The term "overpopulate" is a matter of politics. If all of China had the same political system as the Hong Kong SAR, China's population growth would accelerate AND they would NOT be "overpopulated".
Hong Kong has the highest population density in the world with a per capital standard of living and income comparable to the U.S., and is situated essentially on a rock in the ocean. It also has historically dealt with HUGE waves, along with a steady trickle, of refugees. Its population "problem" is only an issue for its civil engineers and people (I'm not one of them) who simply don't like crowds.
Assuming that we can maintain the current upward trend in productivity presupposes that we have limitless resources. We do not.