Is the Friedman rule optimal when money is an intermediate good?

In contrast to the recent literature on the optimal inflation tax, we show that, in models where money reduces transactions costs, it is optimal to set the inflation tax to zero when seigniorage is replaced by revenue from distortionary taxes. The main reasons for this result are that the variable costs of supplying real balances are negligible and the inflation tax is a unit tax. We also show that the intermediate good optimal taxation rules in the public finance literature cannot be directly applied, both when money is costless and when it requires resources to be produced.