Maćkowiak, Piotr (2010): The existence of equilibrium without fixedpoint arguments. Published in: The existence of equilibrium without fixedpoint arguments , Vol. 46, No. 6 (2010): pp. 11941199.

PDF
MPRA_paper_42044.pdf Download (156kB)  Preview 
Abstract
This paper gives a proof of the existence of general equilibrium without the use of a fixed point theorem. Unlike other results of this type, the conditions we use do not imply that the set of equilibrium prices is convex. We use an assumption on the excess demand correspondence that is related to, but weaker than, the weak axiom of revealed preference (WARP). The proof is carried out for compact and convex valued upper hemicontinuous excess demand correspondences satisfying this WARPrelated condition and some other standard conditions. We also provide an algorithm for finding equilibrium prices.
Item Type:  MPRA Paper 

Original Title:  The existence of equilibrium without fixedpoint arguments 
Language:  English 
Keywords:  existence of economic equilibrium; the weak axiom of revealed preference; excess demand correspondence; distribution economies; law of demand 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium > D50  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  42044 
Depositing User:  Piotr Maćkowiak 
Date Deposited:  18. Oct 2012 14:57 
Last Modified:  22. Feb 2013 02:41 
References:  Arrow K., Hahn F. General Competitive Analysis. HoldenDay: San Francisco; 1971 Barbolla R., Corchon L. An Elementary Proof of the existence of Competitive Equilibrium in a Special Case. The Quarterly Journal of Economics 1989; 104; 385389 Florenzano M., LeVan C. Finite Dimensional Convexity and Optimization. Springer: Berlin Heidelberg New York; 2001 Fraysse J. A simple proof of the existence of an equilibrium when the weak axiom holds. Journal of Mathematical Economics 2009; 45; 767769 Greenberg J. An elementary proof of the existence of a competitive equilibrium with weak gross substitutes. The Quarterly Journal of Economics 1977; 91; 513516 Hildenbrand W. On the ’Law of Demand’ . Econometrica 1983; 51; 9971019 John R. 1998. Variational Inequalities and Pseudomonotone Functions: Some Characterizations. In Crouzeix J.P., Mart´ınezLegaz J.E., Volle M. (Eds), Generalized convexity, generalized monotonicity: recent results. Kluwer Academic Publishers; 1998. p. 291301 John R. AbrahamWald’s equilibrium existence proof reconsidered. Economic Theory 1999; 13; 417428 MasColell A., Whinston M., Green J. Microeconomic Theory. Oxford University Press: New York Oxford; 1995 Moore J. General Equilibrium and Welfare Economics. An Introduction. Springer: Berlin Heidelberg; 2007 Quah J. The Law of Demand when income is price dependent. Econometrica 1997; 65; 14211442 Quah J. The existence of equilibrium when excess demand obeys the weak axiom. Journal of Mathematical Economics 2008; 44; 337343 Toda M. Approximation of Excess Demand on the Boundary and Equilibrium Price Set. Advances in Mathematical Economics 2006; 9; 99107 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/42044 