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Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the mmaximin problem in the case where production and utility are Cobb-Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show taht it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb-Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resoultion of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if doesn't whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/V08031.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number v08031.

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Length: 35 pages
Date of creation: Apr 2008
Handle: RePEc:mse:cesdoc:v08031
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  1. Avinash Dixit & Peter Hammond & Michael Hoel, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 551-556.
  2. Kenneth J. Arrow & Partha Dasgupta & Karl-Göran Mäler, 2003. "The genuine savings criterion and the value of population," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 217-225, 03.
  3. Withagen, Cees & B. Asheim, Geir, 1998. "Characterizing sustainability: The converse of Hartwick's rule," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 159-165, September.
  4. John Hartwick, 1977. "Intergenerational Equity and the Investment of Rents from Exhaustible Resources in a Two Sector Model," Working Papers 281, Queen's University, Department of Economics.
  5. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, Diciembre.
  6. Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2007. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Journal of Environmental Economics and Management, Elsevier, vol. 53(2), pages 213-229, March.
  7. Wolfgang Buchholz & Swapan Dasgupta & Tapan Mitra, 2005. "Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(3), pages 547-561, 09.
  8. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-974, December.
  9. repec:reg:rpubli:132 is not listed on IDEAS
  10. Jeffrey A. Krautkraemer, 1985. "Optimal Growth, Resource Amenities and the Preservation of Natural Environments," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 153-169.
  11. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(03), pages 275-300, June.
  12. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
  13. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 3-28.
  14. Kenneth Stollery, 1998. "Constant Utility Paths and Irreversible Global Warming," Canadian Journal of Economics, Canadian Economics Association, vol. 31(3), pages 730-742, August.
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