We develop a model of monetary exchange that avoids several common criticisms of the recent microfoundations literature. First, rather than random matching, we assume that buyers know the location of all sellers, and hence the process of finding a partner is deterministic, although trade is still stochastic since the number of buyers visiting a given seller is random. Second, given multilateral matching, rather than bargaining, we assume that goods are allocated according to second-price auctions. Third, given this mechanism, we do not have to assume agents can observe each other’s money holdings or preferences, as is necessary for tractability with bargaining. A novel result is that homogeneous buyers hold different amounts of money, leading to equilibrium price dispersion. We find the closed-form solution for the distribution of money holdings. We characterize equilibrium and efficient monetary policy.