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While A.W. Phillips originally observed a downward-sloping short-run trade-off (lower unemployment equals higher inflation), monetarists like Milton Friedman argued this is an illusion. In the long run, workers adjust their inflation expectations and demand higher nominal wages, nullifying any employment gains from inflation. Thus, the Long-Run Phillips Curve is perfectly vertical at the natural rate of unemployment, meaning monetary policy can only dictate inflation, not long-term job levels.