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Intertemporal Complementarity And Optimality: A Study Of A Two-Dimensional Dynamical System

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  • Tapan Mitra
  • Kazuo Nishimura

Abstract

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. Copyright 2005 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 46 (2005)
Issue (Month): 1 (02)
Pages: 93-131

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Handle: RePEc:ier:iecrev:v:46:y:2005:i:1:p:93-131

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Cited by:
  1. Olivier Bruno & Cuong Le Van & Benoît Masquin, 2005. "When does a developing country use new technologies ?," Cahiers de la Maison des Sciences Economiques b05093, Université Panthéon-Sorbonne (Paris 1).
  2. Hiraguchi, Ryoji, 2011. "A two sector endogenous growth model with habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 430-441, April.
  3. GOENKA Aditya & NGUYEN Manh-Hung, 2009. "Existence of competitive equilibrium in an optimal growth model with elastic labor supply and smoothness of the policy function," LERNA Working Papers 09.21.297, LERNA, University of Toulouse.

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