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When a central bank introduces a central bank digital currency, it may lead to an erosion of deposits as the stable funding base of banks and result in challenges regarding the asset side of the central bank. We study the resulting economy and trade-offs in a stylized nominal version of the Diamond-Dybvig (1983) model. The central bank is now involved in maturity transformation, if it so chooses. We posit that the central bank pursues three objectives: price stability, economic efficiency and financial stability. We demonstrate that a CBDC Trilemma arises: out of these three objectives, the central bank can achieve at most two. In particular, a commitment to price stability can cause a run on the central bank. Implementation of the socially optimal allocation requires a commitment to inflation. Keywords: CBDC, currency crises, monetary policy, bank runs, financial intermediation, central bank digital currency, inflation targeting
