Attending the Laboratory sessions 3 + 4 makes sense only if the theory sessions (Wednesday) and lab sessions 1 + 2 have been attended (or if the content of these sessions is known already from previous work.

Some fifty years ago, Nathan Keyfitz (1971) asked for the amount a growing human population would further increase if its fertility rate would be reduced immediately to replacement level and remains there forever. The reason for this demographic momentum is an inertia of age structures containing relatively many potential parents due to past high fertility. Nobody expects such a miraculous reduction of reproductive behavior, but a gradual decline of fertility in fast-growing populations seems inevitable. Since any delay in fertility decline to a stationary level leads to an increase of the momentum, we consider an intertemporal trade-off between costly birth control and the demographic momentum at the end of a planning period. Using the McKendrick partial differential equation for the age-structured population dynamics, an appropriate extension of Pontryagin’s maximum principle is applied. The results of such a distributed parameter control framework can also be applied to determine efficient pro-natalistic measures for shrinking populations.