The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case

Abstract

We consider a multiperiod, additive utility, optimal consumption model with a riskless investment and a stochastic labor income. The main result is that for utility functions belonging to the set F, consumption decreases when we go from any sequence of distribution functions representing labor income to a more risky sequence. It is shown that a concave utility function belongs to F if and only if its first derivative exists everywhere and is convex.