General Equilibrium Analysis: Existence and Optimality Properties of Equilibria

ISBN-13: 9781441953728 / Angielski / Miękka / 2010 / 181 str.

Monique Florenzano

Opis

General Equilibrium Analysis is a systematic exposition of the Walrasian model of economic equilibrium with a finite number of agents, as formalized by Arrow, Debreu and McKenzie at the beginning of the fifties and since then extensively used, worked and studied. Existence and optimality of general equilibrium are developed repeatedly under different sets of hypothesis which define some general settings and delineate different approaches to the general equilibrium existence problem. The final chapter is devoted to the extension of the general equilibrium model to economies defined on an infinite dimensional commodity space. The objective of General Equilibrium Analysis is to give to each problem in each framework the most general solution, at least for the present state of art. The intended readers are graduate students, specialists and researchers in economics, especially in mathematical economics. The book is appropriate as a class text, or for self-study.

Spis treści

Preface. -1: Fixed Points and Maximal Elements. 1.1. From the Knaster-Kuratowski-Mazurkiewicz lemma to the Kakutani-Fan theorem. 1.2. From the Ky Fan lemma to the Kakutani Fan theorem. 1.3. The coincidence theorem and its consequences. 1.4. An application of the previous results: the KKMS lemma. 1.5. Theorems obtained by selection. - 2: Transitive Equilibrium. 2.1. A direct proof of the Debreu-Gale-Nikaido lemma. 2.2. Existence of transitive quasiequilibrium. 2.3. From quasiequilibrium to equilibrium. - 3: Nontransitive Equilibrium. 3.1. Equilibrium and quasiequilibrium of an abstract economy. 3.2. Existence of nontransitive quasiequilibrium. 3.3. From quasiequilibrium to equilibrium. - 4: Optimality Properties of Equilibrium. 4.1. Optimality concepts. 4.2. Nonemptiness theorems. 4.3. Decentralization theorems. - 5: Infinite Dimensional Economies. 5.1. Preliminaries. 5.2. Edgeworth equilibrium existence and nonemptiness of the fuzzy core. 5.3. Decentralizing Edgeworth allocations. 5.4. A brief historical survey and a suggestion for a research agenda. - Appendix: A.1. Upper and lower semicontinuity. A.2. Related concepts. A.3. Operations with correspondences. A.4. Maximum Theorem. Bibliography. Index of symbols. Index.

O autorze

Monique Florenzano was Assistant-Professor at the Math. Department of the University of Paris, Center of Orsay, when she entered in CNRS (Centre National de la Recherche Scientifique). She is currently research director at CNRS and affiliated to CERMSEM. She was a visiting Professor of several universities: University of California at Berkeley (USA), Carlos III de Madrid (Spain), Universidad de Chile at Santiago, Universidad de la Havana (Cuba), The Johns Hopkins University at Baltimore (USA), University of Melbourne (Australia), Purdue University at W. Lafayette (USA), IMPA at Rio de Janeiro (Brazil), she has taught several courses in Mathematical Economics: General equilibrium, Incomplete markets, and in Mathematics: Convexity and Optimization. She publishes in optimization, fixed point theory, and obviously in different areas of finite and infinite dimensional general equilibrium.