  We analyze equilibrium housing prices in an overlapping generations model
with perfect housing and rental markets. The economy exhibits a two-stage phase
transition: as the income of home buyers rises, the equilibrium regime changes
from fundamental to bubble possibility, where fundamental and bubbly equilibria
can coexist. With even higher incomes, fundamental equilibria disappear and
housing bubbles become a necessity. Even with low current incomes, housing
bubbles may emerge if home buyers have access to credit or have high future
income expectations. Contrary to widely-held beliefs, fundamental equilibria in
the possibility regime are inefficient despite housing being a productive
non-reproducible asset.
