A theory of value with non-linear prices - Equilibrium analysis beyond vector lattices

This paper presents a new theory of value with a personalized pricing syste m that naturally induces, a family of non-linear prices. This affords a coo rdinate free theory of value in which the analysis is without any lattice t heoretic considerations. When commodity bundles are perfectly decomposable the generalized prices become linear and the analysis specializes to the Wa lrasian model. This happens, for instance, whenever the commodity space is a vector lattice and consumption sets coincide with the positive cone. Our approach affords theorems on the existence of equilibrium and provides a va lue-based characterization of Pareto optimality and Edgeworth equilibrium w here the Walrasian linear price-based characterization fails. The analysis has applications in the finite as well as the infinite dimensional setting. (C) 2001 Academic Press.