This paper considers the optimal taxation of savings intermediation and payment services in a dynamic general equilibrium setting, when the government can also use consumption and income taxes. When payment services are used in strict proportion to final consumption, and the cost of intermediation services is fixed and the same across firms, the optimal taxes are generally indeterminate. But, when firms differ exogenously in the cost of intermediation services, the tax on savings intermediation should be zero. Also, when household time and payment services are substitutes in transactions, the optimal tax rate on payment services is determined by the returns to scale in the conditional demand for payment services, and is generally different to the optimal rate on consumption goods. In particular, with constant returns to scale, payment services should be untaxed. These results can be understood as applications of the Diamond-Mirrlees production efficiency theorem. Finally, as an extension, we endogenize intermediation, in the form of monitoring, and show that it may be oversupplied in equilibrium when banks have monopoly power, justifying a Pigouvian tax in this case.