Abstract
This note discusses the asymptotic behavior of optimal trajectories in infinite horizon control problems when the objective function is a compromise between two averaged discounted sums of the same stream of rewards. We show that the turnpike associated with the lowest discount rate is the one that will prevail. We also show that, when one discount rate is equal to 0, the problem of the best compromise between a discounted sum and the long term average reward may not admit a solution. We then discuss the implications of these findings for the definition of global climate change mitigation policies.
Research supported by the NCCR—“Cimate” grant of the Swiss NSF.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ainslie, G. and Haslam, N., Hyperbolic discounting, in Loewenstein & Elster (eds), Choice Over Time, Russell Sage Foundation, New York, 1992.
Altman A., Feinberg E. and Schwartz A., Weighted discounted stochastic games with perfect information, in J.A. Filar, V. Gaitsgory and K. Mizukami (eds), Advances in Dynamic Games and Applications,Annals of the International Society of Dynamic Games, 2000.
Arndt, H.W., The rise and fall of economic growth: a study in contemporary thought, Longman Cheshire, Sydney, 1978.
Arrow K. and Kurz, M., Public investment, the rate of return,and optimal investment policies,John Hopkins Press, Baltimore, 1970.
Arrow, K, Bolin, B., Costanza, R., Dasgupta, P., Folke, C., Holling, C., Jansson, B-O., Levin, S., Maler, K-G., Perrings, C., and PimentaL, D., Economic growth carrying capacity and the environment, Science, 268:520–21, 1995.
Arrow, K.J., Cline, W.R., Maeler, K.G., Munasinghe, M., Squitieri, R., and Stiglitz, J.E., Intertemporal equity, discount-ing, and economic efficiency, in J.P. Bruce, H. Lee and E.F. Haites (eds), Climate Change 1995: Economic and Social Dimensions - Contribution of Working Group III to the Second Assessment Report of the Intergovernmental Panel on Climate Change, pp. 125–144, Cambridge University Press, Cambridge, 1996.
Asheim G.B., Buchholz, W. and Tungodden, B., Justifying sustainability, Journal of Environmental Economics and Management, 41:252–268, 2001.
Ayong LE Kama, A., Sustainable growth, renewable resources and pollution, Journal of Economic Dynamics and Control, 25:1911–1918, 2001.
Baumol, W., and Oates, W., Economics, Environmental Policy and the Quality of Life, Prentice Hall, Englewood Cliffs, 1979.
Beltratti A., Chichilnisky G. and Heal G., The green golden rule, Economic Letters, 49:175–179, 1995.
Carlson D., Haurie, A., and Leizarowitz, A., Infinite Horizon Optimal Control: Deterministic and stochastic Systems, Springer Verlag, 1994.
Chichilnisky G., An axiomatic approach to sustainable development, Soc. Choice Welf., 13:231–257, 1996.
Chichilnisky G., What is sustainable development, Land Economy,73:467–49, 1997.
Cline, W.R., Discounting for the very long term, in Portney & Weyant (eds), Discounting and Intergenerational Equity, Resources for the Future, Washington DC, 1999.
Feinstein C.D.,and Luenberger,D.G.,Analysis of the asymptotic behavior of optimal control trajectoriesSIAM Journal on Control and Optimization19:561–585,1981.
Hartwick, J.M., Intergenerational equity and the investing of rents from exhaustible resourcesAmerican Economic Review66:972–4, 1977.
Harvey, C.M., The reasonableness of non-constant discounting, Journal of Public Economics, 53:31–51, 1994.
Haurie A., Environmental coordination in dynamic oligopolistic markets, Group Decision and Negotiation, 4:39–57, 1995.
Heal, G.M., Interpreting sustainability, mimeo Columbia Business School, New York, May 1996.
Heal, G.M., Optimality or sustainability ?, mimeo Columbia Business School, New York, June 2001.
Heal, G.M., Valuing the Future: Economic Theory and Sustain-ability, Columbia University Press, New York, 1998.
IPCC, Climate Change 1995: Economic and Social Dimensions of Climate Change, NY. Cambridge University Pess, 1996.
Kopp,R.J.,and Portney,P.R.,Mock referenda for intergenerational decisionmaking, in P.R. Portney and J. Weyant (eds),Discounting and Intergenerational Effects,Resources for the Future, pp. 87–98, Washington, DC, 1999.
Li C.-Z. and Lofgren, K.-G., Economic growth, environmental quality and hyperbolic discounting, Technical Report, Dept. of Economics, Umea University, Sweden, 2001.
Loewenstein, G. and Prelec, D., Anomalies in intertemporal choice: Evidence and an interpretation, in Loewenstein & Elster (eds), Choice Over Time, Russell Sage Foundation, New York, 1992.
Nordhaus W.D., A market based discount rate, in P.R. Portney and J. Weyant (eds), Discounting and Intergenerational Effects, Resources for the Future, pp. 145–162, Washington, DC, 1999.
Norgaard, R. and Howarth, R., Sustainability and discounting the future, in R. Costanza (ed.), Ecological Economics: The Science and Management of Sustainability, Columbia University Press, New York, 1991.
Peleg B. and Yaari M.E., On the existence of consistent course of action when tastes are changing, Review of Economic Studies, 40:391–401, 1973.
Phelps E.S. and Pollak R., On second best national saving and game-equilibrium growth, Review of Economic Studies, 35:185–199, 1968.
Portney P.R. and Weyant J., eds, Discounting and Intergenerational Effects, Resources for the Future, Washington, DC, 1999.
Weitzman, M.L., Why the far-distant future should be discounted at its lowest possible rate, Journal of Environmental Economics and Management, 36:201–208, 1998.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Haurie, A. (2002). Turnpikes in Multi-Discount Rate Environments and Gcc Policy Evaluation. In: Zaccour, G. (eds) Optimal Control and Differential Games. Advances in Computational Management Science, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1047-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1047-5_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5368-3
Online ISBN: 978-1-4615-1047-5
eBook Packages: Springer Book Archive