EDIT: Okay, "drastic decrease of billions from the current global population" instead of "extinction."

You may have written this with a rhetorical intention, but it's actually significant. If it really gets to that point, culture will change and people will start making more children again. We aren't predictable animals who behave according to a set of instincts. We're reasoning and adaptable creatures, that's what got us at the top of the food chain in the first place.