We study the underlying structure of the two-dimensional dynamical system generated by a class of dynamic optimization models, which allow for intertemporal complementarity between adjacent periods, but which 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 (1971). 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.
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Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number
02-06.
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Boyer, Marcel, 1978.
"A Habit Forming Optimal Growth Model,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 585-609, October.
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