Optimal Provision Of Public Goods Research Articles

On optimal public good provision with tax evasion

It is proved that for public goods with zero income effects (also called Ziff public goods) tax evasion does not affect the optimal level of public expenditure. Further examples show that, in general, tax evasion may lead to less but also to more public expenditure.

Optimal public good provision in the Ramsey tax model: A generalization

For the single-consumer Ramsey tax model, the use of distortionary taxation to finance public good provision is shown to lower the optimal level of public good provision below its optimal value ina first-best economy, where lump sum taxation is available. The assumptions used in the proof include a previous Cobb-Douglas example as a special case.

The Simple Analytics of Pure Public Good Provision

quantities appear in his utility function. Also, the presence of the externality effectively implies a third commodity, the quantity of which influences his optimal choice and/or the maximum attainable utility in any situation. His utility function, therefore, must have three arguments. While this presents no problem for the rigorous analysis of such problems, it does complicate attempts to provide intuitive and geometric expositions of their essential features. The pure public goods model has inspired a number of devices, each useful in illustrating some particular aspect. Bowen (1943) and Samuelson (1955) noted that one could draw a demand, or marginal rate of substitution, curve for each individual, and that their vertical summation was the relevant object to equate with the marginal rate of transformation between public and private goods at a Pareto optimum. This simple construct assumed either a given distribution or a special class of preferences so as to guarantee that the optimal public goods provision was independent of distribution. Likewise, Johansen (1963) produced a graphical treatment of Lindahl equilibrium which again is generally sensitive to income redistribution. An alternative diagram has been used by McGuire and Aaron (1969) to analyse efficient public goods provision when the range of available policy instruments-specifically, the ability to make lump-sum income transfers and to choose individuals' cost shares-is limited. Pauly (1970) depicted inefficient equilibrium allocations in a similar diagram; however, Pauly's diagram does not permit an easy or direct comparison between equilibria and optima. This applies also to the treatment by Atkinson and Stiglitz (1980, p. 507), who used a two-part diagram. Other modern expositions, such as Boadway (1979), avoided diagrams at this point in their discussion. The present paper provides a thorough discussion of a relatively simple diagram which allows one to depict both the orthodox Nash equilibrium and the set of Pareto-optimal allocations in an economy with a pure public good. This diagram also allows for a simple representation of Lindahl equilibrium in such an economy. In the simple two person example, our diagram is analogous to the Edgeworth box treatment of a private goods exchange economy, and in this special case it can accommodate differences in preferences or endowments without complication. For an economy of more than two people, the diagram may still be used if the assumption of identical tastes and endowments across consumers is made. In a private goods economy with

Optimal provision of public goods through Nash equilibria

Optimal provision of public goods through Nash equilibria

Jurisdictional consequences of optimizing public goods

The jointness efficiency of large jurisdictions and the distributional efficiency of small jurisdictions present a dilemma in the organization of a governmental system. Working from the point of view that governments exist to provide services, the two types of efficiency are integrated through Lagrangian methodology. The result is an optimal provision of public goods, an equitable taxing structure, and an efficient distribution system.

On the Optimal Taxation of Consumption Externalities

The conventional theory of the optimal taxation of consumption externalities (see, for instance, Samuelson, 1969) is applicable to a world where lump-sum transfers are available. When externalities affect individual utilities through aggregate consumption only (the aggregation assumption), according to this theory, a social optimum can be attained by a system of lump-sum transfers and uniform taxes-subsidies on the externality-causing goods.1 A tax-subsidy is imposed on each such good; the amount equals the sum across individuals of the marginal rates of substitution (2MRS) between the aggregate consumption of this good and the numeraire good. Diamond (1973), Starrett (1972), and others relaxed the aggregation assumption, while still maintaining the framework of lump-sum transfers. In this paper we derive explicit tax formulae in a more realistic setting, where lump-sum transfers are not available. However, the aggregation assumption is retained. The formal analysis developed here applies to both external economies and diseconomies; in order to avoid needless repetition, the interpretation of the results is confined to the latter case. When lump-sum taxes are not available, we encounter some problems that otherwise do not exist. Fortunately, these problems are similar in nature to those associated with the optimal provision of public goods. In particular, one may conjecture from the treatment of public consumption by Diamond and Mirrlees (1971) in what ways the optimal taxes-subsidies will be different in our case from what is suggested by the conventional theory. First, with no lump-sum transfers available, the marginal social welfare of income is not necessarily equalized across individuals; therefore it is not appropriate to add up the individual willingness to pay for a unit decrease in the aggregate consumption of an externality-causing good (the MRS's). Thus, as in Diamond and Mirrlees (1971) the term 2MRS

Compensation With Induced Factor Movements in a Simple General Equilibrium Model

Interjurisdictional compensation can provide an effective method of achieving an optimal provision of public goods in an independent system of local governments, only if all the major side effects of public goods are included in its computation. Previous studies have suggested compensation levels calculated solely on spillins and spillouts of public goods, but in this framework the provision of public goods may induce migration of productive inputs. To incorporate potential movement of factors of production, we recast the local government expenditures problem in a simple general equilibrium framework and estimate the impact of migration on the suggested compensation level. We show that, within reasonable ranges of parameter values of our model, compensation based entirely on output externalities substantially understates the level necessary to achieve an allocatively efficient provision of public goods.

The Optimal Provision of Public Goods: Yet Another Comment

In his 1966 analysis of the Optimal Provision of Public Goods, Alan concluded that a setting in which local governments are left free to make their own independent decisions about the supply of goods with no compensation being paid for spillovers], the complex interactions that occur even in highly simplified situations make impossible to predict a priori whether undersupply or oversupply will generally (p. 19). This and other conclusions of his have evoked considerable comment. As yet, however, no one has questioned his assertion that it is not implied Ithat aggregate oversupply] will necessarily result in all cases lin which spillovers are uncompensated], but only that is a perfectly conceivable result which does not require any obviously unreasonable assumptions to be made (p. 31). It is with the empirical aspects of this assertion that we deal. More specifically, we address the question, How disparate must communities be in their price and income elasticities of demand for the Williams effect to be observed? That is, under what circumstances would uncompensated spillovers of the type of good considered result in greater output than would eventuate if compensation were paid? As Pauly (1970, p. 577), Brainard and Dolbear (1967), and, indeed, (1966, p. 29) indicate, the class of goods examined is public only in a rather special sense: XWhile these goods may satisfy the Samuelson et al. conditions for pure goods within individual communities, they are pure private goods among communities. That is, if a unit of such a good spills over from one community to a second, the first community completely loses the services of that unit. A stylized mosquito control program provides an example. Suppose that a fraction, cc, of the mosquitoes which breed in community 1 migrate to community 2 and, conversely, that the same fraction of the mosquitoes born in community 2 migrate to community 1. This being the case, if community 1 eradicates

Local Government Tax and Product Competition and the Optimal Provision of Public Goods

The location of any given town has commonly been determined by collusion between"interested parties" with a view to speculation in real estate, and it continues through its life-history (hitherto) to be managed as a real estate "proposition." Its municipal affairs, its civic pride, its community interest, coverage upon its real-estate values.

A Planning Approach to the Public Good Problem

The theory of planning should give new insight into the classical problem of how to achieve an optimal provision of public goods. The point is exhibited by a diagrammatic study of the simple model in which there are just two consumers and two commodities, one private, one public. Besides the procedure proposed by E. Lindahl, two others are discussed; the first uses tax indicators, the second quantity indicators. Consideration is given to three requirements: convergence to an optimum, equitable treatment of the two consumers, incentives for correct revelation of preferences.

The Optimal Provision of Public Goods: A Comment

In a recent issue of this Journal, Alan Williams (1966) presented an analysis of the optimality of public goods supply in a situation in which the public goods are produced by independently operating local governments. By appropriate reference to hitherto neglected income effects, he succeeded in demonstrating that it is possible for too much of the public good to be produced in the aggregate, even though each local government cannot extract payment for the benefits from its public good production which spill out onto other local government areas. The question under discussion is conceptually equivalent to the question of the direction of the distortion resulting under conditions of independent adjustment in a situation of reciprocal externalities of the separable variety,1 and Williams' analysis can be applied equally well to this case. Thus, if A's production of X reduces the total (but not marginal) cost of B's production of X, and B's production of X likewise reduces the total (but not marginal) cost of A's, Williams' result indicates that, where A and B act independently, oversupply of X may result. To those familiar with the work of Buchanan and Kafoglis (1963) and of Baumol (1964), this conclusion may not, in itself, be very surprising. What is perhaps more interesting is Williams' assertion that, although oversupply of public goods can occur in the aggregate, it is not possible for public goods consumption to be overexpanded in every local government area. Or, in the individual case, although too much of X may be produced in toto, simultaneous overproduction by A and B is impossible.2

Welfare Maximization: The Simple Analytics with Public Goods

In his Simple Analytics of Welfare Maximization, Professor Bator has described diagrammatically the meaning of Pareto optimality in the allocation of resources and the maximization of social welfare.1 He has also shown that under certain conditions competitive markets achieve a Pareto-optimal allocation of resources and, given the possibility of making the appropriate nondistorting redistribution of income, the social welfare maximum. By presenting in a form more easily understood by many students of welfare economics the analysis developed elsewhere in a more general but more fornmidable mathematical form (especially by Professor Samuelson),2 Bator has performed a considerable service. In two seminal and apparently definitive articles Samuelson has shown both mathematically and diagrammatically how the conditions for Pareto optimality and welfare maximization are altered by the introduction of public goods, and has emphasized that voluntary exchange cannot be expected to result in the optimal provision of public goods.3 Yet it may remain unclear just how public goods can be incorporated in Bator's extremely useful analysis of welfare maximization. The primary purpose of the present note is to describe how Bator's analysis can be modified to take account of public goods. While the diagrammatic analysis presented here is not fundamentally different from Samuelson's, it may clarify for those who find Bator's analytical framework useful the way public goods fit into the problem of welfare maximization. A secondary purpose is to comment upon several questions raised by Professor Richard Musgrave in his treatise The Theory of Public Finance.4

The Optimal Provision of Public Goods in a System of Local Government

The Optimal Provision of Public Goods in a System of Local Government