2. Assume that consumers and firms have rational expectations of inflation and that the Fed can choose the level of inflation. The loss function of the Fed is L(u, ) = u+22 and the Phillips curve governing the private sector behavior is given by u u"-4(T-ET) where u" 6%. Note: inflation, Tis denoted in percentage terms; that is, 5 means that inflation is 5%. Answer the following questions: (a) If the Fed could commit to 0.5, how much would unemployment be? (b) Is = 0.5 a time consistent policy? Defend your answer.