If expected inflation equals actual inflation what is the

Question

The Phillips curve is given by

π = π_e- 0.5(u - 8) + ν,

where ν is a supply shock.

Price expectations are based on adaptive expectations:

πe = π_-1,

where π_-1 is last year's rate of inflation.

Initially, expected inflation is 4 percent and the supply shock is zero. Answer the following questions:

(a) If expected inflation equals actual inflation, what is the rate of unemployment?

(b) Now suppose in the following year, oil price shocks result in inflation taking a value of six percent and unemployment rising to 10 percent. What value does ν take?

(c) In the year after the oil shock, the value of ν returns to zero. What must happen to inflation to return the economy to the natural rate of unemployment?