suppose that the phillips curve is given bypit

Question

Suppose that the Phillips curve is given by:

Π_t = Π^e_t - (Π_t - 5%)

and expected inflation is given by

Π^e_t = Π_t-1

a. What is the sacrifice ratio in this economy?

Suppose that unemployment is initially equal to the natural rate and Π_t = 8%. The central bank decides that 8% inflation is too high and that, starting in year t, it will maintain the unemployment rate one percentage point above the natural rate of unemployment until the inflation rate has decreased to a new target of 2%.

b.  Compute the rate of inflation for years t, t + 1, t + 2, ...

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.?

d.  Now assume that Π^e_t = 0.5Π^t + 0.SΠ_t-1. For how many years must the central bank keep the unemployment rate above the natural rate of unemployment? What is the sacrifice ratio in this case?

e.  Finally assume that Π^e_t = Π^t. What is the sacrifice ratio in this case? What is the role of central bank credibility in disinflation process?