Housing demand is more elastic than many people suppose. As you indirectly point out, people will generally take the best housing they can afford. If they can only afford a shared apartment or living with their parents, that is what they will do. If they can afford their own apartment, they will do that. If they can afford a mansion with a swimming pool, many will do that. People will sometimes move away from high priced areas and toward lower priced areas if they can manage it. To a certain extent, therefore, demand will increase and decrease relative to supply. So, back to my original thesis, if you want cheaper or better housing, build more of it. Ideally, you do this in places where it is in demand though I acknowledge it may be difficult in the highest demand areas. Alternatively, build rapid transit to increase the effective availability of housing (increase the reasonable commuting distance).