# Question

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*.
(a) 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 that real aggregate output and the inflation rate take over time.
(b) Now, suppose that the central bank takes the drastic strategy in part (a), 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.
(c) Now, suppose that the central bank takes a gradual strategy of reducing the inflation rate in a number of steps to i*. Under a gradual strategy, show what differences there are between adaptive and rational expectations for the path of output and the inflation rate over time.
(d) Explain your results in parts (a) to (c), and comment on the early 1980s period in the United States.

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