IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_6054.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp6054.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, April.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. William Brock & Anastasios Xepapadeas, 2015. "Modeling Coupled Climate, Ecosystems, and Economic Systems," DEOS Working Papers 1508, Athens University of Economics and Business.
    2. Anastasios Xepapadeas, 2012. "Diffusion and Spatial Aspects," DEOS Working Papers 1232, Athens University of Economics and Business.
    3. Fabbri, G. & Faggian, S. & Freni, G., 2018. "Spatial resource wars: A two region example," Working Papers 2018-04, Grenoble Applied Economics Laboratory (GAEL).
    4. Thorsten Upmann & Stefan Behringer, 2017. "Harvesting a Remote Renewable Resource," CESifo Working Paper Series 6724, CESifo.
    5. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2020. "Policy effectiveness in spatial resource wars: A two-region model," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    6. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    7. Eli Fenichel & Timothy Richards & David Shanafelt, 2014. "The Control of Invasive Species on Private Property with Neighbor-to-Neighbor Spillovers," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(2), pages 231-255, October.
    8. Rintaro Yamaguchi, 2021. "Genuine Savings and Sustainability with Resource Diffusion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 80(2), pages 451-471, October.
    9. 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.
    10. Maria Arvaniti & Chandra K. Krishnamurthy & Anne-Sophie Crépin, 2019. "Time-consistent resource management with regime shifts," CER-ETH Economics working paper series 19/329, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    11. Wrzaczek, Stefan & Kuhn, Michael & Prskawetz, Alexia & Feichtinger, Gustav, 2010. "The reproductive value in distributed optimal control models," Theoretical Population Biology, Elsevier, vol. 77(3), pages 164-170.
    12. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    13. Sterner, Thomas, 2007. "Unobserved diversity, depletion and irreversibility The importance of subpopulations for management of cod stocks," Ecological Economics, Elsevier, vol. 61(2-3), pages 566-574, March.
    14. Dieter Grass, 2015. "From 0D to 1D spatial models using OCMat," Papers 1505.03956, arXiv.org.
    15. Christopher Costello & Daniel T. Kaffine, 2010. "Marine protected areas in spatial property-rights fisheries ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(3), pages 321-341, July.
    16. Costello, Christopher & Molina, Renato, 2021. "Transboundary marine protected areas," Resource and Energy Economics, Elsevier, vol. 65(C).
    17. Brito, Paulo B. & Costa, Luís F. & Dixon, Huw, 2013. "Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2287-2306.
    18. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    19. Rauscher, Michael & Barbier, Edward B., 2010. "Biodiversity and geography," Resource and Energy Economics, Elsevier, vol. 32(2), pages 241-260, April.
    20. Hinloopen, J. & Smrkolj, G. & Wagener, F.O.O., 2013. "In Defense of Trusts: R&D Cooperation in Global Perspective," CeNDEF Working Papers 13-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_6054. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.