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Optimal harvesting of a spatial renewable resource

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  • Behringer, Stefan
  • Upmann, Thorsten

Abstract

In this paper we investigate the optimal harvesting of a renewable natural resource. While in most standard approaches the resource is located at a single point, we allow the resource to be distributed spatially. Consequently, an agent who exploits the resource has to travel from one location to another. For a fixed planning horizon, we investigate the speed and the path of harvesting chosen by the agent. We show that the agent adjusts this speed so as to visit each location only once, even in the absence of travelling cost. Since the agent does not return to any location for a second harvest, it is optimal to fully deplete the resource upon arrival. A similar type of bang–bang solution results when we drop the assumption of a constant harvesting rate: allowing for a variable harvesting rate, the agent chooses to fully exploit the resource either in the last or in the first travelling period. A society interested in conserving some of the resource thus has to take measures to limit the exploitative behaviour of the agent.

Suggested Citation

  • Behringer, Stefan & Upmann, Thorsten, 2014. "Optimal harvesting of a spatial renewable resource," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 105-120.
    • Handle: RePEc:eee:dyncon:v:42:y:2014:i:c:p:105-120
    DOI: 10.1016/j.jedc.2014.03.008
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    Citations

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    Cited by:

    1. Anastasios Xepapadeas & Athanasios Yannacopoulos, 2015. "Spatial Resource Management under Pollution Externalities," CEEES Paper Series CE3S-05/15, European University at St. Petersburg, Department of Economics.
    2. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    3. Erik O. Sterner & Elizabeth J. Z. Robinson & H. J. Albers, 2018. "Location choice for renewable resource extraction with multiple non-cooperative extractors: a spatial Nash equilibrium model and numerical implementation," Letters in Spatial and Resource Sciences, Springer, vol. 11(3), pages 315-331, October.
    4. Thorsten Upmann & Stefan Behringer, 2017. "Harvesting a Remote Renewable Resource," CESifo Working Paper Series 6724, CESifo.
    5. Yoshioka, Hidekazu & Yaegashi, Yuta, 2019. "A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 40-66.
    6. 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).
    7. Arabatzis, Garyfallos & Kyriakopoulos, Grigorios & Tsialis, Panagiotis, 2017. "Typology of regional units based on RES plants: The case of Greece," Renewable and Sustainable Energy Reviews, Elsevier, vol. 78(C), pages 1424-1434.
    8. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    9. Upmann, Thorsten & Uecker, Hannes & Hammann, Liv & Blasius, Bernd, 2021. "Optimal stock–enhancement of a spatially distributed renewable resource," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    10. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.

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    More about this item

    Keywords

    Optimal harvesting; Spatial renewable resource; Continuous time; Market failure; Bang–bang solution;
    All these keywords.

    JEL classification:

    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
    • Q28 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Government Policy
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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