On equity with public goods

Existence theorems for envy-free and efficient allocations are derived for economies with public goods. For economies with an arbitrary but finite number of private and public goods, an adaptation of the existence proof of Svensson for private good economies is used. For economies with one private and one public good, a case often studied in theory and applications, two more direct proofs are given, using different conditions and taking advantage of the particularly simple structure of the set of envy-free allocations in this case. These proofs are also shown to apply to the case of excludable public goods with congestion.I am grateful to William Thomson, Marcus Berliant, Robert Gilles, Hervé Moulin, Thomas Palfrey, Tomoichi Shinotsuka, Simon Wilkie, and two anonymous referees for their comments. This paper is a revised version of Chap. 1 of my doctoral dissertation submitted to the University of Rochester in July 1988. The financial support of the University of Rochester in the form of the Raymond N. Ball Dissertation Year Fellowship is gratefully acknowledged. All shortcomings of this paper are solely of my own creation.