Front Page Titles (by Subject) 7.4.: The Nonsurplus Maximizer - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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7.4.: The Nonsurplus Maximizer - 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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Foreword and coauthor note © 2000 Liberty Fund, Inc. © 1980 Cambridge University Press.
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The Nonsurplus Maximizer
Before turning to possible policy implications, it will be useful to modify the analysis in the direction of a more widely shared image of government. What effect will be exerted on rational constitutional choices among tax instruments if the model is changed so as to allow the institutions that supply public goods—be these kings, bureaucrats, politicians, or judges—to be somewhat less intractable than the earlier treatment makes them appear? The most selfish of kings or bureaucrats may supply some public goods, even from purely self-interested motivations, especially if they themselves secure shares in the nonexcludable benefits. Some law and order, some defense, some fireworks, will be supplied by a king for his own benefit; and the masses can then be expected to secure spillover benefits. Beyond this, political decision makers, even if unconstrained directly by the citizenry, may be honorable men and women motivated by a genuine sense of public duty; kings may care about their subjects.
We now want to allow for this, while retaining the assumption that the government will attempt to maximize revenues from any tax base or bases assigned to it. We want to examine a model in which some G will be provided due to the king’s utility function. In Figure 7.5, assume that some arbitrarily chosen tax base yields a maximum revenue to the king of . If the king is a pure surplus maximizer as previously analyzed, he will, of course, retain all of this revenue for personal usage. If, however, G is included as an argument in his utility function, he will want to provide some G. The king’s preferences in this case may be represented in a set of indifference contours defined on B and G and exhibiting the standard properties. The rate at which a dollar’s worth of revenues in the “king’s” hands can be transformed into a dollar’s worth of outlay on public goods is, of course, unity. Hence, the “price line” faced by the king is the 45° line drawn southeasterly from . Equilibrium is attained at H; the amount of revenue “given up” to provide the public good is Z; the amount of revenue retained as surplus is 0Z, with the ratio Z/0 being the a previously discussed, although in this case its value is determined behaviorally rather than exogenously set, as previously assumed. This ratio is simply the king’s average propensity to consume G out of revenues collected.
The curve αα′ in Figure 7.5 is the locus of equilibrium positions as the “king” is assigned more comprehensive bases for tax levies, all of which are independent of spending on G. (Note that an a of unity would imply that this curve lie along the abscissa.)
In the setting depicted in Figure 7.5, what is the effect of substituting a tax base that is complementary to G for the independent tax bases assumed in tracing out the aa’ curve? To answer this question, we may transform Figure 7.2 into Figure 7.5 by relating surplus to levels of G. Recall from Figure 7.2 that, at M′, there is no net surplus, and that this rises to a maximum at E, while falling back to zero at M. We simply translate these results into Figure 7.5 with the same labeling. The curve M′EM now represents the transformation possibilities facing the king. He will attain equilibrium at W, with W′ being the total outlay on G made. Note that this solution involves more public goods and less surplus than the equilibrium at E reached in the surplus-maximizing model.
The dramatic difference between this complementary tax-base constraint and its absence can now be indicated by comparing the costs (in terms of surplus retained by the king) of securing the amount of G shown at W′. In the constrained model, these costs are measured by the vertical distance W′W. But, for the same G, these costs rise to W′V in the unconstrained case. If the potential taxpayer-beneficiary is assumed to be confronted with an unlimited set of choice alternatives, he will conceptually be able to reduce the retained (wasted) surplus to zero in the limiting case, while ensuring that a predicted efficient level of outlay on public goods will be made. In Figure 7.5, if we assume that W′ is the efficient level desired, a tax base may be selected that exhibits the complementarity properties required to generate a curve like the dashed one drawn through W′. Note that, in contrast to the comparable curve in the surplus-maximizing model, this curve can lie above zero along a part of its range. Surplus is reduced to zero (assuming the required properties of the king’s utility function) because the king places an independent marginal valuation on G.