Luigi Brighi

Characterizations of pseudomonotone maps and economic equilibrium

Abstract The paper surveys some recent contributions to the analysis of pseudomonotone maps and their application to economics. It is shown that the concept of pseudomonotonicity is strongly related to a notion of rationality of consumer behaviour which is well known in economics as a weak version of the Weak Axiom of Revealed Preference. In economic models of general equilibrium, a pseudomonotone aggregate excess demand function is seen to guarantee convexity of the set of price equilibria and, in the case of so-called regular economies, even the uniqueness of equilibrium. Some general characterizations of differentiable pseudomonotone maps, which reduce to necessary and sufficient first order conditions under the assumption of regularity, are provided. These conditions are employed in order to prove pseudomonotonicity of aggregate excess demand in economies displaying a particular kind of heterogeneous consumer behaviour.

A stronger criterion for the Weak Weak Axiom

Abstract The Weak Weak Axiom (WWA) is a milder version of the Weak Axiom of Revealed Preference (WA) and is equivalent to pseudomonotonicity of the excess demand function. Since the WWA guarantees uniqueness of the equilibrium in a broad class of general equilibrium models, it is important to have criteria to check when the WWA holds. In this paper, a new and more general characterization of pseudomonotonicity for C 1 maps is provided. Using this result, we obtain a stronger criterion for the WWA than those available in the literature. A complete characterization of the WA for excess demand functions is also offered and other important existing results are obtained in a straightforward fashion.