Linear And Non-Linear Price Decentralization

The present paper provides compendious and thorough solutions to the price equilibrium existence problem, the second welfare theorem, and the limit theorem on the core of an economy for exchange economies whose commodity space is an arbitrary ordered Frechet space. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory commodity spaces that are not vector lattice ordered and whose positive cones have empty interior, a typical situation in models of portfolio trading with incomplete markets. Our assumptions are made on the primitive objects fo the economy. Remarkably, the assumptions that we make on the order structure of the commodity space are indispensable. For w-proper economies, these assumptions are both sufficient and necessary for the existence of equilibrium, the second welfare theorem, and the Edgeworth-Walras equivalence theorem. We take advantage of new developments in the theory of ordered vector spaces, in particular the possibility of embedding the price cone into a lattice cone called the super-order dual of the ordered vector space. Therefore, even though the commodity price duality has no lattice structure important lattice theoretic techniques can be applied outside this duality.