I. Philips Curve

Suppose that the Philips curve is given by π_t = π^e_t + 0.1 -2u_t

1. What is the natural rate of unemployment? 
2. Assume π^et = θπt-1 and suppose that θ is equal to 0. 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. Determine the rate of inflation in years t, t+1, t+2, and t+5.
3. Do you believe the answer given in (b)? Why or why not? (Hint: Think about how people are likely to form expectations of inflation.)
4.  Now suppose that in year t+5, θ increases from 0 to 1. Suppose that the government is still determined to keep u at 3% forever. 
5. Why might θ increase in this way? What will the inflation rate be in years t+5, t+6, and t+7. 
6. Do you believe the answer given in (d)? Why or why not?