This paper presents two sets of conditions under which a sole owner of a renewable resource stock who maximize s a nonlinear benefit function would find it more profitable to harvest the stock to extinction than follow a continuous harvesting strategy. When the minimum viable resource stock is positive, extinction is optimal as long as the initial resource stock is sufficiently small, regardless of the discount rate.
A Note on the Extinction of Renewable ResourcesMaureen Cropper ,
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Journal of Environmental Economics and Management