AN APPROACH FOR MATHEMATICAL FORMULATION OF THE SUSTAINABLE ECONOMY

Abstract

Assuming that the concepts included in the fundamental description level of the sustainable economy are the concepts of sum and direction, a model is formulated herein using a mathematical structure used by the equilibrium Macroscopic Thermodynamic Theory. For this formulation, the following items are considered: an open economy, with a public sector, which produces non-free (goods) and free (conveniences) goods and services. New concepts are introduced which, associated to macroeconomic variables, define a set of variables which are representative of each and every activity performed by the economy. Equilibrium states are conceptualized which an economy can achieve when it evolves in a sustainable manner and with certain restraints. The existence of a function, only defined for equilibrium states, is postulated which has a peak value when the economy achieves the highest welfare state. It is postulated that this function has mathematical properties that allow use the same mathematical tools of Thermodynamic Theory. Then, the model is applied to a simple economy and the equilibrium and equilibrium stability criteria are deduced. It is emphasized in the conclusions that the model provides a useful connection between the Microeconomics and Macroeconomics domains, and numerous equations that are useful for economic analysis; the obtained equilibrium criteria are compared to the traditional ones, and the economic content of the stability criteria is expressed.