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Using UK consumer price microdata, we report that aggregate price flexibility varies substantially over time and induces significant non-linearity in inflation. In a regime of high flexibility, the half-life of inflation drops by 50% and its volatility rises considerably. Such asymmetry arises naturally from state-dependent pricing, of which we find ample evidence in the data, particularly following the Great Recession. Neglecting this property may lead to a systematic underprediction of inflation, as seen in the post-pandemic inflation surge. Tracking real-time movements in price flexibility is crucial for assessing inflation dynamics and informing monetary policy decisions.