Optimal stock–enhancement of a spatially distributed renewable resource

Upmann T, Uecker H, Hammann L, Blasius B (2021)
Journal of Economic Dynamics and Control 123: 104060.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Upmann, ThorstenUniBi ; Uecker, Hannes; Hammann, Liv; Blasius, Bernd
Abstract / Bemerkung
We study the economic management of a renewable resource, the stock of which is spatially distributed and moves over a discrete or continuous spatial domain. In contrast to standard harvesting models where the agent can control the take-out from the stock, we consider the case of optimal stock enhancement. In other words, we model an agent who is, either because of ecological concerns or because of economic incentives, interested in the conservation and enhancement of the abundance of the resource, and who may foster its growth by some costly stock–enhancement activity (e.g., cultivation, breeding, fertilizing, or nourishment). By investigating the optimal control problem with infinite time horizon in both spatially discrete and spatially continuous (1D and 2D) domains, we show that the optimal stock–enhancement policy may feature spatially heterogeneous (or patterned) steady states. We numerically compute the global bifurcation structure and optimal time-dependent paths to govern the system from some initial state to a patterned optimal steady state. Our findings extend the previous results on patterned optimal control to a class of ecological systems with important ecological applications, such as the optimal design of restoration areas.
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Economic Dynamics and Control
Band
123
Art.-Nr.
104060
ISSN
01651889
Page URI
https://pub.uni-bielefeld.de/record/2958437

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Upmann T, Uecker H, Hammann L, Blasius B. Optimal stock–enhancement of a spatially distributed renewable resource. Journal of Economic Dynamics and Control. 2021;123: 104060.
Upmann, T., Uecker, H., Hammann, L., & Blasius, B. (2021). Optimal stock–enhancement of a spatially distributed renewable resource. Journal of Economic Dynamics and Control, 123, 104060. https://doi.org/10.1016/j.jedc.2020.104060
Upmann, T., Uecker, H., Hammann, L., and Blasius, B. (2021). Optimal stock–enhancement of a spatially distributed renewable resource. Journal of Economic Dynamics and Control 123:104060.
Upmann, T., et al., 2021. Optimal stock–enhancement of a spatially distributed renewable resource. Journal of Economic Dynamics and Control, 123: 104060.
T. Upmann, et al., “Optimal stock–enhancement of a spatially distributed renewable resource”, Journal of Economic Dynamics and Control, vol. 123, 2021, : 104060.
Upmann, T., Uecker, H., Hammann, L., Blasius, B.: Optimal stock–enhancement of a spatially distributed renewable resource. Journal of Economic Dynamics and Control. 123, : 104060 (2021).
Upmann, Thorsten, Uecker, Hannes, Hammann, Liv, and Blasius, Bernd. “Optimal stock–enhancement of a spatially distributed renewable resource”. Journal of Economic Dynamics and Control 123 (2021): 104060.

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