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

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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.

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Acknowledgments

The authors are grateful to two anonymous reviewers for valuable comments. Nobuyuki Kato acknowledges the support of the JSPS KAKENHI Grant Number 25400140.

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Authors and Affiliations

  1. Prairie View A&M University, Prairie View, TX, USA

    Natali Hritonenko

  2. Kanazawa University, Kanazawa, Japan

    Nobuyuki Kato

  3. Houston Baptist University, Houston, TX, USA

    Yuri Yatsenko

Authors
  1. Natali Hritonenko
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  2. Nobuyuki Kato
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  3. Yuri Yatsenko
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Correspondence to Natali Hritonenko.

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Hritonenko, N., Kato, N. & Yatsenko, Y. Optimal Control of Investments in Old and New Capital Under Improving Technology. J Optim Theory Appl 172, 247–266 (2017). https://doi.org/10.1007/s10957-016-1022-y

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  • DOI: https://doi.org/10.1007/s10957-016-1022-y

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