Pollution, carrying capacity and the Allee effect

In ecology, one of the simplest representation of population dynamics is the logistic equation. This basic view can be enriched by considering two important variables : (1) the maximal population density Nature can support (carrying capacity) and (2) the critical density threshold under which the population disappear (Allee effect). The economic literature on biodiversity and renewable resources ignores both these variables. Evidence suggests also that these variables are affected by the pollution level due to economic activity. Indeed, a degrated environment is unsuitable for wildlife and reduces the carrying capacity, while the climate chance entails the habitat fragmentation and, lowering the wildlife reproduction possibilites, raise the Allee effect. The present paper aims to incorporate both endogenous carrying capacity and Allee effec in a Ramsay model augmented with biodiversity as a renewable resource. Our extended framework enables us to study the effect of a Pigouvian tax on anthropogenic mass extinction. We find that, when the household overvalues biodiversity with respect to consumption, a higher green-tax rate is beneficial in three respects entailing : (1) a lower pollution and a higher biodiversity, (2) a welfare improvement and (3) a less likely mass extinction.