Optimal stock–enhancement of a spatially distributed renewable resource

Thorsten Upmann, Hannes Uecker, Liv Hammann and Bernd Blasius

Journal of Economic Dynamics and Control, 2021, vol. 123, issue C

Abstract: 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.

Keywords: Breeding; Farming and cultivation; Spatial modelling; Spatial migration; Optimal control theory; Patterned optimal steady states; Optimal diffusion–induced instability (search for similar items in EconPapers)
JEL-codes: C61 Q20 Q22 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:123:y:2021:i:c:s0165188920302281

DOI: 10.1016/j.jedc.2020.104060

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