Consider an Economy in Long-Run Equilibrium with an Inflation Rate

Essay

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 = π^e - 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 π^e = 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 short of 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?