Foundations and Properties of Time Discount Functions

A critical element in all discounted utility models is the specification of a discount function. We extend the standard model to allow for reference points for both out- comes and time. We consider the axiomatic foundations and properties of two main classes of discount functions. The first, the Loewenstein-Prelec discount function, accounts for declining impatience but cannot account for the evidence on subadditivity. A second class of discount functions, the Read-Scholten discount function accounts for declining impatience and subadditivity. We derive restrictions on an individual’s preferences to expedite or to delay an outcome that give rise to the discount functions under consideration. As an application of our framework we consider the explanation of the common difference effect.