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Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

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This paper studies the undiscounted utilitarian optimal paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. We use a Keynes-Ramsey rule wich yields a generalization of Hartwick's rule : if society has a zero discount rate but is ready to accept intertemporal substitution, net investment should not be zero as in the maximin case but should be positive, its level depending on the distance between the current and the long run bliss level of utility. We characterize solutions in the Cobb-Douglas utility and production case, and analyse the influence of the intertemporal elasticity of substitution on the time profile of the optimal paths. We show that, in the Cobb-Douglas case, the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09012.pdf
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Bibliographic Info

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 09012.

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Length: 22 pages
Date of creation: Jan 2009
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Handle: RePEc:mse:cesdoc:09012

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Keywords: Exhaustible resources; Hartwick's rule; intertemporal substitution.;

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Cited by:
  1. d'Autume, Antoine & Hartwick, John M. & Schubert, Katheline, 2010. "The zero discounting and maximin optimal paths in a simple model of global warming," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 193-207, March.
  2. Robert D. Cairns & Vincent Martinet, 2012. "An Environmental-Economic Measure of Sustainable Development," EconomiX Working Papers 2012-2, University of Paris West - Nanterre la Défense, EconomiX.

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