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

Q4. Oil shocks. The Phillips curve is I, =n,_1+BY,+z, Suppose that =1/2, and that in period 0, inflation is 2%. In period 1 there is an unexpected increase in the oil price so Z, =0.03. (a) Calculate inflation in periods 1, 2, 3, 4 and 5 if the output gap is kept at zero all the time. Explain the results. It, =0.02+0+0.03=5% 712 =0.05+0+0=5% 713=0.05+0+0=5% It =0.05+0+0=5% Is =0.05+0+0=5% As people come to expect higher inflation, it will continue. (b) Calculate inflation in periods 1, 2, 3 and 4 if the central bank counteracts the cost- push shock so the output gap is minus 2% in periods 1, 2 and 3 and zero thereafter. 7, =0.02-0.5 x 0.02 +0.03=4% 712 =0.04-0.5 x 0.02+0=3% 73=0.03-0.5 x 0.02 +0=2% It =0.02+0+0=2% Its=0.02+0+0=2% (c) Repeat the calculations from part (a), but now assume that the expected inflation rate is constant at 2%. Explain the results. It, =0.02+0+ 0.03=5% It,=0.02+0+0=2% 73=0.02+0+0=2% TA=0.02+0+0=2% Its =0.02+0+0=2% (d) Central bankers are sometimes accused of being obsessed with "credibility". Contrast the results from parts (a) - (c) and explain how these results might shed light on this apparent obsession. In part (c), we saw that when inflation expectations remain anchored at a constant value, then inflation will return to its previous level after a shock without the need for a recessionary period. But if inflation expectations are not anchored, then either the central bank will need to tolerate permanently higher inflation - as in part (a) - or else they will need to induce a recession to get inflation back in line - as in part (b). This is why central banks are so obsessed with credibility - if the public believes that they will return inflation to the 2% target, then they get to see inflation fall "for free". But if they are not credible, then they will need to pay for bringing inflation down by inducing a recession. And the costs are not small - the cumulative 6% that we found in part (b) is probably in the right ballpark, and this is actually a very big number. The GDP of the UK is about E1.5 trillion, so 6% of this is E90 billion. For reference, the largest skyscraper in Britain (the Shard) was built for just over E0.4 billion, the London Olympics cost about 69 billion, and the annual defence budget in the UK is E38 billion. So with the extra output we get from having credible bankers in just one oil shock, we can host the Olympics for the next