Skip to main content

An Approximation Method for Evolutions of Exchange Economies Making the Evolving Equilibrium Set Nice

  • Chapter
  • 217 Accesses

Abstract

Static equilibrium theory still struggles with the annoying feature of indeterminateness of the equilibrium set. For evolutions of exchange economies, however, there is a certain general well-behavedness property of the evolving equilibrium set (Mas-Colell, Lehmann-Waffenschmidt). Unfortunately, this property is rather weak. Mas-Colell has shown by an abstract argumentation that in principle it must be possible to approximate evolutions so that a significantly stronger well-behavedness property obtains. Our present paper presents an explicit method which achieves the approximation. Based on the familiar polynomial approximation our method seems both natural and intuitive. Major efforts, however, were necessary to verify the well-behavedness of the evolving equilibrium set.

Keywords

  • Analytical Path
  • Exchange Economy
  • Component Function
  • Continuous Path
  • Advanced Result

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The authors are indebted to Prof. R. Selten, University of Bonn, who suggested the issue of polynomial approximation, and to Prof. C. T. C. Wall, University of Liverpool, who indicated the reference to Teissier’s article.

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Allen, B. (1981), “Utility Perturbations and the Equilibrium Price Set,” Journal of Mathematical Economics 8, 277–307.

    CrossRef  Google Scholar 

  • Kehoe, T. (1980), “An Index Theorem for General Equilibrium Models with Production,” Econometrica 48, 1211–1232.

    CrossRef  Google Scholar 

  • Kehoe, T. (1982), “Regular Production Economies,” Journal of Mathematical Economics 10, 147–176.

    CrossRef  Google Scholar 

  • Lang, S. (1969), Analysis I, Addison-Wesley.

    Google Scholar 

  • Lehmann-Waffenschmidt, M. (1983), “Fasernweise algebraische Fixpunktinvarianten und eine Anwendung in stetig-deformierten Walrasianischen Ökonomien,” in: Beckmann, M., Eichhorn, W., Krelle, W. (Hrsg.): Mathematische Systeme in der Ökonomie, Athenaum-Verlag, 383–413.

    Google Scholar 

  • Lehmann-Waffenschmidt, M. (1985), Gleichgewichtspfade für Ökonomien mit variierenden Daten, mathematical systems in economics, vol. 99, Hain-Verlag.

    Google Scholar 

  • Lehmann-Waffenschmidt, M., “On the Equilibrium Price Set of a Continuous Perturbation of Exchange Economies,” Discussionpaper A-147, University of Bonn.

    Google Scholar 

  • Mas-Colell, A. (1977), “On the Equilibrium Price Set of an Exchange Economy,” Journal of Mathematical Economics 4, 117–126.

    CrossRef  Google Scholar 

  • Mas-Colell, A. (1985), The Theory of General Economic Equilibrium. A Differentiable Approach, Econometric Society Monographs vol. 9, Cambridge University Press.

    Google Scholar 

  • Shafer, W. and Sonnenschein, H. (1982), “Market Demand and Excess Demand Functions,” in: Arrow and Intriligator (eds.): Handbook of Mathematical Economics, vol. II, ch. 14, North-Holland.

    Google Scholar 

  • Teissier, B. (1975), “Théorèmes de finitude en géometrie analytique [d’après Heisuke Hironaka],” in: Séminaire Bourbaki 73/74, Exposés 436–452, Lecture Notes in Mathematics vol. 431, Springer-Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1993 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

Bilitewski, F., Lehmann-Waffenschmidt, M. (1993). An Approximation Method for Evolutions of Exchange Economies Making the Evolving Equilibrium Set Nice. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-78508-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78510-8

  • Online ISBN: 978-3-642-78508-5

  • eBook Packages: Springer Book Archive