I study a version of the Lagos-Wright (2003) model of monetary exchange in which buyers have private information about their tastes and sellers make take-it-or-leave-it-offers (i.e., have the power to set prices and quantities). The introduction of imperfect information makes the existence of monetary equilibrium a more robust feature of the environment. In general, the model has a monetary steady state in which only a proportion of the agents hold money. Agents who do not hold money cannot participate in trade in the decentralized market. The proportion of agents holding money is endogenous and depends (negatively) on the level of expected inflation. As in Lagos and Wright’s model, in equilibrium there is a positive welfare cost of expected inflation, but the origins of this cost are very different.