It is commonly asserted that inflation is a jump variable in the New Keynesian Phillips curve, and thus wage-price inertia does not imply inflation inertia. We show that this "inflation flexibility proposition" is highly misleading, relying on the assumption that real variables are exogenous. In a general equilibrium setting (in which real variables not only affect inflation, but are also influenced by it) the phenomenon of inflation inertia re-emerges. Under plausible parameter values, high degrees of inflation persistence (prolonged after-effects of inflation in response to temporary money growth shocks) and under-responsiveness (prolonged effects in response to permanent shocks) can arise in the context of standard wage-price staggering models.