Question

5. Mutations of the Phillips curve

Suppose that the Phillips curve is given by

Pi_t = (Pi_t)^e + 0.1 - 2u_t

(Pi_t)^e = (1-theta) - Pibar + thetaPi_t-1

and suppose that u is initially equal to 0 and pQ is given and does not change. It could be zero or any positive value. Suppose that the rate of unemployment is initially equal to the natural rate. In year t, the authorities decide to bring the unemployment rate down to 3% and hold it there forever.

a. Determine the rate of inflation in periods t + 1, t + 2,t + 3, t + 4, t + 5. How does pQ compare to pibar?

2. Do you believe the answer given in (a)? Why or why not? (Hint: Think about how people are more likely to form expectations of inflation.)
   Nowsupposethatinyeart + 6,uincreasesfrom0to1.Suppose that the government is still determined to keep u at 3% forever.

3. Why might u increase in this way?

4. What will the inflation rate be in years t + 6, t + 7, and

   t + 8?

5. What happens to inflation when u = 1 and unemploy-

   ment is kept below the natural rate of unemployment?

6. What happens to inflation when u = 1 and unemployment

   is kept at the natural rate of unemployment?

Answer 1

e)

Therefore, the inflation rate accelerates each year if the government keep the unemployment rate below the natural level forever.

f)

On the other hand, if the unemployment rate is equal to its natural rate the inflation will be equal to forever.