On the Mitra--Wan Forest Management Problem in Continuous Time

Silvia Faggian, Giorgio Fabbri and Giuseppe Freni

No 2013:28, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: The paper provides a continuous time version of the well known discrete time Mitra-Wan model of optimal forest management, where a forest is harvested to maximize the utility of timber flow over an infinite time horizon. Besides varying with time, the state variable (describing available trees) and the other parameters of the problem vary continuously also with respect to the age of the trees. The evolution of the system is given in terms of a partial differential equation and later rephrased as an ordinary differential equation in an infinite dimensional space. The paper provides a classification of the behavior of optimal and maximal programs when the utility function is linear, convex, or strictly convex and the discount rate is positive or null. Formulas are provided for modified golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and the optimality or maximality of such programs is discussed. In all different sets of data, it is shown that the optimal (or maximal) control is necessarily something more general than a function, i.e. a positive measure. In particular, in the case of strictly concave utility and null discount, when the Faustmann policy is not optimal, it is shown that optimal paths converges over time to the golden rule configuration, while in the case of strictly concave utility and positive discount the Faustmann policy is shown to be not optimal, contradicting the corresponding result in discrete time.

Keywords: Optimal harvesting problems; Forest Management; Measure-valued Control (search for similar items in EconPapers)
JEL-codes: C61 C62 D90 E22 Q23 (search for similar items in EconPapers)
Pages: 58
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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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 (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)
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