There's arguments on both sides of that. The truth is that economics are rough guesses at best and the only way to know if demand will outstrip supply leading to price increases or if supply will increase enough to make up a lot of the difference is to try and see what happens.
What's actually likely to happen is that some places supply won't increase as much because of external limits (a la zoning in SF or space in NYC) and other places the supply will increase enough that there will be only small effects. On top of that it's hard to guess how much more mobile people will be if they have a guarantee of income if they move to the midwest from a big city where their BI will go much further, which would blunt the demand increase in big cities.
It's a huge mess of interdependent factors and effects.
I think the idea is that there would be so much housing and food that there would be no way to compete (without the necessary manufacturing capital if/when BI becomes law) in the lower end market because the supply is so high.
