Friedman meets Becker and Mulligan in a monetary neoclassical growth model

We study a neoclassical growth model with the time preference determined by resources spent on imagining future pleasures along the line of Becker and Mulligan (Q J Econ 112:729–758, 1997). We introduce money into the economy via a cash-in-advance constraint and study the effect of higher seignorage taxes or higher monetary growth rates on capital, consumption and welfare in the long run. We find that if the fraction of investment constrained by cash is smaller than a threshold, the negative-monetary-growth Friedman (The Optimum Quantity of Money and Other Essays, 1969) rule does not hold and the optimal inflation rate is positive. Calibrating our model yields a mild optimal inflation rate per annum with a switch from zero inflation to optimal inflation creating a sizable welfare gain in terms of consumption equivalence.