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Characterizing sustainability in discrete time

Author

Listed:
  • Geir B. Asheim

    (University of Oslo)

  • Tapan Mitra

    (Cornell University)

Abstract

We examine the investment rule that must be satisfied by an efficient and egalitarian path in a discrete-time version of the Dasgupta–Heal–Solow model of capital accumulation and resource depletion. In the discrete-time model, competitive valuation of net investments in terms of early and late pricing differs. We redefine Hartwick’s rule to require zero value of net investments at a valuation rule intermediate between these two. Using this definition, we show that along an efficient and egalitarian path, Hartwick’s rule is followed in all time periods. We thereby establish the converse of Hartwick’s result in discrete time, and we do so under weaker assumptions than those in the existing literature on how output varies as a function of capital and resource use. Our redefinition of Hartwick’s rule follows naturally if discrete time is viewed as providing information at discrete points in time of an underlying continuous-time process.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-020-01250-8
    DOI: 10.1007/s00199-020-01250-8
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    1. Avinash Dixit & Peter Hammond & Michael Hoel, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 551-556.
    2. Doyen, L. & Martinet, V., 2012. "Maximin, viability and sustainability," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1414-1430.
    3. 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.
    4. Geir Asheim & Wolfgang Buchholz & Cees Withagen, 2003. "The Hartwick Rule: Myths and Facts," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 25(2), pages 129-150, June.
    5. 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.
    6. 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.
    7. John Hartwick, 1977. "Intergenerational Equity and the Investment of Rents from Exhaustible Resources in a Two Sector Model," Working Paper 281, Economics Department, Queen's University.
    8. Burmeister, Edwin & Hammond, P J, 1977. "Maximin Paths of Heterogeneous Capital Accumulation and the Instability of Paradoxical Steady States," Econometrica, Econometric Society, vol. 45(4), pages 853-870, May.
    9. 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.
    10. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-974, December.
    11. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
    12. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 29-45.
    13. Fleurbaey, Marc, 2015. "On sustainability and social welfare," Journal of Environmental Economics and Management, Elsevier, vol. 71(C), pages 34-53.
    14. Kenneth J. Arrow & Leonid Hurwicz & Hirofumi Uzawa, 1961. "Constraint qualifications in maximization problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(2), pages 175-191, June.
    15. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    16. Mitra, Tapan, 1978. "Efficient growth with exhaustible resources in a neoclassical model," Journal of Economic Theory, Elsevier, vol. 17(1), pages 114-129, February.
    17. John C. V. Pezzey, 1997. "Sustainability Constraints versus "Optimality" versus Intertemporal Concern, and Axioms versus Data," Land Economics, University of Wisconsin Press, vol. 73(4), pages 448-466.
    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. 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).

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    More about this item

    Keywords

    Intergenerational equity; Sustainable development; Hartwick’s rule;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development

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