Suppose that the economy responds to the real interest rate according to the following equation: Yt = Y* - Y* (1.5) (rt-1 - 0.02). The phillips curve is: pi = pi + 05(Y - Y*)/Y* + v. Potential GDP is S2.25 billion: expectations are adaptive: the 2018 inflation rate was 4%. A price shock sufficient to raise inflation by two percentage points hits the economy in 2019. In an effort to bring inflation down they had set interest rates at 5% in 2018. How should the federal resent react if they desire to bring inflation down to 3%. When will they achieve that goal? (Hint: maintain plenty of decimal places.)