Problems in Equilibrium Theory

Prof. Dr. Uschi Backes-Gellner ist Leiterin des Seminars für Allgemeine Betriebswirtschaftslehre und Personalwirtschaft an der Universität zu Köln.

In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.

Contents: The Arrow-Debreu Model: Preferences and utility functions.- Maximal elements.- Demand functions.- Exchange economies.- Optimality in exchange economies.- Optimality and decentralization.- Production economies.- Riesz Spaces of Commodities and Prices: Partially ordered vector spaces.- Positive linear functionals.- Topological Riesz spaces.- Banach lattices.- Markets With Infinitely Many Commodities: The economic models.- Proper and myopic preferences.- Edgeworth equilibria and the core.- Walrasian equilibria and quasiequilibria.- Pareto optimality.- Examples of exchange economies.- Production With Infinitely Many Commodities: The model of a production economy.- Edgeworth equilibria and the core.- Walrasian equilibria and quasiequilibria.- Approximate supportability.- Properness and the welfare theorems.- The Overlapping Generations Model: The setting of the OLG model.- The OLG commodity-price duality.- Malinvaud optimality.- Existence of competitive equilibria.