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Regeneration under Uncertainty

Author

Listed:
  • Tapan Mitra

    (Cornell University)

  • Santanu Roy

    (Southern Methodist University)

Abstract

In a general one-sector model of stochastic growth where the marginal productivity of capital at zero is finite but can vary widely due to technology shocks, we derive explicitly the limiting optimal propensity to invest (the "slope" of the optimal policy function) at zero. We then derive an explicit condition that ensures it is optimal for capital stocks to regenerate with probability one if they are depleted to levels close enough to zero so that "long run" consumption is strictly positive with probability one. For a widely used class of utility and production functions, a strict violation of our regeneration condition implies almost sure global extinction of capital under the optimal policy. Risk aversion plays an important role in regeneration. Regeneration is likely to be optimal when the degree of risk aversion (near zero) is either high or low, while extinction may be optimal for intermediate levels of risk aversion.

Suggested Citation

  • Tapan Mitra & Santanu Roy, 2021. "Regeneration under Uncertainty," Departmental Working Papers 2101, Southern Methodist University, Department of Economics.
    • Handle: RePEc:smu:ecowpa:2101
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    File URL: ftp://ftp1.economics.smu.edu/WorkingPapers/2021/ROY/ROY-2021-02.pdf
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    More about this item

    Keywords

    Stochastic Growth; Propensity to Invest; Optimal Policy Function; Regeneration; Conservation; Extinction; Risk Aversion.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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