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This book presents the theory of general economic equilibrium from a modern perspective. It gives a systematic exposition of research done by the authors and others on the subject of general equilibrium theory over the last ten years. It is intended to serve both as a graduate text on aspects of general equilibrium theory and as an introduction, for economists and mathematicians working in mathematical economics, to current research in a frontier area of general equilibrium theory. To make the material as accessible as possible to the student, the authors have provided two introductory chapters on the basic Arrow-Debreu economics model and the mathematical framework. Exercises at the end of each section complement the exposition. The monograph addresses the questions of existence and optimality of Walrasian equilibria for economies with a finite number of households and firms, but with an infinite number of commodities. The final chapter of the book presents a comprehensive study of the overlapping generations model. This is the first book to give a unified and mathematically rigorous presentation of the theory of general economic equilibrium in an infinite dimensional setting.
1: The Arrow—Debreu Model.- 1.1. Preferences and Utility Functions.- 1.2. Maximal Elements.- 1.3. Demand Functions.- 1.4. Exchange Economies.- 1.5. Optimality in Exchange Economies.- 1.6. Optimality and Decentralization.- 1.7. Production Economies.- 2: Riesz Spaces of Commodities and Prices.- 2.1. Partially Ordered Vector Spaces.- 2.2. Positive Linear Functionals.- 2.3. Topological Riesz Spaces.- 2.4. Banach Lattices.- 3: Markets with Infinitely Many Commodities.- 3.1. The Economic Models.- 3.2. Proper and Myopic Preferences.- 3.3. Edgeworth Equilibria and the Core.- 3.4. Walrasian Equilibria and Quasiequilibria.- 3.5. Pareto Optimality.- 3.6. Examples of Exchange Economies.- 4: Production with Infinitely Many Commodities.- 4.1. The Model of a Production Economy.- 4.2. Edgeworth Equilibria and the Core.- 4.3. Walrasian Equilibria and Quasiequilibria.- 4.4. Approximate Supportability.- 4.5. Properness and the Welfare Theorems.- 5: The Overlapping Generations Model.- 5.1. The Setting of the OLG Model.- 5.2. The OLG Commodity-Price Duality.- 5.3. Malinvaud Optimality.- 5.4. Existence of Competitive Equilibria.- References.