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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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    1. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-1393, September.
    2. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    3. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    4. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    5. 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.
    6. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-644, August.
    7. 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.
    8. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
    9. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," The Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    10. B. Douglas Bernheim & Debraj Ray, 1987. "Economic Growth with Intergenerational Altruism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 227-243.
    11. 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.
    12. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    13. Peter A. Diamond & Tjalling C. Koopmans & Richard E. Williamson, 1962. "Stationary Utility and Time Preference," Cowles Foundation Discussion Papers 142, Cowles Foundation for Research in Economics, Yale University.
    14. Iwai, Katsuhito, 1972. "Optimal economic growth and stationary ordinal utility --A fisherian approach," Journal of Economic Theory, Elsevier, vol. 5(1), pages 121-151, August.
    15. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    16. Harl E. Ryder & Geoffrey M. Heal, 1973. "Optimal Growth with Intertemporally Dependent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(1), pages 1-31.
    17. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    18. 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.
    19. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
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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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