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Optimal Control of Investments in Old and New Capital Under Improving Technology

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  • Natali Hritonenko

    (Prairie View A&M University)

  • Nobuyuki Kato

    (Kanazawa University)

  • Yuri Yatsenko

    (Houston Baptist University)

Abstract

An optimal control problem for nonlinear integral equations of special kind is analyzed. It considers a firm’s investment into age-dependent capital under improving technology and limited substitutability among capital of different ages. We prove the existence of solutions and analyze their structure. It is shown that the initially bang-bang optimal investment switches to an interior one and eventually converges to a steady-state trajectory that represents balanced economic growth. The obtained analytic outcomes contribute to better understanding of investment policies under technological change.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1022-y
    DOI: 10.1007/s10957-016-1022-y
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    References listed on IDEAS

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    1. Hritonenko, Natali & Yatsenko, Yuri, 2012. "Energy substitutability and modernization of energy-consuming technologies," Energy Economics, Elsevier, vol. 34(5), pages 1548-1556.
    2. V. Barbu & M. Iannelli, 1999. "Optimal Control of Population Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 1-14, July.
    3. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    4. Natali Hritonenko & Yuri Yatsenko, 2013. "Mathematical Modeling in Economics, Ecology and the Environment," Springer Optimization and Its Applications, Springer, edition 2, number 978-1-4614-9311-2, December.
    5. Hart, Rob, 2004. "Growth, environment and innovation--a model with production vintages and environmentally oriented research," Journal of Environmental Economics and Management, Elsevier, vol. 48(3), pages 1078-1098, November.
    6. 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.
    7. Greenwood, Jeremy & Hercowitz, Zvi & Krusell, Per, 1997. "Long-Run Implications of Investment-Specific Technological Change," American Economic Review, American Economic Association, vol. 87(3), pages 342-362, June.
    8. 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.
    9. 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.
    10. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
    11. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, 2014. "Optimal Investment in Heterogeneous Capital and Technology Under Restricted Natural Resource," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 310-331, October.
    12. Kredler, Matthias, 2014. "Vintage human capital and learning curves," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 154-178.
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