But human population hasn't outstripped innovation or our ability to acquire resources up to this point. Why would it now? It's quite evident that worldwide living conditions have generally risen throughout our history. And I don't see why any innovation now would take
longer to affect the world at large. If anything, with our superior communication and transportation (compared to the rest of history), innovation propagates much much faster. Hence things like the industrial and the Green Revolution.[1]
Also population growth worldwide has been declining for a couple decades now. Surely our ability to innovate won't likewise decline. Generally innovation seems to accelerate (more people spend more time thinking and less time acquiring basic necessities).
Just read about Norman Borlaug[2] to see what I am talking about. His work on wheat has been credited with saving over a billion people from starvation.
I am curious though, how would you solve the overpopulation problem? Reproductive controls don't work very well (and make people miserable/rebellious), and you can't just kill off a bunch of people (like you said, not an economics class), so what do we do? The most effective birth control method for a nation so far has been economic success for women (look at birth rates in the West compared to the developing world).
[1] http://en.wikipedia.org/wiki/Green_Revolution
[2] http://en.wikipedia.org/wiki/Norman_Borlaug