An N-dimensional version of Scarf's example

摘要

This paper presents a unification of the contributions of Scarf [Some examples of global instability of competitive equilibrium, Int. Econ. Rev. 1 (1960) 157-172] and Gale [A note on global instability of competitive equilibrium, Nav. Res. Logist. Q. 10 (1963) 81-87] by means of a single class of utility functions. The unification extends Scarf's three-commodity, three-consumer economy to an n-commodity, n-consumer economy. We find that the stability of the extended economy depends on whether the law of demand for exchange economies, i.e., downward sloping excess demand, holds or not. Moreover, it is seen that there is a transition from instability to stability as substitution effect increases or as the desire of each consumer for his own commodity decreases. (c) 2007 Elsevier Ltd. All rights reserved.