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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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    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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