The welfare costs of inflation result from many factors: the potential costs to households and firms that result from efforts to insure themselves against inflation or from confusion regarding real and nominal prices; distortions to the financial system related to inflation; imperfect indexation of the taxation, especially of capital income, and the related distortions to economic activity; and the costs associated with a slow adjustment of nominal prices and wages.
The costs of inflation imply that central banks should aim for low measured inflation.