Stock-dependent uncertainty and optimal resource exploitation

The probability that an agent takes a certain action or a certain event occurs depends often on the actions taken by some agents. If this probability depends not only on current actions but on the sum of all past actions, these stock-dependent risks imply an intertemporal effect. In the present paper, we analyse this problem using an example concerning the exploitation of a non-renewable, exhaustible common-pool resource. The paper discusses resource extraction policies under endogenous closure risks which depend on the accumulated stock of extracted resources. It turns out that the optimal time path of resource extractions requires a tax rate which surmounts both the no-risk and second-best tax which tackles the problem by a mere evaluation of the expected exhaustibility stock: