General equilibrium and optimal taxes

It is shown that if subsidies are not excessive, there exists a general competitive equilibrium in the presence of a complex tax structure. Furthermore, under certain continuity assumptions, a tax structure which is optimal from the social point of view can be determined. Procedures maximize quasi-concave after tax profit functions. Consumers have convex budget sets reflect- ing their income from sales and profits minus taxes on fixed income and progressive sales taxes. Their preferences are interdependent, intransitive and incomplete. The government provides public goods and determines the optimal tax regime on the basis of its preferences on the final competitive consumption allocation.