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Nerlove-Arrow: A New Solution to an Old Problem

Author

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  • Marc Artzrouni

    (LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau] - UPPA - Université de Pau et des Pays de l'Adour - CNRS - Centre National de la Recherche Scientifique)

  • Patrice Cassagnard

    (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour)

Abstract

We use the optimality principle of dynamic programming to formulate a discrete version of the original Nerlove–Arrow maximization problem. When the payoff function is concave, we give a simple recursive process that yields an explicit solution to the problem. If the time horizon is long enough, there is a "transiently stationary" (turnpike) value for the optimal capital after which the capital must be left to depreciate as it takes the exit ramp. If the time horizon is short, the capital is left to depreciate. Simple closed-form solutions are given for a power payoff function.

Suggested Citation

  • Marc Artzrouni & Patrice Cassagnard, 2017. "Nerlove-Arrow: A New Solution to an Old Problem," Post-Print hal-01881901, HAL.
    • Handle: RePEc:hal:journl:hal-01881901
    DOI: 10.1007/s10957-016-1033-8
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    References listed on IDEAS

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    2. Shi, Jianmai & Chen, Wenyi & Verter, Vedat, 2023. "The joint impact of environmental awareness and system infrastructure on e-waste collection," European Journal of Operational Research, Elsevier, vol. 310(2), pages 760-772.

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