Journal of Forest Economics > Vol 24 > Issue 1

Could the Faustmann model have an interior minimum solution?

Peichen Gong, Center of Environmental and Resource Economics, Department of Forest Economics, Swedish University of Agricultural Sciences, Sweden, Peichen.gong@slu.se Karl-Gustaf Löfgren, Center of Environmental and Resource Economics, Department of Economics, Umeå University, Sweden, karl-gustaf.lofgren@umu.se
 
Suggested Citation
Peichen Gong and Karl-Gustaf Löfgren (2016), "Could the Faustmann model have an interior minimum solution?", Journal of Forest Economics: Vol. 24: No. 1, pp 123-129. http://dx.doi.org/10.1016/j.jfe.2016.06.001

Published: 0/8/2016
© 0 2016 Peichen Gong, Karl-Gustaf Löfgren
 
Subjects
 
Keywords
JEL Codes:Q23Q24
Forest economicsOptimal rotation ageS-shaped growth curve
 

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In this article:
Introduction
Necessary and sufficient conditions for the optimal rotation
Proof of the existence of an interior solution
Proof of the uniqueness of the solution
Age-dependent stumpage price
An example
Concluding remarks

Abstract

The growth of an even-aged stand usually follows a S-shaped pattern, implying that the growth function is convex when stand age is low and concave when stand age is high. Given such a growth function, the Faustmann model could in theory have multiple optima and hence an interior local minimum solution. To ensure that the rotation age at which the first derivative of the land expectation value equals zero is a maximum, it is often assumed that the growth function is concave in stand age. Yet there is no convincing argument for excluding the possibility of conducting the final harvest before the growth function changes to concave. We argue that under normal circumstances the Faustmann model does not have any interior minimum. It is neither necessary nor proper to assume that the growth function is concave in the vicinity of the optimal rotation age. When the interest rate is high, the optimal rotation may lie in the interval on which the growth function is convex, i.e. before volume or value growth culminates.

DOI:10.1016/j.jfe.2016.06.001