INTERTEMPORAL COMPLEMENTARITY AND OPTIMALITY: A STUDY OF A TWO‐DIMENSIONAL DYNAMICAL SYSTEM*
研究允许相邻时期跨期互补但保持时间可加分离框架的二维动力系统，识别传统Ramsey型理论结果成立的条件，并建立全局收敛结果，关联局部稳定性与最优政策函数的可微性。
We study the underlying structure of the two‐dimensional dynamical system generated by a class of dynamic optimization models that allow for intertemporal complementarity between adjacent periods, but preserve the time‐additively separable framework of Ramsey models. Specifically, we identify conditions under which the results of the traditional Ramsey‐type theory are preserved even when the intertemporal independence assumption is relaxed. Local analysis of this theme has been presented by Samuelson ( Western Economic Journal 9 (1971), 21–26). We establish global convergence results and relate them to the local analysis, by using the mathematical theory of two‐dimensional dynamical systems. We also relate the local stability property of the stationary optimal stock to the differentiability of the optimal policy function near the stationary optimal stock, by using the Stable Manifold Theorem.