We consider an infinite-horizon inter-generational economy with identical agents differing only in their inherited wealth and with a constant-returns-to-scale technology using capital and labour (called 'effort') and displaying a purely idiosyncratic risk. If effort is contractible, full insurance contracts make the production deterministic and initial wealth inequalities cannot persist (just as in a neoclassical growth model). But if effort is not contractible the ability to commit is an increasing function of initial wealth so that in equilibrium poorer agents face tougher credit rationing and take smaller projects (i.e. use less capital); although there is no poverty trap, the initial distribution may have long-run effects: there can be multiple long-run stationary distributions, and all are continuous and ergodic on the same interval, but have different equilibrium interest rates (and therefore different degrees of intergenerational mobility). This provides an explanation for wealth differentials within a country as well as between countries, and a basis for redistributive policies with long-run effects.