An Optimal Taylor Rule Consider an economy with staggered price setting whose equilibrium dynamics are described by the system 1 . xt = E(% E1773\" P) + Et$t+1 + 5t 1'1": = EtT-\"Hl + H1113: + \"Ht, where at and at are iid, mutually uncorrelated, shocks with variances given by or? and 03, respectively. Here, at can be interpreted as a demand shock. Assume that the monetary authority adopts a simple Taylor rule of the form it = P + 11's\":- (a) Solve for the equilibrium processes for the output gap and ination, as a function of the exogenous supply and demand shocks. (b) Determine the value of the ination coefcient 1,57: that minimizes the central bank's loss function amuarrt) + warren). (c) Discuss and provide intuition for the dependence of the optimal ination coef- cient on the weight an; and the variance ration %. What assumptions on parameter values would warrant an aggressive response to ination implemented through a large 11:\"? Explain