Bank Deposit Pricing in Competitive Oligopoly When Breaking Through the Zero Lower Bound

Low key rates hurt the profits of deposit-taking institutions in a differentiated Bertrand game if there is neither a tax on banknotes, nor a limit on its quantity, nor a reduction of its quality. By making the electronic dollar the unit of account and taxing paper currency, the central bank can escape the zero bound, optimize its seignorage and eliminate systematic profit shortfalls. By following a variant of Friedman's rule, the central bank can remove the market disruption of paper currency. The average rate paid in Nash's unique equilibrium is then bounded from above and below by measures of concentration