  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 calibrate a model with standard constant
relative risk aversion utility and show that zero asymptotic MPCs are
empirically plausible, implying that our mechanism has the potential to
accommodate a large saving rate of the rich and high wealth inequality (small
Pareto exponent) as observed in the data.
