A mathematical model is analyzed to determine the impact of two alternative monetary policies upon the rate of change of prices and the level of real national income. The first is a once and for all change in the rate of growth of the money supply to a new level; the second is found through an optimization analysis using the maximum principle of postaudit. It is found that the second policy not only leads to a final equilibrium position in less time than the first policy, but it also induces less variability in both prices and real income.