IDEAS home Printed from https://ideas.repec.org/p/sfu/sfudps/dp14-01.html
   My bibliography  Save this paper

Convergence of Optimal Harvesting Policies to a Normal Forest

Author

Listed:

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 wood harvested as in Mitra - 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 uniformly bounded 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

  • Terry Heaps, 2014. "Convergence of Optimal Harvesting Policies to a Normal Forest," Discussion Papers dp14-01, Department of Economics, Simon Fraser University.
    • Handle: RePEc:sfu:sfudps:dp14-01
    as

    Download full text from publisher

    File URL: http://www.sfu.ca/repec-econ/sfu/sfudps/dp14-01.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    2. Tapan Mitra & Henry Y. Wan, 1985. "Some Theoretical Results on the Economics of Forestry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 263-282.
    3. Sahashi, Yoshinao, 2002. "The convergence of optimal forestry control," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 179-214, May.
    4. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    5. Salo, Seppo & Tahvonen, Olli, 2002. "On Equilibrium Cycles and Normal Forests in Optimal Harvesting of Tree Vintages," Journal of Environmental Economics and Management, Elsevier, vol. 44(1), pages 1-22, July.
    6. Mitra, Tapan & Wan, Henry Jr., 1986. "On the faustmann solution to the forest management problem," Journal of Economic Theory, Elsevier, vol. 40(2), pages 229-249, December.
    7. 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.
    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.
    9. Heaps, Terry & Neher, Philip A., 1979. "The economics of forestry when the rate of harvest is constrained," Journal of Environmental Economics and Management, Elsevier, vol. 6(4), pages 297-319, December.
    10. Heaps, Terry, 1984. "The forestry maximum principle," Journal of Economic Dynamics and Control, Elsevier, vol. 7(2), pages 131-151, May.
    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. Renan Goetz & Angels Xabadia & Elena Calvo, 2011. "Optimal Forest Management in the Presence of Intraspecific Competition," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(3), pages 151-171.
    13. Salo, Seppo & Tahvonen, Olli, 2003. "On the economics of forest vintages," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1411-1435, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    5. Laukkanen, Matti & Tahvonen, Olli, 2023. "Wood product differentiation in age-structured forestry," Resource and Energy Economics, Elsevier, vol. 73(C).
    6. Ken-Ichi Akao, 2011. "Optimum forest program when the carbon sequestration service of a forest has value," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 13(4), pages 323-343, December.
    7. Piazza, Adriana & Roy, Santanu, 2015. "Deforestation and optimal management," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 15-27.
    8. 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.
    9. Salo, Seppo & Tahvonen, Olli, 2003. "On the economics of forest vintages," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1411-1435, June.
    10. Moriguchi, Kai & Ueki, Tatsuhito & Saito, Masashi, 2020. "Establishing optimal forest harvesting regulation with continuous approximation," Operations Research Perspectives, Elsevier, vol. 7(C).
    11. Meilby, Henrik & Brazee, Richard J., 12. "Sustainibility and Long-term Dynamics of Forests: Methods and Metrics for Detection of Convergence and Stationarity," Scandinavian Forest Economics: Proceedings of the Biennial Meeting of the Scandinavian Society of Forest Economics, Scandinavian Society of Forest Economics, issue 40, May.
    12. Newman, D.H., 2002. "Forestry's golden rule and the development of the optimal forest rotation literature," Journal of Forest Economics, Elsevier, vol. 8(1), pages 5-27.
    13. Dumollard, Gaspard, 2018. "Multiple-stand forest management under fire risk: Analytical characterization of stationary rotation ages and optimal carbon sequestration policy," Journal of Forest Economics, Elsevier, vol. 32(C), pages 146-154.
    14. Khan, M. Ali & Piazza, Adriana, 2011. "Classical turnpike theory and the economics of forestry," Journal of Economic Behavior & Organization, Elsevier, vol. 79(3), pages 194-210, August.
    15. Tahvonen, Olli, 2009. "Economics of harvesting age-structured fish populations," Journal of Environmental Economics and Management, Elsevier, vol. 58(3), pages 281-299, November.
    16. Lintunen, Jussi & Uusivuori, Jussi, 2014. "On The Economics of Forest Carbon: Renewable and Carbon Neutral But Not Emission Free," Climate Change and Sustainable Development 165755, Fondazione Eni Enrico Mattei (FEEM).
    17. Khazri, Olfa & Lasserre, Pierre, 2011. "Forest management: Are double or mixed rotations preferable to clear cutting?," Resource and Energy Economics, Elsevier, vol. 33(1), pages 155-171, January.
    18. 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.
    19. KHAZRI, Olfa & LASSERRE, Pierre, 2008. "Forest Management : Are Double or Mixed Rotations Desirable?," Cahiers de recherche 12-2008, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    20. Adriana Piazza & Bernardo Pagnoncelli, 2015. "The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases," Journal of Economics, Springer, vol. 115(2), pages 175-194, June.

    More about this item

    Keywords

    optimal harvesting; multiple age classes; convergence;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sfu:sfudps:dp14-01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Working Paper Coordinator (email available below). General contact details of provider: https://edirc.repec.org/data/desfuca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.