Or like the US solves it, through immigration. In the US, the fertility rate is at roughly 1.6 children per woman (which is below the 2.1 children per woman required for a stable population), and yet the US population is steadily increasing thanks to immigration. One can talk all day about pros and cons of immigration, but it is ultimately the only solution we have to a falling fertility rate (other than trying to increase it, of course).
Fertility in the migrant source areas is decreasing fast as well. At some point the books won't balance anymore, to provide a reliable flow of workers.
Yea, my comment was looking at it from a global point of view. We simply can't base the global economy on an infinitely growing population--it's ultimately a ponzi scheme.
Many countries don't have a Social Security equivalent, and people rely on their families instead. So not having kids can mean not having anyone to take care of you in old age, but it's maybe still ok if your siblings had kids. It's not that the economy overall relies on that.