Abstract The paper sets out a simple monetary model and uses it to compare alternative monetary systems. Money may be either fiat or gold. Both gold supply and velocity are uncertain. Asset demands are derived from expected utility maximization. I demonstrate the basic argument against a commodity money — that it wastes resources, show why the optimal growth rate of money may be zero, and compare the behavior of the economy under constant money stock, constant price level, and constant gold price rules. Expected utility is typically highest under the constant price level rule.