Center for Economic Research, Department of Economics, University of Minnesota
This paper contains the following results for economies
with infinite dimensional commodity spaces. (i) He establish a core-Walras
equivalence theorem for economies with an atomless measure space
of agents and with an ordered separable Banach commodity space whose
positive cone has a non-empty norm interior. This result includes as a
special case the Aumann (1964) and Hildenbrand (1974) finite dimensional
theorems. (ii) We provide a counterexample which shows that the above
result fails in ordered Banach spaces whose positive cone has an empty
interior even if preferences are strictly convex, monotone and weak*
continuous and initial endowments are strictly positive. (iii) After
introducing a new assumption on preferences called "commodity pair
desirability," (which is automatically satisfied whenever preferences
are monotone and the positive cone of the commodity space has a non-empty
interior), we establish core-Walras equivalence in any arbitrary separable
Banach lattice whose positive cone may have an empty (norm) interior.
(iv) We provide a proof that in some concrete spaces whose positive cone
may have an empty interior, the assumption of an extremely desirable
commodity or uniform properness suffices for core-Walras equivalence.
Finally, (v) we indicate how our methods can be used to obtain core-Walras
equivalence results for the space M(~) of measures on a compact metric
Rustichini, A. and Yannelis, N.C., (1987), "Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities", Discussion Paper No. 238, Center for Economic Research, Department of Economics, University of Minnesota.
Rustichini, Aldo; Yannelis, Nicholas C..
Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities.
Center for Economic Research, Department of Economics, University of Minnesota.
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