The Phillips Curve is given as; IT = Te + (m + z) - au (1) Derive an equation for the natural rate of unemployment from the Phillips Curve First, consider the case where the expected inflation is anchored at the target interest rate n. (Notations: It is the target inflation rate, mis the expected inflation, and It is the inflation for year t.) (2) Suppose It = 3%, m = z = 0.1, and a = 1. What would be the unemployment rate (Ut) when It = 4%?Now, consider the case where the ination expectations are de-anchored. Assume the expected ination it\" is based on last year's ination rate Ht_1 (He 2 Ht 1) (3) Suppose Ht_1 = 3%. "What would he the unemployment rate (Ht) when Ht = 4%? (4) Suppose the production function is given by: Yr 2 N: : LU _ Ht) What happens to the potential output when the markup increases? (5) Suppose there is an increase in oil prices for year t and we model it as an increase in the markup. Draw the changes in the IS-LM-PC model for the following two cases: lCase 1. When the expected ination is anchored (Hf = E)? lCase 2. When the expected ination is de-anchored (Hf = ire1) (6) Suppose the economy stays at the same short-run equilibrium for the next period (t+1). Characterize the inflation rate at period t+1 for Case 1 and Case 2, respectively. (Compare them with the inflation rate at period t) (7) What would be the central bank's policy to stabilize the inflation and move to the NEW medium-run equilibrium