In most models with inÞnitely-lived representative agents (ILRA models), the optimal monetary policy is the Friedman Rule. In overlapping generations (OG) models, in contrast, there are widely used deÞnitions of "optimality" under which the Friedman Rule usually is not optimal. This paper seeks to identify the basic difference between the role of money in ILRA vs. OG models, using their prescriptions for the optimal monetary policy to illustrate the nature and importance of this difference. To this end, we study the welfare properties of monetary policies in an OG model under two different money demand assumptions: reserve requirements and stochastic relocation. In both cases, the optimal policy can be said to deviate from the Friedman Rule. Our analysis of these results indicates that OG models produce different optimal monetary policies from ILRA models because in OG models, the standard method for constructing a monetary regime causes exchanges ∗ We began working on this paper while Russell was visiting Iowa State University, and we completed the current version while Bhattacharya was visiting the University of Texas at Austin. We acknowledge useful discussions with Randy Wright, as well as helpful comments from participants in the Midwest Macro Meetings in Atlanta and seminars at