Consider an economy in long-run equilibrium with an inflation rate, π, of 12% (0.12) per year and a natural unemployment rate, u, of 6% (0.06). The expectations-augmented Phillips curve is
π = π^e - 2(u - u).
Assume that Okun's law holds so that a 1 percentage point increase in the unemployment rate maintained for one year reduces GDP by 2% of full-employment output.
a) Consider two-year disinflation. In the first year π = 0.04 and π^e = 0.08. In the second year π = 0.04 and π^e = 0.04. In the first year, what is the unemployment rate? By what percentage does output fall short of full-employment output? In the second year, what is the unemployment rate? By what percentage does output fall short of full-employment output? What is the sacrifice ratio for this disinflation?
b) Now consider a four-year disinflation according to the following table:
Year 1 2 3 4
π 0.08 0.04 0.04 0.04
π^e 0.10 0.08 0.06 0.04
What is the unemployment rate in each of the four years? By what percentage does output fall short of full-employment output each year? What is the sacrifice ratio for this disinflation?