Overpopulation isn't the problem, it's the distribution of resources. If we place the human race together at one spot, we'd be very surprise that we'll only form a small island in our vast Earth.
Policies of both economic and government origin have created this gap of "rich" and "poor". Now imagine if they were well balanced, we wouldn't really see the problem as much.
Besides, with most of the food we take from the Earth, we grow more through enhanced genetic engineering. It's not like we farm potatoes till the soil is exhausted. Our early attempt at this was seasonal farming.
Seriously though, 1000 years is kind of a cruel fate. I'd get 300-500 but 1000... Man, talk about a life...
Seriously though, people. Don't start telling each other Fuck Off even though he's been proven wrong. You're counter-productive. :V