We consider the problem of allocating objects to a group of agents and how
much agents should pay. Each agent receives at most one object and has
non-quasi-linear preferences. Non-quasi-linear preferences describe
environments where payments influence agents' abilities to utilize objects
or derive benefits from them. The ``minimum price Walrasian
(MPW) rule'' is the rule that assigns a minimum price
Walrasian equilibrium allocation to each preference profile. We establish
that the MPW rule is the unique rule satisfying \textit{strategy-proofness},
\textit{efficiency}, \textit{individual rationality}, and \textit{no subsidy
for losers}. Since the outcome of the MPW rule coincides with that of the
simultaneous ascending (SA) auction, our result supports SA auctions adopted
by many governments.