What Is the Phillips Curve?
The expectations-augmented Phillips curve says inflation equals expected inflation plus a slope times the output gap (or minus the unemployment gap) plus any supply shock, so there is no permanent trade-off between inflation and unemployment.
The Phillips curve is the relationship between inflation and the state of the economy. In its modern, expectations-augmented form (Friedman and Phelps) it is written:
inflation = expected inflation + α·(output gap) + supply shock
What it says
When the economy runs hot (a positive output gap, low unemployment), inflation rises above what people expected. When it runs cold, inflation falls below expectations. The slope α measures how strongly slack feeds into prices.
The crucial twist: expectations
Because expected inflation is in the equation, there is no permanent trade-off between inflation and unemployment. You can buy lower unemployment with surprise inflation only for a while; once expectations catch up, you are left with the higher inflation and unemployment back at its natural rate. The long-run Phillips curve is vertical. This insight, which the 1970s proved the hard way, reshaped macroeconomics.
The flat-curve debate
Empirically the slope α is small and has looked flatter in recent decades, which is why inflation can stay quiet even when unemployment is very low, and why supply shocks and expectations do so much of the work.
Sources: Friedman (1968) and Phelps (1967); see the methodology.