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Uzawa's Transformation and Optimal Control Problems with Variable Rates of Time Preference

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  • Johanna Francis
  • Tom Kompas

Abstract

Uzawa (1968) first introduced a simple and appealing method for reducing problems with variable rates of time preference to single-state systems by transforming the time scale from t to ., a utility discount factor. This transformation has been used extensively, particularly in models of international trade and finance (e.g., Obstfeld, 1981a, 1981b, 1982, Engeland Kletzer, 1989, and Turnovsky, 1997), where the use of a variable rate of time preference avoids some of the ¡°disturbing implications¡± drawn from typical open-economy Ramsey models. The purpose of this paper, however, is to show that Uzawa¡¯s transformation is valid only when the underlying system to be analyzed is autonomous. Unfortunately, except for the simplest control problems, this is rarely the case. In particular, systems with non-autonomous transition equations imply that the correspondence between .and t is no longer unique, and thus Uzawa¡¯s transformation is not applicable.

Suggested Citation

  • Johanna Francis & Tom Kompas, 2001. "Uzawa's Transformation and Optimal Control Problems with Variable Rates of Time Preference," International and Development Economics Working Papers idec01-12, International and Development Economics.
    • Handle: RePEc:idc:wpaper:idec01-12
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    References listed on IDEAS

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    1. Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, December.
    2. Engel, Charles & Kletzer, Kenneth, 1989. "Saving and Investment in an Open Economy with Non-traded Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 735-752, November.
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    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
    • F30 - International Economics - - International Finance - - - General

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