Clifman,
You may be partly right about the behaviour of poor people in times of austerity.  Clearly things have been brutal in countries like Somalia, Ethiopia and Sudan for decades, yet these countries populations keep increasing.  It is hard to know exactly how much more marginal a person's existence needs to become before a person consciously decides not to have children.  Typically though, once a woman's physiology is compromised by lack of adequate food energy their body is either too weak to procreate or conception does not occur.
It is a too-oft forgotten fact that during the oil shocks of the 70s there were short periods of starvation in countries dependent on food aid.  Clearly, countries like Egypt with population sizes that have gone far beyond their  lands carrying capacity will suffer immensely if US & Euro food aid is cut off.  Initially there may be rationing...later there may be an attempted exodus north to Turkey and Greece.