Won't vendors and landlords charge what the market will bare? If all the people not receiving subsidized housing now have +$10,000 per year, they can all bid up to that much more.
In certain places where there is a limit on the supply of housing this will probably happen.
However, when rent prices go up, it encourages people to build more homes/apartments which in turn drives prices down. There is a feedback loop (granted, many times it's interrupted, and there is a delay)
