Decreasing relative impatience

Prelec (2004) showed that the Arrow–Pratt degree of convexity of the logarithm of the discount function can serve as a measure of decreasing impatience and of the corresponding time-inconsistency. In decision under risk and uncertainty the convexity of the utility function itself, not of its logarithm, has empirical meaning in terms of risk attitude. This paper introduces decreasing relative impatience, which is directly related to the degree of convexity of the discount function. By giving empirical meaning to the convexity of the discount function this paper clarifies the relations between several concepts in intertemporal choice. This paper also introduces a concept of spread seeking. Spread seeking and decreasing relative impatience are likely to have distinct underlying psychological motives, but are shown to be equivalent under discounted utility.