Just for fun, I made a quick calc for you: http://tinyurl.com/3xl32bx

In 50 years at 1.3% growth we'll basically double our population, and go from about 8000 m^2 per person to 4000 m^2 per person. After 780 years, the growth starts adding up, you can play with the numbers.

Wow, instacalc is pretty awesome.

The population will increase by a factor of exp(.013780) = 25336.5

So we should be at roughly 25,336 meters / person currently. (But remember that plenty of that is more-or-less unlivable--Siberia and the like.)

In 50 years, the population will have increased by a factor of exp(.013 50) = 1.91554, so in the next 50 years population will roughly double, so that number will go down to about 13k meters/person.

Using data from the 2000 US Census, Manhattan, the United States' most dense city, had 25,836 people per square km or 0.025836 people per square meter.

That's roughly 38 square meters per person. For the most dense city, that's plenty of space.