Characterizations of Pseudomonotone Maps and Economic Equilibrium

The paper surveys some recent contributions to the analysis ofpseudomonotone maps and their application to economics. It is shown that the concept ofpseudomonotonicity is strongly related to a notion of rationalityof consumer's behaviour which is well known in economics as a weakversion of the Weak Axiom of Revealed Preference. In economic models of general equilibrium, a pseudomonotone aggregate excess demand function is seen to guaranteeconvexity of the set of price equilibria and, in the case of so-called regular economies,even the uniqueness of equilibrium. Some generalcharacterizations 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 ofaggregate excess demand in economies displaying a particular kind ofheterogeneous consumer behaviour.