Tradeoff? Inflation and unemployment

The causes are unrelated.
In the short run, under particular conditions, there can be a relationship.

1958, British economist A.W. Phillips, his
research showed correlation between less unemployment and higher wages.

Later, economists found a correlation between less unemployment and higher price inflation.
They called this the Phillips Curve, even though Phillips correlated unemployment and wages.

Some economists thought that the Phillips curve offers a way to exploit this relationship: increase M when unemployment is high.

Some economists think that policymakers face a tradeoff between inflation and unemployment.

1968, Milton Friedman said inflation and unemployment are unrelated in the long run.

The long-run Phillips curve is vertical.

The non-vertical Philips curve is caused by sticky prices. If not stuck, then it is vertical.

Rational expectations is based on past information and expectations of the future.