The Solow model improved through the logistic manpower growth law |
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Authors: | Giovanni Mingari Scarpello Daniele Ritelli |
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Institution: | (1) Present address: via Negroli, 6, 20133 Milano, Italy;(2) Present address: Dipartimento di Matematica per le Scienze Economiche e Sociali, viale Filopanti, 5, 40127 Bologna, Italy |
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Abstract: | In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with
the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated
in closed form via the Hypergeometric function2
F
1. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which
keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested
and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in
the logistic law.
Research supported by MURST grant:Metodi matematici in economia |
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Keywords: | Primary 34A05 Secondary 33C05 |
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