I just ran these numbers to see what they would say. I assumed the upper bound would be absurdly high. If I have not made a mistake, the bound is actually disturbingly close:
A bit of googling tells me that, in a year, the sun puts out 150 EJ.
It is said that people should consume 2000 kCal/day = 3.05 GJ
To get an upper bound on the number of people that can be supported, we take the ratio, to get 4.92e10.
The current world population is 7e9. This is 1/7-th the upper bound.
The doubling time for the world's population, at current growth rates, is (after some more googling), 54 years. That means that it will increase by a factor of 8 -- more than can be supported -- in just 162 years. More precisely, it will increase by a factor of 7 in 152 years.
That's about two human lifetimes.
Either (1) my numbers are wrong, (2) I made an arithmetic mistake, (3) growth will level off very soon, (4) we will learn to practice space agricuture at a massive scale in an implausibly-short timeframe, or (5) we're in for some pain.