Uzawa's Transformation and Optimal Control Problems with Variable Rates of Time Preference
AbstractUzawa (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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Length: 8 pages
Date of creation: 2001
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Other versions of this item:
- Francis, J. & Kompas, T., 1998. "Uzawa's Transformation and Optimal Control Problems With Variable Rates of Time Preference," Papers 354, Australian National University - Department of Economics.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- F30 - International Economics - - International Finance - - - General
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- NEP-ALL-2004-12-12 (All new papers)
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.:
- Robert J. Barro & Paul M. Romer, 1991.
National Bureau of Economic Research, Inc, number barr91-1.
- repec:fth:harver:1504 is not listed on IDEAS
- Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
- 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.
- 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., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
- Maurice Obstfeld, 1980.
"Capital Mobility and Devaluation in an Optimizing Model with Rational Expectations,"
NBER Working Papers
0557, National Bureau of Economic Research, Inc.
- 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, 1991.
"Intertemporal Dependence, Impatience, and Dynamics,"
NBER Working Papers
3028, National Bureau of Economic Research, Inc.
- Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
- 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.
- Maurice Obstfeld, 1981.
"Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation,"
NBER Working Papers
0599, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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, .
- Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, January.
- 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.
- 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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