Closed-Form Solution for the Solow Model with Constant Migration

In this work we deal with the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss' Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

Solow growth model; migration; hypergeometric function