Optimal Exploitation of a Biomass Confronted with the Threat of Partial Extinction

This paper examines how to harvest a biomass confronted with the threat of partial extinction. We show that the uncertainty involved gives rise to two opposing effects determining an optimal steady-state stock of the biomass. A "discount effect", leading to a smaller stock as compared to the certainty case, and a "cushion effect" leading to a larger stock. The net effect is indeterminate and depends on the size of the failure rate and the size of the possible collapse. Furthermore, it is shown that for some combinations of the failure rate and the size of the collapse, a strategy risking total extinction may be optimal even though the biomass could have been saved with certainty. Likewise, for other combinations, a strategy of no harvest may be followed until a mishap has taken place. Finally, both repetitive collapses and stock dependent collapses are shown to lead to a smaller optimal steady state stock as compared to a one shot stock independent collapse.