Size matters: Optimal management of dynamic systems with varying size

Many natural and economic systems are managed to deliver the highest benefits to society but are subject to regime shifts. We specifically consider the variability of the size of the system itself as a key driver of a regime shift. We address the question of how the optimal management of these systems should vary with its size. Put simply, certain management options might work when the system is of a given size, while others might be preferred when the system has grown or shrunk. In this paper, we develop a model that allows us to analyse the effect of the size of the system on its optimal management. We apply this model to a case of water pollution in a reservoir/lake that varies in size over time: sometimes the lake is deep and sometimes it is shallow. Numerical simulations were conducted to compare optimal management of the reservoir with and without explicitly modelling its size variation. The findings show that the overall social costs of optimally managing pollution are significantly smaller when the variability in size is taken into account. This is due to differences in the timing and magnitude of the optimal control. The key implication is that the variability of the size of a system should be explicitly considered in this type of management problems.