Short-run and long-run effects of changes in money in a random matching model

Using an existing random matching model of money, I show that a once-for-all change in the quantity of money has short-run effects that are predominantly real and long-run effects that are in the direction of being predominantly nominal provided (i) the quantity of money is random and (ii) people learn about what happened to it only with a lag. The change in the quantity of money comes about through a random process of discovery that does not permit anyone to deduce the aggregate amount discovered when the change actually occurs.