suppose that the economy is in a long run equilibrium where the inflation rate is greater than the optimal rate i' and then the central bank acts to reduce the inflation rate to i".

(1) suppose that the central bank decides to take drastic action and reduces the inflation rate within one period to i". also suppose that the private sector has adaptive expectations, so that the current expected inflation rate is last period's actual inflation rate. Show in a diagram the path than real aggregate output and the inflation rate take over time.

(2)now, suppose that the central bank takes the drastic strategy in part 1, but that the private sector has rational expectations so that i=ie. again, show in a diagram the path followed by output and the inflation rate over time.