You can't really compare today to the future if the population is meant to increase exponentially... By 2050 it could be the most populated country in the world, the idea that, that population wouldn't immigrate especially when other countries will be in desperate need of workers seems absurd.
Especially when, as you say, they will be uneducated and that education will likely be available in those nations.
I'm a bit confused by your choice of words "subservient" and "obligation", it seems you're trying to imply more but not caring to say it.
Immigrants are cheap labor for europe and the US, even though it's not commonly admitted. Emigrating is not the only option for those countries. For example china, due to its development, did not end up with massive waves of emigration.
Especially when, as you say, they will be uneducated and that education will likely be available in those nations.
I'm a bit confused by your choice of words "subservient" and "obligation", it seems you're trying to imply more but not caring to say it.