Wealth Preferences and the Upper Tail of Consumption

Abstract

We develop a theory of optimal saving when wealth enters utility. Relative curvatures of consumption and wealth utility, $\gamma$ and $\delta$, govern the upper-tail behavior. When $\delta<\gamma$, wealth preferences generate a vanishing asymptotic marginal propensity to consume and power-law consumption, $c(w)\sim w^{\delta/\gamma}$, yielding a thinner upper tail for consumption than for wealth. When $\delta=\gamma$, they lower the positive limiting propensity to consume; when $\delta>\gamma$, they become asymptotically irrelevant. The framework encompasses joy-of-giving/warm-glow bequests under random mortality. A calibrated model shows that the asymptotic characterization is accurate at observed wealth levels and reproduces wealthy households' high saving rates.