Question

Given πt= πt-1 -0.5(Ut -0.06)
I) Supppse the government want to decrease the unemployment rate to 2%(0.02)in perion t+1. The government want to keep that unemployemnt rate for three periods t+1, t+2 and t+3. Using phillips curve above calculate the inflation rate at time t+1, t+2 and t+3.
II) At time t+4 the economy rzturn to natural rate, what happen to the inflation rate t+4 ? What is the main result of the policy implemented by the government.

Answer 1

I) To calculate the inflation rate at time t+1, t+2, and t+3, we need to solve for πt+1, πt+2, and πt+3 in the Phillips curve equation.

Given:
πt = πt-1 - 0.5(Ut - 0.06)

Substitute the desired unemployment rate of 2% (0.02) for Ut.

At time t+1:
πt+1 = πt - 0.5(0.02 - 0.06)
= πt + 0.02

At time t+2:
πt+2 = πt+1 - 0.5(0.02 - 0.06)
= (πt + 0.02) - 0.5(-0.04)
= πt + 0.02 + 0.02
= πt + 0.04

At time t+3:
πt+3 = πt+2 - 0.5(0.02 - 0.06)
= (πt + 0.04) - 0.5(-0.04)
= πt + 0.04 + 0.02
= πt + 0.06

So, the inflation rate at time t+1 is πt + 0.02, at time t+2 is πt + 0.04, and at time t+3 is πt + 0.06.

II) At time t+4, the economy returns to the natural rate of unemployment. This means that Ut is equal to 0.06. Substituting this into the Phillips curve equation:

πt+4 = πt+3 - 0.5(0.06 - 0.06)
= πt+3

Therefore, the inflation rate at time t+4 is the same as the inflation rate at time t+3, which is πt+3.

The main result of the policy implemented by the government is that the inflation rate remains constant at πt+3 after the economy returns to the natural rate of unemployment.