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Age-Structured PDEs in Economics, Ecology, and Demography: Optimal Control and Sustainability

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  • NATALI HRITONENKO
  • YURI YATSENKO

Abstract

Optimal control of partial differential equations arises in population ecology, economics, and demography. The consistency of mathematical treatment is demonstrated for the Lotka-McKendrick model and its nonlinear modifications of increasing complexity. The obtained qualitative optimal dynamics show that the models have either the bang-bang structure of optimal controls or follow balanced growth dynamics.

Suggested Citation

  • Natali Hritonenko & Yuri Yatsenko, 2010. "Age-Structured PDEs in Economics, Ecology, and Demography: Optimal Control and Sustainability," Mathematical Population Studies, Taylor & Francis Journals, vol. 17(4), pages 191-214.
    • Handle: RePEc:taf:mpopst:v:17:y:2010:i:4:p:191-214
    DOI: 10.1080/08898480.2010.514851
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    References listed on IDEAS

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    5. Natali Hritonenko & Yuri Yatsenko, 2006. "Optimization of Harvesting Return from Age-Structured Population," Journal of Bioeconomics, Springer, vol. 8(2), pages 167-179, August.
    6. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    7. Zou, Benteng, 2006. "Vintage technology, optimal investment and technology adoption," Economic Modelling, Elsevier, vol. 23(3), pages 515-533, May.
    8. Natali Hritonenko & Yuri Yatsenko, 2008. "Can Technological Change Sustain Retirement in an Aging Population?," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(2), pages 96-113.
    9. Xepapadeas, Anastasios & de Zeeuw, Aart, 1999. "Environmental Policy and Competitiveness: The Porter Hypothesis and the Composition of Capital," Journal of Environmental Economics and Management, Elsevier, vol. 37(2), pages 165-182, March.
    10. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
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    Cited by:

    1. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, 2013. "Health, Work Intensity, and Technological Innovations," Working Papers halshs-00805199, HAL.
    2. Heaps, Terry, 2015. "Convergence of optimal harvesting policies to a normal forest," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 74-85.
    3. Natali Hritonenko & Nobuyuki Kato & Yuri Yatsenko, 2017. "Optimal Control of Investments in Old and New Capital Under Improving Technology," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 247-266, January.

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