Abstract
An central bank digital currency or CBDC may provide to be an attractive alternative to traditional demand-deposits in private banks. With that, the central bank needs to confront classic issues of banking: maturity transformation and demand-liquidity or 'spending' shocks by its private customers. We analyze these issues in a nominal version of a Diamond and Dybvig (1983) model, with an additional and exogenous price stability objective for the central bank. While the central bank can always deliver on its nominal obligations, runs can nonetheless occur, manifesting themselves either as excessive real asset liquidation or as a failure to maintain price stability. We demonstrate a CBDC Trilemma: of the three goals e ciency, nancial stability (i.e. absence of runs) and price stability, the central bank can achieve at most two.