More on the Green Solow Model with Logistic Population Change

This paper generalizes the model introduced by Ferrara and Guerrini [13], where two different research
lines have been joined together: the one studying the effects of incorporating technological progress in pollution
abatement in the Solow-Swan model (Brock and Taylor [6]), and that analyzing the role of a logistic population
growth rate within the Solow-Swan model (Ferrara and Guerrini [13]). In this framework, the economy is described
by a three dimensional dynamical system, whose solution can be explicitly determined. We note that physical capital
can be expressed in closed-form via Hypergeometric functions. As well, we prove the model’s solution to be
convergent in the log-run. We characterize the economy balanced growth path equilibrium, and find that sustainable
growth occurs if technological progress in abatement is faster than technological progress in production. An
environmental Kuznets curve may result along the transition to the balanced growth path. If there is no technological
progress in abatement, then there is no EKC. Furthermore, the economy has a unique equilibrium (a node),
which is locally asymptotically stable.