If the agent responds to an exogenous increase in risk (i.e. a mean preserving spread of the distribution of (1−s)k for given k) by savingmore, then the first effect would raise expected utility but the second effect would reduce it by further increasing risk.


s is a positive shock with Es=1


it raises the deterministic part a+k but it also changes the distribution of shocks (1−s)k.


This cannot be reconciled with the usual assumptions of constant relative risk aversion and labor income risk. However, it is consistent with risk affecting assets or the return to assets.


It is well known (Leland, 1968) that under these assumptions the effect of risk on savings is positive if the utility function exhibits prudence (u″′>0).