This paper presents a new theory of value with a personalized pricing system that naturally induces a family of non-linear prices. This affords a coordinate free theory of value in which the analysis is without any lattice theoretic considerations. When commodity bundles are perfectly decomposable the generalized prices become linear and the analysis specializes to the Walrasian 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 value-based characterization of Pareto optimality and Edgeworth equilibrium where the Walrasian linear price-based characterization fails. The analysis has applications in the finite as well as the infinite dimensional setting. Journal of Economic Literature Classification Numbers: C62, C71, D46, D51, D61.