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Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System

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  • Mitra, Tapan

    (Cornell U)

  • Nishimura, Kazuo

    (Institute of Economic Research, Kyoto U)

Abstract

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.

Suggested Citation

  • Mitra, Tapan & Nishimura, Kazuo, 2002. "Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System," Working Papers 02-06, Cornell University, Center for Analytic Economics.
    • Handle: RePEc:ecl:corcae:02-06
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    References listed on IDEAS

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    Cited by:

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    2. Olivier Bruno & Cuong Van & Benoît Masquin, 2009. "When does a developing country use new technologies?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 275-300, August.
    3. Jean-Pierre Drugeon & Thai Ha-Huy & Thi-Do-Hanh Nguyen, 2018. "On Maximin Optimization Problems & the Rate of Discount: a Simple Dynamic Programming Argument," Working Papers halshs-01761997, HAL.
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    5. 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.
    6. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2022. "Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos," Journal of Economic Theory, Elsevier, vol. 201(C).

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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