What does the Long Run Phillips Curve suggest about the relationship between inflation and unemployment when adaptive expectations are considered?

The Long Run Phillips Curve suggests that there is no trade-off between inflation and unemployment in the long run, especially when we consider adaptive expectations. This means that while people might think they can benefit from lower unemployment by accepting higher inflation, over time, they adjust their expectations. For example, if the government tries to lower unemployment by increasing inflation, workers will eventually expect higher prices and demand higher wages. As a result, any short-term decrease in unemployment will not last, and the economy will return to a natural rate of unemployment, regardless of inflation levels. Therefore, in the long run, the curve is vertical, indicating that inflation does not affect unemployment.