Remarks on criticality and crisis in pure exchange economies

TL;DR

This paper rigorously defines crisis transitions in pure exchange economies and provides criteria to distinguish unavoidable crises from other critical points, using advanced mathematical tools.

Contribution

It introduces a formal definition of crisis transitions and infinitesimal criteria within the equilibrium manifold framework, advancing theoretical understanding.

Findings

Defined crisis transitions rigorously

Established criteria to identify unavoidable crises

Linked mathematical notions to economic criticality

Abstract

In the framework of the theory of Equilibrium Manifold of a Pure Exchange Economy, introduced by Balasko, we give a rigorous definition of a crisis transition and establish some infinitesimal criteria which distinguish unavoidable crises from other critical equilibria. Our approach builds on the relationship between the mathematical notions of branching, envelopes, and the intrinsic derivative.