Math. Model. Nat. Phenom.
Volume 14, Number 1, 2019
Economics and the environment: distributed optimal control models
|Number of page(s)||13|
|Published online||15 February 2019|
Optimal harvesting of a spatially distributed renewable resource with endogenous pricing
Alexandru Ioan Cuza University of Iasi,
2 “Octav Mayer” Institute of Mathematics, Iasi, Romania.
3 SciencesPo, Paris, France.
4 Helmholtz-Institute for Functional Marine Biodiversity at the University of Oldenburg, Oldenburg, Germany.
5 Faculty of Business Administration and Economics, Bielefeld University, Bielefeld, Germany.
6 CESifo, Munich, Germany.
* Corresponding author: firstname.lastname@example.org
Accepted: 27 June 2018
In this paper, we focus on the exploitation of a renewable resource in a spatial setting. Building upon the spatial harvesting model of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120], we endogenize the price for the resource assuming that after harvesting the good is non-durable, i.e. the harvesting yield must be supplied on the market instantaneously. We find necessary optimality conditions and use them to derive an iterative algorithm to improve at each step the harvesting effort. We find that with endogenous prices the full exploitation result of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120] may cease to hold.
Mathematics Subject Classification: 49K99 / 91B76 / 65K10 / 49M05
Key words: Optimal control / optimality conditions / spatial harvesting / renewable resources / iterative algorithms
© EDP Sciences, 2019
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