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A viability theory approach to a two-stage optimal control problem of technology adoption

Author

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  • KRAWCZYK, Jacek B.
  • SEREA, Oana-Silvia

Abstract

A new technology adoption problem can be modelled as a two-stage control problem, in which model parameters ("technology") might be altered at some time. An optimal solution to utility maximisation for this class of problems needs to contain information on the time, at which the change will take place (0, finite or never), along with the optimal control strategies before and after the change. For the change, or switch, to occur the "new technology" value function needs to dominate the "old technology" value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and we study when the graphs can intersect. If they do not, the switch cannot occur at a positive time. Using this characterisation we analyse a technology adoption problem and showmodels, for which the switch will occur at time zero or never.

Suggested Citation

  • KRAWCZYK, Jacek B. & SEREA, Oana-Silvia, 2009. "A viability theory approach to a two-stage optimal control problem of technology adoption," LIDAM Discussion Papers CORE 2009004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2009004
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2009.html
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    Citations

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    Cited by:

    1. Krawczyk, Jacek B & Pharo, Alastair & Simpson, Mark, 2011. "Approximations to viability kernels for sustainable macroeconomic policies," Working Paper Series 1531, Victoria University of Wellington, School of Economics and Finance.
    2. Krawczyk, Jacek B & Pharo, Alastair & Simpson, Mark, 2011. "Approximations to viability kernels for sustainable macroeconomic policies," Working Paper Series 18551, Victoria University of Wellington, School of Economics and Finance.
    3. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 18839, Victoria University of Wellington, School of Economics and Finance.
    4. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 3432, Victoria University of Wellington, School of Economics and Finance.
    5. Krawczyk, Jacek B., 2011. "Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems," Working Paper Series 21186, Victoria University of Wellington, School of Economics and Finance.
    6. Krawczyk, Jacek B & Pharo, Alastair S, 2011. "Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems," Working Paper Series 1878, Victoria University of Wellington, School of Economics and Finance.

    More about this item

    Keywords

    technology adoption; value function; viability kernel; viscosity solutions;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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