Asymptotic Behaviors Analysis of the Spatial AK Model with Trade Costs

Abstract

We consider a spatial economic growth model with trade costs whose spatial-temporal dynamics of the capital stock are governed by a parabolic partial differential equation and analyze the effects of the trade costs on the asymptotic behaviors of the capital in the framework of spatial AK model, where the technology is time-varying. Taking advantage of the good properties of the Green function, we formulate an explicit solution to the auxiliary partial differential equation of the original problem and derive the sufficient conditions on the consumption function that guarantee the existence and the uniqueness of the solution and obtain the convergence properties of the capital in the long run for the spatial AK model with trade costs.