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An Exercise on Discrete-Time Intertemporal Optimization

Author

Listed:
  • Fidelina B. Natividad-Carlos

    (School of Economics, University of the Philippines Diliman)

Abstract

This paper, using the different alternative methods of dynamic optimization - the Lagrange/Kuhn-Tucker (LKT) method, the substitution method, the Hamiltonian method, and the dynamic programming approach - derives the conditions that must be satisfied by the solution to the so-called Ramsey problem, hopefully in a way that can be understood by advanced undergraduate economics students. This is done by assuming that time is discrete and that, for simplicity but without loss of generality, there are only three periods.

Suggested Citation

  • Fidelina B. Natividad-Carlos, 2013. "An Exercise on Discrete-Time Intertemporal Optimization," UP School of Economics Discussion Papers 201306, University of the Philippines School of Economics.
    • Handle: RePEc:phs:dpaper:201306
    as

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    File URL: http://www.econ.upd.edu.ph/dp/index.php/dp/article/view/710/184
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    References listed on IDEAS

    as
    1. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, December.
    2. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    3. Dorfman, Robert, 1969. "An Economic Interpretation of Optimal Control Theory," American Economic Review, American Economic Association, vol. 59(5), pages 817-831, December.
    4. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
    5. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Ramsey problem; dynamic optimazation; Lagrange method; Substitution method; Hamiltonian method; dynamic programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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