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This paper shows that deviations from long-run price stability are optimal in the presence
of price stickiness whenever profit and utility flows are discounted at a different rate. In that
case, a monetary authority acting under commitment will choose a path for the inflation rate
that ends with a non-zero value. Such a property is relevant in a wide range of macroeconomic
environments. I first illustrate this by studying optimal monetary policy in a New Keynesian
model with a perpetual youth structure. In this setting, profit flows are discounted more heavily
than utility flows and the optimal inflation target is equal to 3.2% in a baseline calibration of the
model. I also show that this property leads to a positive long-run inflation rate in models with
firm entry and exit and in environments with search and matching frictions in the labor market
and another form of nominal rigidity, wage stickiness.
