An Equivalence Result for the Core of an Economy with a Public Good

The central result of this paper is a refinement of an equivalence theorem in Mas-Colell (1980) for the core of a finite economy with a public good. It is shown that an allocation belongs to the core if and only if it is a cost share equilibrium. A further characterization of core elements which can be supported by a strictly monotonic cost sharing method is also provided. An application of these results allows a complete characterization of core allocations which can be supported by a linear cost share system. The set of linear cost share equilibria, which are in one-to-one correspondence with the Lindahl-Foley equilibria, is determined by uniform upper and lower bounds on the elasticity of substitution for the public good. In contrast to cost share equilibria, Lindahl-Foley equilibria are based on profit maximization.