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Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result

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  • John Kennan

    (University of Wisconsin, Madison)

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)

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File URL: http://dx.doi.org/10.1006/redy.2001.0139
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Bibliographic Info

Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 4 (2001)
Issue (Month): 4 (October)
Pages: 893-899

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Handle: RePEc:red:issued:v:4:y:2001:i:4:p:893-899

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Keywords: fixed points; concavity.;

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Citations

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Cited by:
  1. Baetz, Oliver, 0. "Social activity and network formation," Theoretical Economics, Econometric Society.
  2. 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, Exeter University, Department of Economics.
  3. Laurence Ales & Francesca Carapella & Pricila Maziero & Warren E. Weber, 2006. "A model of banknote discounts," Working Papers 641, Federal Reserve Bank of Minneapolis.
  4. Katzman,B. & Kennan,J. & Wallace,N., 2001. "Output and price level effects of monetary uncertainty in a matching model," Working papers 1, Wisconsin Madison - Social Systems.
  5. repec:hal:wpaper:hal-00294828 is not listed on IDEAS
  6. Yann Rébillé & Lionel Richefort, 2014. "Influence and Social Tragedy in Networks," Working Papers hal-00924017, HAL.
  7. John Kennan, 2005. "Private Information, Wage Bargaining and Employment Fluctuations," 2005 Meeting Papers 555, Society for Economic Dynamics.
  8. Timo Hiller & Timo Hiller, 2013. "Peer Effects in Endogenous Networks," STICERD - Theoretical Economics Paper Series /2013/564, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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