1. Consider a simple Taylor rule with an ination target of zero: it 2 17+ @3th + gbyt, where it is the nominal interest rate, F > 0 is the natural real interest rate, 71'; is ination, and Q. is the output gap. The aggregate demand and supply equations are given by Q: = 5(rt_1 f) + pgt_1 + a? and Tl't : m4 + 053:}: + 8?, where a? and 5;? are demand and supply shocks, respectively. The relationship between it and art is given by the Fisher identity (assuming expected ination is equal to current ination): rt : it 7rt. All parameters (f, g6,\" gay, ,6, p, 0:) are > 0. Further, assume that the following parameters (0:, B, p, qy O. (c) Suppose that w > 1. Show that it is possible to stabilize ination after only one period (i.e., 1T1 = 0). At what value of gt.\" would this occur? (d) What can you say about the role of the value of gt\" for ination stabilization? But what is the cost of a higher ratio of gag/(by