I don't think you can make simple rules like this, or expect complex systems like economies to behave according to such simple rules. What you can know is that

I don't think you can make simple rules like this, or expect complex systems like economies to behave according to such simple rules. What you can know is that in expensive areas, they will need to pay a premium, but does the premium need to be as high to allow teachers to buy houses there instead of commuting in? And if you did pay them that much, many would prefer to keep the money and commute a bit longer because they may not value housing as much as the people living in the community. So people have different values and we should let them make their own trade offs. If a community can't hire enough teachers because cost of living is high, then they will need to raise wages. Once they can hire enough, then let people chose for themselves where they want to work and live.