Closed-Form Solutions to an Economic Growth Logistic Model with Migration

17 Pages Posted: 30 Mar 2010

See all articles by J. P. Juchem Neto

J. P. Juchem Neto

Universidade Federal do Rio Grande do Sul (UFRGS)

J. C. R. Claeyssen

Universidade Federal do Rio Grande do Sul (UFRGS)

Daniele Ritelli

University of Bologna - Department of Mathematics for Economic and Social Sciences

Giovanni Mingari Scarpello

Free University of Bozen-Bolzano

Date Written: March 24, 2009

Abstract

This paper presents a Solow Growth Model with the labor force ruled by the logistic equation added by a constant migration rate, I. We prove the global asymptotic stability of the capital and production per capita. Considering a Cobb-Douglas production function, we show this model to have a closed-form solution. This transient behavior is expressed in terms of the Beta and Appell F1 functions. We also show that if I > 0, it implies in a higher (minor) output of the economy, and in a minor (greater) capital and production per capita in the short term (middle and long term); furthermore, these ratios converge to the same steady-state value of the no-migration model; if I < 0 the behavior is the opposite; and if I = 0 we recover the solution obtained by Mingari Scarpello and Ritteli [12] for the pure logistic case. Finally, we replace the Cobb-Douglas by a Perfect Substitution CES Production Function, accompanied with sample problems.

Keywords: Solow Growth Model, Logistic Labor Force, Migration, Appell Function

JEL Classification: C61, C62, O41

Suggested Citation

Juchem Neto, Joao Plinio and Claeyssen, Julio Cesar Ruiz and Ritelli, Daniele and Mingari Scarpello, Giovanni, Closed-Form Solutions to an Economic Growth Logistic Model with Migration (March 24, 2009). Available at SSRN: https://ssrn.com/abstract=1578338 or http://dx.doi.org/10.2139/ssrn.1578338

Joao Plinio Juchem Neto (Contact Author)

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Av. João Pessoa, 52 - Centro Histórico
Porto Alegre, RS 90040-000
Brazil

HOME PAGE: http://professor.ufrgs.br/plinio/

Julio Cesar Ruiz Claeyssen

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Av. Carlos Gomes 1111
Porto Alegre, Rio Grande do Sul 90480-004
Brazil

Daniele Ritelli

University of Bologna - Department of Mathematics for Economic and Social Sciences ( email )

Piazza Scaravilli 2
40139 Bologna
Italy

Giovanni Mingari Scarpello

Free University of Bozen-Bolzano ( email )

Via Sernesi 1
39100 Bolzano
Italy

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