A spatial Solow model with transport cost

In this paper we introduce capital transport cost in an unidimensional unbounded economy described by a spatial Solow model with capital-induced labor migration. Proceeding with a linear stability analysis of its spatially homogeneous equilibrium solution, we show that exists a critical value for the capital transport cost where the dynamic behavior of the economy changes, provided the capital-induced labor migration intensity is big enough. On one hand, if capital transport cost is bigger than this critical value, the homogeneous equilibrium of the model is stable, and the economy converges to this spatially homogeneous state in the long run; on the other hand, if transport cost is smaller than this critical value, the equilibrium is unstable, and the economy may develop distinct spatio-temporal dynamics, including the formation of stable economic clusters and spatio-temporal economic cycles, depending on the other parameters of the model. This result, though obtained using a different formalism, is consistent with the main results of the standard core-periphery model used in the New Economic Geography literature, where a small transport cost is essencial to the formation of spatial economic agglomeration. Finally, we close this work validating the linear stability analysis results through numerical simulations, and verifying that the introduction of a positive transport cost in the model causes a break in the symmetry of the spatial economic agglomerations generated.