(Revised August 2023)

This paper examines whether the two key functions of central banks—ensuring price stability and lending during crises —must be in conflict. We develop a nominal model of bank runs à la Diamond and Dybvig (1983) in which individuals can store the money they withdraw “under the mattress” or use it to buy assets. In this setting, lending of last resort does not need be inflationary. Whether it is inflationary depends on the interest rates the central bank charges. Our results suggest central banks should not charge low rates to ensure price stability, and should charge a high rate to robustly attain the ex-ante efficient outcome. These results are in line with the Bagehot rule of charging high interest rates on loans during a crisis.