The Demand and Supply of Public Goods
1. Paul A. Samuelson, "The Pure Theory of Public Expenditure," Review of Economics and Statistics 36 (November 1954): 387-89; "Diagrammatic Exposition of a Theory of Public Expenditure," Review of Economics and Statistics 37 (November 1955): 350-56; and "Aspects of Public Expenditure Theories," Review of Economics and Statistics 40 (November 1958): 332-38. James M. Buchanan, The Limits of Liberty: Between Anarchy and Leviathan (Chicago: University of Chicago Press, 1975), volume 7 in the series.
2. James M. Buchanan and W. C. Stubblebine, "Externality," Economica 29 (November 1962): 371-84; James M. Buchanan, "An Economic Theory of Clubs," Economica 32 (February 1965): 1-14. Both papers are included in volume 15 in the series, Externalities and Public Expenditure Theory. James M. Buchanan, The Demand and Supply of Public Goods (Chicago: Rand-McNally, 1968), volume 5 in the series. Samuelson, "The Pure Theory," 387-89; "Diagrammatic Exposition," 350-56; and "Expenditure Theories," 332-38; Richard A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill, 1959). John G. Head, Public Goods and Public Welfare (Durham: Duke University Press, 1974).
4. Richard A. Musgrave, "The Voluntary Exchange Theory of Public Economy," Quarterly Journal of Economics 53 (February 1939): 213-37; Erik Lindahl, Die Gerechtigkeit der Besteuerung (Lund: Gleerupska Universitets-Bokhandeln, 1919); Knut Wicksell, Finanztheoretische Untersuchungen (Jena: Fischer, 1896).
6. This statement suggests one important aspect of public-goods supply that may have been overlooked by some scholars. The theory of public goods can be applied even in those cases where congestion arises in the usage of a public facility. A road, street or highway provides the best illustration of this point. The facility, once constructed, is made equally available to all users, and the theory of public goods can be used to determine, conceptually, the appropriate extension in the capacity of the facility. Each facility embodies, however, a certain congestion probability as one of its physical dimensions, and this will be taken into account in the individual marginal evaluations. For example, an individual will place a different marginal evaluation on a toll-free, congested thoroughfare than on a toll-charging, noncongested throughway of the same physical attributes. Even in the toll-charging case, however, the facility is equally available to all potential users.
7. Under the restricted assumption of linearity in the two cost functions under separate production, the convexity of the iso-cost contours implies net efficiency in joint production. If, however, this linearity assumption is dropped, convex iso-cost contours may exist even where there is no jointness advantage. For this more general model, a redefinition of quantity units in terms of dollars of cost is required to convert the independent-production cost functions into effectively linear form. Once this step is taken, the analysis proceeds as it does in the simpler model.
8. The set of points that qualify as Pareto-optimal meet the same general conditions in the two-person and the three-person cases. Any point outside this set is dominated by at least one point in the set for all persons, and no point inside the set dominates any other point in the set for all persons. These conditions may be stated differently by reference to potential moves among points. From any nonoptimal point, there must exist at least one means of shifting to a point in the optimal set of points in such a way that at least one person is benefited and no one is harmed. In other words, it must be possible to shift from any nonoptimal point to some optimal point in a Pareto-optimal manner. Once a point within the Pareto set is attained, however, any shift must harm at least one person; no Pareto-optimal moves can be made.
9. This chapter is not well integrated with the other parts of this book, and earlier attempts to locate the material elsewhere in the manuscript were not successful. Although the analysis builds on the models previously discussed, a new question is introduced which cannot be adequately explored in all of its complexities. Despite this acknowledged incompleteness, I have decided to include the chapter because of its relevance for the interpretations that many scholars, correctly or incorrectly, have placed on the modern theory of public goods, and finally, because of the fundamental and general interest of the question itself.
10. This is an important and necessary qualification. For goods and services exhibiting publicness over large groups (and inoculations may be excellent examples here) the way in which any available quantity is distributed may affect the degree and extent of spillover benefits generated. This is only one type of difficulty that is likely to be encountered in any attempt to classify goods and services by criteria that are inherent in the descriptive characteristics of the goods themselves.
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