Existence and Regularity of Equilibria in a General Equilibrium Model with Private Provision of a Public Good

Abstract

We prove existence and generic regularity of equilibria in a general equilibrium model of a completely decentralized pure public good economy. Competitive rms using private goods as inputs produce the public good, which is privately provided by households. Previous studies on private provision of public goods typically use one private good, one public good models in which the public good is produced through a constant returns to scale technology. As two distinguishing features of our model, we allow for the presence of several private goods and non-linear production technology. In that framework, we use an homotopy argument to prove existence of equilibria and we show that economies are generically regular. 1 Introduction In this paper, we prove the existence and regularity of equilibria in a general equilibrium model of a completely decentralized pure public good economy. The model studied extends the standard pure exchange model with private goods by allowing households to make voluntary purchases of (or “privately provide”) a public good that is produced by competitive rms using private goods as inputs. The interest in a general equilibrium model with private provision of public goods lies in the fact that it serves as a benchmark extension of an analysis of completely decentralized private good economies to public good economies. Moreover, there are some relevant situations in which public goods are in fact We would like to thank the Editor and three anonymous referees for their helpful comments. In particular, we are very grateful to one of the referees for very stimulating and thoughtful comments and suggestions that helped improve the paper greatly. We would also like to express our gratitude to late Murat Sertel for a helpful discussion on the paper yCorresponding author. Department of Mathematics for Decision Theory (Di.Ma.D), University of Florence, via Lombroso 6/17, 50134 Firenze, Italy; e-mail: villanac@uni .it. zDepartment of Economics, Bo1⁄4 gazici University, 80815 Bebek, Istanbul, Turkey; e-mail: zenginob@boun.edu.tr.