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Dynamic spatial theory has been a fruitful approach in understanding economic phenomena involving time and space. However, this new field has opened a set of questions still unresolved in the literature. For instance, the identification of the temporal and spatial social optimal allocation of economic activity has not been ensured yet in economic growth. By means of a monotone method we study in this paper the optimal solution of spatial Ramsey-type models. The iterative nature of this approach also allows us to present a new algorithm to simulate the optimal trajectories of the economy. We provide two economic illustrations of our method. Firstly, in order to investigate the importance of capital mobility in economic growth, we consider the spatial Ramsey model. We point out the spatial dynamic implications in social welfare and income inequality. Secondly, under fairly general assumptions, we analytically prove the existence of a unique social optimum in this framework. We also apply the outcome to the spatial growth model and to a set-up for optimal land-use planning, concluding that these problems are well-posed.
