Using fast and slow processes to manage resources with thresholds

Economists have relied on convexity assumptions for a long time but many natural resources that stem from ecosystems have non-convexities in their dynamics. This article illustrates the consequences of relaxing convexity assumptions for management and the role of fast and slow variables. The paper presents a general framework to handle systems with fast and slow variables, and illustrates the method using a model of coral reefs subject to fishing pressure. The insights obtained are used to discuss alternative management strategies.