Consider the expectations adjusted Phillips’s curve and assume that expected inflation is given by πet = πt-1. Suppose that unemployment is initially equal to the natural rate and that π=10%. The central bank decides that inflation is too high and that, starting in year t, it will maintain the unemployment rate 1% point above the natural rate until the inflation rate has decreased to 2%. (a) What is the sacrifice ratio in this economy [Hint: the sacrifice ratio is the percentage of a year’s excess unemployment needed to reduce inflation by 1%. For a Philips curve given as πet − πt −1 = −α (ut − un ), the sacrifice ratio is 1/α]? (b) Compute the rate of inflation for year t, t+1, t+2, t+3, …, t+8. (c) For how many years must the central bank keep the unemployment rate above the natural rate of unemployment? Is the implied sacrifice ratio consistent with your answer to (a)?
Consider the expectations adjusted Phillips’s curve and assume that expected inflation
is given by πet = πt-1. Suppose that
and that π=10%. The central bank decides that inflation is too high and that, starting in
year t, it will maintain the unemployment rate 1% point above the natural rate until the
inflation rate has decreased to 2%.
(a) What is the sacrifice ratio in this economy [Hint: the sacrifice ratio is the percentage of
a year’s excess unemployment needed to reduce inflation by 1%. For a
given as πet − πt −1 = −α (ut − un ), the sacrifice ratio is 1/α]?
(b) Compute the rate of inflation for year t, t+1, t+2, t+3, …, t+8.
(c) For how many years must the central bank keep the unemployment rate above the natural rate of unemployment? Is the implied sacrifice ratio consistent with your answer to (a)?
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