Question

4. (2.5 PTS) Assume the following Phillips curve: where π is the inflation rate, π et is the expected inflation rate, ut the unemployment rate, un the natural rate of unemployment. The rule of expectations is π e.-π t-1 The economy is initially (t-0) in medium term equilibrium, with the unemployment rate equal to 10% and the inflation rate equal to 8%. a) Suppose the monetary authority decides to lower the inflation rate to 2%. It faces two options: i) carry out this reduction in 3 years (2 point reduction per year) or ii) do it in 2 years (3 point reduction per year). Estimate the consequences on the unemployment rate of both policies. Comment on the pros and cons of both policies. b) Suppose the expected inflation was π.-0,5 explain this new expected inflation formation? + 0,5 -1. what reasons could c) Solve again the question in part a) and comment on the results comparing them to the ones from using the first way of forming expectations. Explain your results and use graphics and a table to present them

Answer 1

The equation of Phillips curve is given as:
$\pi {_{t}} - \pi_{t}^{e} = -(0.6)\times (u{_{t}}-u{_{n}}})$
First, we try to find the natural rate of unemployment, which occurs when the inflation rate and expected inflation rate are the same. Therefore, natural rate of employment is equal to the rate of employment given at t=0 (since it is in medium term equilibrium).

Thus, we find $u{_{n}$ = 10%
We use the given inflation rate as the expected inflation for the next year. The government reduces inflation using one of two methods: let us explore each.

Case I] Inflation rate reduced to 2% (from 8%) over a period of 3 years : a two point decrease every year. In such a case, the three years pan out in the following way.

Year 1 : $\pi {_{t}} - \pi_{t}^{e} = -(0.6)\times (u{_{t}}-u{_{n}}})$
inflation rate is now 6%, expected inflation rate is 8%, natural rate of unemployment is 10%.
6-8 = -(0.6)x(u - 10)
20/6 = u - 10
u = 13.33%

Year 2: inflation rate is now 4%, expected inflation rate is 6%, natural rate of employment is 10%.
4-6 = (-0.6)x(u-10)
u = 13.33%

Similarly, Year 3 also yields an unemployment rate of 13.33%. The unemployment rate remains constant over the course of three years.

Case II] Inflation rate reduced to 2% (from 8%) over a period of 2 years : a three point decrease every year. In such a case, the three years pan out in the following way.

Year 1 : $\pi {_{t}} - \pi_{t}^{e} = -(0.6)\times (u{_{t}}-u{_{n}}})$
inflation rate is now 5%, expected inflation rate is 8%, natural rate of unemployment is 10%.
5-8 = -(0.6)x(u - 10)
30/6 = u - 10
u = 15%

Year 2: inflation rate is now 2%, expected inflation rate is 5%, natural rate of unemployment is 10%.
2-5 = (-0.6)x(u-10)
u = 15%

Again, rate of unemployment remains constant, however, the rate is higher than the one we witnessed in the case prior to this.

If the relation between expected rate of inflation and actual inflation rate changes to:
$\pi_{t}^{e} = 0.5{\pi_{t}} + 0.5{\pi_{t-1}}$

Repeating the cases again, we have

Case I b]

Year 1 : $\pi {_{t}} - \pi_{t}^{e} = -(0.6)\times (u{_{t}}-u{_{n}}})$
inflation rate is now 6%, expected inflation rate is 7%, natural rate of unemployment is 10%.
6-7 = -(0.6)x(u - 10)
10/6 = u - 10
u = 11.66%

Year 2: inflation rate is now 4%, expected inflation rate is 5%, natural rate of unemployment is 10%.
4-5 = (-0.6)x(u-10)
u = 11.66%

Year 3: inflation rate is now 2%, expected inflation rate is 3%, natural rate of unemployment is 10%.
u = 11.66%

Case II b]

Year 1 : $\pi {_{t}} - \pi_{t}^{e} = -(0.6)\times (u{_{t}}-u{_{n}}})$
inflation rate is now 5%, expected inflation rate is 6.5%, natural rate of unemployment is 10%.
5-6.5 = -(0.6)x(u - 10)
2.5 = u - 10
u = 12.5 %

Year 2: inflation rate is now 2%, expected inflation rate is 3.5%, natural rate of unemployment is 10%.
2-3.5 = -(0.6)x(u-10)
u = 12.5%

You can see this phenomena on the graph here: