COMMODITY PAIR DESIRABILITY AND THE CORE EQUIVALENCE THEOREM

Publisher Summary This chapter discusses the core-Walras equivalence in economies with a continuum of agents and with an infinite-dimensional commodity space. It discusses the general importance of infinite-dimensional commodity spaces in economics. Infinite-dimensional commodity spaces arise quite naturally in economics. In particular, an infinite-dimensional commodity space may be desirable in problems involving an infinite time horizon, uncertainty about the possibly infinite number of states of nature of the world, or infinite varieties of commodity characteristics. The chapter discusses core-Walras equivalence results for perfectly competitive economies with an infinite-dimensional commodity space that is sufficiently general to include all of the spaces that have been found most useful in equilibrium analysis. In infinite-dimensional commodity space whose positive cone has a nonempty—norm—interior, core-Walras equivalence results can be obtained under quite mild assumptions. The chapter also reviews notation, definitions, and some results on Banach lattices and the integration of correspondences.

[1]  Robert J. Aumann,et al.  EXISTENCE OF COMPETITIVE EQUILIBRIA IN MARKETS WITH A CONTINUUM OF TRADERS , 2020, Classics in Game Theory.

[2]  Nicholas C. Yannelis,et al.  Fatou’s lemma in infinite-dimensional spaces , 1988 .

[3]  F. Hiai,et al.  Integrals, conditional expectations, and martingales of multivalued functions , 1977 .

[4]  Application of Functional Analysis to Models of Efficient Allocation of Economic Resources , 1980 .

[5]  Nicholas C. Yannelis,et al.  Edgeworth's conjecture in economies with a continuum of agents and commodities , 1991 .

[6]  A Limit Theorem on the Core of an Economy with a Continuum of Commodities , 1991 .

[7]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[8]  M. A. Khan,et al.  Equilibria in Markets with a Continuum of Agents and Commodities , 1991 .

[9]  Charalambos D. Aliprantis,et al.  When is the core equivalence theorem valid? , 1991 .

[10]  Nicholas C. Yannelis,et al.  Perfect Competition , 2009 .

[11]  Bezalel Peleg,et al.  MARKETS WITH COUNTABLY MANY COMMODITIES. , 1970 .

[12]  T. Bewley.  Equilibrium theory with an infinite dimensional commodity space , 1970 .

[13]  L. M. Court.  Entrepreneurial and Consumer Demand Theories for Commodity Spectra: Part I , 1941 .

[14]  Graciela Chichilnisky.  The cone condition, properness, and extremely desirable commodities , 1993 .

[15]  T. Bewley,et al.  The Equality of the Core and the Set of Equilibria in Economies with Infinitely Many Commodities and a Continuum of Agents , 1973 .

[16]  Metric measure spaces of economic agents , 1972 .

[17]  A counterexample and an exact version of Fatou's lemma in infinite dimensional spaces , 1986 .

[18]  Andreu Mas-Colell,et al.  The Price Equilibrium Existence Problem in Topological Vector Lattice s , 1986 .

[19]  Mukul Majumdar,et al.  Weak sequential convergence in L1(μ, X) and an approximate version of Fatou's Lemma , 1986 .

[20]  G. Debreu.  VALUATION EQUILIBRIUM AND PARETO OPTIMUM. , 1954, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Andreu Mas-Colell,et al.  A model of equilibrium with differentiated commodities , 1975 .

[22]  N. Yannelis.  Equilibria in noncooperative models of competition , 1987 .

[23]  N. Yannelis.  Integration of Banach-Valued Correspondence , 1991 .

[24]  T. Bewley.  A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many Commodities , 1991 .