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
?
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), 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)
Notation: Tl(t) is pai (inflation) at time t.
1.What is the natural rate of unemployment u
?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
), 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)