Well, if the world were a simple mathematical model it might go as follows: there's enough food to feed ten billion people, so one day a baby is born taking us up to ten billion and one and oops -- somebody dies of starvation. From that moment on, the death rate due to starvation is equal to the birth rate minus the death rate due to non-starvation causes, and that's not _too_ bad.
In practice, though, that's not the way it's gonna happen. For starters, we have a bunch of food stored up, so the population will overshoot the limit by eating stored food, maybe for a bunch of years, enabling the population to get way above what it should. (I'm not just talking about canned beans here -- living animals are "stored food" too). Secondly, food production varies from year to year -- in a good year we might be able to feed eleven billion, and in a bad year only nine... that's gonna cause some problems when a bad year rolls around. Finally, a world where everybody has _just_ enough food to not die is still a pretty miserable and malnourished world... plus you've got the whole "hungry people with guns vs hungry people without guns" problem which leads to a whole bunch of other bad stuff happening.
Anyway, I hope that has been enough to convince you that awful things happen anytime you get a population anywhere near the very fuzzy and variable limit which is the maximum agriculturally sustainable population.