Solve the problem in the image, showing work

III- Dynamic inconsistency (8 points) Suppose a central bank has the following loss function over inflation 7 and unemployment u: L = 12 + 2(u - U)2 and the Phillips curve is given by u = un - a(1 - me ) where u is unemployment target, u" is the natural unemployment, and me is expected inflation. Suppose that inflation expectations are anchored 2 percent. If a = 1 = 1 and u = u", what rate of inflation will the central bank choose? Show your work