In our previous paper, "Optimal Allocation of Public Goods...," [5] we presented a mechanism for determining efficient public goods allocations when preferences are unknown and consumers are free to misrepresent their demands for public goods. We proved the basic welfare theorem for this model: If consumers are competitive in markets for private goods and follow Nash behavior in their choice of demands to report to the mechanism, then equilibria will be Pareto optimal. In this paper we show this result is not vacuous by proving that an equilibria will be Pareto optimal. In this paper we show this result is not vacuous by proving that an equilibrium will exist for a wide class of economies. Our conditions are slightly stronger than those required to prove the existence of a Lindahl equilibrium. In order to rule out the possibility of bankruptcy, we assume additionally that at all Pareto optimal allocations, private goods consumption is bounded away from zero.