Browsing by Author "Rustichini, Aldo"
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Item Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities(Center for Economic Research, Department of Economics, University of Minnesota, 1987-04) Rustichini, Aldo; Yannelis, Nicholas C.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 space.Item A Counterexample and an Exact Version of Fatou's Lemma in Infinite Dimension(Center for Economic Research, Department of Economics, University of Minnesota, 1986-09) Rustichini, AldoAn example is presented to show that approximate versions of Fatou's Lemma in infinite dimension cannot be improved, and a sufficient condition for an exact version is provided.Item An Elementary Proof of Fatou's Lemma in Finite Dimensional Spaces(Center for Economic Research, Department of Economics, University of Minnesota, 1986-11) Rustichini, Aldo; Yannelis, Nicholas C.We provide an elementary and very short proof of the Fatou Lemma in n-dimensions. In particular, we show that the latter result follows directly from Aumann's (1976) elementary proof of the fact that integration preserves upper-semicontinuity.