Local Public Good Equilibrium

Abstract

We extend the ratio equilibrium concept (Kaneko, 1977a,b) to local public good economies by defining and analyzing Local Public Good Equilibrium (LPGE). Similar to ratio equilibrium, LPGE is based on agents paying shares of the cost of the production of public goods. We show existence of LPGE for a far wider class of economies than prior work seeking to extend ratio equilibrium to local public good economies. In particular, we prove LPGE existence with (i) heterogeneous agents, (ii) finite agents and jurisdictions, (iii) endogenous jurisdictional revenues and expenditures, and (iv) robustness against coalitional deviations. We employ “share functions” for individual agents that allow easy comparisons of consumption utility, both across consumption bundles and across jurisdiction memberships; these share functions furthermore aggregate for parsimonious calculation of equilibrium public good provision within each potential jurisdiction. This allows us to establish a link with hedonic games and deploy results from that literature. LPGE admits wide-ranging jurisdiction structures, and we obtain results on sorting, segregation, and snob effects that have attracted interest in the extant literature.

Keywords: Local public good economy, Ratio equilibrium, Share function, Hedonic game, Tiebout sorting.

JEL Classification: H41, D7