The correct answer is given in red, but i struggled to understand , please explain it step by step, thank you!

Q6. Assume that B=1, n; = 1,_,, and z, =0, so the Phillips curve is (a) Suppose the inflation rate is 9% and the central bank wants to bring it down to 3% in the next year. What output gap should it try to achieve? 0.03=0.09+Y Y=-0.06 They need to achieve a 6% output gap. (b) Suppose the situation is as above but the central bank wants to bring down inflation within three periods. What path for the output gaps would you suggest it aims for? Why? On the one hand, a smaller output gap over several periods may be preferred to a large output gap in one period. If expected inflation is equal to inflation in the previous period, an output gap of - 2% will give It =0.09-0.02=7% JI,=0.07-0.02=5% 72=0.05-0.02=3% On the other hand, a clear policy to quickly reduce inflation may affect inflation expectations if they are not completely backward-looking. In this way, a "big bang" approach may lead to a lower total loss in terms of production and employment