On variable discounting in dynamic programming: applications to resource extraction and other economic models
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This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.
KeywordsDynamic programming Variable discounting Bellman equation Resource extraction Growth theory
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- Becker, R. A., & Boyd, J. H. III (1997). Capital theory, equilibrium analysis and recursive utility. New York: Blackwell. Google Scholar
- Berge, C. (1963). Topological spaces. New York: MacMillan. Google Scholar
- Dugundji, J., & Granas, A. (2003). Fixed point theory. New York: Springer. Google Scholar
- Hinderer, K. (1970). Foundations of non-stationary dynamic programming with discrete time parameter. In Lecture notes in oper. res., Vol. 33. New York: Springer. Google Scholar
- Jaśkiewicz, A., Matkowski, J., & Nowak, A. S. (2011). Persistently optimal policies in stochastic dynamic programming with generalized discounting. Working Paper. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Poland. Google Scholar
- Matkowski, J. (1975). Integral solutions of functional equations. Dissertationes Mathematicae, 127, 1–68. Google Scholar
- Ramsey, F. P. (1928). A mathematical theory of saving. Econometrics Journal, 38, 543–599. Google Scholar
- Stokey, N. L., Lucas, R. E., & Prescott, E. (1989). Recursive methods in economic dynamics. Cambridge: Harvard University Press. Google Scholar
- Uzawa, H. (1968). Time preference, the consumption function, and optimum asset holding. In J. N. Wolfe (Ed.), Value, capital and growth: papers in honor of Sir John Hicks (pp. 485–504). Edinburgh: Edinburgh University Press. Google Scholar