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Understanding Fixed Point Theorems


  • Arnold, Lutz G.


Fixed point theorems are the standard tool used to prove the existence of equilibria in mathematical economics. This paper shows how to prove a slight generalization of Brouwer's and Kakutani's fixed point theorems using the familiar techniques of drawing and shifting curves in the plane and is, therefore, intelligible without advanced knowledge of topology. This makes proofs of fixed point theorems accessible to a broader audience.Kurvenverschieben in der Ebene' beweisen lassen. Das wichtigste Instrument für Existenzsätze in der mathematischen Volkswirtschaftslehre sind Fixpunkttheoreme. Dieses Papier zeigt, wie sich Brouwers Fixpunktsatz und einige geringfügige Verallgemeinerungen durch 'Kurvenverschieben in der Ebene' beweisen lassen. Weil keine tiefen topologischen Vorkenntnisse notwendig sind, ist der grafische Beweis für einen breiten Adressatenkreis zugänglich.

Suggested Citation

  • Arnold, Lutz G., 2003. "Understanding Fixed Point Theorems," University of Regensburg Working Papers in Business, Economics and Management Information Systems 379, University of Regensburg, Department of Economics.
  • Handle: RePEc:bay:rdwiwi:139

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    References listed on IDEAS

    1. Holmlund, Bertil, 1998. " Unemployment Insurance in Theory and Practice," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 113-141, March.
    2. Nickell, Stephen & Layard, Richard, 1999. "Labor market institutions and economic performance," Handbook of Labor Economics,in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 46, pages 3029-3084 Elsevier.
    3. Danthine, Jean-Pierre & Hunt, Jennifer, 1994. "Wage Bargaining Structure, Employment and Economic Integration," Economic Journal, Royal Economic Society, vol. 104(424), pages 528-541, May.
    4. Blanchard, Olivier & Wolfers, Justin, 2000. "The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence," Economic Journal, Royal Economic Society, vol. 110(462), pages 1-33, March.
    5. Lars Ljungqvist & Thomas J. Sargent, 1998. "The European Unemployment Dilemma," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 514-550, June.
    6. Nickell, Stephen, 1999. "Product markets and labour markets1," Labour Economics, Elsevier, vol. 6(1), pages 1-20, March.
    7. Pissarides, Christopher A., 1998. "The impact of employment tax cuts on unemployment and wages; The role of unemployment benefits and tax structure," European Economic Review, Elsevier, vol. 42(1), pages 155-183, January.
    8. Laszlo Goerke, 2000. "Bismarck versus Beveridge. Flat-Rate and Earnings-Related Unemployment Insurance in a General Efficiency Wage Framework," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 57(3), pages 243-243, May.
    9. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    10. Goerke, Laszlo & Madsen, Jakob B., 2003. "Earnings-related unemployment benefits and unemployment," Economic Systems, Elsevier, vol. 27(1), pages 41-62, March.
    11. Richard Layard & Stephen Nickell, 1990. "Is Unemployment Lower if Unions Bargain over Employment?," The Quarterly Journal of Economics, Oxford University Press, vol. 105(3), pages 773-787.
    12. Manning, Alan, 1998. " Comment on B. Holmlund, "Unemployment Insurance in Theory and Practice."," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 143-145, March.
    13. Robert J. Flanagan, 1999. "Macroeconomic Performance and Collective Bargaining: An International Perspective," Journal of Economic Literature, American Economic Association, vol. 37(3), pages 1150-1175, September.
    14. Stephen Nickell, 1997. "Unemployment and Labor Market Rigidities: Europe versus North America," Journal of Economic Perspectives, American Economic Association, vol. 11(3), pages 55-74, Summer.
    15. Manning, Alan, 1993. "Wage Bargaining and the Phillips Curve: The Identification and Specification of Aggregate Wage Equations," Economic Journal, Royal Economic Society, vol. 103(416), pages 98-118, January.
    16. Blanchard, Olivier Jean & Kiyotaki, Nobuhiro, 1987. "Monopolistic Competition and the Effects of Aggregate Demand," American Economic Review, American Economic Association, vol. 77(4), pages 647-666, September.
    17. Thomas Beissinger & Oliver Büsse, 2001. "Bismarck versus Beveridge: Which Unemployment Compensation System is more Prone to Labor Market Shocks?," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 58(1), pages 1-78, December.
    18. Manning, Alan, 1991. "The Determinants of Wage Pressure: Some Implications of a Dynamic Model," Economica, London School of Economics and Political Science, vol. 58(231), pages 325-339, August.
    19. Goerke, Laszlo, 1998. "Bismarck versus Beveridge: Flat- and earnings-related unemployment insurance in an efficiency wage framework," Discussion Papers, Series I 291, University of Konstanz, Department of Economics.
    20. John A. Abowd & Thomas Lemieux, 1993. "The Effects of Product Market Competition on Collective Bargaining Agreements: The Case of Foreign Competition in Canada," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 983-1014.
    21. Thomas Beissinger & Hartmut Egger, 2004. "Dynamic wage bargaining if benefits are tied to individual wages," Oxford Economic Papers, Oxford University Press, vol. 56(3), pages 437-460, July.
    22. Burkhard Heer & Albrecht Morgenstern, 2005. "The Labor Market Effects of Indexing Unemployment Benefits to Previous Earnings," Public Finance Review, , vol. 33(3), pages 385-402, May.
    23. Atkinson, Anthony B & Micklewright, John, 1991. "Unemployment Compensation and Labor Market Transitions: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 29(4), pages 1679-1727, December.
    24. Amitava Dutt & Anindya Sen, 1997. "Union bargaining power, employment, and output in a model of monopolistic competition with wage bargaining," Journal of Economics, Springer, vol. 65(1), pages 1-17, February.
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    More about this item


    Brouwerscher Fixpunktsatz ; Allgemeines Gleichgewicht ; Nash-Gleichgewicht; ; Fixed Point Theorems ; General Equilibrium ; Nash Equilibrium;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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