Spatio-Temporal Dynamics of the Spatial AK Model with Trade Costs

Abstract

In this paper, we introduce trade costs into the spatial AK model of economic growth and investigate the effects of trade costs on the spatio-temporal dynamics. We formulate an optimal control problem and obtain the evolution of the capital distribution along the optimal consumption trajectory via dynamic programming and semigroup theory. We also consider the convergence of the physical capital in the long-run and derive a value range for the cost coefficient that guarantee the convergence of the detrended capital across the location. Finally, we perform numerical simulations to support the analytical results and illustrate the spatiotemporal dynamics generated by the model.