This paper develops a model of safety first consumption behavior in which the likelihood of survival to the next period depends on current consumption levels. Below a threshold asset level, individuals follow a decumulation path, and above that level they follow an accumulation path. Saving rates then vary discontinuously with asset level, generating a poverty trap and divergence in incomes. Reduction of risk raises saving rates. A more equitable distribution of assets can be consistent with greater aggregate savings and growth because of declining marginal propensity to save over some asset intervals.