1. Optimal monetary policy at the zero lower bound under discretion. Consider the standard New Keynesian model with a zero lower bound constraint It = Et$t+1 9161: Ett+1 H} [1) 1T: = BEtWHl + El": (2) 7'it = max [0: rt + t + 95337:] [3) Assume that rt follows a two state Markov process 15 a where D U in the high state. {a} (b) {C} {d} Show that when we are in the high state such that r; 2 TH it must be the case that 333:0, x320, andz'ter. Show that when we are in low state such that r; 2 TL