Munich Personal RePEc Archive

On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models

Jaśkiewicz, Anna and Matkowski, Janusz and Nowak, Andrzej S. (2011): On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models. Forthcoming in: Annals of Operations Research : pp. 1-15.

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Abstract

This paper generalizes the classical discounted utility model introduced by Samuelson 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 growth with unbounded utility functions.

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