Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.

Browsing by Subject "Banach lattice"

Now showing 1 - 1 of 1
  • Thumbnail Image
    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.