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Optimal Harvesting Of Forest Age Classes: A Survey Of Some Recent Results

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  • OLLI TAHVONEN

Abstract

Dynamic optimization problems with vintage or age class structures involve complexities that are not encountered in economic models with fewer state variables. These problems have been faced for centuries in forest harvesting decisions, and the earliest ideas for tackling them date from the early 15th century. However, only recently has the harvesting problem with multiple age classes been specified in a form that is fruitful for economic analysis. This survey discusses some of the main properties of the nonlinear discrete time forestry model, which has proven to be tractable in analytical studies and has been used in empirical policy-oriented research. It is shown that the model's stationary state is represented by a set of cyclic solutions and that the maximum radius of the cycle depends on the period length applied in the model specification. The result suggests that it is essential to note that implications of using continuous or discrete variables in specifying time and age structure in age class models with economic optimization.

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  • 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.
    • Handle: RePEc:taf:mpopst:v:11:y:2004:i:3-4:p:205-232
    DOI: 10.1080/08898480490513616
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    1. Wan, H.Jr., 1989. "Durable Assets And Replacement Cycles," Papers 419, Cornell - Department of Economics.
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    Cited by:

    1. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2015. "On the Mitra–Wan forest management problem in continuous time," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1001-1040.
    2. Viitala, Esa-Jussi, 2006. "An early contribution of Martin Faustmann to natural resource economics," Journal of Forest Economics, Elsevier, vol. 12(2), pages 131-144, June.
    3. Couture, Stéphane & Cros, Marie-Josée & Sabbadin, Régis, 2016. "Risk aversion and optimal management of an uneven-aged forest under risk of windthrow: A Markov decision process approach," Journal of Forest Economics, Elsevier, vol. 25(C), pages 94-114.
    4. Laukkanen, Matti & Tahvonen, Olli, 2023. "Wood product differentiation in age-structured forestry," Resource and Energy Economics, Elsevier, vol. 73(C).
    5. Koster, Roman & Fuchs, Jasper M., 2022. "Opportunity costs of growing space – an essential driver of economical single-tree harvest decisions," Forest Policy and Economics, Elsevier, vol. 135(C).
    6. Terry Heaps, 2014. "Convergence of Optimal Harvesting Policies to a Normal Forest," Discussion Papers dp14-01, Department of Economics, Simon Fraser University.
    7. Morag F. Macpherson & Adam Kleczkowski & John R. Healey & Nick Hanley, 2018. "The Effects of Disease on Optimal Forest Rotation: A Generalisable Analytical Framework," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 70(3), pages 565-588, July.
    8. 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.
    9. Adriana Piazza, 2009. "The optimal harvesting problem with a land market: a characterization of the asymptotic convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 113-138, July.
    10. Sloggy, Matthew R. & Kling, David M. & Plantinga, Andrew J., 2020. "Measure twice, cut once: Optimal inventory and harvest under volume uncertainty and stochastic price dynamics," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    11. 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.
    12. Terry Heaps, 2016. "Multiple Use Values and Convergence of Optimal Harvesting Policies," Discussion Papers dp16-09, Department of Economics, Simon Fraser University.
    13. COUTURE Stephane & REYNAUD Arnaud, 2006. "Multi-stand Forest Management Under a Climatic Risk: Do time and Risk Preferences Matter?," LERNA Working Papers 06.17.210, LERNA, University of Toulouse.
    14. Max Bruciamacchie & Marielle Brunette & Jacques-Alexandre Laye & Anne Stenger-Letheux & Arnaud Reynaud, 2008. "Instruments économiques pour une gestion optimale d’un peuplement forestier exploité par sa production ligneuse et son captage du gaz carbonique en situation risquée," Working Papers hal-01189362, HAL.
    15. Adriana Piazza & Bernardo Pagnoncelli, 2014. "The optimal harvesting problem under price uncertainty," Annals of Operations Research, Springer, vol. 217(1), pages 425-445, June.
    16. Stéphane S. Couture & Marie-Josée Cros & Régis Sabbadin, 2014. "Risk preferences and optimal management of uneven-aged forests in the presence of climate change: a Markov decision process approach," Post-Print hal-02741407, HAL.
    17. B. Ainseba & L. Louison & A. Omrane, 2022. "A Population Harvesting Model with Time and Size Competition Dependence Function," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 647-665, November.
    18. Adriana Piazza & Santanu Roy, 2020. "Irreversibility and the economics of forest conservation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 667-711, April.
    19. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.
    20. Couture, Stéphane & Reynaud, Arnaud, 2011. "Forest management under fire risk when forest carbon sequestration has value," Ecological Economics, Elsevier, vol. 70(11), pages 2002-2011, September.
    21. Piazza, Adriana & Roy, Santanu, 2015. "Deforestation and optimal management," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 15-27.

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