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The Reproductive Value in Distributed Optimal Control Models

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Author Info

  • Stefan Wrzaczek
  • Michael Kuhn
  • Alexia Prskawetz
  • Gustav Feichtinger

Abstract

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology.

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File URL: http://www.oeaw.ac.at/vid/download/WP2009_04.pdf
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Bibliographic Info

Paper provided by Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna in its series Working Papers with number 0906.

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Length: 20 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:vid:wpaper:0904

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Web page: http://www.oeaw.ac.at/vid/

Related research

Keywords: Reproductive value; distributed optimal control theory; McKendrick; shadow price; indirect effect; health economics; epidemiology; population biology.;

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Cited by:
  1. Theresa Grafeneder-Weissteiner & Klaus Prettner, 2010. "Agglomeration processes in ageing societies," Working Papers 1005, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
  2. Klaus Prettner & Alexia Prskawetz, 2010. "Demographic Change in Models of Endogenous Economic Growth. A Survey," Working Papers 1008, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
  3. Bilal Barakat & Johannes Holler & Klaus Prettner & Julia Schuster, 2010. "The Impact of the Economic Crisis on Labour and Education in Europe," Working Papers 1006, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.

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