In the theory of endogenous time preference, one of the most common and most controversial assumptions is that the degree of impatience, measured by the rate of time preference, is increasing in wealth. Although this empirically-unjustified assumption often helps ease dynamic analyses by ensuring stability, it has never been discussed why decreasing impatience is theoretically problematic. We first show that under certain conditions there exists no optimal solution when impatience is decreasing. By considering problem-proof, well-behaved models, we examine implications of decreasing impatience for three issues that have been discussed in the literature: (i) long-run tax incidence of capital taxation; (ii) the effect of inflation on growth; and (iii) wealth distribution dynamics in the two-country world.