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On the Mitra–Wan forestry model: A unified analysis

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  • Ali Khan, M.
  • Piazza, Adriana

Abstract

We present a substantive and far-reaching generalization of the principal results in the economics of forestry, as formalized by Mitra and Wan (1986). Rather than a polarized dichotomy of linear and strictly concave, differentiable benefit (felicity) functions, we develop the theory in the context of functions that are supported at the golden-rule consumption and are not necessarily concave. Through a non-interiority condition on the set of zeroes of a resulting “discrepancy function,” we show the equivalence of finitely-maximal, maximal, minimal value-loss and optimal programs, and thereby answer questions left open by Brock and Mitra. Our synthesizing criterion is new to the capital theory literature, and in the concave setting, proves to be necessary and sufficient for the asymptotic convergence of good programs.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 1 ()
Pages: 230-260

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:1:p:230-260

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Forest management; Good programs; Finitely-maximal programs; Maximal programs; Optimal programs; Value-loss; Discrepancy function; Non-interiority; Asymptotic convergence;

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References

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  1. Nyarko, Yaw & Olson, Lars J., 1991. "Stochastic dynamic models with stock-dependent rewards," Journal of Economic Theory, Elsevier, vol. 55(1), pages 161-168, October.
  2. Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 37(2), pages 275-80, April.
  3. Basu, Kaushik & Mitra, Tapan, 2003. "Aggregating Infinite Utility Streams with Inter-generational Equity: The Impossibility of Being Paretian," Working Papers 03-03, Cornell University, Center for Analytic Economics.
  4. Miller, Robert A. & Voltaire, Karl, 1980. "A sequential stochastic tree problem," Economics Letters, Elsevier, vol. 5(2), pages 135-140.
  5. 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.
  6. 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.
  7. Ronald Wendner, 2003. "Existence, uniqueness, and stability of equilibrium in an OLG economy," Economic Theory, Springer, vol. 23(1), pages 165-174, December.
  8. Li, Jinlu & Lin, Shuanglin, 2008. "Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model," Journal of Economic Theory, Elsevier, vol. 141(1), pages 255-275, July.
  9. 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.
  10. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson-Solow-Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110.
  11. Basu, Kaushik & Mitra, Tapan, 2003. "Utilitarianism for Infinite Utility Streams: A New Welfare Criterion and Its Axiomatic Characterization," Working Papers 03-05, Cornell University, Center for Analytic Economics.
  12. Mitra, Tapan, 1983. "Sensitivity of optimal programs with respect to changes in target stocks: The case of irreversible investment," Journal of Economic Theory, Elsevier, vol. 29(1), pages 172-184, February.
  13. Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-92, December.
  14. 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.
  15. 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.
  16. Mitra, Tapan & Wan, Henry Y, Jr, 1985. "Some Theoretical Results on the Economics of Forestry," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 263-82, April.
  17. Adriana Piazza, 2009. "The optimal harvesting problem with a land market: a characterization of the asymptotic convergence," Economic Theory, Springer, vol. 40(1), pages 113-138, July.
  18. Hartl, R.F. & Kort, P.M., 2003. "History dependence without unstable steady state: A non-differentiable framework," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123061, Tilburg University.
  19. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  20. Seppo Salo & Olli Tahvonen, 2004. "Renewable Resources with Endogenous Age Classes and Allocation of Land," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 513-530.
  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.
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Cited by:
  1. Silvia Faggian & Giorgio Fabbri & Giuseppe Freni, 2013. "On the Mitra--Wan Forest Management Problem in Continuous Time," Working Papers 2013:28, Department of Economics, University of Venice "Ca' Foscari".

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