Consider an economy in long-run equilibrium with an inflation rate (?) 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
? = ?e - 2.5 (u - 0.05).
Consider a two-year disinflation. In the first year, ? = 0.06 and ?e = 0.08. In the second year, ? = 0.04 and ?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?
(a) .06 = .08 - 2.5(u - .05), so u = .058.
(b) .058 - .05 = .008 = 0.8%; 0.8 × 2% = 1.6%.
(c) .04 = .05 - 2.5(u - .05), so u = .054.
(d) .054 - .05 = .004 = 0.4%; 0.4 × 2% = 0.8%.
(e) sacrifice ratio = output shortfall/change in inflation rate = (1.6% + 0.8%)/(8% - 4%) = 2.4/4 = 0.6.
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