Subadditivity, Patience, and Utility: The Effects of Dividing Time Intervals

Abstract

Previous work has demonstrated that time discounting is subadditive; individuals are more impatient when a delay is divided into sub-intervals. This paper demonstrates that subdivision affects both components of intertemporal choice, the utility function as well as the intertemporal discount function. In my first experiment, I demonstrate that differential concavity of utility for gains and convexity for losses implies that the discounting of losses is even more subadditive than the discounting of gains. Individuals display even more relative impatience over divided time intervals for negative amounts of money than for positive amounts of money. My second experiment utilizes alternative elicitation methods, which impose an intertemporal status quo, to highlight these utility effects. Subadditivity is stronger when delaying an early gain than for hastening a later gain. The reverse pattern holds for losses; discounting is more subadditive when hastening a later loss than for delaying an earlier loss.