Question 1 Suppose that the Phillips curve is given by 71} = TIT: + 0.1 2.2th, where an is the ination rate, at? is the expected ination rate, and at is the unemployment rate. The ination expectations are formulated by 71'? = 61114 and 6 is initially equal to zero. a) What is the natural rate of unemployment? Suppose that the actual 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. b) Calculate the rate of ination in years if, t + 1, t + 2, t + 3 and t + 4. c) How long does it take the natural rate of unemployment to decline to 3%? d) Do you believe the answer given in (b)? Why or why not? (Hint: Think about how people are likely to form expectations of ination.) Now suppose that in year t + 5, 6 increases from 0 to 1. Suppose that the government is still determined to keep the unemployment rate at 3% forever. e) What expectations formation does 9 = 1 represent? Why might 6 increase in this way? What will the ination rate be in years t + 5, t + 6,15 -l 7? f) How does the natural rate of unemployment depend on 8? g) Do you believe the answer given in (e)? Why or why not