Biological Productivity and Optimal Harvesting of a Biological Resource – an Uncomplicated Exercise in Comparative Dynamics

The paper presents a very simple mathematical proposition that enables easy examination of comparative dynamics when the stock of a renewable biological resource is very low. The proposition is used to prove that in the canonical schooling fisheries model the optimal harvest rate is a decreasing function of the biological productivity of the resource for low stock levels even if the optimal steady state harvest rate is an increasing function of biological productivity. The results presented here carries over to the effect of technological change in the Ramsey model the as the fisheries model used here and the Ramsey model are formally equivalent