2. Consider the following model of an open economy. =E+1+ky + ut = ye Etye+1 are + a + ve r = +E+9+1-9 + & (1) (2) All disturbances are white noise and have a constant variance. All parameters are positive. a. Briefly describe equations (1), (2) and (3). b. Suppose the central bank's objective function consists of a weighted sum of the variance of inflation and the output gap, respectively: V(y) + V(). (4) Suppose further that the central bank announces that it conducts optimal policy by discretion, and that it intends to ensure that the contemporaneous output gap and the rate of inflation are related as follows: Byt + = 0 (5) Elaborate on equation (5). What purpose does this equation serve? What type of rule does it represent? Are equations (4) and (5) independent of each other? c. Derive the reduced form equations for y, and z,. d. Can the central bank perfectly stabilize inflation and the output gap against demand-side disturbances? Comment on the way the output gap and the rate of inflation behave if the central bank bases the conduct of policy on equation (5). e. Suppose that instead of following equation (5), the central bank adopts an alternative rule: What kind of a rule is equation (6)? What are and ? (6) f. Derive the reduced form equations for y, and z, when policy is based on equation (6). Can the central bank perfectly stabilize inflation and the output gap against all three disturbances? (36 points) TURN OVER