Low income housing in Manhattan?

I don't think its fair that renters pay for luxury apartments $2000 - $5000/month and right across the street there is government housing projects where people have apartments for $400/month. I'm not saying we should not have low income housing in general I'm just saying its not fair that they get to live in Manhattan. There is a limited supply of land obviously and the prices of the luxury buildings are artificially high because a lot of the spaces are occupied by low income housing. They should kick them out and build low income housing in far rockaway or the last stop somewhere very far in Brooklyn. If you want to live in Manhattan you should have to pay for it like everyone else. otherwise move far away.