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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. Charles Engel & Kenneth Kletzer, 1987. "Saving and Investment in an Open Economy with Non-Traded Goods," NBER Working Papers 2141, National Bureau of Economic Research, Inc.
  2. repec:fth:harver:1504 is not listed on IDEAS
  3. Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1.
    • Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1.
  4. 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.
  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 1142-61, December.
  6. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
  7. Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, December.
  8. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
  9. Maurice Obstfeld, 1981. "Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?," NBER Working Papers 0686, National Bureau of Economic Research, Inc.
  10. Obstfeld, Maurice, 1981. "Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations," American Economic Review, American Economic Association, vol. 71(2), pages 217-21, May.
  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. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
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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, vol. 9(2), pages 293-313, November.
  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.

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