IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

On The Mitra-Wan Forest Management Problem in Continuous Time

  • Giorgio Fabbri

    ()

    (EPEE, Université d’Evry-Val-d’Essonne (TEPP, FR-CNRS 3126))

  • Silvia Faggian

    ()

    (Università di Venezia “Ca’ Foscari”)

  • Giuseppe Freni

    ()

    (University of Naples Parthenope)

The paper provides a continuous-time version of the discrete-time Mitra- Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with respect to both time and age of the trees, so that the system is ruled by a partial differential equation. The behavior of optimal or maximal couples is classified in the cases of linear, concave or strictly concave utility, and positive or null discount rate. All sets of data share the common feature that optimal controls need to be more general than functions, i.e. positive measures. Formulas are provided for golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann poli- cies, and their optimality/maximality is discussed. The results do not always confirm the corresponding ones in discrete time.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://epee.univ-evry.fr/RePEc/2014/14-04.pdf
Download Restriction: no

Paper provided by Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne in its series Documents de recherche with number 14-04.

as
in new window

Length: 47 pages
Date of creation: 2014
Date of revision:
Handle: RePEc:eve:wpaper:14-04
Contact details of provider: Postal:
4, bld Francois Mitterand, 91025 Evry Cedex

Phone: +33 1 69 47 71 77
Fax: +33 1 69 47 70 50
Web page: http://epee.univ-evry.fr

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. BOUCEKKINE, Raouf & GERMAIN, Marc & LICANDRO, Omar & MAGNUS, Alphonse, . "Creative destruction, investment volatility, and the average age of capital," CORE Discussion Papers RP 1376, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
  3. R. M. Solow & J. Tobin & C. C. von Weizsäcker & M. Yaari, 1966. "Neoclassical Growth with Fixed Factor Proportions," Review of Economic Studies, Oxford University Press, vol. 33(2), pages 79-115.
  4. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
  5. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
  6. Licandro, Omar & Germain, Marc & Boucekkine, Raouf, 1996. "Replacement echoes in the vintage capital growth model," UC3M Working papers. Economics 4096, Universidad Carlos III de Madrid. Departamento de Economía.
  7. Dasgupta, Swapan & Mitra, Tapan, 2010. "On Optimal Forest Management: A Bifurcation Analysis," Working Papers 10-04, Cornell University, Center for Analytic Economics.
  8. Ben J. Heijdra & Ward E. Romp, 2007. "Retirement, Pensions, and Ageing," CESifo Working Paper Series 1974, CESifo Group Munich.
  9. M. Ali Khan & Adriana Piazza, 2010. "On uniform convergence of undiscounted optimal programs in the Mitra-Wan forestry model: The strictly concave case," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 57-76.
  10. Tahvonen, Olli & Salo, Seppo, 1999. "Optimal Forest Rotation within SituPreferences," Journal of Environmental Economics and Management, Elsevier, vol. 37(1), pages 106-128, January.
  11. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
  12. Peleg, Bezalel, 1973. "A Weakly Maximal Golden-Rule Program for a Multi-Sector Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 574-79, October.
  13. Terry Heaps, 2014. "Convergence of Optimal Harvesting Policies to a Normal Forest," Discussion Papers dp14-01, Department of Economics, Simon Fraser University.
  14. HRITONENKO, Natali & YATSENKO, Yuri, . "From linear to nonlinear utility in vintage capital models," CORE Discussion Papers RP 2148, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Foley, Duncan K, 1975. "On Two Specifications of Asset Equilibrium in Macroeconomic Models," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 303-24, April.
  16. Salant, Stephen W., 2013. "The equilibrium price path of timber in the absence of replanting: does Hotelling rule the forests too?," Resource and Energy Economics, Elsevier, vol. 35(4), pages 572-581.
  17. Tahvonen, Olli, 2009. "Economics of harvesting age-structured fish populations," Journal of Environmental Economics and Management, Elsevier, vol. 58(3), pages 281-299, November.
  18. 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.
  19. Silvia Faggian & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
  20. 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.
  21. 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.
  22. 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.
  23. Mitra, Tapan & Ray, Debraj & Roy, Rahul, 1991. "The economics of orchards: An exercise in point-input, flow-output capital theory," Journal of Economic Theory, Elsevier, vol. 53(1), pages 12-50, February.
  24. Khan, M. Ali & Piazza, Adriana, 2010. "On the non-existence of optimal programs in the Robinson-Solow-Srinivasan (RSS) model," Economics Letters, Elsevier, vol. 109(2), pages 94-98, November.
  25. 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.
  26. Wan, Henry, Jr, 1994. "Revisiting the Mitra-Wan Tree Farm," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(1), pages 193-98, February.
  27. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V.M., 2006. "Anticipation effects of technological progress on capital accumulation : A vintage capital approach," Other publications TiSEM 9a8debb0-5030-46fa-b89e-b, Tilburg University, School of Economics and Management.
  28. repec:cor:louvrp:-2148 is not listed on IDEAS
  29. Cass, David & Shell, Karl, 1976. "Introduction to Hamiltonian dynamics in economics," Journal of Economic Theory, Elsevier, vol. 12(1), pages 1-10, February.
  30. Cass, David, 1973. "On the Wicksellian Point-Input, Point-Output Model of Capital Accumulation: A Modern View (or, Neoclassicism Slightly Vindicated)," Journal of Political Economy, University of Chicago Press, vol. 81(1), pages 71-97, Jan.-Feb..
  31. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
  32. Silvia Faggian & Luca Grosset, 2013. "Optimal advertising strategies with age-structured goodwill," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 259-284, October.
  33. BOUCEKKINE, Raouf & DE LA CROIX, David & LICANDRO, Omar, 2006. "Vintage capital," CORE Discussion Papers 2006024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  34. 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.
  35. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
  36. E. Barucci & F. Gozzi, 1999. "Optimal advertising with a continuum of goods," Annals of Operations Research, Springer, vol. 88(0), pages 15-29, January.
  37. Heaps, Terry, 1984. "The forestry maximum principle," Journal of Economic Dynamics and Control, Elsevier, vol. 7(2), pages 131-151, May.
  38. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
  39. Tahvonen, Olli & Salo, Seppo & Kuuluvainen, Jari, 2001. "Optimal forest rotation and land values under a borrowing constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1595-1627, October.
  40. Kemp, Murray C. & Moore, Elvin J., 1979. "Biological capital theory: a question and a conjecture," Economics Letters, Elsevier, vol. 4(2), pages 141-144.
  41. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eve:wpaper:14-04. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Samuel Nosel)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.