The theory of externalities, public goods, and club goods: Alternative mechanisms for provision of public goods

TL;DR: A review of the literature on Pareto-optimal allocation of public goods can be found in this paper, where the authors focus on the problem of finding the optimal level of provision of a public good without any explicit assumption concerning the distribution of private goods and hence of utility.

Abstract: The systematic tendency toward underprovision of a public good that seems to be implied by the model of Nash-Cournot equilibrium has encouraged extensive analysis of alternative allocative mechanisms and their evaluation against the yardstick provided by the set of Pareto-efficient allocations. The aim of this chapter, which is necessarily highly selective, is to review some of this large and varied literature. We begin with a closer look at the set of Pareto-efficient, or Paretooptimal, allocations. Pareto-optimal provision of public goods In the public goods economy, just as in its private goods counterpart, the optimality criterion typically identifies not one, but an infinite number of allocations – all the points on the utility possibilities frontier between R and S in Figure 7.1. Any discussion of “the optimum” must presuppose either a very special structure, so that there is, indeed, a single optimal level of Q associated with every allocation along the frontier RS , or else the introduction of some kind of social welfare function that enables us to rank optima and pick out the optimum optimorum. Economists have, however, often expressed and relied upon the hope that certain allocation decisions can be made without reference to distributional considerations. In the present context, this is reflected in many treatments that refer to the optimal level of provision of a public good without any explicit assumption concerning the distribution of private goods and hence of utility.