Optimal Cyclic Exploitation of Renewable Resources

Belyakov, Anton O.; Davydov, A. A.; Veliov, Vladimir M.

doi:10.1007/s10883-015-9271-x

Cited by 25 publications

(21 citation statements)

References 10 publications

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“…As shown by Belyakov, Davydov, and Veliov (2013), a similar spatial setup with a different growth process and different long run objectives can lead to situations in which the renewable resource is completely depleted in some areas but not in others. Hence, the feasibility of a sustainability doctrine that is based on the persistent existence of the renewable resource in all its original locations is put into question and important issues about adequate alternative definitions are raised.…”

Section: Resultsmentioning

confidence: 99%

“…This approach, which is usually referred to as a search model, has been followed by a series of papers, among them Robinson, Williams, and Albers (2002) and Robinson, Albers, and Williams (2008) in a resource extraction (timber gathering) model. A similar approach has been chosen by Belyakov, Davydov, and Veliov (2013), whose paper is the closest to ours. These authors make similar assumptions about the spatial dimension of the renewable resource (that is, it is a single-aged, homogeneous population of a motionless resource) 2 and the harvesting technology.…”

Section: Introductionmentioning

confidence: 99%

“…In our setting, though, the speed and the harvesting intensity are treated as separate choice variables (this was motivated by thinking about fishing nets as harvesting tools), while temporary waiting is not allowed. Also, in Belyakov, Davydov, and Veliov (2013) there is no discounting of future yield. Still, their approach has important similarities in method and intuition and should be seen as highly complementary to our paper.…”

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confidence: 99%

“…Therefore, only if we allowed for a heterogeneous population and diffusion would movements affect the age-structure of the resource. Since the focus of our paper, similar to Belyakov, Davydov, and Veliov (2013), is on the movement of the agent, not that of the resource, we refrain from adding these additional complications at this point to the benefit of clear cut analytical results.…”

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confidence: 99%

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Optimal harvesting of a spatial renewable resource

Behringer

Upmann

2014

Journal of Economic Dynamics and Control

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Optimal harvesting of a spatial renewable resource

Behringer

Upmann

2014

Journal of Economic Dynamics and Control

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“…There are various particular formulations, but the mathematical problems that arise are usually non-standard; see e.g. [18,20].…”

Section: Harvestingmentioning

confidence: 99%

Distributed optimal control models in environmental economics: a review

Augeraud-Véron¹,

Boucekkine²,

Veliov³

2019

Math. Model. Nat. Phenom.

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We review the most recent advances in distributed optimal control applied to Environmental Economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the Environmental Economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in Environmental Economics.

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Optimal Cyclic Dynamic of Distributed Population Under Permanent and Impulse Harvesting

Davydov

Vinnikov

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Optimal Cyclic Exploitation of Renewable Resources

Cited by 25 publications

References 10 publications

Optimal harvesting of a spatial renewable resource

Optimal harvesting of a spatial renewable resource

Distributed optimal control models in environmental economics: a review

Optimal Cyclic Dynamic of Distributed Population Under Permanent and Impulse Harvesting

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