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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.

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Bibliographic Info

Paper provided by International and Development Economics in its series International and Development Economics Working Papers with number idec01-12.

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Length: 8 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:idc:wpaper:idec01-12

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  1. Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1.
    • Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1.
  2. repec:fth:harver:1504 is not listed on IDEAS
  3. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
  4. Obstfeld, Maurice, 1982. "Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?," The Quarterly Journal of Economics, MIT Press, vol. 97(2), pages 251-70, May.
  5. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
  6. Maurice Obstfeld, 1980. "Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations," NBER Working Papers 0557, National Bureau of Economic Research, Inc.
  7. Maurice Obstfeld, 1991. "Intertemporal Dependence, Impatience, and Dynamics," NBER Working Papers 3028, National Bureau of Economic Research, Inc.
  8. 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 735-52, November.
  9. Maurice Obstfeld, 1981. "Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation," NBER Working Papers 0599, National Bureau of Economic Research, Inc.
  10. 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 611-35, August.
  11. 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 628-52, Part II, .
  12. Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, January.
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Cited by:
  1. 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.
  2. 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, vol. 9(2), pages 293-313, November.

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