Here's the question.

Question 1. Suppose output, the price level, and money in an economy are given by '9': = F'l' Mm; Et-lCmrtl) Pr = Et-1(mt) + (1 b)(mt Etl (mrll mt = X+P08r +P15tl Where y; is output, p; is the price level, m; is money, and 37, A, p0, p1, and b are constants. Lower case variables are in logs, and the shocks 8: are mean zero and independent over time. a) Find the level of output in this economy. (Hint: nd the difference between actual and expected money supply and substitute into yt.) b) Find the level of ination in this economy. (Hint: use your answer in part a and the denition of ination 11} := p; pt_1.) c) What should the de choose for p0 and p1 if its goal is to maintain output stability? (Hint: minimize the variance of output by choosing the parameters appropriately.) d) What should the Fed choose for pa and p1 if its goal is to maintain ination stability? e) What should p9 and p1 be if the goal is to have both output and ination stability