A THEORY OF CONVEX DIFFERENTIALS IN ECONOMICS

Abstract

This paper proposes a concept of convex and linear functions as convex differentials among subsets of commodity and price spaces in a convex and Euclidean space linearity. These subsets are tied together in the whole commodity and price space through fixed-points' equilibrium structure in the form of nonnegative price functions under General Equilibrium Theory. The Economic outcome is a necessarily mutual pricing imperative between a new technology and its market development aspect implying imports and exports to be complements, not substitutes. The theoretical method adopted here is for a mathematical existence result.