Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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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.