Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T16:55:15.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of production economies

Part of: Maps and general types of spaces defined by maps Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

Kok-Keong Tan ,
Jian Yu  and
Xian-Zhi Yuan
Kok-Keong Tan
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie UniversityHalifax, Nova Scotia B3H 3J5Canada e-mail: [email protected]
Jian Yu
Affiliation:
Institute of Applied Mathematics Guizhou Institute of TechnologyGuiyang, Guizhou 550003, China
Xian-Zhi Yuan
Affiliation:
Department of Mathematics University of QueenslandBrisbane Queensland 4072, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, the concept of essential equilibria for production economies is first given. We then prove that in ‘most’ production economies (in the sense of Baire category) all equilibria are essential.

MSC classification

Secondary: 54C60: Set-valued maps 54E52: Baire category, Baire spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 162 - 170
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Border, K. C., Fixed point theorems with applications to economies and game theory (Cambridge University Press, Cambridge, 1985).Google Scholar
[2]Debreu, G., ‘Economies with a finite set of equilibria’, Econometrica 38 (1970), 387–392.CrossRefGoogle Scholar
[3]Debreu, G., ‘Existence of competitive equilibrium’, in: Handbook of mathematical economies (Arrow, K. J. and Intrilligator, M. D., eds.) vol. II (North-Holland, Amsterdam, 1982).Google Scholar
[4]Dierker, E., Topological methods in Walrasian economics (Springer, Berlin, 1974).CrossRefGoogle Scholar
[5]Dugundji, J., Topology (Allyn and Bacon, Boston, 1967).Google Scholar
[6]Fort, M. K., ‘Points of continuity of semicontinuous functions’, Publ. Math. Debrecen 2 (1951), 100–102.CrossRefGoogle Scholar
[7]Grandmont, J. M., ‘Temporary general equilibrium theory’, Econometrica 45 (1977), 535–572.CrossRefGoogle Scholar
[8]Klein, E. and Thompson, A., Theory of correspondences (Wiley, New York, 1984).Google Scholar
[9]Oxtoby, J. C., ‘Cartesian products of Baire spaces’, Fund. Math. 49 (1961), 157–166.CrossRefGoogle Scholar
[10]Tarafdar, E. and Thompson, B., ‘On the existence of the price equilibrium by different methods’, Comment. Math. Univ. Carolin. 34 (1993), 413–417.Google Scholar