Existence of an equilibrium with arbitrary tax schemes for financing local public goods

The existence of a public competitive equilibrium for any arbitrary (nondistortive) tax schemes (in particular, proportional taxes) for economies with local public goods, is proved. Allowing preferences to be both nontransitive and noncomplete enables an explicit introduction of the government as an (additional) agent in the economy. Moreover, we allow for “spillovers” of the public goods among localities, and for the production sets to depend on the amount of public goods produced in the economy. The only restriction on the tax system is that every individual is able to afford it and that the government's budget never runs a surplus. Since every equilibrium allocation is a Pareto optimum, every tax scheme is optimal (in the sense that its equilibrium allocation is a Pareto optimum).