Equilibrium selection under changes in endowments: A geometric approach

Abstract

In this paper we propose a geometric approach to the selection of the equilibrium price. After a perturbation of the parameters, the new price is selected thorough the composition of two maps: the projection on the linearization of the equilibrium manifold, a method that underlies econometric modeling, and the exponential map, that associates a tangent vector with a geodesic on the manifold. As a corollary of our main result, we prove the equivalence between zero curvature and uniqueness of equilibrium in the case of an arbitrary number of goods and two consumers, thus extending the previous result by Loi and Matta (2018).