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Nerlove–Arrow: A New Solution to an Old Problem

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  • Marc Artzrouni

    (University of Pau (Mathematics))

  • Patrice Cassagnard

    (University of Pau (Economics))

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," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 267-280, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1033-8
    DOI: 10.1007/s10957-016-1033-8
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