Dynamic optimization in natural resources management

Halkos, George (2010): Dynamic optimization in natural resources management.

Abstract

Dynamic modeling is general and recently the most interesting perspective to solve a dynamic economic problem based on Pontryagin’s maximum principle. Moreover traditional economic theory, up to the middle of twentieth century, builds up the production functions regardless the inputs’ scarcity. Nowadays it is clear that both the inputs are depletable quantities and a lot of constraints are imposed in their usage in order to ensure economic sustainability. For example the input “oil” used in the production is a non renewable resource so it can be exhausted. In a same way every biomass resides in ecosystems is a resource that can be used in a generalized production function for capital accumulation purposes but the latter resource is a renewable one. The purpose of this paper is the presentation of some natural resources dynamic models in order to extract the optimal trajectories of the state and control variables for the optimal control economic problem. We show how methods of infinite horizon optimal control theory developed for natural resources models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic optimization; optimal control; maximum principle; natural resources
• Subjects: Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q32 - Exhaustible Resources and Economic Development; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

References

Benchekroun, H. and N.V. Long (2001) Tranboundary Fishery: A Differential Game Model, Economica, 69, 207 – 221.

Brock W.A. and D. Starrett (2003) Managing Systems with Non – convex Positive Feedback, Environmental and Resource Economics, 26, 575 – 602.

Dasgupta P. and G.M. Heal (1974), The optimal depletion of exhaustible sources. Review of Economic Studies, Symposium of the Economics of Exhaustible Resources, 3 – 28.

Dasgupta P. and K.G. Maler (2003) The Economics of Non – Convex Ecosystems: Introduction, Environmental and Resource Economics, 26, 499 – 525.

Dockner E.J., Jorgensen S. and Long N. V. – Sorger G. (2000) Differential Games in Economics and Management Science, Cambridge, Cambridge University Press.

Hotelling H. (1931), The economics of exhaustible resources, Journal of Political Economy 39, 137 – 175.

Levhari D, Mirman L. (1980) The great fish war. Bell Journal of Economics, 322-344.

Pontryagin et al (1961), The Mathematical Theory of Optimal Processes, Gordon and Breach Science Publishers (translated by K.N. Trirogoff)

Stiglitz, J. (1976), Monopoly and the Rate of Extraction of Exhaustible Resources, The American Economic Review, 66 (4) 655 – 661.