Topology of utility possibility frontiers of economies with Ramsey taxation

Abstract

This paper establishes the generic size and structure of the second-best Pareto frontier and its various components in private ownership economies with Ramsey taxation. It provides conditions under which the second-best Pareto frontier of an economy with H consumers will have the expected structure of a H . 1-dimensional manifold. In a class of economies, it shows that, generically, while the jointly production and consumption ine cient component of the second-best Pareto manifold is a submanifold that also has a dimension equal to H . 1, the production e cient, consumption e cient, and the rstbest components are lower dimensional, and hence negligible in size, submanifolds. Thus, it formally demonstrates that the economies usually studied in the literature, where all second-best are production e cient, are extremely rare. Market prices cannot be used in lieu of social shadow prices in most economies for cost-bene t tests. This begs further research for recovering the true social shadow prices from the data in such economies.Ramsey taxation ; second-best ; production e ciency ; general equilibrium ; private ownership ; di erential topology ; transversality theorem.