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The Reproductive Value in Distributed Optimal Control Models

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  • 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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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, July.
    2. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2011. "Externalities in a life cycle model with endogenous survival," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 627-641.
    3. Christian Almeder & Gustav Feichtinger & Warren Sanderson & Vladimir Veliov, 2007. "Prevention and medication of HIV/AIDS: the case of Botswana," 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. 15(1), pages 47-61, March.
    4. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    5. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    6. Barro, Robert J & Becker, Gary S, 1989. "Fertility Choice in a Model of Economic Growth," Econometrica, Econometric Society, vol. 57(2), pages 481-501, March.
    7. Kuhn, Michael & Wrzaczek, Stefan & Oeppen, Jim, 2010. "Recognizing progeny in the value of life," Economics Letters, Elsevier, vol. 107(1), pages 17-21, April.
    8. Ehrlich, Isaac, 2000. "Uncertain lifetime, life protection, and the value of life saving," Journal of Health Economics, Elsevier, vol. 19(3), pages 341-367, May.
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    Citations

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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. 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.
    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. Feichtinger, Gustav & Wrzaczek, Stefan, 2024. "The optimal momentum of population growth and decline," Theoretical Population Biology, Elsevier, vol. 155(C), pages 51-66.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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