The Phillips curve hypothesis suggests there is an inverse relationship between unemployment and inflation, where lower unemployment leads to higher inflation. This relationship was observed in UK data from 1861-1957. The Keynesian explanation is that as aggregate demand increases, output and employment rise along the aggregate supply curve, leading to higher prices and wages. On a graph with inflation on the y-axis and unemployment on the x-axis, this shows as a negatively sloped Phillips curve. The government faces a dilemma of balancing unemployment and inflation levels.