An overlapping generations model for monetary policy analysis

We integrate an overlapping generations model into a new monetarist framework and show that the Friedman rule is not optimal. This is because inflation makes saving for retirement less attractive, such that young agents optimally choose to increase their consumption at the expense of lower savings. On the other hand, old agents consume less due to the inflation tax. We show that for low inflation rates, the former effect dominates the latter, such that the Friedman rule is not optimal. However, this effect disappears for higher inflation rates such that the optimal rate is at an intermediate level.