A+ CATEGORY SCIENTIFIC UNIT

Demand continuity and equilibrium in Banach commodity spaces

Volume 71 / 2006

Anthony Horsley, A. J. Wrobel Banach Center Publications 71 (2006), 163-183 MSC: Primary 91B50; Secondary 46B42, 46E30. DOI: 10.4064/bc71-0-13

Abstract

Norm-to-weak* continuity of excess demand as a function of prices is proved by using our two-topology variant of Berge's Maximum Theorem. This improves significantly upon an earlier result that, with the extremely strong finite topology on the price space, is of limited interest, except as a vehicle for proving equilibrium existence. With the norm topology on the price space, our demand continuity result becomes useful in applications of equilibrium theory, especially to problems with continuous commodity spectra. Some auxiliary results are also given, including closedness of the total production set and additivity of the asymptotic cone operation. Both are needed in proving equilibrium existence by the use of the Debreu-Gale-Nikaido Lemma.

Authors

  • Anthony HorsleyDepartment of Economics
    London School of Economics
    Houghton Street
    London WC2A 2AE
    United Kingdom
    e-mail
  • A. J. WrobelDepartment of Economics
    London School of Economics
    Houghton Street
    London WC2A 2AE
    United Kingdom
    e-mail

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