Consistent voting rules for competitive local public goods economies

We establish the existence of a "voting-market equilibrium" for a large class of local public goods economies where, faced with prices of the private goods and with the public goods produced by the local governments, each firm maximizes its profits and each individual maximizes his utility subject to his budget constraint. In addition, each local government, taking the prices of private goods as given, (i) has a balanced budget and (ii) chooses its production of public goods in such a way that no group that contains more than q (q + 1) of its residents, where q denotes the number of public goods produced, will unanimously prefer another affordable vector of public goods.