Question

Consider an economy in long-run equilibrium with an inflation rate π of 12%(0.12) per year and a natural unemployment rate uˉ

of 6%(0.06). The expectationsaugmented Phillips curve is π = πᵉ−2(u−uˉ ) Assume that Okun's law holds so that a 1 percentage point increase in the unemployment rate maintained for one year reduces GDP by 2,0% of full-employment output.
a. Consider a two-year disinflation. In the first year, π=0.04 and πᵉ = 0.08. In the second year, π=0.04 and πᵉ = 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 fullemployment output?

Answer 1

In the first year of disinflation, the unemployment rate rises to 8%, causing output to fall short of full employment by 4%. In the second year, the unemployment rate remains at the natural rate of 6%, and there is no shortfall in output.

Step-by-step explanation:

The student has asked about the implications of disinflation in an economy based on the expectations-augmented Phillips Curve and Okun's Law. According to the given equations, in the first year with an actual inflation rate (π) of 4% and expected inflation rate (πē) of 8%, the unemployment rate can be calculated with the formula π = πē - 2(u - ſu), where ſu is the natural rate of unemployment. Plugging in the values, we get 0.04 = 0.08 - 2(u - 0.06), which simplifies to u - 0.06 = 0.02, giving us an unemployment rate (u) of 8%. Using Okun's Law, a 2 percentage point increase in unemployment (from 6% to 8%) would result in a 4% reduction in GDP, meaning output falls short of full-employment output by 4%.In the second year, with an actual inflation rate of 4% and expected inflation rate now aligned at 4%, using the same formula, we have 0.04 = 0.04 - 2(u - 0.06). This simplifies to u = ſu, which means the unemployment rate remains at the natural rate of 6%, and therefore, the output does not fall short of full-employment output.