Trichotomic discounted utility

Recent evidence on intertemporal choice suggests that decision-makers may exhibit both increasing and decreasing impatience simultaneously, called inverse-S discounting. This paper introduces trichotomic discounted utility to model inverse-S discounting. Under trichotomic discounted utility the decision-maker distinguishes between short-term delays, medium-term delays, and long-term delays. Exponential discounting holds within each category, but not necessarily across each category. We provide preference foundations for trichotomic discounted utility in the timed outcomes framework and in the consumption streams framework. The key axiom is a weakening of the time consistency axiom that allows for both increasing and decreasing impatience. We also consider a weak, local version of time consistency, and show that this plausible condition is satisfied only by discount functions with exponential “pieces”.