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A Note On The Optimal Control Of Stocks Accumulating With A Delay


  • Winkler, Ralph


We study a generic optimal control problem with a stock that accumulates with constant delay. We show that the optimal system dynamics reduces to a system of ordinary differential equations, implying monotonic optimal paths, if the objective function is additively separable in the stock and the control. This is, however, not true for general objective functions, which may exhibit nonmonotonic and oscillatory optimal paths. The reason is that the impact of the stock on the objective depends on the current level of the control, whereas the control influences the dynamics of the stock with a delay.

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  • Winkler, Ralph, 2011. "A Note On The Optimal Control Of Stocks Accumulating With A Delay," Macroeconomic Dynamics, Cambridge University Press, vol. 15(04), pages 565-578, September.
  • Handle: RePEc:cup:macdyn:v:15:y:2011:i:04:p:565-578_00

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    Cited by:

    1. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
    2. Richard Hartl & Peter Kort, 2010. "Delay in finite time capital accumulation," 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. 18(4), pages 465-475, December.
    3. Cyril Bourgeois & Pierre-Alain Jayet, 2010. "Revisited water-oriented relationships between a set of farmers and an aquifer: accounting for lag effect," Working Papers 2010/06, INRA, Economie Publique.

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