The article explores the best long-term inflation rate when using a mix of backward-looking and forward-looking Phillips curves in an economic model. By analyzing a basic New Keynesian model with sticky prices and rule-of-thumb behavior by price setters, the researchers found that having a small positive inflation rate is optimal under commitment by the monetary authority. The study shows that inflation starts from zero with a purely forward-looking Phillips curve and increases to its highest point with a purely backward-looking curve. Positive long-term inflation can lead to increased output when using a hybrid Phillips curve.