Front Page Titles (by Subject) Appendix - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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Appendix - 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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The purpose of this appendix is to extend the analysis of Section 4.4 to a simplified general equilibrium approach somewhat more in keeping with the modern optimal-tax literature. Consider, for example, one of the simpler and more familiar discussions, that provided by Harberger.15 The tax rule derived by Harberger is designed for minimizing the welfare loss of a system of excises, given a revenue constraint, in a three-good setting in which one of the goods (leisure presumably) is tax-free. Let X1, X2, and X3 be the three goods, following Harberger’s formulation, and suppose X3 to be tax-free leisure. Then the change in X1 and X2 in response to taxes t1 and t2, respectively, is given by
In the Harberger case, W is minimized with respect to t1 and t2, given a revenue constraint. Harberger does not allow for the effect of changes in the tax base on revenue, but this can be done without changing the nature of his solution. For we seek to minimize
For our purposes, however, we note that R is given by
We note further that the left-hand side of (13) is ΔX1* from (1), and the left-hand side of (14) is ΔX2* from (2). So we have
We can on this basis conclude that optimal-tax rules and maximum revenue rules are indeed identical, even in this simple general equilibrium setting; and further, that under maximum revenue assumptions, total revenue remains exactly twice the welfare loss, just as in the partial equilibrium case, even where discrimination between goods is permitted and general equilibrium effects allowed for.
Taxation through Time
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
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.
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.
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?
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.
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.
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.
[15. ] Harberger, “Taxation, Resource Allocation and Welfare,” sec. 4.3.