The Pure Theory of Public Goods: Efficiency, Decentralization, and the Core

We extend the results of Mas-Colell (1980) and Weber and Wiesmeth (1991) on valuation equilibria and the relationship of cost share equilibria with the core. We allow for any finite number of private goods and a set of public projects without any structure. We show the two welfare theorems for valuation equilibrium, the inclusion of the set of cost share equilibria in the core, and the nonequivalence of these two sets for an economy with a finite number of agents. In the case that the set of public projects is endowed with a topological structure, we provide conditions under which the price system needed to decentralize a Pareto efficient allocation as a valuation equilibrium is continuous.