2. Consider the following model of an economy. t Ett+1+Kyt + ut Yt EtYt+1-a(ie-Et+1) + Ve it = 0.5y + 1.5m (3) E(L) = V(v) + uV () (4) Both disturbances are white noise and have a constant variance. All parameters are positive. a. Briefly describe equations (1) and (2). b. Elaborate on equation (3). What purpose does this equation serve? What type of rule does it represent? c. What purpose does equation (4) serve? d. Derive the reduced form equations of y, and r,. e. Can the central bank perfectly stabilize inflation and the output gap? Comment on the way the output gap and the rate of inflation behave if the central bank bases the conduct of policy on equation (3). g. f. Do you believe that equation (3) is consistent with optimal policy? Explain. Friedman (2013) discusses how the central bank conducts monetary policy during a financial crisis. Briefly elaborate on the changes to the model he proposes. Why are those changes necessary? (36 points) 2. Consider the following model of an economy. t Ett+1+Kyt + ut Yt EtYt+1-a(ie-Et+1) + Ve it = 0.5y + 1.5m (3) E(L) = V(v) + uV () (4) Both disturbances are white noise and have a constant variance. All parameters are positive. a. Briefly describe equations (1) and (2). b. Elaborate on equation (3). What purpose does this equation serve? What type of rule does it represent? c. What purpose does equation (4) serve? d. Derive the reduced form equations of y, and r,. e. Can the central bank perfectly stabilize inflation and the output gap? Comment on the way the output gap and the rate of inflation behave if the central bank bases the conduct of policy on equation (3). g. f. Do you believe that equation (3) is consistent with optimal policy? Explain. Friedman (2013) discusses how the central bank conducts monetary policy during a financial crisis. Briefly elaborate on the changes to the model he proposes. Why are those changes necessary? (36 points)