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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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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