> If financing (of some kind or another) is available for housing, education or health care, prices go up.
But if there's no financing for housing, builders are realistic about their chances of selling something that's that expensive, stop building, and prices go up due to the lack of supply.
Yes, of course. The technical way is to say that financing pushes the equilibrium price upward. (Because it's just pure inflation, since it's new money created by the bank, and now people have more money to buy houses. The housing market then of course tries to correct, so the price goes up.) What you wrote is a hypothetical overcorrection when financing suddenly stops, the price crashes. (Sound familiar?) And then the supply of new houses reacts eventually, which then sets a new equilibrium.
But if there's no financing for housing, builders are realistic about their chances of selling something that's that expensive, stop building, and prices go up due to the lack of supply.