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The Reproductive Value in Distributed Optimal Control Models

Author

Listed:
  • 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.

Suggested Citation

  • Stefan Wrzaczek & Michael Kuhn & Alexia Prskawetz & Gustav Feichtinger, 2009. "The Reproductive Value in Distributed Optimal Control Models," VID Working Papers 0906, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
    • Handle: RePEc:vid:wpaper:0904
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    Cited by:

    1. Simon, C. & Belyakov, A.O. & Feichtinger, G., 2012. "Minimizing the dependency ratio in a population with below-replacement fertility through immigration," Theoretical Population Biology, Elsevier, vol. 82(3), pages 158-169.
    2. Herbert Dawid & Engelbert Dockner & Richard Hartl & Josef Haunschmied & Ulrike Leopold-Wildburger & Mikulas Luptacik & Alexander Mehlmann & Alexia Prskawetz & Marion Rauner & Gerhard Sorger & Gernot T, 2010. "Gustav Feichtinger celebrates his 70th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 437-451, December.
    3. Grafeneder-Weissteiner, Theresa & Prettner, Klaus, 2010. "Agglomeration processes in aging societies," Department of Economics Working Paper Series 131, WU Vienna University of Economics and Business.
    4. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.
    5. Feichtinger, Gustav & Wrzaczek, Stefan, 2024. "The optimal momentum of population growth and decline," Theoretical Population Biology, Elsevier, vol. 155(C), pages 51-66.
    6. Bilal Barakat & Johannes Holler & Klaus Prettner & Julia Schuster, 2010. "The Impact of the Economic Crisis on Labour and Education in Europe," VID Working Papers 1006, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
    7. Klaus Prettner & Alexia Prskawetz, 2010. "Demographic change in models of endogenous economic growth. A survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 593-608, December.
    8. Karsten, Richard & Teismann, Holger & Vogels, Angela, 2013. "Reproductive value, sensitivity, and nonlinearity: Population-management heuristics derived from classical demography," Theoretical Population Biology, Elsevier, vol. 85(C), pages 20-25.

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