Economic Equilibrium under Deformation of the Economy

Abstract

A philosophical problem arises when one attempts to predict a competitive economy's response to a fundamental change in its structure with the aid of a competitive equilibrium model. Unless the model is known to admit unique solutions, there is little basis for assuming that the computed equilibrium will be attained, even though the model accurately describes the economy's structure and the behavior of its agents. If, however, one is able to arrive at the new model by continuously deforming the old one, then the two versions generally admit solutions which are connected by a path of equilibria arising from the continuum of intermediate economies. By ascribing a suitable dynamic interpretation to the deformation, one obtains a rationale for expecting the path-connected solutions to be mutually attained.