This paper demonstrates that an optimizing model of a monetary economy can produce perfect foresight equilibria, in which the price level fluctuates forever. Cyclically or chaotically fluctuating equilibria are more likely to exist when the rate of money supply growth is high. Furthermore, the set of equilibrium prices may have a complicated topological structure, which poses a more serious problem concerning the validity of comparative statics method than any sort of indeterminacy previously discussed in the literature.