Estimating the welfare gains from ending inflation requires taking a stand on the shape of the money demand function. A form of the money demand function that seems to describe U.S. experience—known in technical jargon as the double log form—seems to work well in countries and times where inflation was moderate. The author argues that the double log form would not likely work well in extreme cases, where policy was set to achieve Milton Friedman’s optimal money stock, or at the other extreme, hyperinflation. The author concludes that this simple functional form should not be used to calculate the welfare gains associated with implementing the optimal policy.