Front Page Titles (by Subject) 7.1.: The Model - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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7.1.: The Model - 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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Because the focus of analysis is somewhat different from that in preceding chapters, it will be useful to restate our basic model. The quantity of the public good (or public-goods bundle), G, provided by the monopoly government (Leviathan) is defined as
The restrictive effects of assuming a to be fixed should be clear. It is evident that the value of a may depend on the tax institutions selected, and it is this relationship that we address directly in this chapter. Let us suppose that we envisage the constitutional process as one that establishes a “monarchy,” under which a “king” may be treated as a utility maximizer in the standard manner. Both the monarchy and the king here are, of course, artifacts constructed solely for convenience in exposition. The king becomes a shorthand expression for the appropriately chosen collection of politicians and bureaucrats whose behavior generates outcomes in postconstitutional political settings, or even the decisive majority in a context of revolving coalitions where that majority exploits the minority. In any case, this collection acts “as if” it were a utility-maximizing entity, or king.
We ascribe to this behavioral unit the maximand, Yk, where
Before explaining this strategy in some depth, it is necessary to specify carefully the relationship of the king to other members of the political community. If the goods and services expected to be provided by government, G, are genuinely “public” in the nonexcludable sense, and, further, if the king shares in the benefits along with others, a may not be reduced to zero, even if its value remains wholly within the control of the king. That is, if the king’s utility function, Uk, contains an argument for G as well as for privately divisible goods that may be enjoyed exclusively, a strict maximizing calculus would imply some provision of G, and hence some value for a, assuming the absence of lumpiness. Largely for purposes of simplifying our discussion here, we shall initially assume that the king is wholly external to the other members of the community in the sense that he does not secure any positive benefits from the provision of G, even though the latter may be described as a collective-consumption good for all other persons. A somewhat more complex model which allows the king to be among the sharers of public-goods benefits and/or which allows for G as a direct argument in the king’s own utility function is presented in Section 7.4. In Sections 7.2 and 7.3, we shall assume that the king does not benefit from public-goods supply and that the surplus that accrues to the king is pure loss to the society. Both assumptions can be considerably weakened without the central results being lost—but initially it is convenient to deal with the more extreme case.
[3. ] In a Niskanen model, Leviathan achieves its surrogate equivalent of “surplus” by producing excessive quantities of G. See William Niskanen, Bureaucracy and Representative Government (Chicago: Aldine-Atherton, 1971). The model has been subjected to criticism precisely because it fails to allow for any diversion of revenues away from the financing of genuine public goods. See Jean Luc Migué and Gérard Bélanger, “Toward a General Theory of Managerial Discretion,” Public Choice, 17 (Spring 1974), 27-42.