Could the Faustmann model have an interior minimum solution? |
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| Institution: | 1. Center of Environmental and Resource Economics, Department of Forest Economics, Swedish University of Agricultural Sciences, SE-901 83 Umeå, Sweden;2. Center of Environmental and Resource Economics, Department of Economics, Umeå University, SE-901 87 Umeå, Sweden;1. Federal University of Paraná—MSc, Caspar-Schrenk-Weg 21, 79117 Freiburg im Breisgau, Germany;2. Federal University of Paraná—Prof. Dr. Department of Forest Sciences, Av. Prof. Lothário Meissner, 900, Campus III Jardim Botânico/UFPR-Bloco B3, Gabinete 3 Jardim Botânico 80210170, Curitiba, PR, Brazil;3. Federal University of Paraná—Prof. Dr. Department of Mathematics, ACF Centro Politécnico Jardim das Américas 81531980, Curitiba, PR, Brazil;1. Forest Economics and Policy, School of Forestry and Wildlife Sciences, Auburn University, Auburn, AL, 36849-5418, United States;2. BETA - UMR 7522 CNRS Université de Strasbourg, 61, avenue de la Forêt Noire, 67085 Strasbourg Cedex, France;3. INRA, UMR 356 Economie Forestière - AgroParisTech, Laboratoire d’Economie Forestière, Nancy, France;4. Pinchot Institute for Conservation, Washington, DC, United States;1. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Architecture and Environment, Sichuan University, Chengdu 610065, China;2. Sino-German Centre for Water and Health Research, Sichuan University, Chengdu 610065, China;3. Institute of Environmental Engineering, RWTH Aachen University, Aachen, Germany;1. College of Architecture and Urban-Rural Planning, Sichuan Agricultural University, Dujiangyan 611830, China;2. Business School, Sichuan University, Chengdu 610064, China;3. College of Economics, Southwestern Poverty Reduction and Development Research Center, Sichuan Agricultural University, Chengdu 611130, China;4. LeBow College of Business, Drexel University, Philadelphia 19104, USA;5. College of Management, Sichuan Center for Rural Development Research, Sichuan Agricultural University, Chengdu 611130, China |
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| 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. |
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| Keywords: | Forest economics Optimal rotation age S-shaped growth curve |
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