MULTIPLE EQUILIBRIA AND HYSTERESIS IN SIMPLE EXCHANGE MODELS

This paper presents a simple two-good general equilibrium model of exchange in which demands are linear functions of relative prices. The solution of the model is represented by a cubic equation which can have either a single root which corresponds to a unique equilibrium price or three roots corresponding to multiple equilibria. The major properties of the model are that the relative price can make large discrete jumps in response to small parameter changes, and can display hysteresis. The paper shows how recent developments in non-linear methods can be used to examine the equilibrium properties of the model and establish conditions under which multiple equilibria can arise. The model is compared with that used by Shapley and Shubik.