Existence and Optimality of Competitive Equilibria

This monograph is a systematic exposition of the authors' research on general equi­ librium models with an infinite number of commodities. 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 this end, we have pro­ vided two introductory chapters on the basic economic model and the mathematical framework. The exercises at the end of each section complement the main exposition. Chapter one is a concise but substantiative discussion of the questions of exis­ tence and optimality of competitive equilibria in the Walrasian general equilibrium model of an economy with a finite number of households, firms and commodities. Our extension of this model to economies with an infinite number of commodities constitutes the core material of this book and begins in chapter three. Readers fa­ miliar with the Walrasian general equilibrium model as exposited in [13], [23J or [52J may treat chapter one as a handy reference for the main economic concepts and notions that are used throughout the book.

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.