The Aggregate Weak Axiom in a Financial Economy through Dominant Substitution Effects

Consider a two period financial economy with incomplete markets and with agents having von Neumann-Morgenstern utility functions. It is well known that when the economy’s endowments are collinear, its excess demand function will obey the weak axiom when certain mild restrictions are imposed on agents’ coefficient of relative risk aversion. This result is obtained through the application of a theorem on the law of demand (for individual demand) formulated independently by Milleron (1974), and Mitjuschin and Polterovich (1978). In this paper, we develop their arguments further and apply them to economies without collinear endowments. We identify conditions which guarantee that the economy’s excess demand function obeys the weak axiom near an equilibrium price. Keywords: income effects, substitution effects, monotonicity, law of demand, weak axiom.