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Characterizing the Sustainability Problem in an Exhaustible Resource Model

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

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 & Geir B. Asheim & Wolfgang Buchholz & Cees A. Withagen, 2012. "Characterizing the Sustainability Problem in an Exhaustible Resource Model," CESifo Working Paper Series 3758, CESifo.
    • Handle: RePEc:ces:ceswps:_3758
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    14. 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.
    15. 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. & Martinet, Vincent, 2021. "Growth and long-run sustainability," Environment and Development Economics, Cambridge University Press, vol. 26(4), pages 381-402, August.
    2. Daniel Grainger, 2025. "Natural Asset Beta," Papers 2502.20706, arXiv.org.
    3. Daniel Grainger, 2023. "Sustainability criterion implied externality pricing for resource extraction," Papers 2306.04065, arXiv.org.
    4. 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.
    5. Bazhanov, Andrei V., 2022. "Extraction path and sustainability," Resources Policy, Elsevier, vol. 76(C).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. 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.
    14. 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.
    15. Cairns, Robert D. & Martinet, Vincent, 2014. "An environmental-economic measure of sustainable development," European Economic Review, Elsevier, vol. 69(C), pages 4-17.
    16. 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.
    17. Grainger, Daniel, 2024. "Sustainability criterion implied externality pricing for resource extraction," Economics Letters, Elsevier, vol. 234(C).
    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).
    21. 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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