The Phillips Curve and a Supply Shock
An economy has been at its natural rate of unemployment (5%) with inflation of 2% for several years, and inflation expectations are firmly anchored at 2%. Then a sharp energy price increase pushes actual inflation to 6%. Workers, seeing higher prices, revise their expected inflation upward to 5%. The central bank must decide whether to accommodate the shock or fight it. The sacrifice ratio is estimated at 2 (two percentage points of unemployment for one year to reduce inflation by one point).
1. Using the expectations-augmented Phillips curve, explain what happens to the short-run tradeoff as expectations adjust, and predict the long-run unemployment rate if the central bank does nothing.
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The expectations-augmented Phillips curve is π = πᵉ − β(u − u*) + shock. Initially πᵉ = 2%, and the energy shock shifts the curve up. When workers revise πᵉ to 5%, the short-run Phillips curve shifts upward: at any given unemployment rate, inflation is now 3 points higher. The short-run tradeoff exists only because expectations are temporarily fixed; once expectations fully adjust, the tradeoff disappears.
If the central bank does nothing and expectations settle at the new higher rate, unemployment returns to the natural rate (5%) but at a higher inflation rate (roughly 5–6%). The long-run Phillips curve is vertical at u* = 5% - there is no long-run tradeoff between inflation and unemployment. The judgment: accommodation buys lower unemployment only temporarily at the cost of permanently higher inflation expectations.
2. Suppose the central bank decides to reduce inflation back to 2%. Using the sacrifice ratio of 2, calculate the unemployment cost and explain the mechanism.
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To reduce inflation from 6% to 2% requires a 4-percentage-point disinflation.
Sacrifice ratio = 2 means 2 point-years of excess unemployment per 1 point of disinflation. So total excess unemployment = 4 × 2 = 8 point-years.
If spread over 2 years, that is 4 extra points of unemployment per year (e.g., unemployment rises from 5% to 9% for two years). If spread over 4 years, 2 extra points per year.
Mechanism: contractionary monetary policy raises interest rates, reduces investment and consumption, AD shifts left, output falls and unemployment rises above the natural rate. The slack weakens workers' bargaining power, so wage growth slows and inflation expectations fall. As πᵉ declines, the short-run Phillips curve shifts down and inflation falls. The cost is the cumulative excess unemployment - the sacrifice ratio captures this tradeoff.
3. A policymaker claims the central bank should not fight the shock because 'unemployment is already too high.' Evaluate this claim using the concept of credibility.
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The claim conflates the short-run and long-run. If the central bank accommodates the 6% inflation, expectations rise to 5% and become entrenched; future policy must then fight higher inflation at greater cost (the sacrifice ratio applies to a larger disinflation). Credibility matters: if the central bank is known to defend its 2% target, expectations stay anchored, the short-run Phillips curve shifts back down quickly, and the inflation spike is temporary with little output cost.
Conversely, if the central bank has a reputation for accommodation, expectations adjust upward faster and the inflation persists. The judgment: fighting the shock protects credibility and lowers the long-run cost, while accommodating it risks unanchoring expectations. However, if the shock is purely temporary and the central bank's credibility is strong, a modest, communicated tolerance may be optimal - the decision hinges on credibility, not on the current unemployment level alone.