Harvesting a remote renewable resource
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ORIGINAL PAPER
Harvesting a remote renewable resource Thorsten Upmann1,2,3
· Stefan Behringer4
Received: 14 June 2019 / Accepted: 20 February 2020 © The Author(s) 2020
Abstract In standard models of spatial harvesting, a resource is distributed over a continuous domain with an agent who may harvest everywhere all the time. For some cases though (e.g., fruits, mushrooms, algae), it is more realistic to assume that the resource is located at a fixed point within that domain so that an agent has to travel in order to be able to harvest. This creates a combined travelling–and–harvesting problem where slower travel implies a lower travelling cost and, due to a later arrival, a higher abundance of the resource at the beginning of the harvesting period; this, though, has to be traded off against less time left for harvesting, given a fixed planning horizon. Possible bounds on the controls render the problem even more intricate. We scrutinise this bioeconomic setting using a two-stage optimal control approach, and find that the agent economises on the travelling cost and thus avoids to arrive at the location of the resource too early. More specifically, the agent adjusts the travelling time so as to be able to harvest with maximum intensity at the beginning and the end of the harvesting period, but may also find it optimal to harvest at a sustainable level, where the harvesting and the growth rate of the stock coincide, in an intermediate time interval. Keywords Optimal travelling–and–harvesting decision · Spatial renewable resource · Bioeconomic model · Two-stage optimal control problem · Sustainable harvesting
Introduction The spatial dimension has recently attracted substantial attention in the economic literature on management of renewable resources. Frequently, this literature focuses on how much effort is required to harvest a resource when that resource is moving (e.g., fish or game).1 In this paper, we 1 See, for example, Neubert (2003), Neubert and Herrera (2008), Brock
and Xepapadeas (2008), Brock and Xepapadeas (2010), Ding and Lenhart (2009), Moeller and Neubert (2013), Kelly et al. (2016), and Grass et al. (2019). Thorsten Upmann
[email protected] Stefan Behringer [email protected] 1
Helmholtz-Institute for Functional Marine Biodiversity at the University of Oldenburg (HIFMB), Ammerl¨ander Heerstraße 231, 23129 Oldenburg, Germany
2
Bielefeld University, Bielefeld, Germany
3
CESifo, Munich, Germany
4
Sciences Po, Department of Economics, 28 rue des Saints P`eres, 75007 Paris, France
reverse this premise: we consider the case where an agent is required to move in order to harvest an immobile resource. Since travelling is a pre-requisite of harvesting, this implies a spatio-temporal interdependence of both policies, which is the focus of this paper. The management of renewable natural resources has been a central issue in economics for many decades, and meanwhile the early models have been extended and generalised in various respects.2 While the temporal dimension of bioeconom
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