Abstract

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans :287–309, 1960, 1972) and Koopmans et al. :82–100, 1964) with subsequent contributions by several other authors, including Bleichrodt et al. :341–347, 2008). The papers by Hayashi :343–352, 2003) and Olea and Strzalecki :1449–1499, 2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn and Harvey :1123–1139, 1986), we show that Anscombe and Aumann’s :199–205, 1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.