Comparative Statics of the Weak Axiom

This paper examines the comparative statics of Walrasian economies with excess demand functions which obey the weak axiom. We show that in these economies there is a precise sense in which goods that are in excess supply (demand) after some perturbation will experience a fall (rise) in its price. We apply this to an exchange economy with additive utility functions, which can be interpreted as a financial economy with von Neumann-Morgenstern utility functions. We show that when the subjective probabilities which agents attribute to a particular state falls, so will the price of consumption in that state. Another interesting issue is the impact of changes to the endowment on the equilibrium price. We develop conditions under which, for an exchange economy, this equilibrium map - from endowment to equilibrium price - will obey the weak axiom and another stronger, monotonicity property.