For this question, consider the DAD-DAS framework of the macroeconomy. The following equations hold throughout the parts of the question. IS Curve: Yi = Y+ (2 - ri )+ mite Aggregate Supply: M= * + ( Y - Y ) +v. Taylor Rule: it = (* + 2 ) + 0. ( 1 - 7" ) + dy ( Yi - Y ) Fisher Equation: Variable/Parameter Description Y Output at time t Y Natural level of output Real interest rate at time Shock to the money supply Demand shock Rate of inflation at time t Expected inflation for time VI Supply shock Nominal interest rate Inflation target (constant over time) Monetary policy parameter, positive Monetary policy parameter, positive The variables are described in the table above. The three shock terms, my, et, and 14, are stochastic and uncorrelated, with expected value of zero. Consider m, to be an arbitrary deviation from the intended monetary policy. (a) (3 A4 sheets, both sides) Suppose initially that ? = 71-1, so that expectations are adaptive. Solve for the equilibrium output and inflation at time t. Find the long run equilibrium output and inflation, and the long run real interest rate.(2 A4, front and back) Suppose initially that the Taylor rule is targeted for an inflation goal of 4%, so that #* = 4. Suppose that at time f - 1, the economy is at the long run equilibrium. At time t, the central bank decides instead to target an inflation rate of 2%, so that ** = 2. Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change. Y Short Run Long Run Illustrate your answer with a graph of the DAD-DAS model. Your graph should include the old equilibrium (period # - 1), the short run (period (), and the long run (well after period (). (2 A4 sheets, both sides) Suppose instead that consumers have rational expectations. Consider again the change in policy from the previous part of the question, lowering the inflation target from 4% to 2%. In particular, assume that the central bank announced the policy change. Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change. Y Short Run Long Run Illustrate your answer with a similar graph to the previous part of the question. (1 A4 sheet, one side) Which of the two types of expectations (adaptive or rational) yields higher output? Name one policy that the government can follow to help make expec- tations fit your answer (that is to say, name a policy that can help make expectations adaptive or rational, whichever was your answer). Briefly explain why