The economic concept describing the inverse short-run relationship between inflation and unemployment is the Phillips curve.
Economist A. W. Phillips identified an apparent inverse relationship between wage inflation and unemployment in a 1958 study of the United Kingdom. Later economists applied the idea to price inflation, producing the familiar trade-off: stronger demand can reduce unemployment while increasing inflationary pressure.
The qualification “in the short run” matters. Expectations-augmented versions of the model allow the curve to shift when people and businesses revise their inflation expectations. In the long run, economists such as Milton Friedman and Edmund Phelps argued that unemployment tends toward a natural rate, so permanently higher inflation cannot reliably buy permanently lower unemployment.
The Phillips curve is often confused with a claim that inflation and unemployment must always move in opposite directions. Supply shocks, such as an oil-price surge, can produce both high inflation and high unemployment—a combination known as stagflation.