Abstract: AK-type models with habit formation have been used in the literature to address a wide variety of issues. For example, through numerical simulations, Carroll et al have shown that the introduction of habit formation in the standard AK endogenous growth model may cause this model to exhibit transitional dynamics, while Gomez has proved that the convergence speed of the AK model with external habits is higher than that in the AK model with internal habits. It is known that usually standard economic growth theory assumes that labor (population) force grows at a positive constant rate (Malthusian model). However, this assumption is not a good approximation to reality as population exponentially grows without limits, which is clearly unrealistic. To remove the prediction of unbounded population size in the very long-run, Verhulst wrote an alternative model, known as the logistic growth model, where the population stock evolves according to an elongated S-curve. Recent forecasts (e.g., United Nations) confirm that the annual growth rate of population is expected to fall gradually until 2100, and that world population will stabilize at a level of about eleven billion people by 2200. Thus, not only theoretically but also empirically, it seems reasonable to model population size as following a logistic process. Bucci and Guerrini, Ferrara and Guerrini, Germana’ and Guerrini, and Guerrini, have recently explored the implications of studying some economic growth models within a framework where the change over time of the labor force is non constant but governed by the logistic law or by a bounded population growth rate. In this paper, we wish to investigate the dynamic effects of assuming a logistic population growth hypothesis in Gomez’s model. This set-up leads the economy to be described by a four dimensional dynamical system, whose unique non-trivial steady state equilibrium is a saddle point with a two dimensional stable manifold. Two stable roots, rather than only one as in Gomez, determine the speed of convergence. Now, the crucial determinant of the asymptotic speed of convergence is the larger of the two negative eigenvalues. As a result, contrary to Gomez, the asymptotic speed of convergence may be not necessarily decreasing as the value of some parameter increases.

Brief Biography of the Speaker:
Massimiliano Ferrara is Associate Professor of Mathematical Economics at "Mediterranea" University of Reggio Calabria where he was also Dean of the degree in Economics (2007-2010). Actually he is the Director of Department - Culture, Education, Research and University at Regione Calabria. He was the Founder and Director of MEDAlics (2009) – Research Centre for Mediterranean Studies - and Vice Rector at "Dante Alighieri" University of Reggio Calabria. He was also Visiting Professor at Morgan State University in Baltimore (USA), Western Michigan University (USA), New Jersey Institute of Technology in Newark (NJ) (USA).He is co-author of the research work on "Knowledge flows and technological trajectories in the Mediterranean Area" published in 2009 on African Journal of Science, Technology, Innovation and Development, and for volume "Economics and International Cooperation in the Mediterranean Area" for Rubbettino Editore. 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 105 publications on international journals many of them "high impact Scientific International (ISI)" and 5 monographs. 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 technological 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. His main research interests are: dynamical systems, patterns of growth and sustainable development, mathematical economics, game theory, optimization theory, applied Economics.