This paper is an attempt at studying the neoclassical Solow-Swan model within a framework where the change over time of the labor-force is given by the logistic population model. In the canonical Solow-Swan model, the growth rate of population is constant, yielding an exponential behavior of population size over time, which is clearly unrealistic and unsustainable in the very long-run. A more realistic approach would be to consider a logistic law for the population growth rate. In this framework, the model is proved to have a unique equilibrium (a node), which is globally asymptotically stable, and its solution is shown to have a closed-form expression via Hypergeometric functions.
The neoclassical model of Solow and Swan with logistic population growth / Ferrara M.; Guerrini L.. - STAMPA. - (2008), pp. 119-127. (Intervento presentato al convegno 2nd International Conference of IMBIC on “Mathematical Sciences for Advancement of Science and Technology" (MSAST-2008) tenutosi a Kolkata (Calcutta), India nel December 22-23, 2008).
The neoclassical model of Solow and Swan with logistic population growth
GUERRINI, LUCA
2008
Abstract
This paper is an attempt at studying the neoclassical Solow-Swan model within a framework where the change over time of the labor-force is given by the logistic population model. In the canonical Solow-Swan model, the growth rate of population is constant, yielding an exponential behavior of population size over time, which is clearly unrealistic and unsustainable in the very long-run. A more realistic approach would be to consider a logistic law for the population growth rate. In this framework, the model is proved to have a unique equilibrium (a node), which is globally asymptotically stable, and its solution is shown to have a closed-form expression via Hypergeometric functions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
