Monetary Policy (MP) is a powerful tool to lean against fluctuations in aggregate demand. But the episode of high and persistent inflation in the wake of thepandemic has highlighted that it faces significant challenges when confronted with other sources of shocks. Shocks to energy prices and disruptions in supply chains and shocks to inflation expectations have introduced a trade-off for central banks between letting inflation rise temporarily to preserve employment or accepting a recession to stabilize inflation. Distributional conflicts, either opportunistic increases in profit margins, known as “greedflation,” or persistent wage-price spirals as emphasized by Werning and Lorenzoni (2023), have further contributed to the challenges of managing inflation. Financial instability triggered by a fast monetary tightening has also been a source of concerns among central bankers and complicates the conduct of monetary policy. In the perspective of broadening the set of tools to regulate inflation, this paper analyzes the effectiveness of a tax on inflation policy (TIP), which would require firms to pay a tax proportional to the increase in their prices or wages. By giving direct incentives to firms to moderate their price increases without exacerbating

relative price distortions, we show that TIP is an effective instrument to control aggregate inflation, especially in the face of markups and shocks to inflation expectations. We do so by embedding a TIP in a workhorse New Keynesian model that includes several exogenous drivers of inflation and by deriving the optimal combination of MP and TIP in response to these shocks.