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Characterizing the Sustainability Problem in an Exhaustible Resource Model

Author

Listed:
  • Tapan, Mitra

    (Department of Economics, Cornell University)

  • Asheim, Geir B.

    (Dept. of Economics, University of Oslo)

  • Buchholz, Wolfgang

    (Department of Economics, University of Regensburg)

  • Withagen, Cees

    (Department of Economics, VU University Amsterdam)

Abstract

The Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion poses the following sustainability problem: is it feasible to sustain indefinitely a level of consumption that is bounded away from zero? We provide a complete technological characterization of the sustainability problem in this model without reference to the time path. As a byproduct we show general existence of a maximin optimal path under weaker conditions that those employed in previous work. Our proofs yield new insights into the meaning and significance of Hartwick's reinvestment rule.

Suggested Citation

  • Tapan, Mitra & Asheim, Geir B. & Buchholz, Wolfgang & Withagen, Cees, 2012. "Characterizing the Sustainability Problem in an Exhaustible Resource Model," Memorandum 08/2012, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2012_008
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    File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2012/Memo-08-2012.pdf
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    References listed on IDEAS

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    4. 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.
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    9. 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.
    10. 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.
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    13. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
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    Cited by:

    1. 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.
    2. 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.
    3. Daniel Grainger, 2023. "Sustainability criterion implied externality pricing for resource extraction," Papers 2306.04065, arXiv.org.
    4. 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.
    5. 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.
    6. Cairns, Robert D. & Martinet, Vincent, 2014. "An environmental-economic measure of sustainable development," European Economic Review, Elsevier, vol. 69(C), pages 4-17.
    7. 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.
    8. Bazhanov, Andrei V., 2022. "Extraction path and sustainability," Resources Policy, Elsevier, vol. 76(C).
    9. 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.
    10. Grainger, Daniel, 2024. "Sustainability criterion implied externality pricing for resource extraction," Economics Letters, Elsevier, vol. 234(C).
    11. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    12. 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.
    13. 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.
    14. Asheim, Geir B. & Hartwick, John M. & Yamaguchi, Rintaro, 2023. "Sustainable per capita consumption under population growth," Resource and Energy Economics, Elsevier, vol. 73(C).
    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. 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.
    18. 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).
    19. 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.
    20. 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).

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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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