Existence of voting and housing equilibrium in a system of communities with property taxes

Abstract

Considerable attention has recently been devoted to general equilibrium analysis of local public good allocation in a system of jurisdictions. While there are differences in approach and emphasis, all the models with a substantial degree of generality essentially ignore political processes for allocating local public goods. It is fairly clear from these models, however, that - at least for the time being - explicit modeling of the political process will require imposing more structure on the economics of the model. The framework of this paper forgoes the generality of the ‘apolitical’ models in order to be able to consider both economic and political aspects of the problem. We develop a formal model of a continuum of non-identical individuals, in which each individual must choose among a finite number of communities. In each community, the provision of the public good is financed by taxing residents on the amount of housing they choose to consume. The tax rate and amount of public good supplied in the community are determined by a vote of residents of the community. An equilibrium is said to exist whenever individuals are located in communities such that each community is populated and it is in an ‘internal equilibrium’, and no individual would become better off by migrating to a different community. Standard restrictions on individual preferences are not sufficient to guarantee the existence of an equilibrium with an arbitrary number of communities. In order to ensure existence, fairly severe assumptions must be placed upon individual preferences and technology. We develop these restrictions, and prove existence of equilibrium.