We consider a market with a set of unit demand buyers and a set of
heterogeneous goods. We assume that the utility of each buyer $i$ from a good
$j$ can be any arbitrary but continuous and decreasing function of price of $j$
and is not necessarily quasi-linear (note that we can model any \emph{smooth
budget constraint} in this form). We give a constructive proof for the
existence of Walrasian equilibria and show that set of Walrasian equilibria
form a complete lattice.