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

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Abstract

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.

Suggested Citation

  • Antoine d'Autume & Katheline Schubert, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Documents de travail du Centre d'Economie de la Sorbonne v08031, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:v08031
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    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.
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    Cited by:

    1. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
    2. Verchère, Alban, 2011. "Le développement durable en question : analyses économiques autour d’un improbable compromis entre acceptions optimiste et pessimiste du rapport de l’Homme à la Nature," L'Actualité Economique, Société Canadienne de Science Economique, vol. 87(3), pages 337-403, septembre.
    3. Antoine d’Autume & Katheline Schubert, 2008. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," Revue d'économie politique, Dalloz, vol. 118(6), pages 827-845.
    4. Lucas Bretschger, 2013. "Population Growth and Natural-Resource Scarcity: Long-Run Development under Seemingly Unfavorable Conditions," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(3), pages 722-755, July.
    5. Louis Dupuy, 2012. "International Trade and Sustainability: A survey," Larefi Working Papers 1201, Larefi, Université Bordeaux 4.
    6. Robert D. Cairns & Stellio Del Campo & Vincent Martinet, 2016. "Sustainability of an economy relying on two reproducible assets," Working Papers 2016/03, INRA, Economie Publique.
    7. Bazhanov, Andrei, 2011. "Investment and resource policy under a modified Hotelling rule," MPRA Paper 32428, University Library of Munich, Germany.
    8. John Gowdy & Roxana Juliá, 2010. "Global Warming Economics in the Long Run: A Conceptual Framework," Land Economics, University of Wisconsin Press, vol. 86(1), pages 117-130.
    9. 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.
    10. Greasley, David & Hanley, Nicholas & McLaughlin, Eoin & Oxley, Les & Warde, Paul, 2012. "Testing for long-run "sustainability": Genuine Savings estimates for B ritain, 1760-2000," Stirling Economics Discussion Papers 2012-05, University of Stirling, Division of Economics.
    11. Andrei V. Bazhanov, 2009. "A constant-utility criterion linked to an imperfect economy affected by irreversible global warming," EERI Research Paper Series EERI_RP_2009_03, Economics and Econometrics Research Institute (EERI), Brussels.
    12. Bazhanov, Andrei, 2011. "Investment and current utility change in dynamically inefficient economies," MPRA Paper 35487, University Library of Munich, Germany.
    13. Susan Randolph & Patrick Guyer, 2011. "Tracking the Historical Evolution of States' Compliance with their Economics and Social Rights Obligations of Result: Insights from the Historical SERF Index," Economic Rights Working Papers 18, University of Connecticut, Human Rights Institute.
    14. Bazhanov, Andrei, 2012. "Disregarded inefficiency may dominate sustainability policies," MPRA Paper 43621, University Library of Munich, Germany.
    15. repec:bla:afrdev:v:29:y:2017:i:s1:p:42-55 is not listed on IDEAS
    16. repec:eee:jrpoli:v:52:y:2017:i:c:p:114-121 is not listed on IDEAS
    17. Sachverständigenrat zur Begutachtung der Gesamtwirtschaftlichen Entwicklung & Conseil d'Analyse Écon (ed.), 2010. "Monitoring economic performance, quality of life and sustainability. Joint report as requested by the Franco-German Ministerial Council," Occasional Reports / Expertisen, German Council of Economic Experts / Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung, number 75366.
    18. Cairns, Robert D. & Tian, Huilan, 2010. "Sustained development of a society with a renewable resource," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1048-1061, June.
    19. Heijnen, P., 2008. "The Hartwick rule as a conservation law," CeNDEF Working Papers 08-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    20. Bazhanov, Andrei V., 2015. "Inefficiency and sustainability," Resources Policy, Elsevier, vol. 45(C), pages 210-216.
    21. repec:hal:journl:halshs-00976395 is not listed on IDEAS
    22. Andrei Bazhanov, 2012. "A Closed-Form Solution to Stollery’s Problem with Damage in Utility," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 365-386, April.
    23. repec:laf:wpaper:201201 is not listed on IDEAS
    24. Bazhanov, Andrei, 2010. "A closed form solution to Stollery's global warming problem with temperature in utility," MPRA Paper 22406, University Library of Munich, Germany.

    More about this item

    Keywords

    Exhaustible resources; sustainability; Hartwick's rule.;

    JEL classification:

    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development
    • Q3 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation

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