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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, 7) = u + 272 and the Phillips curve governing the private sector behavior is given by u = u" -4(7 -Ex) where u" = 6%. Note: inflation, 7 is denoted in percentage terms; that is, 7 = 5 means that inflation is 5%. Answer the following questions: (a) If the Fed could commit to 7 = 0.5, how much would unemployment be? (b) Is 7 = 0.5 a time consistent policy? Defend your