That is the title of an excellent book by demographer Joel Cohen. Though it's over a decade old, I still highly recommend it for getting the big picture.
Apparently there is a quasi-official UN estimate in answer to this question. The relevant web page explicitly forbids hotlinking or reproduction, so please just go have a look. Apparently the sustainable population at western consumption levels is under 2 billion, and at under 6 billion at "medium" consumption levels. The demographers' consensus prospect that the population will settle at perhaps less than 10 billion over this century is therefore not really all that reassuring.
There are some source documents listed in text embedded in the graphic. It would be interesting to see how they arrived at these numbers.
The only thing we can be sure of about the future is that it will be absolutely fantastic. So if what I say now seems to you to be very reasonable, then I have failed completely. Only if what I tell you appears absolutely unbelievable, have we any chance of visualizing the future as it really will happen.
- Arthur C. Clarke (h/t Brin)