Convergence of iterative tâtonnement without price normalization

Abstract

This paper presents global convergence conditions for a non-normalized fixed-point iteration in computing the equilibria of exchange economies. The usual conditions for the stability of Walras’ tâtonnement are obtained as a limiting case from these conditions. The iteration leads to an equilibrium under a strengthened form of the weak axiom of revealed preferences introduced in the paper. Results for economies with global gross substitutability and no trade at equilibrium are also presented. Furthermore, it is shown that a rather general class of non-normalized iterations converges under the same conditions as the fixed-point iteration.