Optimal monetary policy with the cost channel and monopolistically-competitive banks

•I study the optimal policy interest rate with imperfectly-competitive banks.•Due to the market power of banks, the deposit interest rate is relatively low.•The Friedman Rule is not optimal even when prices are fully flexible.•Taxing money is optimal because it is an imperfect substitute for deposits.•This increases the level of deposits and encourages intermediation. This paper studies the optimal nominal policy interest rate in a model with the cost channel and imperfect competition in the banking sector. Due to this market power, the interest rate on deposits is relatively low; in particular it is lower than the policy interest rate. This, in turn, leads to a suboptimal level of deposits and, as a result, to a low level of intermediation. Deviations from the Friedman Rule are optimal in this setup regardless of the assumption about price rigidity; since households can hold their assets in the form of cash or deposits, taxing money, which is an imperfect substitute for deposits, is optimal in order to increase the level of deposits and encourage intermediation. The main results of the paper are robust to the introduction of market power in the loan market as well as stickiness in both the deposit and the loan markets.