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

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  • 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
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    File URL: http://www.ssc.wisc.edu/~jkennan/research/FixedPoint21.pdf
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    Cited by:

    1. John Kennan, 2010. "Private Information, Wage Bargaining and Employment Fluctuations," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 633-664.
    2. Ales, Laurence & Carapella, Francesca & Maziero, Pricila & Weber, Warren E., 2008. "A model of banknote discounts," Journal of Economic Theory, Elsevier, vol. 142(1), pages 5-27, September.
    3. Romano, Richard E. & Tampieri, Alessandro, 2016. "Arts vs engineering: Choosing consumption of and investment in education," Research in Economics, Elsevier, vol. 70(3), pages 493-510.
    4. Yann Rébillé & Lionel Richefort, 2015. "Influence and Social Tragedy in Networks," Revue d'économie politique, Dalloz, vol. 125(6), pages 811-833.
    5. Katzman, Brett & Kennan, John & Wallace, Neil, 2003. "Output and price level effects of monetary uncertainty in a matching model," Journal of Economic Theory, Elsevier, vol. 108(2), pages 217-255, February.
    6. Baetz, Oliver, 2015. "Social activity and network formation," Theoretical Economics, Econometric Society, vol. 10(2), May.
    7. Bergé, Laurent & Carayol, Nicolas & Roux, Pascale, 2018. "How do inventor networks affect urban invention?," Regional Science and Urban Economics, Elsevier, vol. 71(C), pages 137-162.
    8. Belhaj, Mohamed & Bramoullé, Yann & Deroïan, Frédéric, 2014. "Network games under strategic complementarities," Games and Economic Behavior, Elsevier, vol. 88(C), pages 310-319.
    9. repec:eee:mateco:v:70:y:2017:i:c:p:154-165 is not listed on IDEAS
    10. Hiller, Timo, 2013. "Peer effects in endogenous networks," LSE Research Online Documents on Economics 58176, London School of Economics and Political Science, LSE Library.
    11. Satoshi Nakano & Kazuhiko Nishimura, 2017. "Structural propagation in a production network with restoring substitution elasticities," Papers 1701.02216, arXiv.org, revised Apr 2018.
    12. Daron Acemoglu & Pablo D. Azar, 2017. "Endogenous Production Networks," NBER Working Papers 24116, National Bureau of Economic Research, Inc.
    13. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation," Discussion Papers 0803, University of Exeter, Department of Economics.
    14. Francois de Soyres, 2016. "Trade and Interdependence in International Networks," 2016 Meeting Papers 157, Society for Economic Dynamics.
    15. repec:cep:stitep:/2013/564 is not listed on IDEAS
    16. Gustavo Peralta & Ricardo Crisóstomo, 2016. "Financial contagion with spillover effects: a multiplex network approach," ESRB Working Paper Series 32, European Systemic Risk Board.
    17. repec:eee:gamebe:v:105:y:2017:i:c:p:349-367 is not listed on IDEAS
    18. Mathieu Taschereau-Dumouchel, 2017. "Cascades and Fluctuations in an Economy with an Endogenous Production Network," 2017 Meeting Papers 700, Society for Economic Dynamics.
    19. Timo Hiller & Timo Hiller, 2013. "Peer Effects in Endogenous Networks," STICERD - Theoretical Economics Paper Series 564, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    20. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Working Papers hal-00294828, HAL.

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    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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