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.
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.
I) To calculate the inflation rate at time t+1, t+2, and t+3, we will use the Phillips curve equation:
πt = πt-1 - 0.5(Ut - 0.06)
Given that the government wants to decrease the unemployment rate to 2% (0.02) in period t+1, we can substitute this value into the equation:
π(t+1) = πt - 0.5(U(t+1) - 0.06)
Substituting the desired unemployment rate:
π(t+1) = πt - 0.5(0.02 - 0.06)
Simplifying:
π(t+1) = πt - 0.5(-0.04)
π(t+1) = πt + 0.02
Therefore, the inflation rate at time t+1 is equal to the current inflation rate (πt) plus 0.02.
To calculate the inflation rate at time t+2 and t+3, we can apply the same equation:
π(t+2) = π(t+1) + 0.02 = πt + 0.02 + 0.02 = πt + 0.04
π(t+3) = π(t+2) + 0.04 = πt + 0.04 + 0.04 = πt + 0.08
So, the inflation rate at time t+2 is equal to the current inflation rate (πt) plus 0.04, and the inflation rate at time t+3 is equal to the current inflation rate (πt) plus 0.08.
II) At time t+4, the economy returns to the natural rate of unemployment. Since the Phillips curve equation represents the relationship between inflation and the deviation of unemployment rate from its natural rate, when the economy returns to the natural rate, the unemployment gap (Ut - 0.06) becomes zero. As a result, the equation simplifies to:
π(t+4) = π(t+3) - 0.5(0 - 0.06)
π(t+4) = π(t+3) + 0.03
This implies that the inflation rate at time t+4 will be equal to the inflation rate at time t+3 plus 0.03.
The main result of the policy implemented by the government is that it leads to an increase in inflation over time (from t+1 to t+3) in order to decrease the unemployment rate to the desired level. However, once the economy returns to the natural rate of unemployment at t+4, the inflation rate stabilizes, suggesting that the government's policy has achieved its goal of reducing unemployment without causing a sustained increase in inflation.