Skip to main content

Advertisement

Log in

The optimal harvesting problem with a land market: a characterization of the asymptotic convergence

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

We study the asymptotic behavior of the optimal harvesting policies for a multiple species forest with a land market, i.e., any fraction of the land can be traded at any time stage. We prove the existence of sustainable states and we discuss the conditions under which any optimal trajectory converges in the long run towards one of these states or towards the set of optimal periodic cycles. We also discuss briefly a more general problem that includes costs of converting land between the different species.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Boldrin, M., Montrucchio, L.: On the indeterminacy of capital accumulation paths. J Econ Theory 40(1), 26–39 (1986)

    Article  Google Scholar 

  • Cominetti, R., Piazza, A.: Asymptotic convergence of optimal harvesting policies for a multiple species forest. CMM Technical Report no. 158, 1–18 (2006)

  • Dana, R.-A., Van, C.L., Mitra, T., Nishimura, K. (eds): Handbook on Optimal Growth 1, Discrete Time, pp. 477. Springer, Berlin

    Google Scholar 

  • Faustmann, M.: Berechnung des Werthes, welchen Waldboden, sowie noch nicht haubare Holzbestände für die Waldwirtschaft besitzen, Allgemeine Forst- and Jagdzeitung (1849); (translated into English as: Calculation of the value which forest land and immature stands possess for forestry. J For Econ 1(1), 7–44 (1995))

    Google Scholar 

  • Majumdar, M., Mitra, T., Nishimura, K.: Optimization and Chaos, Studies in Economic Theory, vol.11. Berlin, Springer (2000)

    Google Scholar 

  • McKenzie, L.W.: Optimal economic growth, turnpike theorems and comparative dynamics, Handbook of mathematical economics vol III, pp. 1281–1355. North-Holland, Amsterdam (1986)

    Google Scholar 

  • McKenzie, L.W.: Classical general equilibrium theory. MIT Press, Cambridge (2002)

    Google Scholar 

  • Mitra, T., Nishimura, K.: Discounting and long-run behavior: global bifurcation analysis of a family of dynamical systems. J Econ Theory 96(1–2), 256–293 (2001)

    Article  Google Scholar 

  • Mitra, T., Wan, H.W.: Some theoretical results on the economics of forestry. Rev Econ Stud LII, 263–282 (1985)

  • Mitra, T., Wan, H.W.: On the Faustmann solution to the forest management problem. J Econ Theory 40, 229–249 (1986)

    Article  Google Scholar 

  • Montrucchio, L.: Complexity of optimal paths in strongly concave problems. Nonlinear dynamics in economics and social sciences (Siena, 1991), Lecture Notes in Econom. and Math. Systems, vol. 399, 272–282. Berlin, Springer (1993)

    Google Scholar 

  • Montrucchio, L.: A new turnpike for discounted programs. Econ Theory 5, 371–382 (1995)

    Article  Google Scholar 

  • Ohlin, B.: Till frågan om skogarnas omloppstid. Ekonomisk Tidskrift, 22, (1921); (translated into English as: Concerning the question of the rotation period in forestry. J For Econ 1(1), 89–114 (1995))

    Google Scholar 

  • Rapaport, A., Sraidi, S., Terreaux, J.P.: Optimality of greedy and sustainable policies in the management of renewable resources. Optim Control Appl Methods 24, 23–44 (2003)

    Article  Google Scholar 

  • Salo, S., Tahvonen, O.: On equilibrium cycles and normal forests in optimal harvesting of tree vintages. J Environ Econ Manage 44, 1–22 (2002)

    Article  Google Scholar 

  • Salo, S., Tahvonen, O.: On the economics of forests vintages. J Econ Dyn Control 27, 1411–1435 (2003)

    Article  Google Scholar 

  • Salo, S., Tahvonen, O.: Renewable resources with endogenous age classes and allocation of the land. Am J Agric Econ 86(2), 513–530 (2004)

    Article  Google Scholar 

  • Samuelson, P.A.: Economics of forestry in an evolving society, Econ Inquiry, 16 (1976)

  • Tahvonen, O.: Optimal harvesting of forest age classes: a survey of some recent results. Math Popul Stud 11, 205–232 (2004)

    Article  Google Scholar 

  • Zaslavski, A.J.: Turnpike properties in the calculus of variations and optimal control, Nonconvex Optimization and its Applications, vol. 80. New York, Springer (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adriana Piazza.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Piazza, A. The optimal harvesting problem with a land market: a characterization of the asymptotic convergence. Econ Theory 40, 113–138 (2009). https://doi.org/10.1007/s00199-008-0362-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00199-008-0362-8

Keywords

JEL Classification

Navigation