Integrating biodiversity indices into a multi-species optimal control model

Biodiversity is often adversely affected by human activities. This reduces social welfare but may be external to private economic decisions. Consequently, these external effects on biodiversity need to be considered explicitly in economic models, which is only partly reflected in the literature. So far, biodiversity is mostly treated only implicitly in multiple renewable resource models, or it is considered in terms of (genetic) variability or species richness only, but not in terms of indices that simultaneously account for species richness and evenness. However, both constitute important dimensions of biodiversity. This paper integrates such biodiversity indices into an optimal control model, thus accounting for non-use values derived from the existence of multiple living resources. Main findings include that a unique equilibrium satisfying sufficient optimality conditions can be determined although the biodiversity index is non-concave. Compared to a model set-up with a monotonically increasing, concave utility function, steady state stocks are distributed more evenly and biodiversity is higher but the total number of individuals is lower when the biodiversity index is applied.