Advertisement

Economic Theory

, Volume 36, Issue 3, pp 453–469 | Cite as

Controlling a biological invasion: a non-classical dynamic economic model

  • Lars J. OlsonEmail author
  • Santanu Roy
Open Access
Research Article

Abstract

This paper analyzes the optimal intertemporal control of a biological invasion. The invasion growth function is non-convex and control costs depend on the invasion size, resulting in a non-classical dynamic optimization problem. We characterize the long run dynamic behavior of an optimally controlled invasion and the corresponding implications for public policy. Both control and the next-period invasion size may be non-monotone functions of the current invasion size; the related optimal time paths may not be monotone or convergent. We provide conditions under which eradication, maintenance control, and no control are optimal policies.

Keywords

Intertemporal allocation Nonconvexities Biological invasion Invasive species Renewable resource economics 

JEL Classification

D9 Q2 

References

  1. 1.
    Benveniste L.M. and Scheinkman J.A. (1979). On the differentiability of the value function in dynamic models of economics. Econometrica 47(3): 727–732 CrossRefGoogle Scholar
  2. 2.
    Clark C.W. (1990). Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd edn. Wiley, New York Google Scholar
  3. 3.
    Dawid H. and Kopel M. (1999). On optimal cycles in dynamic programming models with convex return function. Econ. Theory 13(2): 309–327 CrossRefGoogle Scholar
  4. 4.
    Dechert W.D. and Nishimura K. (1983). A complete characterization of optimal growth paths in an aggregated model with non-concave production function. J. Econ. Theory 31: 332–354 CrossRefGoogle Scholar
  5. 5.
    Inada K.-I. (1963). On a two-sector model of economic growth: comments and a generalization. Rev. Econ. Stud. 30(2): 119–127 CrossRefGoogle Scholar
  6. 6.
    Jaquette D.L. (1972). A discrete time population control model. Math. Biosciences 15: 231–252 CrossRefGoogle Scholar
  7. 7.
    Majumdar M. and Mitra T. (1982). Intertemporal allocation with a non-convex technology. J. Econ. Theory 27: 101–136 CrossRefGoogle Scholar
  8. 8.
    Majumdar M. and Mitra T. (1994). Periodic and chaotic programs of optimal intertemporal allocation in an aggregative model with wealth effects. Econ. Theory 4(5): 649–676 CrossRefGoogle Scholar
  9. 9.
    Majumdar M., Mitra T., Nishimura K. (eds). (2000). Optimization and Chaos. Springer-Verlag, Berlin Google Scholar
  10. 10.
    Mirman L.J. and Zilcha I. (1975). On optimal growth under uncertainty. J. Econ. Theory 11(3): 329–339 CrossRefGoogle Scholar
  11. 11.
    Mitra T. and Roy S. (2006). Optimal exploitation of renewable resources under uncertainty and the extinction of species. Econ. Theory 28(1): 1–23 CrossRefGoogle Scholar
  12. 12.
    Nyarko Y. and Olson L.J. (1994). Stochastic growth when utility depends on both consumption and the stock level. Econ. Theory 4(5): 791–797 CrossRefGoogle Scholar
  13. 13.
    Olson L.J. and Roy S. (1996). On conservation of renewable resources with stock-dependent return and non-concave production. J. Econ. Theory 70(1): 133–157 CrossRefGoogle Scholar
  14. 14.
    Olson L.J. and Roy S. (2002). The economics of controlling a stochastic biological invasion. AJAE 84(5): 1311–1316 Google Scholar
  15. 15.
    Olson L.J. and Roy S. (2006). The economics of controlling a biological invasion, WP03-06, Dept. of Agricultural and Resource Economics. University of Maryland, College Park Google Scholar
  16. 16.
    Pimentel D., Lach L., Zuniga R. and Morrison D. (2000). Environmental and economic costs of nonindigenous species in the United States. BioScience 50(1): 53–65 CrossRefGoogle Scholar
  17. 17.
    Rockafellar R.T. and Wets R.J.-B. (2004). Variational Analysis. Springer, Berlin Google Scholar
  18. 18.
    Simberloff D. (1996). Impacts of introduced species in the United States. Consequences 2(2): 13–22 Google Scholar
  19. 19.
    Strauch R.E. (1966). Negative dynamic programming. Ann. Math. Stat. 37(4): 871–890 CrossRefGoogle Scholar
  20. 20.
    Topkis D.M. (1978). Minimizing a submodular function on a lattice. Oper. Res. 26: 305–321 CrossRefGoogle Scholar
  21. 21.
    Vitousek P.M., D’Antonio C.M., Loope L.L. and Westbrooks R. (1996). Biological invasions as global environmental change. Am. Scientist 84: 468–478 Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Agricultural and Resource EconomicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of EconomicsSouthern Methodist UniversityDallasUSA

Personalised recommendations