A theory of the saving rate of the rich
Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we consider an income fluctuation problem with homothetic preferences and general shocks and prove that consumption functions are asymptotically linear, with an exact analytical characterization of asymptotic marginal propensities to consume (MPC). We provide necessary and sufficient conditions for the asymptotic MPCs to be zero. We solve a calibrated model with standard constant relative risk aversion utility and show that asymptotic MPCs can be zero in empirically plausible settings, implying an increasing and large saving rate of the rich.