We introduce ex-post heterogeneity into monetary search models with lotteries. Heterogeneity allows lotteries over goods to exist in equilibrium. These lotteries over goods create an intensive margin (expected production in a match) that is non-existent in all indivisible goods monetary search models. We then show there can be a tradeo¤ between the intensive margin and extensive margin (number of matches) when choosing the optimal monetary stock. We would like to thank the participants of the 1