Translating AD-AS into the Phillips Curve

AD-AS and the Phillips curve are two pictures of the same economy. AD-AS plots the price level against real output. The Phillips curve plots the inflation rate against the unemployment rate. Because shifts in aggregate demand move price level and output together in a predictable pattern, each AD-AS equilibrium corresponds to exactly one point on the Phillips curve. When AD increases, the price level rises and output rises toward or beyond potential; that shows up on the Phillips curve as higher inflation and lower unemployment. When AD falls, the reverse happens on both diagrams at once.

The mapping runs through two relationships, not one. Rising output pulls unemployment down because firms hire more workers to produce more, roughly following Okun's rule of thumb. Rising output also pushes the price level up along the upward-sloping short-run AS curve, which shows up as inflation. So output doesn't become the Phillips curve's horizontal axis directly; it gets translated into unemployment first, while the price level change gets translated into an inflation rate. A recessionary gap, output below potential, means idle labor and capital, so unemployment sits above its natural rate and inflation is low or falling. An inflationary gap flips both.

This translation sets up everything else in the unit: short-run movements along the Phillips curve versus long-run shifts of it, the natural rate of unemployment anchoring the long-run vertical curve, and how expected inflation shifts the whole short-run curve when expectations catch up.