Monetary uncertainty and information lags are put into a random matching model so that the resulting setting has some meetings in which producers are relatively informed and others in which consumers are relatively informed. For that setting, the ex ante socially optimal way to conduct trade is characterized. The optimum can display a variety of relationships between money and total output and the price level. While the price level is always sticky, even the direction of its response and that of total output depend on the magnitude of the lag and on subtle features of the serial correlation properties of the money supply.