Uzawa's Transformation and Optimal Control Problems with Variable Rates of Time Preference
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.
|Date of creation:||2001|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +61 2 6125 4705
Fax: +61 2 6125 5448
Web page: https://crawford.anu.edu.au/research/papers/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, June.
- Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
- Robert J. Barro & Paul Romer, 1993.
National Bureau of Economic Research, Inc, number barr93-1, December.
- repec:tpr:qjecon:v:97:y:1982:i:2:p:251-70 is not listed on IDEAS
- 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.
- Maurice Obstfeld, 1980. "Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation," NBER Working Papers 0599, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Obstfeld, Maurice, 1990.
"Intertemporal dependence, impatience, and dynamics,"
Journal of Monetary Economics,
Elsevier, vol. 26(1), pages 45-75, August.
- Maurice Obstfeld, 1989. "Intertemporal Dependence, Impatience, and Dynamics," NBER Working Papers 3028, National Bureau of Economic Research, Inc.
- 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, .
- 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.
- Maurice Obstfeld, 1980. "Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations," NBER Working Papers 0557, National Bureau of Economic Research, Inc.
- repec:fth:harver:1504 is not listed on IDEAS
- Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
When requesting a correction, please mention this item's handle: RePEc:idc:wpaper:idec01-12. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tom Kompas)
If references are entirely missing, you can add them using this form.