The article explores how monetary policy should react to changes in oil prices caused by supply and demand shocks. It suggests that when wages are flexible, it's best to stabilize core inflation by adjusting interest rates in response to demand or supply shocks. If prices and wages are sticky, core inflation moves in the opposite direction to the shock. The study finds that stabilizing CPI inflation only leads to small welfare losses if demand shocks drive oil prices. Analysis of U.S. data shows that both types of shocks have had minimal effects on core inflation. The federal funds rate goes up with a demand shock but down with a supply shock, aligning with the model's predictions for a policy that maintains core inflation stability.