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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)

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File URL: http://www.ssc.wisc.edu/~jkennan/research/FixedPoint21.pdf
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Bibliographic Info

Paper provided by Wisconsin Madison - Social Systems in its series Working papers with number 2.

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Date of creation: 2001
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Handle: RePEc:att:wimass:20012

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Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.

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Citations

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Cited by:
  1. 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.
  2. Laurence Ales & Francesca Carapella & Pricila Maziero & Warren E. Weber, 2006. "A model of banknote discounts," Working Papers 641, Federal Reserve Bank of Minneapolis.
  3. John Kennan, 2006. "Private Information, Wage Bargaining and Employment Fluctuations," NBER Working Papers 11967, National Bureau of Economic Research, Inc.
  4. Yann Rébillé & Lionel Richefort, 2014. "Influence and Social Tragedy in Networks," Working Papers hal-00924017, HAL.
  5. repec:hal:wpaper:hal-00294828 is not listed on IDEAS
  6. Baetz, Oliver, 0. "Social activity and network formation," Theoretical Economics, Econometric Society.
  7. repec:hal:cesptp:hal-00294828 is not listed on IDEAS
  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.
  9. 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.

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