latter half of the population finds themselves unable to afford a second generation

The technical term for that is "starving to death", so let's call it what it is. Don't worry, I won't judge you-- I'm a pragmatist deeply skeptical of prescriptive morality. I respect someone who frankly doesn't give a damn about the less fortunate more than I respect someone who pretends to give a damn. From a pragmatic point of view, though, that starving half will resort to the other standard response to scarcity: violence.

Which brings us to...

Normal political mechanisms

Do we live in a world where normal political mechanisms operate? Uh-oh, we do. Does the impact of political mechanisms outweigh the opposite impact of market mechanisms to limit family size? Uh-oh, we don't know.

So, for you to continue believing that the markets will prevent overpopulation without any specific person thinking or doing anything about it, it's your turn to come up with estimates on the net effect government has on technological progress and population growth, and the net effect an pure free market would have on technological progress and population growth.