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?
What will be an ideal response?
| (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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