Have you learned the squared Loss function of central bank, it is just a trade off between output target and inflation.
The best solution is not possible , zero inflation but also zero output growth, stational or stagnation.
Then people try to get the second best solution, a little inflation and also a little output growth, but it should let the utility from growth greater than loss of the confidence of market.And it is also not possible, because the market will not be always fooled by the central bank. They adjust their inflation expectation at next period automatically. It is a process without end, then the second best solution is also not possible
The third best solution, that means the president of central bank weights inflation bigger than government, to reduce the inflationsbias.
I think it is quite useful to derive these squared loss function.
For your reference