Consider the Phillips curve: Tl(t) = ETl(t) + 4 - 0.5u(t), where Tl(t) is inflation rate at t, ETl(t) is expected inflation for t, and u(t) is unemployment at t.
Notation: Tl(t) is pai (inflation) at time t.

1.What is the natural rate of unemployment u(n)?
2. If inflation expectation is static, by how much unemployment must rise in order to reduce inflation by 1%?
3.Combining Okun's law: gY = 3.5 - 2(u - u(n)), to reduce inflation by 1%, by how much GDP growth must be sacrificed (i.e., what is the sacrifice ratio)?
4. Suppose expectation is static with ETl(t) = 3(%). At t, unemployment u(t) is at the natural level. The authorities decide to bring the unemployment rate to 6% from time t+1 on, i.e., u(t+1) = u(t+2) = u(t+3) = ... = 6%. What is the rate of inflation at t+3?
5.Now suppose the public has adaptive expectation: ETl(t) = Tl(t-1), ETl(t+1) = Tl(t), and so on. Inflation at time t-1 is Tl(t-1) = 3%; the rate of unemployment u(t) at time t is at the natural level. The authorities decide to bring the unemployment rate to 6% from time t+1 on. What is the rate of inflation at t+3? (hint: derive inflation rate for t+1 and t+2 first)