We consider the nature of optimal cyclical monetary policy in three different stochastic models with various shocks. The first is a pure liquidity effect model, the second is a cost of changing prices model, and the third is an optimal seinorage model. In each case we solve for the optimal monetary policy and describe how money growth and interest rates respond to shocks under the optimal policy. The shocks we consider are money demand shocks, productivity shocks, and government consumption shocks. All of the models have the feature that the Friedman rule of setting the nominal interest rate to zero is not optimal. Optimal policies are always time inconsistent even though lump sum taxation is allowed. At least in some instances we find that optimal policy dictates responses of money growth and interest rates which run counter to conventional wisdom.