The population will balance out at the capacity the Earth will allow and how effectively we utilise our resources. It's no coincidence that the population grows almost symbiotically with advances in agricultural science. You can't really have significantly more people than you can sustain.
For example, right now rearing livestock consumes 30% of our land. But meat production is about to be revolutionised with things like lab grown meat. That will allow the amount of meat produced per land unit to be rapidly increased, boosting our overall production greatly. We could probably expect a similar boom to that found after the Haber-Bosch process was first used.
For over a century people have thought the world will be overpopulated in what they called the near future, but it's never happened. They often consider a future population using current technology, which I believe is the pitfall.
