The Phillips curve is given by
π = πe- 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?