Optimal Policy When the Inflation Target is not Optimal

I assess the optimal policy to be followed by a welfare-concerned central bank when assigned an inflation target that is not necessarily welfare-optimal. I treat the inflation target as the trend inflation and I have three main contributions: (i) a welfare-based loss function fully derived under trend inflation, showing how the non-optimal inflation target acts as an extra inefficiency source; (ii) I show that the trend inflation does affect the relative weight of the output gap: they are inversely related; (iii) under trend inflation, I derive time consistent optimal policies with both unconditional and timeless commitment, and I show how to translate the pursuit of the inflation target into an additional constraint in the minimization step.