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Capital Accumulation and Embodied Technological Progress

Author

Listed:
  • Dieter Grass

    (Vienna University of Technology)

  • Richard F. Hartl

    (University of Vienna)

  • Peter M. Kort

    (Tilburg University
    University of Antwerp)

Abstract

This paper combines technology adoption with capital accumulation taking into account technological progress. We model this as a multi-stage optimal control problem and solve it using the corresponding maximum principle. The model with linear revenue can be solved analytically, while the model with market power is solved numerically. We obtain that investment jumps upwards right at the moment that a new technology is adopted. We find that, if the firm has market power, the firm cuts down on investment before a new technology is adopted. Furthermore, we find that larger firms adopt a new technology later.

Suggested Citation

  • Dieter Grass & Richard F. Hartl & Peter M. Kort, 2012. "Capital Accumulation and Embodied Technological Progress," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 588-614, August.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0042-5
    DOI: 10.1007/s10957-012-0042-5
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Saglam, Cagri & Valléee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 250-271, April.
    2. repec:ucp:bknber:9780226304557 is not listed on IDEAS
    3. 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.
    4. Farzin, Y. H. & Huisman, K. J. M. & Kort, P. M., 1998. "Optimal timing of technology adoption," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 779-799, May.
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    6. Stephen L. Parente, 2000. "Learning-by-Using and the Switch to Better Machines," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 675-703, October.
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    8. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    9. Tomiyama, Ken & Rossana, Robert J., 1989. "Two-stage optimal control problems with an explicit switch point dependence : Optimality criteria and an example of delivery lags and investment," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 319-337, July.
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    12. Robert J. Gordon, 1990. "The Measurement of Durable Goods Prices," NBER Books, National Bureau of Economic Research, Inc, number gord90-1, March.
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    Cited by:

    1. M. Chahim & D. Grass & R. F. Hartl & P. M. Kort, 2017. "Product innovation with lumpy investment," 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. 25(1), pages 159-182, March.
    2. Thorsten Upmann & Stefan Behringer, 2017. "Harvesting a Remote Renewable Resource," CESifo Working Paper Series 6724, CESifo.
    3. Johanna Grames & Dieter Grass & Peter M. Kort & Alexia Prskawetz, 2019. "Optimal investment and location decisions of a firm in a flood risk area using impulse control theory," 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. 27(4), pages 1051-1077, December.
    4. Seidl, Andrea, 2019. "Zeno points in optimal control models with endogenous regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 353-368.
    5. Elke Moser & Andrea Seidl & Gustav Feichtinger, 2014. "History-dependence in production-pollution-trade-off models: a multi-stage approach," Annals of Operations Research, Springer, vol. 222(1), pages 457-481, November.

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