An intersectoral migration and growth model with distinct population growth rates

In this paper we propose a generalization of the Mas-Colell and Razin two-sector migration and growth model, introducing distinct population growth rates for the industrial and agricultural sectors. We show that the proposed generalized model has an unique economically feasible stable steady-state for the distribution of the labor force between the sectors, as well as for the per capita capital of the economy. Besides, we obtain the signal of the impact of marginal changes in the intersectoral differential population growth rate in the steady-state values of the endogenous variables implied by the model, ceteris paribus. In particular, we show that an increase in the intersectoral differential population growth rate, which happens when the population growth rate of the industrial sector inscreases in relation to the agricultural sector, causes an increase in the proportion of the total labor force employed in the industrial sector, and in the per capita capital of the economy at the steady-state, provided the population growth rate at the agricultural sector is higher than a certain critical value.