Lindahl Equilibrium as a Collective Choice Rule

TL;DR

This paper explores Lindahl equilibrium as a collective choice rule, establishing its existence, efficiency, and relation to bargaining solutions and Walrasian equilibria in various economic settings.

Contribution

It introduces the equitable solution as a set-valued solution concept, characterizes it axiomatically, and links Lindahl equilibrium payoffs to Nash bargaining and Walrasian equilibria.

Findings

Lindahl equilibrium allocations are shown to exist and be efficient.

The equitable solution contains the Nash bargaining solution.

Lindahl equilibrium payoffs coincide with Walrasian equilibrium payoffs in certain markets.

Abstract

A collective choice problem is a finite set of social alternatives and a finite set of economic agents with vNM utility functions. We associate a public goods economy with each collective choice problem and establish the existence and efficiency of (equal income) Lindahl equilibrium allocations. We interpret collective choice problems as cooperative bargaining problems and define a set-valued solution concept, {\it the equitable solution} (ES). We provide axioms that characterize ES and show that ES contains the Nash bargaining solution. Our main result shows that the set of ES payoffs is the same a the set of Lindahl equilibrium payoffs. We consider two applications: in the first, we show that in a large class of matching problems without transfers the set of Lindahl equilibrium payoffs is the same as the set of (equal income) Walrasian equilibrium payoffs. In our second application, we show that in any discrete exchange economy without transfers every Walrasian equilibrium payoff is a Lindahl equilibrium payoff of the corresponding collective choice market. Moreover, for any cooperative bargaining problem, it is possible to define a set of commodities so that the resulting economy's utility possibility set is that bargaining problem {\it and} the resulting economy's set of Walrasian equilibrium payoffs is the same as the set of Lindahl equilibrium payoffs of the corresponding collective choice market.