clear that the decisive majority will always apply the revenue-maximizing tax rate to the minority’s income. To do otherwise would be to forgo transfers that the majority coalition could obtain. This will not, however, drive the minority’s net money income to zero; tax rates will necessarily fall short of 100 percent. To apply a tax rate in excess of the revenue-maximizing rate will, by definition, reduce the revenues available for transfer to the majority. At the same time, the majority will never willingly impose taxes on itself, because taxes involve an excess burden. Even if the revenue were to be returned to the taxpayer group in lump-sum form, the group would still receive less than would be required to compensate for the imposition of the tax.
Consider, for example, the case where A is in the minority, and B and C are in the majority. Then A will face the revenue-maximizing tax rate and receive a net total income of na, whereas B and C will pay no taxes and will receive R*a to divide between them in some proportion. That is, the resultant outcome will be JA = [na, mb + Sb, mc + Sc], where Sb + Sc = R*a. Analogously, when B is the minority, the outcome will be JB = [ma + S’a, nb, mc + S’c], where S’a + S’c = R*b. The result would be equivalent if C were the minority.
As in the case of unrestricted majoritarianism, we cannot predict which majority coalition will prevail. No outcome exists that cannot be defeated under majority rule. “Cycling” can be expected, as the identity of the decisive coalition continuously shifts. Such cycling is here bounded, however, in the sense that no one’s income can be reduced to a level below ni. Obversely, the best that any group can conceivably do is to receive maximum revenue from both of the other groups. This is, of course, unlikely, but a majority member may have to consent to be taxed in order to provide sufficient revenue to bribe another group to join the majority coalition. Suppose, for example, that JA prevails and that the maximum revenue R*a is split equally between B and C. Then A will seek to form a coalition that is best for himself. If there is more maximum revenue to be obtained from B than C (that is, R*b > R*c), A will attempt to form a coalition with C. In order to do so, however, he may need to pay C more than R*b (if R*b < ½R*a, for example), and A will therefore have to pay some positive tax himself.
Because of the revolving cycles and the general distributional indeterminacy involved here, it is difficult to specify exactly what the expected income will be for each group over the long electoral sequence. However, we can make certain general remarks. First, unlike the case of unrestricted majoritarianism, differential productivity, thrift, and so forth will exercise some influence on the expected distribution because the minimal income that each will receive when in the minority can be expected to reflect basic income-earning capability. There is, then, some substantive meaning here in the notion that some are richer than others. Second, and as in the unrestricted case, the effect of government transfer activity seems likely to be in the direction of equalizing expected incomes. In general, we expect the maximum revenue obtainable from any group to be positively related to the tax-free income of that group. If so, the amount the poorest can expect to receive in transfers will exceed the amount the richest can expect to receive as transfers in absolute terms (and hence a fortiori as a proportion of pretax total income). The net effect is to condense the distribution of expected income over the long electoral sequence, but not to equalize it. In this sense, unrestricted majoritarianism generates expected income that is closer to equality; on the other hand, at each point in the electoral sequence, the observed distribution of income will be more nearly equal in the presence of the tax restriction than in its absence. And, of course, the aggregate of incomes will be predictably higher.
Uniform proportional income tax
We now add to the previous tax restrictions the requirement that taxes be uniform across taxpayers. Under this restriction, the majority must face the same tax rate on money income that the minority faces. However, since there are no restrictions on the use of tax revenues, the majority will rationally appropriate all tax revenues for itself; no transfer at all will be paid to the minority. Accordingly, there will still be cycling in this case. No particular majority coalition will be intrinsically stable, for any outcome can always be confronted with another that is preferred by two of the three individuals.
If it were not for the presence of excess burden in the tax system, this case would not differ from unrestricted majoritarianism. Uniform nondistorting taxes would be imposed by the majority so as to appropriate all the income of each individual. Revenues would then be divided in some proportions strictly among majority coalition members. In other words, the requirement of tax uniformity, in the absence of distortions within the tax system, does not constrain outcomes in any way. But because the tax system does distort—because it imposes an excess burden on majority members that increases at the margin with the tax rate—the majority will not rationally push the tax rate to its maximum revenue limits. Rather, the majority coalition will push taxes to the point where the cost to itself of the marginal dollar raised, including the excess burden imposed on majority members, is exactly one dollar. It is relatively simple to see that this will imply taxation at a rate lower than that required to generate maximum revenue from the minority. Specifically, let us consider tax-rate increases in the neighborhood of that maximum revenue level. An increase in the tax rate adds only a small amount to the net revenue collected from the minority (and hence to the net transfer received by the majority members) but adds substantially to the excess burden of taxation that majority members themselves face.
Specifically, the cost to individual i of raising an additional dollar of revenue consists of two elements: the individual’s share of the tax revenue and the marginal excess burden he faces. That is, Ci = ri + (dWi/dR), where ri is i’s share in the marginal dollar of tax revenue raised. Under a proportional money income tax, ri is simply the ratio of i’s money income to aggregate money income. It is clear that dWi/dR tends to infinity as we approach the revenue maximum, because dR becomes zero at the maximum revenue level. Therefore, the marginal cost to i of an additional dollar of transfer also rises to infinity at maximum revenue. If each majority member shares equally in the tax proceeds (that is, each majority group receives half of each dollar of revenue received), each group will desire a tax rate at which Ci takes the value ½.
Since ri is larger for those with larger money incomes, and given that money income and total income are positively related, tax rates will be predictably lower when the rich are in the majority coalition than when the poor are. The poor therefore will lose relatively less when in the minority than the rich will lose when in the minority. Furthermore, although tax rates will in general be lower than in the nonuniform case, aggregate revenue will tend to be higher than in the nonuniform case since all must pay taxes. This means in turn that gross transfers will be larger.
In summary, the poor will tend to do rather better under the uniformity restriction: They will receive larger transfers on average than in the nonuniform case when in the majority and pay lower taxes when in the minority. The requirement of tax uniformity works in favor of greater redistribution on average and yet toward smaller variation over the long electoral sequence in the fortunes of any individual. The richest can do less well and the poorest less badly over the electoral cycle.
This is an important result and merits some emphasis. The requirement of tax uniformity in the presence of majority rule (without any corresponding uniformity restrictions on the transfer side) leads to a more equitable outcome, both in terms of expected income and in terms of the outcome at any point in the electoral cycle, than emerges in the absence of the uniformity requirement.
Uniform proportional income tax plus demogrant
Consider now the case in which uniformity restrictions are imposed on both the tax and the transfer side of the budget. The transfer uniformity is taken to require that revenues be divided equally among all citizens, in the form of an individual payment to all. Each group therefore receives thirty-three cents of each dollar of tax revenue raised. Uniformity on the tax side is defined, as in the preceding section, to involve a proportional income tax levied at the same flat rate on all individuals.
Given these restrictions, there will be some desired tax rate for each individual. This rate will be lower for any individual the higher his income, because he will be contributing a higher pro rata share of any dollar of tax revenue raised. In fact, any individual with income above the average will desire a zero tax rate—and hence a zero demogrant. Such an individual will contribute to revenue raised in proportion to his share of national income and will receive in return a per capita share enduring a net loss. Obversely, an individual with less than average income will desire a positive tax rate, one at which the cost to him of raising an additional dollar of revenue, including the marginal excess burden, will be equal to his per capita share of one-third. Clearly, the lower the individual’s income, the higher will be the desired tax rate (and concomitantly tax revenue and demogrant). Here we have no cycles. Preferences over the single parameter t can be arrayed along a single spectrum, and majority rule will lead to the median income earner, in this case B, being decisive in determining the tax rate to be applied. There is no scope for a decisive coalition between A and C, because given the restrictions on taxes and transfers there is no arrangement that will make both A and C better off: A wants lower tax rates, C higher ones. Hence, the tax rate levied will be the tax rate desired by the median-income individual. As we have indicated, only if income of the median-income earner is less than average will he desire positive transfers; and he will desire more transfers the lower his income is. The extent of redistribution will depend, therefore, on the extent to which the income distribution is skewed toward the lower end.
In contrast with the earlier cases, then, the pattern of transfers in this case is entirely determinate and emerges identically at every point in the electoral sequence. The extent of such redistribution depends solely on the difference between mean and median income. Whereas the focus of normative analysis is on the variance of the income distribution, or some equivalent measure of inequality, the extent of redistribution under majority rule, so restricted, depends solely on the degree of skewness. In other words, majority rule, with uniformity restrictions on both tax and transfer sides, serves to connect redistribution to the wrong parameter. Changes in the distribution of income that are essentially irrelevant to redistributive ethics can generate substantial changes in the pattern of political transfers, whereas changes in the income distribution that are of considerable normative significance may either leave the extent of transfers from rich to poor unchanged or alter them in a “perverse” direction. Some simple comparative static results from our three-person analysis suffice to support these claims. Suppose, for example, that the income of the poorest falls, ceteris paribus. Then average income will by definition also fall. Median income will remain unchanged, however, so the extent of transfers will fall. Obversely, if the income of the poorest rises, ceteris paribus, transfers will rise. Consider, on the other hand, an increase in median income, ceteris paribus. In this case, transfers will fall, even though the relative share of the poorest in the total pie has declined. Of course, some changes in the income distribution will generate changes in the transfer pattern that are consistent with the dictates of distributive justice as conventionally interpreted. For example, as the income of the richest increases or decreases, ceteris paribus, the level of transfers will rise or fall. But as we have shown, the simple median voter model does not generate patterns of political redistribution that are an appropriate expression of what distributive justice requires.
[9. ]See Geoffrey Brennan and James Buchanan, The Power to Tax (Cambridge University Press, 1980), ch. 3, for a detailed exposition of this point.
[10. ]Under inadequate indexing provisions, inflation makes it possible for taxing authorities to appropriate part of the real value of the assets themselves (by driving the net-of-tax real rate of return below zero). Here, we assume that monetary authorities are constitutionally restricted from engineering inflation for redistributive purposes, or at least are independent of in-period political pressures. See Brennan and Buchanan, Power to Tax, chs. 5 and 6.
[11. ]See, for example, ibid., chs. 3 and 4.