Your [1] does not imply your [2]. If 200,000 refugees show up in Vienna tomorrow and are allowed to work and be economically productive they'll look for and fin

Your [1] does not imply your [2]. If 200,000 refugees show up in Vienna tomorrow and are allowed to work and be economically productive they'll look for and find housing, bidding up prices. Housing supply does not automatically increase with demand. If the private sector provides 100,000 new dwelling places it'll have a very similar effect to the public sector doing so. Who owns the provider has limited economic effect.