Power and Taxes in a multi-commodity economy

Taxation and redistribution in a democratic majority-rule society are analyzed, using the Harsanyi-Shapley non-transferable utility value. The context is that of a multi-commodity pure exchange economy. Two approaches are treated: one in which taxes are in kind and exchange takes the form of barter; and one in which taxes are in money, exchange takes the form of sale and purchase, and prices are determined by a process of supply and demand. It is shown that in the presence of a non-atomic continuum of agents, the two approaches are equivalent, but that this is not so when there are only finitely many agents. It is also shown that the value exists under both approaches, and a characterization is found in the non-atomic case.