On the Mitra–Wan forest management problem in continuous time

Giorgio Fabbri, Silvia Faggian and Giuseppe Freni

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Abstract: The paper provides a continuous-time version of the discrete-time Mitra–Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with respect to both time and age of the trees, so that the system is ruled by a partial differential equation. The behavior of optimal or maximal couples is classified in the cases of linear, concave or strictly concave utility, and positive or null discount rate. All sets of data share the common feature that optimal controls need to be more general than functions, i.e. positive measures. Formulas are provided for golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and their optimality/maximality is discussed. The results do not always confirm the corresponding ones in discrete time.

Keywords: Optimal harvesting; Forest management; Measure-valued controls (search for similar items in EconPapers)
Date: 2015-05
Note: View the original document on HAL open archive server: https://hal.science/hal-01615431
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Citations: View citations in EconPapers (3)

Published in Journal of Economic Theory, 2015, 157, pp.1001 - 1040. ⟨10.1016/j.jet.2015.03.004⟩

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Related works:
Journal Article: On the Mitra–Wan forest management problem in continuous time (2015)
Working Paper: On the Mitra-Wan Forest Management Problem in Continuous Time (2014)
Working Paper: On The Mitra-Wan Forest Management Problem in Continuous Time (2014)
Working Paper: On the Mitra--Wan Forest Management Problem in Continuous Time (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01615431

DOI: 10.1016/j.jet.2015.03.004

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