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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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    File URL: https://crawford.anu.edu.au/degrees/idec/working_papers/IDEC01-12.pdf
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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, January.
    2. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, pages 45-75.
    3. 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.
    4. Maurice Obstfeld, 1982. "Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?," The Quarterly Journal of Economics, Oxford University Press, pages 251-270.
    5. Obstfeld, Maurice, 1981. "Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation," Journal of Political Economy, University of Chicago Press, vol. 89(6), pages 1142-1161, December.
    6. Clotfelter, Charles T. & Ehrenberg, Ronald G. & Getz, Malcolm & Siegfried, John J., 1992. "Economic Challenges in Higher Education," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226110509.
      • Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1.
    7. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, pages 45-75.
    8. repec:fth:harver:1504 is not listed on IDEAS
    9. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    10. Maurice Obstfeld, 1982. "Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?," The Quarterly Journal of Economics, Oxford University Press, pages 251-270.
    11. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    12. Uzawa, H, 1969. "Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 77(4), pages 628-652, Part II, .
    13. Obstfeld, Maurice, 1981. "Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations," American Economic Review, American Economic Association, pages 217-221.
    14. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
    15. Obstfeld, Maurice, 1981. "Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations," American Economic Review, American Economic Association, pages 217-221.
    16. Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1.
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    Cited by:

    1. Xiaoyong Cui & Liutang Gong & Ziguan Zhuang, 2008. "Macroeconomic Policies and Foreign Asset Accumulation in a Finite-Horizon Model," Annals of Economics and Finance, Society for AEF, pages 293-313.
    2. Tom Kompas & Omar Abdel-Razeq, 2001. "A Simple Monetary Growth Model with Variable Rates of Time Preference," International and Development Economics Working Papers idec01-10, International and Development Economics.

    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
    • 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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