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Optimal Fishery with Coastal Catch

Author

Listed:
  • Hannes Uecker
  • Thorsten Upmann

Abstract

In many spatial resource models it is assumed that the agent is able to determine the harvesting activity over the complete spatial domain. However, agents frequently have only access to a resource at particular locations at which the moving biomass, such as fish or game, may be caught or hunted. To analyse this problem, we set up a simple optimal control model of boundary harvesting. Using the Pontryagin’s Maximum Principle we derive the associated canonical system, and numerically compute canonical steady states and optimal time dependent paths, and characterise the optimal control and the associated stock of the resource. Finally, we extend our model to a predator-prey model of the Lotka-Volterra type, and show how the presence of two species enriches the results of our basic model. For both models we illustrate the dependence of the optimal steady states and the optimal paths on the cost parameters.

Suggested Citation

  • Hannes Uecker & Thorsten Upmann, 2016. "Optimal Fishery with Coastal Catch," CESifo Working Paper Series 6054, CESifo.
    • Handle: RePEc:ces:ceswps:_6054
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    References listed on IDEAS

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    1. William Brock & Anastasios Xepapadeas, 2005. "Spatial Analysis in Descriptive Models of Renewable Resource Management," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 141(III), pages 331-354, September.
    2. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, December.
    3. Sanchirico, James N. & Wilen, James E., 1999. "Bioeconomics of Spatial Exploitation in a Patchy Environment," Journal of Environmental Economics and Management, Elsevier, vol. 37(2), pages 129-150, March.
    4. Xepapadeas, Anastasios, 2010. "The spatial dimension in environmental and resource economics," Environment and Development Economics, Cambridge University Press, vol. 15(6), pages 747-758, December.
    5. Quaas, Martin F. & Requate, Till & Ruckes, Kirsten & Skonhoft, Anders & Vestergaard, Niels & Voss, Rudi, 2013. "Incentives for optimal management of age-structured fish populations," Resource and Energy Economics, Elsevier, vol. 35(2), pages 113-134.
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    Cited by:

    1. Behringer, Stefan & Upmann, Thorsten, 2017. "Harvesting a Remote Renewable Resource," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168250, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    boundary control; bioeconomics; optimal harvesting; coastal fishing; infinite time horizon; predator-prey model; Lotka-Volterra;
    All these keywords.

    JEL classification:

    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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