IDEAS home Printed from https://ideas.repec.org/p/att/wimass/20012.html
   My bibliography  Save this paper

Uniqueness of positive fixed points for increasing concave functions on Rn : an elementary result

Author

Listed:
  • Kennan,J.

    (University of Wisconsin-Madison, Social Systems Research Institute)

Abstract

The square root function has a unique positive fixed point. This function has the following properties: it is strictly increasing and strictly concave, with f(0)=0, and there are points a>0 and b>0 such that f(b)>a and b>f(b). It is shown that any function from Rn to Rn satisfying these properties has a unique positive fixed point. (Copyright: Elsevier)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kennan,J., 2001. "Uniqueness of positive fixed points for increasing concave functions on Rn : an elementary result," Working papers 2, Wisconsin Madison - Social Systems.
    • Handle: RePEc:att:wimass:20012
    as

    Download full text from publisher

    File URL: http://www.ssc.wisc.edu/~jkennan/research/FixedPoint21.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mulligan Casey B, 2001. "Aggregate Implications of Indivisible Labor," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-35, April.
    2. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    3. Simon Anderson & Michael Devereux, 1985. "Trade Unions and the Choice of Capital Stock," Working Paper 600, Economics Department, Queen's University.
    4. Benhabib, Jess & Rogerson, Richard & Wright, Randall, 1991. "Homework in Macroeconomics: Household Production and Aggregate Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1166-1187, December.
    5. Horn, Henrik & Wolinsky, Asher, 1988. "Worker Substitutability and Patterns of Unionisation," Economic Journal, Royal Economic Society, vol. 98(391), pages 484-497, June.
    6. repec:wop:calsdi:97-23 is not listed on IDEAS
    7. Gomes, Joao & Greenwood, Jeremy & Rebelo, Sergio, 2001. "Equilibrium unemployment," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 109-152, August.
    8. 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.
    9. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007, Elsevier.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    12. Rogerson, Richard, 1988. "Indivisible labor, lotteries and equilibrium," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 3-16, January.
    13. Pencavel, John, 1985. " Wages and Employment under Trade Unionism: Microeconomic Models and Macroeconomic Applications," Scandinavian Journal of Economics, Wiley Blackwell, vol. 87(2), pages 197-225.
    14. Garey Ramey & Wouter J. den Haan & Joel Watson, 2000. "Job Destruction and Propagation of Shocks," American Economic Review, American Economic Association, vol. 90(3), pages 482-498, June.
    15. Keane, Michael P & Runkle, David E, 1990. "Testing the Rationality of Price Forecasts: New Evidence from Panel Data," American Economic Review, American Economic Association, vol. 80(4), pages 714-735, September.
    16. Francesco Daveri & Marco Maffezzoli, "undated". "A numerical approach to fiscal policy, unemployment and growth in Europe," Working Papers 155, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    18. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    19. Palokangas,Tapio, 2010. "Labour Unions, Public Policy and Economic Growth," Cambridge Books, Cambridge University Press, number 9780521144056.
    20. Westermark, Andreas, 1999. "A Model of Union Formation," Working Paper Series 1999:8, Uppsala University, Department of Economics.
    21. Danthine, J.P. & Donaldson, J.B., 1993. "Non-Walrassian Economies," Papers 93-02, Columbia - Graduate School of Business.
    22. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
    23. Jordi Gali, 1995. "Non-Walrasian Unemployment Fluctuations," NBER Working Papers 5337, National Bureau of Economic Research, Inc.
    24. Merz, Monika, 1995. "Search in the labor market and the real business cycle," Journal of Monetary Economics, Elsevier, vol. 36(2), pages 269-300, November.
    25. Gali, Jordi, 1996. "Unemployment in dynamic general equilibrium economies," European Economic Review, Elsevier, vol. 40(3-5), pages 839-845, April.
    26. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    27. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    28. Rogerson, Richard & Wright, Randall, 1988. "Involuntary unemployment in economies with efficient risk sharing," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 501-515.
    29. Hall, Robert E., 1999. "Labor-market frictions and employment fluctuations," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 17, pages 1137-1170, Elsevier.
    30. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    31. Horn, Henrik & Svensson, Lars E O, 1986. "Trade Unions and Optimal Labour Contracts," Economic Journal, Royal Economic Society, vol. 96(382), pages 323-341, June.
    32. Manning, Alan, 1987. "An Integration of Trade Union Models in a Sequential Bargaining Framework," Economic Journal, Royal Economic Society, vol. 97(385), pages 121-139, March.
    33. Andolfatto, David, 1996. "Business Cycles and Labor-Market Search," American Economic Review, American Economic Association, vol. 86(1), pages 112-132, March.
    34. Oswald, Andrew J, 1982. "The Microeconomic Theory of the Trade Union," Economic Journal, Royal Economic Society, vol. 92(367), pages 576-595, September.
    35. Anderson, Simon P & Devereux, Michael, 1988. " Trade Unions and the Choice of Capital Stock," Scandinavian Journal of Economics, Wiley Blackwell, vol. 90(1), pages 27-44.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marco Maffezzoli, 2001. "Non-Walrasian Labor Markets and Real Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 860-892, October.
    2. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007, Elsevier.
    3. Aleksandar Vasilev, 2020. "Are labor unions important for business cycle fluctuations? Lessons from Bulgaria," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 10(1), pages 143-161, March.
    4. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present, and Future," NBER Working Papers 11401, National Bureau of Economic Research, Inc.
    5. Aleksandar Vasilev, 2019. "Are Labor Unions Important for Business Cycle Fluctuations: Lessons from Bulgaria (1999-2016)," Bulgarian Economic Papers bep-2019-02, Faculty of Economics and Business Administration, Sofia University St Kliment Ohridski - Bulgaria // Center for Economic Theories and Policies at Sofia University St Kliment Ohridski, revised Jan 2019.
    6. Lawrence Christiano & Mathias Trabandt & Karl Walentin, 2021. "Involuntary Unemployment and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 26-54, January.
    7. Zanetti, Francesco, 2011. "Labor market institutions and aggregate fluctuations in a search and matching model," European Economic Review, Elsevier, vol. 55(5), pages 644-658, June.
    8. Christiano, Lawrence J. & Trabandt, Mathias & Walentin, Karl, 2010. "DSGE Models for Monetary Policy Analysis," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 7, pages 285-367, Elsevier.
    9. Fabrizio Mattesini & Lorenza Rossi, 2008. "Productivity Shocks And Optimal Monetary Policy In A Unionized Labor Market Economy," Manchester School, University of Manchester, vol. 76(5), pages 578-611, September.
    10. Sergio Rebelo, 2005. "Real Business Cycle Models: Past, Present and Future," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(2), pages 217-238, June.
    11. Lawrence Christiano & Mathias Trabandt & Karl Walentin, 2021. "Involuntary Unemployment and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 26-54, January.
    12. Fang Yao, 2008. "Lumpy Labor Adjustment as a Propagation Mechanism of Business Cycles," SFB 649 Discussion Papers SFB649DP2008-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Ester Faia & Lorenza Rossi, 2013. "Union Power, Collective Bargaining, And Optimal Monetary Policy," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 408-427, January.
    14. Mattesini, Fabrizio & Rossi, Lorenza, 2009. "Optimal monetary policy in economies with dual labor markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(7), pages 1469-1489, July.
    15. Rossi, Lorenza & Mattesini, Fabrizio, 2007. "Optimal Monetary Policy in a Dual Labor Market Economy," MPRA Paper 2468, University Library of Munich, Germany, revised 15 Mar 2007.
    16. Rossi, Lorenza & Mattesini, Fabrizio, 2007. "Productivity Shock and Optimal Monetary Policy in a Unionized Labor Market. Forthcoming: The Manchester School," MPRA Paper 8414, University Library of Munich, Germany, revised 2008.
    17. Yongsung Chang & Sun-Bin Kim, 2006. "From Individual To Aggregate Labor Supply: A Quantitative Analysis Based On A Heterogeneous Agent Macroeconomy ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(1), pages 1-27, February.
    18. Ellen R. McGrattan, 2006. "Real business cycles," Staff Report 370, Federal Reserve Bank of Minneapolis.
    19. Paul Gomme & Richard Rogerson & Peter Rupert & Randall Wright, 2005. "The Business Cycle and the Life Cycle," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 415-592, National Bureau of Economic Research, Inc.
    20. Federico Etro & Andrea Colciago, 2010. "Endogenous Market Structures and the Business Cycle," Economic Journal, Royal Economic Society, vol. 120(549), pages 1201-1233, December.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:att:wimass:20012. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ailsenne Sumwalt (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.