The paper studies the role of subsitence thresholds in the emergence of poverty traps, in a two-country overlapping generations model. If consumption is lower than the subsitence level, people may die after the first period of their life. Given the presence of a survival threshold, and given a difference in productivity between the rich and the poor economy, perfect capital mobility cannot prevent the poor economy from falling into a poverty trap. The higher the level of the survival threshold, the higher the productivity gap, of the more unequal the world population distribution, the more likely the poor economy is to be caught into a poverty trap. By correcting the market allocation of resources or by introducing an international solidarity tax, an international organization can eliminate the poverty trap.