On variable discounting in dynamic programming: applications to resource extraction and other economic models |
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Authors: | Anna Ja?kiewicz Janusz Matkowski Andrzej S Nowak |
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Institution: | 1. Institute of Mathematics and Computer Science, Wroc?aw University of Technology, Wybrze?e Wyspiańskiego 27, 50-370, Wroc?aw, Poland 2. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland 3. Institute of Mathematics, Silesian University, Bankowa 14, Katowice, Poland 4. Institute of Finance, PWSZ Nysa, Poland
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Abstract: | 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. |
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