Dynamic spatial theory has been a fruitful approach to understanding economic phenomena involving time and space. However, several central questions still remain unresolved in this field. The identification of the social optimal allocation of economic activity across time and space is particularly problematic, not been ensured yet in economic growth. Developing a monotone method, we study the optimal solution of the spatial Ramsey model. Under fairly general assumptions, we prove the existence of unique social optimum. Considering a numerical implementation of our algorithm, we study the role played by capital mobility in the neoclassical growth environment. With capital irreversibility and economic openness, space allows for transitional dynamics. Moreover, in this context, capital mobility is beneficial as well in terms of social welfare and inequality. We also consider an application of our method to an extension of the spatial Ramsey model for optimal land-use planning.

动态空间理论是理解涉及时间和空间的经济现象的一种富有成效的方法。然而，该领域的几个核心问题仍未解决。跨时间和空间的经济活动的社会最优分配的确定尤其成问题，在经济增长中尚未得到保证。我们开发了一种单调方法，研究了空间 Ramsey 模型的最优解。在相当普遍的假设下，我们证明了独特的社会最优的存在。考虑到我们算法的数值实现，我们研究了资本流动在新古典增长环境中所起的作用。由于资本的不可逆性和经济的开放性，空​​间允许过渡动态。此外，在这种情况下，资本流动在社会福利和不平等方面也有好处。我们还考虑将我们的方法应用于空间 Ramsey 模型的扩展，以实现最佳土地利用规划。