[2) [24 points] An eccncrm' is described by the following equations: AD : y: = m: p: SEAS: yz=+b [PaP3) The natural logarithm of a variable is denoted in lower case. Suppose that the economy is initially at the longrun equilibrium, m = 5', and l5 2 . Next1| suppose that the monejr supply is expected to grow at some constant rate a. That is, the log money supply In follows the stochastic processI m=a+m_1 +5:. (1) Where E: is unexpected monetary policy shock with zero mean. (a) [8 points] The central bank unexpectedly reduces money supply. Briey,r explain what happens to Equation (1}I and illustrate graphically whether money is neutral or not in the short run. (h) [8 points] Use the imperfect-information model to explain how the central banks action in part (a) above can inuence the output gap (y, g} in the short run. (c) [8 points] Suppose that the economy has return to the original shortrun equilibrium, '90 = y. Now consider an increase in o in Equation (1). How, if at all1 does this affect cyclical unemploym-t? Use the Phillips curve to illustrate graphically