Consider an economy in long-run equilibrium with an inflation rate (π) of 0.08 per year and a natural unemployment rate of 0.05. Suppose Okun's law holds and a one percentage point increase in the unemployment rate reduces real output by 2% of full-employment output. The expectations-augmented Phillips curve is given by π=πe -2.5(u-0.05). Consider a two-year disinflation. In the first year, π = 0.06 and π e = 0.08. In the second year, π = 0.04 and πe =0.05.
(a) In the first year, what is the value of the unemployment rate?
(b) In the first year, by what percentage does output fall shor to full-employment output?
(c) In the second year, what is the value of the unemployment rate?
(d) In the second year, by what percentage does output fall short of full-employment output?
(e) What is the sacrifice ratio for this disinflation?