STABILITY OF EXCESS DEMAND FUNCTIONS WITH RESPECT TO A STRONG VERSION OF WALD'S AXIOM

In this paper, a use of s-quasimonotonicity [introduced in Optimization, Vol. 55 (2006)] in an economics model is presented. We introduce a strong version of Wald's Axiom of excess demand functions $Z : P \subset \mathbb{R}_{>0}^n \to \mathbb{R}^n$, namely "there exists σ > 0 such that p, q ∈ P, qT Z(p) - δ ≤ 0,|δ| < σ, and Z(q) ≠ Z(p) imply pTZ(q) + δ > 0". Under some assumptions, Z satisfies the strong version of Wald's Axiom iff -Z is a s-quasimonotone function. Consequently, an excess demand function Z satisfies the strong version of Wald's Axiom iff -Z is stable with respect to the pseudomonotonicity property (i.e. there exists ∊ > 0 such that -Z + a fulfills the pseudomonotonicity property for all a ∈ ℝn satisfying ‖a‖ < ∊). Some properties on the measure of the strong version of Wald's Axiom of excess demand functions are also presented.