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INTERTEMPORAL COMPLEMENTARITY AND OPTIMALITY: A STUDY OF A TWO‐DIMENSIONAL DYNAMICAL SYSTEM*
Author(s) -
Mitra Tapan,
Nishimura Kazuo
Publication year - 2005
Publication title -
international economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.658
H-Index - 86
eISSN - 1468-2354
pISSN - 0020-6598
DOI - 10.1111/j.0020-6598.2005.00311.x
Subject(s) - differentiable function , separable space , mathematical economics , dynamical systems theory , complementarity (molecular biology) , stationary point , economics , stock (firearms) , mathematics , mathematical optimization , pure mathematics , mathematical analysis , physics , mechanical engineering , quantum mechanics , biology , engineering , genetics
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.