Capital-induced labor migration in a spatial Solow model

In this work we consider labor mobility in the spatial Solow model for economic growth. Besides considering that labor diffuses from regions with higher density to regions with lower density of labor, we consider that workers move from regions with lower density of capital to regions with higher density of capital, and that the labor force grows following a logistic law. Through stability analysis, we show that the introduction of capital-induced labor migration in the Solow model is a necessary condition for reaching an unstable regime that can generate a rich spatio-temporal dynamics. Numerical simulations show that, depending on the migration intensity and on the size of the economy, this modified Solow model can develop, endogenously, four kinds of behavior for the economy: (i) convergence to a homogeneous steady-state; (ii) convergence to a non-homogeneous steady-state; (iii) development of periodic spatio-temporal cycles; and (iv) development of irregular and aperiodic spatio-temporal cycles.