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Existence of General Equilibrium

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Abstract

This article summarizes the history of the attempts to prove the existence of general equilibrium from those of Wald and others in Vienna in the 1930s to those of von Neumann and Nash, and of the solutions provided by Arrow, Debreu and McKenzie in the 1950s and their subsequent development.

This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume

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Bibliography

  • Arrow, K.J., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290.

    Article  Google Scholar 

  • Arrow, K.J., and M.D. Intriligator, eds. 1981–6. Handbook of mathematical economics. Vol. I–III. Amsterdam: North-Holland.

    Google Scholar 

  • Cassel, K.G. 1918. Theoretische Sozialökonomie. Leipzig: C.F. Winter.

    Google Scholar 

  • Debreu, G. 1952. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences 38: 886–893.

    Article  Google Scholar 

  • Debreu, G. 1956. Market equilibrium. Proceedings of the National Academy of Sciences 42: 876–878.

    Article  Google Scholar 

  • Debreu, G. 1982. Chapter 15: Existence of competitive equilibrium. In Arrow and Intriligator (1981–6).

    Google Scholar 

  • Dierker, E. 1972. Two remarks on the number of equilibria of an economy. Econometrica 40: 951–953.

    Article  Google Scholar 

  • Dierker, E. 1974. Topological methods in Walrasian economics. Berlin/New York: Springer-Verlag.

    Book  Google Scholar 

  • Gale, D. 1955. The law of supply and demand. Mathematica Scandinavica 3: 155–169.

    Article  Google Scholar 

  • Kakutani, S. 1941. A generalization of Brouwer’s fixed point theorem. Duke Mathematical Journal 8: 457–459.

    Article  Google Scholar 

  • McKenzie, L.W. 1954. On equilibrium in Graham’s model of world trade and other competitive systems. Econometrica 22: 147–161.

    Article  Google Scholar 

  • Nash, J.F. 1950. Equilibrium points in N-person games. Proceedings of the National Academy of Sciences of the USA 36: 48–49.

    Article  Google Scholar 

  • Neisser, H. 1932. Lohnhöhe und Beschäftigungsgrad im Marktgleichgewicht. Weltwirtschaftliches Archiv 36: 415–455.

    Google Scholar 

  • Nikaidô, H. 1956. On the classical multilateral exchange problem. Metroeconomica 8: 135–145.

    Article  Google Scholar 

  • Schlesinger, K. 1933–4. Über die Produktionsgleichungen der ökonomischen Wertlehre. Ergebnisse eines mathematischen Kolloquiums 6: 10–20.

    Google Scholar 

  • Smale, S. 1976. A convergent process of price adjustment and global Newton methods. Journal of Mathematical Economics 3: 107–120.

    Article  Google Scholar 

  • Smith, A. 1776. An inquiry into the nature and causes of the wealth of nations, vol. 2, ed. R.H. Campbell, A.S. Skinner, and W.B. Todd. Oxford: Clarendon Press, 1976.

    Google Scholar 

  • von Neumann, J. 1935–36. Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. Ergebnisse eines mathematischen Kolloquiums 8: 73–83. Trans. by G. Morgenstern as ‘A model of general economic equilibrium’. Review of Economic Studies 13(1), 1945, 1–9.

    Google Scholar 

  • von Stackelberg, H. 1933. Zwei kritische Bemerkungen zur Preistheorie Gustav Cassels. Zeitschrift für Nationalökonomie 4: 456–472.

    Article  Google Scholar 

  • Wald, A. 1933–4. Über die eindeutige positive Lösbarkeit der neuen Produktionsgleichungen. Ergebnisse eines mathematischen Kolloquiums 6: 12–20.

    Google Scholar 

  • Wald, A. 1934–5. Über die Produktionsgleichungen der ökonomischen Wertlehre. Ergebnisse eines mathematischen Kolloquiums 7: 1–6.

    Google Scholar 

  • Wald, A. 1936. Über einige Gleichungssysteme der mathematischen ökonomie. Zeitschrift für Nationalökonomie 7: 637–670. Trans. by Otto Eckstein as ‘On some systems of equations of mathematical economics’. Econometrica 19(4), 1951, 368–403.

    Google Scholar 

  • Walras, L. 1874–7. Éléments d’économie politique pure. Lausanne: L. Corbaz. Trans. by William Jaffé as Elements of pure economics. Homewood: Richard D. Irwin, 1954.

    Google Scholar 

  • Zeuthen, F. 1932. Das Prinzip der Knappheit, technische Kombination und ökonomische Qualität. Zeitschrift für Nationalökonomie 4: 1–24.

    Article  Google Scholar 

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  1. http://link.springer.com/referencework/10.1057/978-1-349-95121-5

    Gerard Debreu

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  1. Gerard Debreu
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    Debreu, G. (2008). Existence of General Equilibrium. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_487-2

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    • DOI: https://doi.org/10.1057/978-1-349-95121-5_487-2

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    • Online ISBN: 978-1-349-95121-5

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    Chapter history

    1. Latest

      Existence of General Equilibrium
      Published:
      31 March 2017

      DOI: https://doi.org/10.1057/978-1-349-95121-5_487-2

    2. Original

      Existence of General Equilibrium
      Published:
      28 November 2016

      DOI: https://doi.org/10.1057/978-1-349-95121-5_487-1

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