Given πt= πt-1 -0.5(Ut -0.06)
I) where economy start at inflation rate of zero at t-1. And at time t unemployment rate is at natural level, what is the inflation rate at time t ?
If the economy starts at an inflation rate of zero at t-1 and the unemployment rate is at its natural level at time t, we can substitute these values into the equation to find the inflation rate at time t:
πt = πt-1 - 0.5(Ut - 0.06)
Since πt-1 (inflation rate at t-1) is zero, we have:
πt = 0 - 0.5(Ut - 0.06)
If the unemployment rate is at its natural level, we can assume that Ut = 0.06. Substituting this into the equation, we get:
πt = 0 - 0.5(0.06 - 0.06)
πt = 0 - 0.5(0)
πt = 0
Therefore, the inflation rate at time t is zero.
To find the inflation rate at time t using the given equation πt = πt-1 - 0.5(Ut - 0.06):
1) Given that the economy starts at an inflation rate of zero at t-1, we can substitute πt-1 = 0 into the equation:
πt = 0 - 0.5(Ut - 0.06)
2) Since at time t the unemployment rate is at the natural level, we can substitute Ut = Un (where Un is the natural unemployment rate) into the equation:
πt = -0.5(Un - 0.06)
Therefore, the inflation rate at time t is -0.5 multiplied by the difference between the natural unemployment rate and 0.06.