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Convergence of optimal harvesting policies to a normal forest

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  • Heaps, Terry

Abstract

This paper extends the forestry maximum principle of Heaps (1984) to allow the benefits of harvesting to be the utility of the volume of the wood harvested as in Mitra and Wan (1985, 1986). Unlike those authors, however, time is treated as a continuous rather than as a discrete variable. Existence of an optimal harvesting policy is established. Then necessary conditions are derived for the extended model which are also sufficient. The conditions are used to show that under certain boundedness conditions, sequences of optimal harvesting policies contain subsequences which converge pointwise a.e. and in net present value to an optimal harvesting policy. This result is then used to show that any optimal logging policy must converge in harvesting age to a constant rotation period given by modified Faustmann formula. The associated age class distribution converges to a normal forest.

Suggested Citation

  • Heaps, Terry, 2015. "Convergence of optimal harvesting policies to a normal forest," Journal of Economic Dynamics and Control, Elsevier, vol. 54(C), pages 74-85.
    • Handle: RePEc:eee:dyncon:v:54:y:2015:i:c:p:74-85
    DOI: 10.1016/j.jedc.2015.03.001
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    References listed on IDEAS

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    8. Olli Tahvonen, 2004. "Optimal Harvesting Of Forest Age Classes: A Survey Of Some Recent Results," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 205-232.
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    10. Xabadia, Angels & Goetz, Renan U., 2010. "The optimal selective logging regime and the Faustmann formula," Journal of Forest Economics, Elsevier, vol. 16(1), pages 63-82, January.
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    Cited by:

    1. Han Zhang & Jari Kuuluvainen & Hongqiang Yang & Yi Xie & Can Liu, 2017. "The Effect of Off-Farm Employment on Forestland Transfers in China: A Simultaneous-Equation Tobit Model Estimation," Sustainability, MDPI, vol. 9(9), pages 1-14, September.
    2. Terry Heaps, 2016. "Multiple Use Values and Convergence of Optimal Harvesting Policies," Discussion Papers dp16-09, Department of Economics, Simon Fraser University.
    3. González-González, José Mario & Vázquez-Méndez, Miguel Ernesto & Diéguez-Aranda, Ulises, 2022. "Multi-objective models for the forest harvest scheduling problem in a continuous-time framework," Forest Policy and Economics, Elsevier, vol. 136(C).
    4. Moriguchi, Kai & Ueki, Tatsuhito & Saito, Masashi, 2020. "Establishing optimal forest harvesting regulation with continuous approximation," Operations Research Perspectives, Elsevier, vol. 7(C).

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    More about this item

    Keywords

    Optimal harvesting; Multiple age classes; Convergence; Normal forest;
    All these keywords.

    JEL classification:

    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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