A theory of the saving rate of the rich

Empirical evidence suggests that the rich have higher propensity to save than do poor. While this observation may appear contradict homotheticity of preferences, we theoretically show is not case. Specifically, consider an income fluctuation problem with homothetic preferences and general shocks prove consumption functions are asymptotically linear, exact analytical characterization asymptotic marginal propensities consume (MPC). We provide necessary sufficient conditions for MPCs be zero. calibrate a model standard constant relative risk aversion utility zero empirically plausible, implying our mechanism has potential accommodate large saving rate high wealth inequality (small Pareto exponent) as observed in data.