This paper models the dynamics of the earnings distribution among successive generations of workers as a stochastic process. The process arises from the random assignment of abilities to individuals by nature, together with the utility maximizing bequest decisions of their parents. A salient feature of the model is that parents cannot borrow to make human capital investments in their offspring. Consequently the allocation of training resources among the young people of any generation depends upon the distribution of earnings among their parents. This implies in turn that the often noted conflict between egalitarian redistributive policies and economic efficiency is mitigated. A number of formal results are proven which illustrate this fact.