The Optimum Quantity of Money: Theory and Evidence

with Xavier X. Sala-i-Martin


In this paper we propose a simple and general model for computing the Ramsey optimal inflation tax, which includes several models from the previous literature as special cases. We show that it cannot be claimed that the Friedman Rule is always optimal (or always non-optimal) on theoretical grounds. The Friedman rule is optimal or not, depending on conditions relating to the shapes of various relevant functions. One contribution of this paper is to relate these conditions to measurable variables such as the interest rate or the consumption elasticity of money demand. We find that it tends to be optimal to tax money when there are economies of scale in the demand for money (the scale elasticity is smaller than one) and/or when money is required for the payment of consumption or wage taxes. We find that it tends to be optimal to tax money more heavily when the interest elasticity of money demand is small. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields a optimal nominal interest rate of less than 1%/year, although that finding is sensitive to the calibration.

You cannot download a copy of this paper. It was published as:
Mulligan, Casey B. and Xavier X. Sala-i-Martin. "The Optimum Quantity of Money: Theory and Evidence." Journal of Money, Credit, and Banking, November 1997, Part 2: 687-715.

A longer version of the paper was circulated as:
NBER Working Paper No. 5954, March 1997.

© copyright 1997 by Casey B. Mulligan and Xavier X. Sala-i-Martin.