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Convergence of Optimal Harvesting Policies to a Normal Forest

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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
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    File URL: http://www.sfu.ca/econ-research/RePEc/sfu/sfudps/dp14-01.pdf
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    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," Review of Economic Studies, Oxford University Press, 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.
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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.

    More about this item

    Keywords

    optimal harvesting; multiple age classes; convergence;

    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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