Decreasing impatience and the magnitude effect jointly contradict exponential discounting

The experimental literature on time preference finds that the manner in which subjects discount money (as opposed to utility) exhibits properties known as Decreasing Impatience and the Magnitude Effect. While these findings are often referred to as anomalies for the Exponential Discounting model, several authors have demonstrated that each of these qualitative findings can be explained by the curvature of utility and thus are not anomalies. We prove that, under basic regularity conditions, the two findings jointly imply the existence of Preference Reversals, and thus jointly contradict the Exponential Discounting model.