How does the long-run Phillips Curve illustrate the relationship between inflation and unemployment in the context of monetary policy and aggregate supply?

The long-run Phillips Curve shows that there is no trade-off between inflation and unemployment in the long run. This means that while in the short term, increasing demand can lower unemployment by causing inflation, in the long run, the economy adjusts. For example, if a government tries to reduce unemployment by increasing money supply, it might create short-term jobs but eventually, prices will rise, leading to inflation without reducing unemployment. In the long run, the economy finds its natural rate of unemployment, where inflation stabilizes. Therefore, monetary policy must focus on maintaining stable prices rather than trying to lower unemployment through inflationary measures.