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A NOTE ON THE CONSEQUENCES OF AN ENDOGENOUS DISCOUNTING DEPENDING ON THE ENVIRONMENTAL QUALITY

Published online by Cambridge University Press:  19 March 2007

ALAIN AYONG LE KAMA  and
KATHELINE SCHUBERT
ALAIN AYONG LE KAMA
Affiliation:
MEDEE, Université de Lille 1 and Commissariat général du Plan
KATHELINE SCHUBERT
Affiliation:
Centre d'Economie de la Sorbonne
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Abstract

Our intention is to study, in the framework of a very simple optimal growth model, the consequences on the optimal paths followed by consumption and the environmental quality of an endogenous discounting. Consumption directly comes from the use of environmental services and so is a direct cause of environmental degradation. The environment is valued both as a source of consumption and as an amenity. For a sustainability concern, we introduce an endogenous discount rate growing with the environmental quality, and compare the optimal growth paths with the ones obtained in the usual case of exogenous and constant discounting. We show that the convergence of the environmental quality toward a steady state occurs only for a very special configuration of the parameters in the exogenous discounting case, whereas it occurs generically in the endogenous discounting one. This happens for a utility discount rate becoming sufficiently high when the environmental quality is high and sufficiently low when the environmental quality is poor. In this case, then, endogenous discounting with a positive marginal discount rate allows us to avoid the depletion of the environment.

Keywords

Endogenous DiscountingSustainabilityEnvironment
Type
NOTES
Information
Macroeconomic Dynamics , Volume 11 , Issue 2 , April 2007 , pp. 272 - 289
Copyright
© 2007 Cambridge University Press

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References

Arrow K. and M. Kurz 1970 Public Investment, the Rate of Return and Optimal Fiscal Policy. Baltimore: Johns Hopkins University Press.
Ayong Le Kama A. 2001 Sustainable growth, renewable resources and pollution. Journal of Economic Dynamics and Control 25 (12), 1911– 1918.Google Scholar
Barro R. 1999 Ramsey meets Laibson in the neoclassical growth model. Quarterly Journal of Economics 114, 1125– 1152.Google Scholar
Becker R., J. Boyd and B. Sung 1989 Recursive utility and optimal capital accumulation: I. Existence. Journal of Economic Theory 47, 76– 100.Google Scholar
Chichilnisky G. 1996 An axiomatic approach to sustainable development. Social Choice and Welfare 13, 231– 257.Google Scholar
Das M. 2003 Optimal growth with decreasing marginal impatience. Journal of Economic Dynamics and Control 27, 1881– 1898.Google Scholar
Epstein L. 1987 A simple dynamic general equilibrium model. Journal of Economic Theory 41, 68– 95.Google Scholar
Gollier C. 2002a Time horizon and the discount rate. Journal of Economic Theory 107, 463– 473.Google Scholar
Gollier C. 2002b Discounting an uncertain future. Journal of Public Economics 85, 149– 166.Google Scholar
Harrod R. 1948 Towards a Dynamic Economy. London: Macmillan Press.
Harvey C. 1994 The reasonableness of non-constant discounting. Journal of Public Economics 53, 31– 51.Google Scholar
Heal G. 1998 Valuing the future: Economic Theory and Sustainability. New York: Columbia University Press.
Koopmans T. 1960 Stationary ordinal utility and impatience. Econometrica 28, 287– 309.Google Scholar
Laibson D. 1996 Hyperbolic Discount Functions, Undersaving, and Savings Policy. NBER Working Paper 5635.Google Scholar
Laibson D. 1997 Golden eggs and hyperbolic discounting. Quarterly Journal of Economics 112, 443– 477.Google Scholar
Li C.-Z. and K.-G. Löfgren 2000 Renewable resources and economic sustainability: A dynamic analysis with heterogeneous time preferences. Journal of Environmental Economics and Management 40, 236– 249.Google Scholar
Loewenstein G. and D. Prelec 1992 Anomalies in intertemporal choice: Evidence and an interpretation. Quarterly Journal of Economics 107, 573– 598.Google Scholar
Michel P. 1982 On the transversality conditions in infinite horizon problems. Econometrica 50 (4), 975– 985.Google Scholar
Obstfeld M. 1990 Intertemporal dependence, impatience, and dynamics. Journal of Monetary Economics 26, 45– 75.Google Scholar
Palivos T., P. Wang and J. Zhang 1997 On the existence of balanced growth equilibrium. International Economic Review 38 (1), 205– 223.Google Scholar
Pittel K. 2002 Sustainability and Endogenous Growth. Cheltenham, UK: Edward Elgar.
Portney P.R. and J.P. Weyant 1999 Discounting and Intergenerational Equity. Washington, DC: Resources for the Future.
Ramsey F.P. 1928 A mathemathical theory of saving. Economic Journal 138, 543– 559.Google Scholar
Seierstad A. and K. Sydsaeter 1987 Optimal Control Theory with Economic Applications. Amsterdam: North Holland.
Smulders S. and R. Gradus 1996 Pollution abatement and long-term growth. European Journal of Political Economy 12, 505– 532.Google Scholar
Weitzman M. 1998 Why the far distant future should be discounted at its lowest possible rate. Journal of Environmental Economics and Management 36, 201– 208.Google Scholar