Consider an economy in long-run equilibrium with an inflation rate, \(\pi\), of \(12 \%(0.12)\) per year and a natural unemployment rate, \(u_{n}\), of \(4 \%(0.04)\). The expectations-augmented Phillips curve iswhere \(\alpha\) is wage flexibility and \(u\) is the unemployment rate in the current year. Assume that Okun's law holds so that a 1 percentage point increase in the cyclical unemployment rate maintained for one year reduces GDP by 3\% of full-employment output.

a. Consider a two-year disinflation. In the first year, \(\pi=0.06\) and \(\pi^{e}=0.09\). In the second year, \(\pi=0.06\) and \(\pi^{e}=0.06\). What are the unemployment rates in the first and second years? By what percentage does output exceed the full-employment in the first and second year respectively? What is the sacrifice ratio for this disinflation?

b. Now consider a four-year disinflation according to the following table:

What is the unemployment rate in each of the four years? By what percentage does output fall short of the full-employment output each year? What is the sacrifice ratio for this disinflation?

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