The Tiebout Hypothesis: Near Optimality in Local Public Good Economies

Abstract

Over two decades ago, Charles Tiebout conjectured that in economies with local public goods, consumers vote with their feet and that this voting creates an approximate market-type equilibrium. He hypothesized that this approximate equilibrium is and, the smaller the moving costs, the closer the equilibrium is to an optimum. This paper provides a formal model of an economy with a local public good and endogenous jurisdiction structures (partitions of the set of agents into jurisdictions) which permits proofs of Tiebout's conjectures. Analogues of classical results pertaining to private-good economies, such as existence of equilibrium and convergence of the core to equilibrium states of the economy, are obtained for the approximate equilibrium and approximate cores. IN HIS SEMINAL PAPER Charles Tiebout [12] argued that the movement of consumers to jurisdictions where their wants are best satisfied, subject to their budget constraints and given (lump sum) taxes within jurisdictions, would lead to near optimal provision of a local public good. In addition, he hypothesized that the larger the economy and the number of jurisdictions and the smaller the moving costs, the nearer the equilibrium would be to an state of the economy. This paper provides proofs of Tiebout's conjectures for local public good economies with endogenous jurisdiction structures (partitions of the set of agents into jurisdictions). An E-core, similar to the Shapley-Shubik weak E-core (in [10]), is defined and it is shown that the E-core is non-empty for all sufficiently large economies. For small E and large economies, points in the E -core have the property that the utilities of consumers are nearly equal to the utilities they would realize at a point in the core of an associated economy with a non-empty core (an economy where agents can be appropriately partitioned into jurisdictions); informally, the E-core shrinks to the core. An E-equilibrium is defined and shown to be in the E -core; therefore, for small E, the E -equilibrium states of the economy are Pareto optimal. In addition, for small E, an s-equilibrium has the properties that: the utilities of consumers are nearly 2 equal to their utilities in a local public equilibrium allocation; and the lump sum taxes paid by most consumers are equal to the Lindahl prices times the quantities consumed of the local public good minus profit shares (the profit shares consumers nearly receive are the per capita profits in local public good