1. Suppose the aggregate demand for an economy is given by the following equation: y = m - P The nominal money stock is xed at t = 2500. There are 100 rms (N = 100} in the economy indexed with i and with the following demand and supply schedules: at 3,-.- Xi N+c 2m m 1 t 2 .E i. a 9+5@ lash where C is normal i.i.d. random variable with 0 mean, and p is the aggregate price index P = :er.11%- (a) Derive the Lucas aggregate supply function. (h) Assuming perfect information (E [p] = p) and using your answer in (a), solve for the level of aggregate output and the price level in equilibrium. (c) Now assume that rms have imperfect information on the price level p but es- timate it according to the following rational expectations forecast: E [pl pi] = 0.51%- + 0.5E [p]. Derive the Lucas aggregate supply function as a function of E [p]. Derive the goods market equilibrium and explain the economic intuition behind why this diifers from {a}. (d) Assuming an initial equilibrium as given (b), what would happen if there is an unanticipated and permanent increase in the nominal money supply to m' = 3000 (Le, E {m} = 2500)? Calculate the short-run level of aggregate output and the price level. (e) Graph your answer to (d) and discuss what would happen as the economy tran- sitions to the long-run