This work provides a rigorous treatment concerning the formation of rational expectations equilibria in a general class of spatial economic models under the effect of externalities, using techniques from calculus of variations and optimal control. Using detailed estimates for a parametric optimisation problem, the existence of rational expectations equilibria is proved via a fixed-point theorem, and they are characterised in terms of a nonlocal Euler-Lagrange equation. The study of the individual optimisation problem, formulated according to Ramsey's model, is performed via a convex relaxation to the space of BV capital paths and measure-valued consumptions, and allows to obtain existence, uniqueness, regularity and stability properties for the optimisers in a rigorous and original way.

这项工作使用变化演算和最优控制技术，对在外部性影响下在一般一类空间经济模型中合理期望均衡的形成提供了严格的处理。使用参数优化问题的详细估计，通过不动点定理证明有理期望均衡的存在，并根据非局部Euler-Lagrange方程对它们进行表征。根据Ramsey模型建立的个体优化问题的研究是通过对BV资本路径的空间和度量值的消耗进行凸松弛来进行的，并允许获得优化器中的存在性，唯一性，规则性和稳定性。严格而原始的方式。