Sticky price models featuring heterogeneous firms and systematic firm-level productivity trends deliver radically different predictions for the optimal inflation rate than their popular homogenous-firm counterparts: (1) the optimal steady-state inflation rate generically differs from zero and (2) inflation optimally responds to productivity disturbances. We show this by aggregating a heterogenous-firm model with sticky prices in closed form. Using firm-level data from the U.S. Census Bureau, we estimate the historically optimal inflation path for the U.S. economy. In the year 1977, the optimal inflation rate stood at 1.5%, but subsequently declined to around 1.0% in the year 2015. Inflation rates up to twice these numbers can be rationalized if one considers product demand elasticities more in line with the trade literature or if one considers firms that (partially) index prices to lagged inflation rates.