AD - AS Model with stabilizing monetary policy

1. Suppose the aggregate demand for an economy is given by the following equation: Yt = mt - Pt + Vt where v = {vt-1+nt and nt is an i.i.d. random variable with 0 mean and o- variance. Aggregate supply is given by Yt = Pt Wt where wages are determined by previous expectations of the price at t Wt = (p<-1 + p<-2). The central bank tries to stabilize the economy from the shocks by setting the money supply as follows: 3 1 mt = A +-1t irre 4 where y is a policy parameter that the central bank sets. time t|t- (a) If workers knew pt (the price level at time t) when setting their wage wt, how would output and price be affected by the aggregate demand shocks? Graphically show the equilibrium. (b) Derive the equilibrium solutions for Yt and pt as functions of the previous shocks (V11, Vt-2, Nz), expected prices (p