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On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions

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  • Winkler, Ralph
  • Brandt-Pollmann, Ulrich
  • Moslener, Ulf
  • Schlöder, Johannes

Abstract

We formulate an optimal control capital accumulation model with a Leontief-type production function and an exogenously given time-lag between investment and the accumulation of the capital stock, to analyze the qualitative and quantitative influence of time-lags on the system dynamics. As known from the time-to-build literature, optimal investment paths for positive and finite time-lags are in general cyclical, in contrast to the monotonic optimal paths for instantaneous capital accumulation. We show that the transition between instantaneous and time-lagged capital accumulation is continuous, in the sense that the greater is the time-lag between investment and capital accumulation, the more likely and more pronounced becomes cyclical behavior of the optimal paths.

Suggested Citation

  • Winkler, Ralph & Brandt-Pollmann, Ulrich & Moslener, Ulf & Schlöder, Johannes, 2005. "On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions," ZEW Discussion Papers 05-30, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:3185
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    References listed on IDEAS

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    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    3. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    4. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    5. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    6. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-1146, November.
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    Cited by:

    1. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    2. Christoph Heinzel & Ralph Winkler, 2011. "Distorted Time Preferences and Time-to-Build in the Transition to a Low-Carbon Energy Industry," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 49(2), pages 217-241, June.
    3. Heinzel, Christoph & Winkler, Ralph, 2006. "Gradual versus structural technological change in the transition to a low-emission energy industry: How time-to-build and differing social and individual discount rates influence environmental and tec," Dresden Discussion Paper Series in Economics 09/06, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.

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    More about this item

    Keywords

    cyclical optimal paths; numerical optimization; time-lagged optimal control; time-to-build;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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