We explore steady‐state inequality in an intergenerational model with altruistically linked individuals who experience privately observed taste shocks. When the welfare function depends only on the initial generation, efficiency requires immiseration: inequality grows without bound and everyone’s consumption converges to zero. We study other efficient allocations in which the welfare function values future generations directly, placing a positive but vanishing weight on their welfare. The social discount factor is then higher than the private one, and for any such difference we find that consumption exhibits mean reversion and that a steady‐state, cross‐sectional distribution for consumption and welfare exists, with no one trapped at misery.