Phillips Curve Explorer 2D: Inflation vs. Unemployment Plane

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 red line): you cannot buy permanently lower unemployment with inflation once expectations catch up. Hold the stimulus and watch the amber trail spiral outward in inflation; 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.

This 2D plotter drops the 3D version's depth (time) axis and instead draws the trajectory directly on the u–π plane, where the accelerationist spiral is easier to read at a glance — drag to pan, scroll/pinch to zoom.

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

Drag to pan · Scroll to zoom