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

  • Antoine D'Autume


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

  • Katheline Schubert


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00367910.

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Date of creation: Feb 2009
Date of revision:
Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2009.12 - ISSN : 1955-611X. 2009
Handle: RePEc:hal:cesptp:halshs-00367910
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  1. Antoine D'Autume & Katheline Schubert, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308793, HAL.
  2. John Hartwick, 1976. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," Working Papers 220, Queen's University, Department of Economics.
  3. Mitra, Tapan, 1980. "On Optimal Depletion of Exhaustible Resources: Existence and Characterization Results," Econometrica, Econometric Society, vol. 48(6), pages 1431-50, September.
  4. repec:oup:restud:v:52:y:1985:i:1:p:153-70 is not listed on IDEAS
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