Macroeconomics question for AD-AS equation:

1. Consider the European economy with the following AD-AS equations: AD: 1", = a, Err1m, 73') where E = 0.5.717 = 2 A5171} = II? + 1717', where = 0.5 a. The European Central Bank's inflation target is it = 2. Find the equilibrium GDP gap, 17,, and inflation, 71}, as a function of 1:5, and 5,. b. Assume 7:? = nt_1, and initial no = 2. The economy is at the long run equilibrium with a, = 0 except for period t = 1 when there is a temporary AD shock and 311 = 1. Find what happens to the GDP gap and inflation for periods 1 and 2 [you can either do Excel or solve algebraically). c. Assume that the US economy has the exact same equations for AD and AS as Europe, but the Federal Reserve is more dovish against inflation, so that their 771 = 0.5. Facing the same one-period shock of 11 = 1, what happens to the US's GDP gap and inflation for periods 1 and 2? Who has the deeper recession in period 1 and who appears to recover faster in the subsequent periods? d. Back to the European economy, if inflation expectations are rational and the Central Bank's policy is partially credible so that at? = 0.5(7rr_1) + 0.5(1'r), how does your answer in part be change? Calculate and state whetherthe recession is worse or not