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)?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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)?

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