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Characterizing the sustainability problem in an exhaustible resource model

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  • Mitra, Tapan
  • Asheim, Geir B.
  • Buchholz, Wolfgang
  • Withagen, Cees

Abstract

We provide a general condition under which consumption can be sustained indefinitely bounded away from zero in the continuous time Dasgupta–Heal–Solow–Stiglitz model, by letting augmentable capital substitute for a non-renewable resource. The assumptions made on the production function are mild, thus generalizing previous work. By showing that Hartwickʼs rule minimizes the required resource input per unit of capital accumulation, and integrating the required resource input with respect to capital, we obtain a complete technological characterization without reference to the time path. We also use the characterization result to establish general existence of a maximin path.

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  • Mitra, Tapan & Asheim, Geir B. & Buchholz, Wolfgang & Withagen, Cees, 2013. "Characterizing the sustainability problem in an exhaustible resource model," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2164-2182.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:5:p:2164-2182
    DOI: 10.1016/j.jet.2013.04.019
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    1. Mitra, Tapan & Asheim, Geir B. & Buchholz, Wolfgang & Withagen, Cees, 2013. "Characterizing the sustainability problem in an exhaustible resource model," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2164-2182.
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    4. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(3), pages 275-300, June.
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    8. Martinet, V. & Doyen, L., 2007. "Sustainability of an economy with an exhaustible resource: A viable control approach," Resource and Energy Economics, Elsevier, vol. 29(1), pages 17-39, January.
    9. 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.
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    15. 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.
    16. 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, September.
    17. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
    18. Dasgupta, Swapan & Mitra, Tapan, 1983. "Intergenerational Equity and Efficient Allocation of Exhaustible Resources," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 133-153, February.
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    Cited by:

    1. Daniel Grainger, 2023. "Sustainability criterion implied externality pricing for resource extraction," Papers 2306.04065, arXiv.org.
    2. Antony, Jürgen & Klarl, Torben, 2019. "Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203640, Verein für Socialpolitik / German Economic Association.
    3. Bazhanov, Andrei V., 2022. "Extraction path and sustainability," Resources Policy, Elsevier, vol. 76(C).
    4. Cairns, Robert D. & Del Campo, Stellio & Martinet, Vincent, 2019. "Sustainability of an economy relying on two reproducible assets," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 145-160.
    5. Yu, Yun & Lei, Yalin, 2017. "China's provincial exhaustible resources rent and produced capital stock—Based on Hartwick's rule," Resources Policy, Elsevier, vol. 52(C), pages 114-121.
    6. Cairns, Robert D. & Martinet, Vincent, 2021. "Growth and long-run sustainability," Environment and Development Economics, Cambridge University Press, vol. 26(4), pages 381-402, August.
    7. John M. Hartwick & Ngo Van Long, 2020. "Sustainability with endogenous discounting," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(2), pages 216-221, June.
    8. Jean‐François Fagnart & Marc Germain & Bruno Van der Linden, 2023. "Working time reduction and employment in a finite world," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(1), pages 170-207, January.
    9. Mitra, Tapan & Asheim, Geir B. & Buchholz, Wolfgang & Withagen, Cees, 2013. "Characterizing the sustainability problem in an exhaustible resource model," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2164-2182.
    10. Cairns, Robert D. & Martinet, Vincent, 2014. "An environmental-economic measure of sustainable development," European Economic Review, Elsevier, vol. 69(C), pages 4-17.
    11. Grainger, Daniel, 2024. "Sustainability criterion implied externality pricing for resource extraction," Economics Letters, Elsevier, vol. 234(C).
    12. Geir B. Asheim, 2017. "Sustainable growth," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 825-848, December.
    13. Antony, Jürgen & Klarl, Torben, 2023. "Subsistence consumption and natural resource depletion: Can resource-rich low-income countries realize sustainable consumption paths?," Journal of Macroeconomics, Elsevier, vol. 77(C).
    14. Jürgen Antony & Torben Klarl, 2019. "Non-Renewable Resources in a Ramsey Economy with Subsistence Consumption, Human and Physical Capital Accumulation: A full Characterization," Bremen Papers on Economics & Innovation 1904, University of Bremen, Faculty of Business Studies and Economics.
    15. Asheim, Geir B. & Hartwick, John M. & Mitra, Tapan, 2021. "Investment rules and time invariance under population growth," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    16. Geir B. Asheim & Tapan Mitra, 2021. "Characterizing sustainability in discrete time," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 461-481, March.
    17. Hartwick, John M. & Long, Ngo Van, 2018. "Sustainability with endogenous discounting when utility depends on consumption and amenities," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 31-36.
    18. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    19. Asheim, Geir B. & Hartwick, John M. & Yamaguchi, Rintaro, 2023. "Sustainable per capita consumption under population growth," Resource and Energy Economics, Elsevier, vol. 73(C).
    20. Bazhanov, Andrei V., 2022. "A comment on Hamilton (2016) “Measuring sustainability in the UN System of Environmental-Economic Accounting”," Resources Policy, Elsevier, vol. 76(C).

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    More about this item

    Keywords

    Sustainability; Maximin;

    JEL classification:

    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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