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Stochastically Induced Critical Depensation and Risk of Stock Collapse

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  • Diwakar Poudel
  • Leif K. Sandal
  • Sturla F. Kvamsdal
Abstract
This article investigates the risk of stock collapse due to stochastically induced critical depensation in managed fisheries. We use a continuous-time surplus production model and an economic model with downward-sloping demand and stock-dependent costs. First, we derive an optimal exploitation policy as a feedback control rule by applying the Hamilton-Jacobi-Bellman approach and analyze the effects of stochasticity on the optimal policy. Then, we characterize the long-term sustainable optimal state and estimate the risk of stock collapse due to stochastically induced critical depensation. We find that the optimal harvest policy in the stochastic setting is conservative at low stochasticity and approaches the myopic solution at high stochasticity. The risk of stock collapse is increasing with the stochasticity and decreasing with stock sizes.

Suggested Citation

  • Diwakar Poudel & Leif K. Sandal & Sturla F. Kvamsdal, 2015. "Stochastically Induced Critical Depensation and Risk of Stock Collapse," Marine Resource Economics, University of Chicago Press, vol. 30(3), pages 297-313.
    • Handle: RePEc:ucp:mresec:doi:10.1086/680446
    DOI: 10.1086/680446
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    References listed on IDEAS

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    1. R. Quentin Grafton & Leif K. Sandal & Stein Ivar Steinshamn, 2000. "How to Improve the Management of Renewable Resources: The Case of Canada's Northern Cod Fishery," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 82(3), pages 570-580.
    2. José Da Rocha & María Gutiérrez, 2012. "Endogenous Fishery Management in a Stochastic Model: Why Do Fishery Agencies Use TACs Along with Fishing Periods?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(1), pages 25-59, September.
    3. Moxnes, Erling, 2003. "Uncertain measurements of renewable resources: approximations, harvesting policies and value of accuracy," Journal of Environmental Economics and Management, Elsevier, vol. 45(1), pages 85-108, January.
    4. Robert J. Johnston & Jon G. Sutinen, 1996. "Uncertain Biomass Shift and Collapse: Implications for Harvest Policy in the Fishery," Land Economics, University of Wisconsin Press, vol. 72(4), pages 500-518.
    5. Clark, Colin W. & Kirkwood, Geoffrey P., 1986. "On uncertain renewable resource stocks: Optimal harvest policies and the value of stock surveys," Journal of Environmental Economics and Management, Elsevier, vol. 13(3), pages 235-244, September.
    6. José-María Da-Rocha & Linda Nøstbakken & Marcos Pérez, 2014. "Pulse Fishing and Stock Uncertainty," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(2), pages 257-274, October.
    7. Poudel, Diwakar & Sandal, Leif K. & Kvamsdal, Sturla F. & Steinshamn, Stein I., 2011. "Fisheries Management under Irreversible Investment: Does Stochasticity Matter?," Discussion Papers 2011/20, Norwegian School of Economics, Department of Business and Management Science.
    8. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 1-23, May.
    9. Ragnar Arnason & Leif K. Sandal & Stein Ivar Steinshamn & Niels Vestergaard, 2004. "Optimal Feedback Controls: Comparative Evaluation of the Cod Fisheries in Denmark, Iceland, and Norway," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 531-542.
    10. Kanaganayagam Kugarajh & Leif Sandal & Gerhard Berge, 2006. "Implementing a Stochastic Bioeconomic Model for the North-East Arctic Cod Fishery," Journal of Bioeconomics, Springer, vol. 8(1), pages 35-53, April.
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    Cited by:

    1. Ni, Yuanming & Steinshamn, Stein I. & Kvamsdal, Sturla F., 2022. "Negative shocks in an age-structured bioeconomic model and how to deal with them," Economic Analysis and Policy, Elsevier, vol. 76(C), pages 15-30.
    2. Jules Selles, 2018. "Fisheries management: what uncertainties matter?," Working Papers hal-01824238, HAL.
    3. Kvamsdal, Sturla, 2023. "An exploratory analysis of warming effects on wealth in the Barents Sea fisheries," Economic Analysis and Policy, Elsevier, vol. 77(C), pages 34-50.
    4. Kvamsdal, Sturla F. & Sandal, Leif K. & Poudel, Diwakar, 2020. "Ecosystem wealth in the Barents Sea," Ecological Economics, Elsevier, vol. 171(C).

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