The five equations that make up the dynamic AD-AS model are Y =Y, -a(r, -p)+, X, = EX, + #(Y, - F) +4, i =x+p+0_(x - x ) ) +8, ( X - F).a) Derive the long-run equilibrium for the dynamic AD-AS model. Assume there are no shocks to demand or supply (e, = v, = 0) and inflation has stabilized (It = nit-1). Be sure to show each step you follow. b) If the central bank decides to reduce the target inflation rate from 5% to 2%. Using a graph of the dynamic AD-AS model, show the effect of this change. What happens to the nominal interest rate immediately after the policy change and in the long run? Explain. c) Suppose that there is a shock to aggregate supply (for example, a sudden increase in the oil price), which causes v, rise to 1 percent for one period and subsequently returns to zero. Using a graph of the dynamic AD-AS model, show the effect of this change on output and inflation rate. What happens to the nominal interest rate immediately after the policy change and in the long run? d) Assume that the central bank decides to increase the response of interest rate to inflation (by increasing 0,), how does this change in policy alter the response of the economy to a supply shock you discussed in part c)? Give an economic explanation