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

In: Nonlinear Dynamics in Equilibrium Models

Author

Listed:
  • Tapan Mitra

    (Cornell University)

  • Kazuo Nishimura

    (Kyoto University)

Abstract

The theory of optimal intertemporal allocation has been developed primarily for the case in which the objective function of the planner or representative agent can be written as $$U(c1, c2\ldots) \equiv {{{\sum}^\infty}_{t=1}} {{\delta}^{t-1}}w(c_{t})$$ where c t represents consumption at date t, w the period felicity function, and $$\delta\,\,\epsilon$$ (o,1) a discount factor, representing the time preference of the agent.

Suggested Citation

  • Tapan Mitra & Kazuo Nishimura, 2012. "Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 195-233, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-22397-6_9
    DOI: 10.1007/978-3-642-22397-6_9
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    References listed on IDEAS

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    10. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
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    12. 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.
    13. Lane, John & Mitra, Tapan, 1981. "On Nash Equilibrium Programs of Capital Accumulation under Altruistic Preferences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 309-331, June.
    14. Wan, Henry, 1970. "Optimal Saving Programs under Intertemporally Dependent Preferences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 521-547, October.
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    16. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
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    Cited by:

    1. 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," TSE Working Papers 09-064, Toulouse School of Economics (TSE).
    2. Hippolyte d'Albis & Jean-Pierre Drugeon, 2020. "On Investment and Cycles in Explicitely Solved Vintage Capital Models," PSE Working Papers halshs-02570648, HAL.
    3. 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.
    4. 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.
    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

    Keywords

    Utility Function; Euler Equation; Discount Factor; Characteristic Root; Optimal Program;
    All these keywords.

    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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