The optimum quantity of money: Theory and evidence

Our model for computing the Ramsey optimal inflation tax includes several models from the previous literature as special cases. The model highlights the various assumptions in that literature that have led to such different results, assumptions that relate to the interest and scale elasticities of money demand and how they vary with the interest rate, whether money is required to pay taxes, and the nature of transactions when interest rates are very low. Calibrating the model to a variety of empirical studies yields an optimal nominal interest rate of less than 1 percent per year, although that finding is sensitive to the calibration.