Singular Optimal Control Model of Stock-Dependent Environmental Policies

  • K. Erdlenbruch
  • M. Tidball


In many countries, forest policies consist of a system of various regulations, taxes, and subsidies. In this article, we focus on those policies that regulate selective harvesting and study the example of Central Africa. We use a deterministic singular optimal control model of renewable resources to assess these policies with respect to a first best situation which integrates a social surplus or externality function. In particular, in contrast to earlier articles, we analyze a stock dependent tax, for which the objective function is piecewise differentiable. We use a theorem proposed by Hartl and Feichtinger to solve the mathematical problem. We show that this tax is the most flexible instrument with respect to fund collection.


Singular optimal control environmental taxation renewable resource economics stock dependency 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    CLARK, C. W., and MUNRO G. R., The Economics of Fishing and Modern Capital Theory: A Simplified Approach, Journal of Environmental Economics and Management, Vol. 2, pp. 92–106, 1975.Google Scholar
  2. 2.
    CLARK, C. W., Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Wiley and Sons, New York, NY, 1990.MATHGoogle Scholar
  3. 3.
    MUNRO, G. R., The Optimal Management of Transboundary Renewable Resources. Canadian Journal of Economics, Vol. 12, pp. 355–376, 1979.CrossRefGoogle Scholar
  4. 4.
    CLARK, C. W., The Effect of Fishermen’s Quotas on Expected Catch Rate, Marine Resource Economics, Vol. 1, pp. 419–427, 1985.Google Scholar
  5. 5.
    BERCK, P., Optimal Management of Renewable Resources with Growing Demand and Stock Externalities, Journal of Environmental Economics and Management, Vol. 8, pp.105–117, 1981.Google Scholar
  6. 6.
    MONTGOMERY, C. A., and ADAMS, D. M., Optimal Timber Management Policies, Handbook of Environmental Economics, Edited by D. W. Bromley, Basil Blackwell, Oxford, UK, pp. 3–14, 1995.Google Scholar
  7. 7.
    FARZIN, Y. H., Optimal Pricing of Environmental and Natural Resource Use with Stock Externalities, Journal of Public Economics, Vol. 62, pp. 31–57, 1996.CrossRefGoogle Scholar
  8. 8.
    VAN SOEST, D., and LENSINK, R., Foreign Transfers and Tropical Deforestation: What Terms of Conditionality? American Journal of Agricultural Economics, Vol. 82, pp. 389–399, 2000.CrossRefGoogle Scholar
  9. 9.
    HYDE, W. F., AMACHER, G. S., and MAGRATH, W., Deforestation and Forest Land Use: Theory, Evidence, and Policy Implications, The World Bank Research Observer, Vol. 11, pp. 223–248, 1996.Google Scholar
  10. 10.
    VINCENT, J. R., Rent Capture and the Feasibility of Tropical Forest Management, Land Economics, Vol. 66, pp. 212–223, 1990.CrossRefGoogle Scholar
  11. 11.
    ENGLIN, J. E., and KLAN, M. S., Optimal Taxation: Timber and Externalities Journal of Environmental Economics and Management, Vol. 18, pp. 263–275, 1990.CrossRefGoogle Scholar
  12. 12.
    GAMPONIA, V., and MENDELSOHN, R., The Economic Efficiency of Forest Taxes, Forest Science, Vol. 33, pp. 367–378, 1987.Google Scholar
  13. 13.
    LEVHARI, D., and MIRMAN, L. J., The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution, Bell Journal of Economics, Vol. 11, pp. 322–334, 1980.CrossRefMathSciNetGoogle Scholar
  14. 14.
    MUNRO, G. R., Differential Games and the Optimal Management of Transboundary Fisheries, Lecture Notes in Control and Information Sciences, Springer. Berlin, Germany, Vol. 157, pp. 95–101, 1991.Google Scholar
  15. 15.
    STIGLITZ, J. E., and DASGUPTA, P., Differential Taxation, Public Goods, and Economic Efficiency, Review of Economic Studies, Vol. 38, pp. 151–174, 1971.CrossRefGoogle Scholar
  16. 16.
    MIRRLEES, J. A., Optimal Tax Theory: A Synthesis, Journal of Public Economics. Vol. 6, pp. 327–358, 1976.CrossRefGoogle Scholar
  17. 17.
    CREMER, H., and GAHVARI, F., Second-Best Taxation of Emissions and Polluting Goods, Journal of Public Economics, Vol. 80, pp. 169–197, 2001.CrossRefGoogle Scholar
  18. 18.
    CHANG, S. J., An Economic Analysis of Forest Taxation’s Impact on Optimal Rotation Age, Land Economics, Vol. 58, pp. 310–323, 1982.CrossRefGoogle Scholar
  19. 19.
    JOHANSSON, P. O., and LÖFGREN, K. G., The Economics of Forestry and Natural Resources, Basil Blackwell, Oxford, UK, 1985.Google Scholar
  20. 20.
    HARTL, R. F., and FEICHTINGER, G., A New Sufficient Condition for Most Rapid Approach Paths, Journal of Optimization Theory and Applications, Vol. 54, pp. 403–411, 1987.CrossRefMathSciNetGoogle Scholar
  21. 21.
    KOLSTAD, C., Environmental Economics, Oxford University Press, Oxford, UK. 2001.Google Scholar
  22. 22.
    VOUSDEN, N., Basic Theoretical Issues of Resource Depletion, Journal of Economic Theory, Vol. 6, pp. 126–143, 1973.CrossRefMathSciNetGoogle Scholar
  23. 23.
    AMACHER, G. S. and BRAZEE, R. J., Designing Forest Taxes with Varying Government Preferences and Budget Targets, Journal of Environmental Economics and Management, Vol. 32, pp. 323–340, 1997.CrossRefGoogle Scholar
  24. 24.
    KOSKELA, E., and OLLIKAINEN, M., Optimal Forest Taxation under Private and Social Amenity Valuation, Forest Science, Vol. 49, pp. 596–607, 2003.Google Scholar
  25. 25.
    BAUMOL, W. J., and OATES, W. E., The Theory of Environmental Policy, Cambridge University Press, Cambridge, UK, 1988.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • K. Erdlenbruch
    • 1
  • M. Tidball
    • 2
  1. 1.Cemagref, UMR G-EAU and LAMETAMontpellierFrance
  2. 2.INRA, UMR LAMETAMontpellierFrance

Personalised recommendations