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: (i) the optimal steady-state inflation rate generically differs from zero and (ii) inflation optimally responds to productivity disturbances. We show this by aggregating a heterogeneous-firm model with sticky prices in closed form. Using firm-level data from the US Census Bureau, we estimate the historically optimal inflation path for the US economy: the optimal inflation rate ranges between 1 percent and 3 percent per year and displays a downward trend over the period 1977–2015.