Costs of high inflation, costs of low inflation

In the early 1980s, central banks switched to inflation targeting (an inflation objective) at a time when inflation was high. The objective of monetary policies was then to reduce the costs of high inflation: loss of purchasing power for holders of non-indexed incomes, distortions of relative prices, excessive taxation of holders of money. But nowadays , central banks have maintained inflation targeting (the inflation target: 2%) while inflation has become low, lower than the target. This means that they have to restore inflation. Keeping inflation targeting means that central banks believe that the costs of low inflation are as high as those of high inflation. But what are the costs of low inflation? The inflation tax is low, which makes it necessary to increase other taxes; at equilibrium, nominal interest rates are low, which limits the ability of monetary policy to react in the event of a recession. Central banks’ choice shows that they believe these costs are significant .