Phillips Curve Explorer: Inflation vs. Unemployment

Policy Controls

Demand stimulus 0.0

Supply shock (oil, etc.) 0.0%

Adaptive-expectations speed λ 0.30

Natural unemployment rate uₙ 5.0%

Economy State

Unemployment u

5.0%

Inflation π

2.0%

Expected πᵉ

2.0%

Quarter 0 — economy resting at the natural rate.

How it works

The expectations-augmented (Friedman–Phelps) Phillips curve links inflation to the unemployment gap, shifted by what people already expect prices to do:

π = πᵉ − β(u − uₙ) + ε
πᵉ(t+1) = πᵉ(t) + λ·(π(t) − πᵉ(t))

π — actual inflation this quarter. πᵉ — expected inflation, β = 1 (Phillips-curve slope). ε — a one-off supply shock (e.g. an oil-price spike).
Demand stimulus pushes unemployment below uₙ (Okun's-law shorthand: u = uₙ − 0.8·stimulus), sliding the economy down the current short-run curve — inflation rises above what people expected.
Adaptive expectations: each quarter people revise πᵉ toward the inflation they just observed, at speed λ. That revision shifts the whole short-run curve up, so the same low unemployment now needs even higher inflation to sustain — the accelerationist result.
The long-run Phillips curve is vertical at u = uₙ (the green plane): you cannot buy permanently lower unemployment with inflation once expectations catch up. Hold the stimulus and watch the trajectory spiral outward in inflation before any correction; release it and expectations slowly decay back toward the natural rate.
A supply shock shifts π directly (stagflation): unemployment and inflation can rise together, something the original 1958 Phillips curve could not explain.

Real-world relevance: this is the mechanism central banks target when they say policy must "anchor inflation expectations" — the same logic explains the 1970s stagflation and why disinflation (Volcker, 1980s) required a deliberate recession to reset πᵉ.

Current state (u, π) Short-run Phillips curve Long-run curve (u = uₙ) Trajectory trail

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