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.
Highlights
With the development of new economic geography, capital flows and trade costs in line with the economic reality have attracted extensive attentions of researchers
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 perform numerical simulations to support the analytical results and illustrate the spatiotemporal dynamics generated by the model
Summary
With the development of new economic geography, capital flows and trade costs in line with the economic reality have attracted extensive attentions of researchers. We explore the impacts of trade costs from the perspective of spatial economic growth model. As far as we concerned, most of the related literatures focus on how to solve the economic growth model with spatial variables and analyze the effect of spatial factor on consumption or the dynamics of capital accumulation across space. The combination of trade cost and spatial economic growth model is our literature contribution. The main contribution of the present paper is to analyze the effects of trade costs on the spatio-temporal dynamics and the convergence of the physical capital in the long-run. We carry out numerical illustrations to show the dynamics of the detended capital with different trade costs.
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