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

2009 ◽  
Vol 26 (04) ◽  
pp. 523-532
Author(s):  
PHAN THANH AN ◽  
VUONG THI THAO BINH
Keyword(s):  
Demand Function ◽  
Excess Demand ◽  
Strong Version ◽  
Demand Functions ◽  
Economics Model

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 [Formula: see text], 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.

scholarly journals Regular Infinite Economies

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Enrique Covarrubias
Keyword(s):  
Demand Function ◽  
Excess Demand ◽  
Natural Projection ◽  
Banach Manifold ◽  
Equilibrium Manifold ◽  
Equilibrium Set ◽  
Regular Economies

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.

Market Excess Demand Functions

Econometrica ◽  
1972 ◽  
Vol 40 (3) ◽  
pp. 549 ◽  
Author(s):  
Hugo Sonnenschein
Keyword(s):  
Excess Demand ◽  
Demand Functions

scholarly journals LEARNING TO PLAY BEST RESPONSE IN DUOPOLY GAMES

2004 ◽  
Vol 06 (03) ◽  
pp. 443-459 ◽  
Author(s):  
JAN WENZELBURGER
Keyword(s):  
Demand Function ◽  
Optimal Strategies ◽  
Market Demand ◽  
Response Behavior ◽  
Estimation Errors ◽  
Demand Functions ◽  
Best Response ◽  
Game Theoretic ◽  
Payoff Functions ◽  
Duopoly Market

We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response behavior of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, a firm is able to play best response in the usual game theoretic sense.

scholarly journals On the Disaggregation of Excess Demand Functions

Econometrica ◽  
1980 ◽  
Vol 48 (2) ◽  
pp. 315 ◽  
Author(s):  
J. D. Geanakoplos ◽  
H. M. Polemarchakis
Keyword(s):  
Excess Demand ◽  
Demand Functions

WHAT A DIFFERENCE A SUM (∑) MAKES: SUCCESS AND FAILURE IN THE RATIONALIZATION OF DEMAND

2012 ◽  
Vol 34 (3) ◽  
pp. 379-396 ◽  
Author(s):  
D. WADE HANDS
Keyword(s):  
General Equilibrium ◽  
Excess Demand ◽  
Previous Literature ◽  
Equilibrium Theory ◽  
General Equilibrium Theory ◽  
Success Story ◽  
Demand Functions ◽  
Individual Demand

This paper discusses the Sonnenschein–Mantel–Debreu (SMD) theorems in general equilibrium theory. It argues that the SMD results were related to the previous literature on the integrability of demand. The integrability question involved rationalizing individual demand functions, and the SMD theorems asked the same question about aggregate (market) excess demand functions. The paper’s two goals are to demonstrate how the SMD results followed naturally from the earlier work on integrability, and to point out that the profession’s reception was quite different; the integrability results were considered a success story, while the SMD results were quite negative.

A characterization of community excess demand functions

1974 ◽  
Vol 9 (4) ◽  
pp. 361-374 ◽  
Author(s):  
Daniel McFadden ◽  
Andreu Mas-Colell ◽  
Rolf Mantel ◽  
Marcel K Richter
Keyword(s):  
Excess Demand ◽  
Demand Functions
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