The global LeChatelier Principle and multimarket equilibria

Abstract

LeChatelier (Comptes Rendus 99:786, 1884) and LeChatelier (Ann Mines 13(2):157, 1888) proposed that the adjustment of a physical system to a disturbance in its equilibrium was smaller as constraints are added to the adjustment process. Samuelson (Econometrica 28:368–379, 1960) showed that this Principle applied to a stable multimarket equilibrium for the case that all commodities are gross substitutes. We note that the Principle also applies to the stable equilibria of markets for which commodities can also be gross complements as formulated by Morishima (Osaka Econ Pap 1:101–113, 1952). Further, the Morishima and gross substitute cases are the only cases to which the Principle can apply, based only upon the stability hypothesis and a specification of the gross substitute/complement relations among commodities. We show that the Milgrom and Shannon (Econometrica 62:157–180, 1994) single crossing conditions specified for monotone comparative statics can be configured appropriate to the Morishima case to give global conditions for the LeChatelier Principle to apply to a multimarket equilibrium.