Due to the ageing process, the provision of long-term care (LTC) to the dependent elderly has become a major challenge of our epoch. But our societies are also characterized, since the 1970s, by a postponement of births, which, by raising the intergenerational age gap, can affect the provision of LTC by children. In order to examine the impact of those demographic trends on the optimal policy, we develop a four-period OLG model where individuals, who receive children's informal LTC at the old age, must choose, when being young, how to allocate births along their life cycle. It is shown that, in line with empirical evidence, early children provide more LTC to their elderly parents than late children, because of the lower opportunity cost of providing LTC when being retired. When comparing the laissez-faire with the long-run social optimum, it appears that individuals have, at the laissez-faire, too few early births, and too many late births. We then study, in first-best and second-best settings, how the social optimum can be decentralized by encourageing early births, in such a way as to reduce the social burden of LTC provision.