Closed-form Solution to an Economic Growth Logistic Model With Constant Migration

João Plínio Juchem Neto, Julio Cesar Ruiz Claeyssen, Daniele Ritelli, Giovanni Mingari Scarpello


This paper considers a Solow-Swan economic 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, which is expressed in terms of the Beta and Appell F1 special functions. We also show, through simulations, that if I>0, it implies in a smaller capital and product per capita in the short term, but in a higher  capital and product per capita in the middle and long terms. In both cases, these per capita variables converge to the same steady-state given by the model without migration. If I<0 the transient behavior is the opposite. Finally, if I=0, we recover the solution for the pure logistic case, involving Gauss' Hypergeometric Function 2F1.


Solow economic growth model. Logistic labor growth. Migration. Beta function. Appell function.

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