The authors begin by summarizing some popular arguments for positive steady-state rates of inflation based on the idea that a certain amount of inflation stabilizes economic performance. Then, synthesizing a number of disparate results in a single framework and using a general class of money-demand functions, they find that the stability-through-inflation arguments have either been completely replaced (by potent but unsettling results based on rational expectations) or called into question (by more sophisticated treatments of the adaptive expectations hypothesis).