Halkos, George and Papageorgiou, George (2008): Extraction of nonrenewable resources: a differential game approach. Published in: Archieves of Economic History , Vol. 1, No. XXI (2008): pp. 522.

PDF
MPRA_paper_37596.pdf Download (285kB)  Preview 
Abstract
Exploitation of non–renewable resources is an intensively studied field of environmental economics in the last century. Since the influential Hotelling’s paper a huge progress is made in the depletable resources literature. Although a variety of methodologies is used in that problem’s solutions a basic question of time inconsistency arises in the solution process. We show the sources of dynamical time inconsistency in a leader – follower game for which the buyer leads while the extractor follows and the players employ open loop strategies. Also we make use of Markovian informational structure, in a non – renewable resource Nash game, in order to extract strategies that are time consistent. Finally we enlarge the utility function space from the logarithmic utility to the utility functions that exhibits relative risk aversion with the same, with respect to time consistency, strategies.
Item Type:  MPRA Paper 

Original Title:  Extraction of nonrenewable resources: a differential game approach 
Language:  English 
Keywords:  Nonrenewable resources; time consistency; Markovian strategies; leaderfollower 
Subjects:  Q  Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q0  General > Q00  General C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C70  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis Q  Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q3  Nonrenewable Resources and Conservation > Q30  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C60  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  37596 
Depositing User:  G.E. Halkos 
Date Deposited:  23. Mar 2012 13:42 
Last Modified:  12. Feb 2013 05:40 
References:  Barnett, H.J. and Morse C. (1963), Scarcity and Economic Growth: The Economics of Natural Resource Availability. John Hopkins University Press: Baltimore. Basar T., Olsder G. (1998) Dynamic Noncooperative Game Theory, SIAM edition New York, Academic Press. Bergstrom T., Cross J., Porter R. (1981), Efficiency – inducing taxation for a monopolistically supplied depletable resource, Journal of Public Economics, 15, 23 – 32. 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. Dockner E., Wagener F. (2008) Markov – Perfect Nash Equilibria in Models With a Single Capital Stock, Working paper 08 – 09, University of Amsterdam Halkos G. E., (2007), Environmental thinking in Economics, Archives of Economic History XIX (2) 5 – 17. Hotelling H. (1931), The economics of exhaustible resources, Journal of Political Economy 39, 137 – 175. Karp L., (1984), Optimality and consistency in a differential game with non – renewable resources. Journal of Economic Dynamics and Control, 8, 73 – 97. Kemp, M.C. Long, N.V., (1980) Optimal tariffs and exhaustible resources, in: M.C. Kemp and N.V. Long eds, Exhaustible resources, optimality and trade (North Holland, Amsterdam). Kydland, F. Prescott, E. (1977), Rules rather than discretion: The inconsistency of optimal plans, Journal of Political Economy, 85, 479 – 491. Lewins, Tracy R., Mathews S. Burness, S., (1979), Monopoly and the rate of extraction of exhaustible resources: Note, American Economic Review, 69, 227 – 230. Malthus, T.R. (1798), An essay on the Principle of Population. Ed. By P. Appleman New York, London: W.W. Norton and Company. Malthus, T.R. (1820), Principles of Political Economy: Considered with a view to their practical application. John Murray: London. Marshall, A. (1890), Principles of Economics. MacMillan London. Ramsey F. (1928), A mathematical theory of saving. Economic Journal 38, 543559. Ricardo, D. (1973), The principles of Political Economy. J.M. Dent and Sons: London. Simaan, M. and J.B. Cruz, Jr (1973), Additional aspects of the Stackelberg strategy in non – zero sum games, Journal of Optimization Theory and Applications, 11, 613 – 626. Smith, A. (1776), The Wealth of Nations (1961 edition, edited by Cannan, E.). Methuen, London. Stiglitz J. (1976), Monopoly and the Rate of Extraction of Exhaustible Resources, The American Economic Review, 66 (4) 655 – 661. Varian R. H. , (1992), Microeconomic Analysis Third Edition W – W. Norton New York. Ulph A.M. & Folie, G.M. 1980. Exhaustible Resources and Cartels: An Intertemporal NashCournot Model, Canadian Journal of Economics, Canadian Economics Association, vol. 13(4), pages 64558. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/37596 