We present an optimal control model of three stages of resources allocation for managing invasive species. Three types of temporal uncertainty are considered, involving the timing of discovery of an invasive pest, the timing of an induced technology development after the establishment and dispersion of an invasive species, and the timing of farmer adoption of induced technology as the costs of controlling the invasive species increase. Using a bioeconomic optimal control model of managing invasive species, where models in previous studies are subset within our model, we show that when sub-structured models not including all three stages are used for managing invasive species, resource allocation for adopting preventive measures before the initial discovery of an invasive pest would be supra-optimalwhile resource allocation for adopting conventional control measures after establishment and dispersion would be sub-optimal.
References
[1]
C. S. Kim, R. N. Lubowski, J. Lewandrowski and M. E. Eiswerth, “Prevention or Control: Optimal Government Policies for Invasive Species Management,” Agricultural and Resource Economics Review, Vol. 35, No. 1, 2006, pp. 29-40.
[2]
L. J. Olson and S. Roy, “On Prevention and Control of an Uncertain Biological Invasion,” Review of Agricultural Economics, Vol. 27, No. 3, 2005, pp. 491-497.
doi:10.1111/j.1467-9353.2005.00249.x
[3]
K. Kotani, M. Kakinaka and H. Matsuda, “Dynamic Economic Analysis on Invasive Species Management: Some Policy Implications of Catchability,” Mathematical Biosciences, Vol. 220, No. 1, 2009, pp. 1-14.
doi:10.1016/j.mbs.2009.03.009
[4]
C. S. Kim, G. D. Schaible, J. Lewandrowski and U. Vasavada, “Managing Invasive Species in the Presence of Endogenous Technological Change with Uncertainty,” Risk Analysis, Vol. 30, No. 2, 2010, pp. 250-260.
doi:10.1111/j.1539-6924.2009.01312.x
[5]
M. Grubb, J. Kohler and D. Anderson, “Induced Technical Change in Energy and Environmental Modeling: Analytic Approaches and Policy Implications,” Annual Review of Energy and the Environment, Vol. 27, No. 1, 2002, pp. 271-308.
doi:10.1146/annurev.energy.27.122001.083408
[6]
C. S. Kim, D. Lee, G. Schaible and U. Vasavada, “Multiregional Invasive Species Management: Theory and an Application to Florida’s Exotic Plants,” Journal of Agricultural and Applied Economics, Vol. 39, Special Issue, 2007, pp. 111-124.
[7]
M. E. Eiswerth and W. S. Johnson, “Managing Nonindigenous Invasive Species,” Environmental and Resource Economics, Vol. 23, No. 3, 2002, pp. 319-342.
doi:10.1023/A:1021275607224
[8]
B. Leung, D. M. Ludge, D. Finnoff, J. F. Shogren, M. A. Lewis and G. Lamberti, “An Ounce of Prevention or a Pound of Cure: Bioeconomic Risk Analysis of Invasive Species,” Royal Society, Vol. 269, No. 1508, 2002, pp. 2407-2413. doi:10.1098/rspb.2002.2179
[9]
N. M. Kieffer, “Economic Duration Data and Hazard Functions,” Journal of Economic Literature, Vol. 26, No. 2, 1988, pp. 646-679.
[10]
M. I. Kamien and N. L. Schwartz, “Limit Pricing and Uncertain Entry,” Econometrica, Vol. 39, No. 3, 1971, pp. 441-454. doi:10.2307/1913258
[11]
N. L. Rose and P. L. Joskow, “The Diffusion of New Technologies: Evidence from the Electric Utility Industry,” Rand Journal of Economics, Vol. 21, No. 3, 1990, pp. 354-373. doi:10.2307/2555614
[12]
K. J. Arrow and A. C. Enthoven, “Quasi-Concave Programming,” Econometrica, Vol. 29, No. 4, 1961, pp. 779-800. doi:10.2307/1911819
[13]
A. Seierstad and K. Sydsaeter, “Sufficient Conditions in Optimal Control Theory,” International Economic Review, Vol. 18, No. 2, 1977, pp. 367-391.
doi:10.2307/2525753
[14]
R. F. Stengel, “Optimal Control and Estimation,” 2nd Edition, Dover Publication Inc., New York, 1994.
