[drats]

As another answer says, global carrying capacity depends on people's living standards. Wars normally start when there is a regression in standards. I am sympathetic to the idea that in the West this might not apply as much, i.e. regressing to 1970s living from 2011 wouldn't be a huge tragedy even if it was a loss. However, as current protests and riots in the West show, there is also a psychological element. Additionally, large portions of the world do not have that padding, and regression actually means physical pain (food shortages) rather than psychological pain. Large groups in that category are also nuclear-equipped (Russia, Pakistan, India and China) and so I guess your sine-wave of population gently dipping down from carrying capacity after briefly going over might actually be a very sharp movement downward, measured in the units of the nuclear age: megadeaths.[1]

[1]http://en.wikipedia.org/wiki/Megadeath