The demographic transition is introduced into the otherwise standard Ramsey model to generate multiple equilibria, poverty traps, and demography-driven cycles. The model is calibrated for global data to explore the demographic conditions under which multiplicity is realized. Three cases arise, referring either to unique or multiple equilibria, and to transitional cycles. The calibrated model shows that multiple equilibria can explain a considerable fraction of the global income gap. The model provides a test to distinguish the trapped countries from those which just suffer from a long-lasting demographic recession, showing that the latter are more common than the former. Therefore, the economic effects of the demographic transition, even though considerable, are temporary rather than permanent.