Abstract: The traditional neoclassical model of economic growth, first developed by Solow (1956) and Swan (1956), who independently proposed similar one-sector models, provides a theoretical framework for understanding world-wide growth of output and the persistence of geographical differences in per capita output. The key concept of this model, famously known as the Solow-Swan model, is the neoclassical form of production function with declining returns to capital combined with a fixed saving rate. On the basis of these assumptions, an economy, regardless of its starting point, converges to a balanced growth path, where long-run growth of output and capital are determined solely by the rate of labor-augmenting technological progress and the rate of population growth (see, for example, Barro and Sala-i-Martin, 1995). Ferrara and Guerrini (2008) have analyzed the role of a variable population growth rate within the Solow-Swan model by assuming a logistic-type population growth law. Within this set up, the model is proved to have a unique equilibrium, which is globally asymptotically stable. As well, its solution is shown to have a closed-form expression via Hypergeometric functions. As is typical in the neoclassical model, the human population size is assumed to be equal to the labor force. An assumption of that model, however, is that the growth rate of population is constant, yielding an exponential behavior of population size over time. Clearly, this type of time behavior is unrealistic and, more importantly, unsustainable in the very longrun. A more realistic approach would be to consider a logistic law for the population growth rate.
Brock and Taylor (2004) have demonstrated that the Solow-Swan model and the environmental Kuznets curve (hereafter EKC) are intimately related (for the EKC, see, for example, Grossman and Krueger, 1995). Amending the Solow-Swan model to incorporate technological progress in abatement, the EKC is a necessary by-product of convergence to a sustainable growth path. The resulting model, which they called the Green-Solow model, generates an EKC relationship between the flow of pollution emissions and income per capita, and the stock of environmental quality and income per capita.
The main objective of this paper is to combine within the same framework these two different research lines that have been analyzed separately in the recent past. The two research lines we aim at joining together are, respectively, the one studying the effects of including emissions, abatement and a stock of pollution in the Solow-Swan model (Brock and Taylor, 2004), and that analyzing the role of a variable population growth rate within the Solow-Swan model (Ferrara and Guerrini, 2008). Within this framework, the economy is described by a three dimensional dynamical system, whose solution can be explicitly determined, and proved to be convergent in the long-run. Finally, we prove that sustainable growth occurs if technological progress in abatement is faster than technological progress in production. An EKC may result along the transition to the balanced growth path.

Brief Biography of the Speaker:
MASSIMILIANO FERRARA, was born in Pisa (Italy) on June 8, 1972. He graduated cum laude in 1995 in Economics at the University of Messina. Ph.D. (2001) with academic honors in "Mathematical Economics and Finance". Professor in "Mathematical Economics" since 2002. Chief of the Chairs of Mathematical Economics and Economic Statistics at the Faculty of Law - Economics Degree - Mediterranean University of Reggio Calabria since 2007. Professor in the degree course on European Economics at the Faculty of Political Science, University of Milan, where he also is Professor of Decision Theory on the Master by title "Marketing Intelligence and Data Analysis". Head of the Economics Degree of the Mediterranean University of Reggio Calabria. Invited Speaker by WSEAS Conferences (Baltimora MACMESE '09 Morgan State University) by American Mathematical Society (Western Michigan University, USA) and Calcutta Mathematical Society, INDIA and Visiting Professor at the Lomonosov Moscow State University (Department of Mathematics), at the New Jersey Institute of Technology in NewArk (NJ) (USA), (Department of Mathematical Sciences), at the Eotvos Lorand University of Budapest (Department of Atomic Physics, Faculty of Sciences), at Politehnica of Bucharest (Department of Mathematics). Author of 80 publications on international journals many of them "high impact Scientific International (ISI)" and 4 monographs. His biography appeared on Who's Who in the world 2006, 2007 and 2008 published by Marquis (since 1899) in the United States, in the collection 2000 Outstanding Intellectuals of the 21st century (years 2006 and 2007), published by the Biographical Centre, University of Cambridge, England and on the prestigious collection Accomplished International Profiles of Leaders, published by American Biographical Institute, Inc. (Year 2008). Member of Indian Academy of Mathematics (2008- current), Member of Accademia Peloritana dei Pericolanti (2003-current), Member of the Balkan Society of Geometers (2003- current), Member of AMASES - Associazione di Matematica Applicata alle Scienze Economiche e Sociali - (2003- current), Member of the Scientific SET - Advances Center for Studies on Economic Theory - (Center for Advanced Studies Theoretical Economics) at the University of Milan Bicocca (2005-current), Member of the Mathematical Association of America (2007-current), Member of the SIEP (Societa italiana di Economia Pubblica) (2008-current). Scientific Coordinator of international projects financed by the Ministry of Foreign Affairs:the Executive Programme of scientific and techonological cooperation between Italy and Romania during 2006- 2008 and of the Executive Programme of scientific and techonological cooperation between Italy and Estonia during 2005-2007. Editor and referree of several International Journals. Official Reviewer of Mathematical Reviews (MathSciNet), Division of the American Mathematical Society and Zentralblatt MATH, reviews scientific journal published by the European Mathematical Society, the Heidelberg Academy of Sciences and Fachinformationszentrum Karlshruhe.