Comparative statics for the private provision of normal and inferior public good

Abstract

This paper studies a standard model of the private provision of public goods which can be either normal or inferior. Using new tools from monotone comparative statics, the paper fully characterizes the Nash equilibria for each case and shows that the condition for the normality (inferiority) of the public good is sufficient for the extremal total equilibrium contribution to be increasing (decreasing) in the group size. When the public good is inferior, there always exists a “monopoly provision” equilibrium involving one contributor and n-1 free riders, which surprisingly supplies the highest amount of public good among all possible equilibria, also generating the highest social welfare if the utility function is convex in the private good. The lattice-theoretic methodology allows a generalization of the classical results by showing that the assumption of quasi-concavity of the utility function is not “critical” and therefore can be relaxed.