This paper develops an overlapping-generations (OLG) model to analyze the consequences of demographic structure changes induced by an exogenous shift in the birth rate. We first show that a finite growth rate of the population that maximizes long-run capital per capita exists. Then, we examine the theoretical properties of this growth rate by showing that: (i) it corresponds to the demographic structure such that the average ages of capital holders and workers are equal; (ii) it is associated to an efficient steady state; (iii) it increases with compulsory transfers from younger to older generations. Finally, we explain why standard OLG models do not exhibit such a growth rate.