The Phillips Curve is given as; 1= n+(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 m. (Notations: It is the target inflation rate, " is the expected inflation, and n is the inflation for year t.) (2) Suppose 1 = 3%, m = z = 0.1, and a = 1. What would be the unemployment rate (up) when T = 4%?Now, consider the case where the inflation expectations are de-anchored. Assume the expected inflation or is based on last year's inflation rate At-1 (n = It-1) (3) Suppose It-1 = 3%. What would be the unemployment rate (Ut ) when it = 4%? (4) Suppose the production function is given by: Yt = Nt = L(1 - ut) What happens to the potential output when the markup increases? (5) Suppose there is an increase in oil prices for year f and we model it as an increase in the markup. Draw the changes in the IS-LM-PC model for the following two cases: Case 1. When the expected inflation is anchored (; = 1)? Case 2. When the expected inflation is de-anchored (nf = It-1)(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