Stability in a discrete time model of the Walrasian tâtonnement

Abstract

Almost all of the extensive literature on the stability of the Walrasian tâtonnement models the process in continuous rather than discrete time. Since the motivation for the use of continuous time is primarily mathematical, not economic, and since stability for a continuous time model does not imply the stability of its discrete time analogue, it is of interest to investigate the stability of the Walrasian tâtonnement modeled in discrete time. The question is of particular importance since much of the recent literature on topics such as expectations, disequilibrium trading, and temporary equilibrium utilizes discrete time. This paper demonstrates that for a certain class of models, conditions known to be sufficient for stability in continuous time are also sufficient in a discrete time formulation of the price adjustment mechanism. Excess demand functions having the properties of gross substitution, dominant diagonals, and the ‘Morishima system’ of complementary commodities, are analyzed.