(1) [24 points) An economy is described by the following equations AD : 1 = W - PI SRAS : 1 =7 +6 (p. - Pi) (1) (2) The natural logarithm of a variable is denoted in lower case. Suppose that the economy is initially at the long-run equilibrium, 30 = 7, and b > 0. Next, suppose that the money supply is expected to grow at some constant rate a. That is, the log money supply m follows the stochastic process, my=a+ m-1+ en (3) where & is unexpected monetary policy shock with zero mean. (a) [8 points] The central bank unexpectedly raises money supply. Briefly explain what happens to Equation (3), and illustrate graphically whether money is neutral or not in the short run. (b) [8 points] Use sticky-price model to explain how the central bank's action in part (a) above can influence the output gap (yr - 7) in the short run. (c) [8 points] Suppose that the economy has return to the original short-run equilibrium, 30 = 7- Now the central bank announces that it will increase in a in Equation (3). How, if at all, does this affect cyclical unemployment, when a actually rises? Use the Phillips curve to illustrate graphically