Halkos, George (2010): Harvesting natural resources: management and conflicts.

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Abstract
It is reasonable to consider the stock of any renewable resource as a capital stock and treat the exploitation of that resource in much the same way as one would treat accumulation of a capital stock. This has been done to some extent in earlier papers containing a discussion of this point of view. However, the analysis is much simpler than it appears in the literature especially since the interaction between markets and the natural biology dynamics has not been made clear. Moreover renewable resources are commonly analyzed in the context of models where the growth of the renewable resource under consideration is affected by two factors: the size of the resource itself and the rate of harvesting. This specification does not take into account that human activities other than harvesting can have an impact on the growth of the natural resource. Furthermore, natural resource harvesting are not productive factories. Fishery economic literature (based on the foundations of Gordon, 1954; Scott, 1955; and Smith, 1963) suggests particular properties of the ocean fishery which requires tools of analysis beyond those supplied by elementary economic theory. An analysis of the fishery must take into account the biological nature of fundamental capital, the fish and it must recognize the common property feature of the open sea fishery, so it must allow that the fundamental capital is the subject of exploitation. The purpose of this paper is the presentation of renewable resources dynamic models in the form of differential games aiming to extract the optimal equilibrium trajectories of the state and control variables for the optimal control economic problem. We show how methods of infinite horizon optimal control theory may be developed for renewable resources models.
Item Type:  MPRA Paper 

Original Title:  Harvesting natural resources: management and conflicts 
Language:  English 
Keywords:  Renewable resources; exploitation of natural resources; dynamic optimization; optimal control 
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 
Item ID:  24119 
Depositing User:  Nickolaos Tzeremes 
Date Deposited:  27. Jul 2010 15:03 
Last Modified:  13. Feb 2013 13:21 
References:  Berck, P., (1981), Optimal management of renewable resources with growing demand and stock externalities, Journal of Environmental Economics and Management, 8, 105–117. Clark, C., (1973), Profit maximization and the extinction of animal species, Journal of Political Economy, 81, 950 – 961. Clark, C., (1990), Mathematical Bioeconomics, 2nd , Wiley Interscience. Clark, C.W., Munro, G.R., (1975), Economics of fishing and modern capital theory: a simplified approach, Journal of Environmental Economics and Management, 2, 92 – 106. Cohen, D., Michel, P., (1998) How should control theory be used to calculate a time–consistent government policy?. Review of Economic Studies, 55, 2, 263 – 274. Dockner, E., Jorgensen, S., Long, N.V., Sorger, G., (2000), Differential games in economics and management science, Cambridge University Press. Grass, D., Caulkins, J., Feichtinger, G., Trangler, G., Behrens, D., (2008), Optimal Control of Nonlinear Processes, Springer. Dockner, E.J., Feichtinger, G., (1991), On the optimality of limit cysles in dynamic economic systems. Journal of Economics, 53, 31 – 50. Gordon, H.S., (1954), The economic theory of a common property resource, Journal of Political Economy, 62, 124 – 142. Hartl, P.F., (1987), A simple proof of the monotonicity of the state strajectories in autonomous control problems. Journal of Economic Theory, 40, 211 – 215. Hartman, P., (1963), On the local linearization of differential equations. In: Proceedings of the American Mathematical Society, pp. 568 – 573. Kydland, F., Prescott, E., (1977), Rules rather discretion: The inconsistency of optimal plans. Journal of Political Economy, 85, 473 – 492. Kuznetsov, Y., (1997). Elements of Applied Bifurcation Theory. Springer, Berlin. Levhari, D., Withagen, C., (1992), Optimal Management of the Growth Potential of Renewable Resources, Journal of Economics, 3, 297 – 309. Lewis, T., Schmalensee, R., (1980), On Oligopolistic Markets of Nonrenewable Natural Resources, Quarterly Journal of Economics, 95, 475 – 491. Plourde, C.G., (1970), A simple model of replenishable natural resource exploitation, American Economic Review, 62, 518 – 521. Schafer, M., (1994), Exploitation of natural resources and pollution. Some differential game models, Annals of Operations Research, 54, 237 – 262. Scott, A., 1955, Natural resources: The economics of conservation, Univ. of Toronto Press, Toronto, Canada. Smith, V.L., (1969), On models of commercial fishing, Journal of Political Economy, 77, 181 – 198. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/24119 