Money and banking with reserves and CBDC

We analyze retail central bank digital currency (CBDC) in a two-tier monetary system with bank deposit market power and externalities from liquidity transformation. Resource costs of liquidity provision determine the optimal monetary architecture and modified Friedman (1969) rules the optimal monetary policy. Optimal interest rates on reserves and CBDC differ. A calibration for the U.S. suggests a weak case for CBDC in the baseline but a much clearer case when too-big-to-fail banks, tax distortions or instrument restrictions are present. Depending on central bank choices CBDC raises U.S. bank funding costs by up to 1.5 percent of GDP.