Nerlove-Arrow: A New Solution to an Old Problem

Marc Artzrouni () and Patrice Cassagnard ()
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Patrice Cassagnard: CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour

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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.

Keywords: Optimization; Turnpike; Nerlove–Arrow; Dynamic programming (search for similar items in EconPapers)
Date: 2017-01
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Citations: View citations in EconPapers (2)

Published in Journal of Optimization Theory and Applications, 2017, 172 (1), pp.267-280. ⟨10.1007/s10957-016-1033-8⟩

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Journal Article: Nerlove–Arrow: A New Solution to an Old Problem (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01881901

DOI: 10.1007/s10957-016-1033-8

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