Integrating biodiversity indices into a multi-species optimal control model

This paper extends economic models of optimal resource extraction by integrating biodiversity indicators. So far, biodiversity was only implicitly treated in models of multiple renewable resources, or it was considered in terms of (genetic) diversity or species richness only, but not in terms of biodiversity indicators that account for both species richness and evenness. Biodiversity is threatened in many cases where non-renewable resources are extracted by man, and it needs to be considered explicitly. This paper integrates non-use values derived from the existence of multiple living resources, expressed by a biodiversity indicator that accounts for both species richness and species evenness, into a social welfare function. An optimal control model with one non-renewable and two living resources is set up and conditions for optimal management are derived. Main findings are that multiple equilibria are possible when a biodiversity indicator is considered explicitly in the model. The optimal program involves a stable rate of resource extraction that is adjusted according to the damage it causes. In steady state, the biodiversity indicator will be below its maximum value, which implies that the shadow price of at least one living resource is positive while the other one can be negative. Contrary to models with strictly increasing value functions, steady states with low stocks of both living resources are possible when a biodiversity indicator is applied.