why is the long-run Phillips curve vertical

A. the long-run Phillips curve is vertical because it represents a relationship between two real variables in the long run
B. the long-run Phillips curve is vertical because the inflation rate is always the same
C. the long-run Phillips curve is vertical because any level of inflation can occur at the full-employment rate of unemployment in the long run
D. the long-run Phillips curve is vertical because the natural rate of unemployment never changes
E. the long-run Phillips curve is vertical because any level of unemployment can occur at the full-employment rate of inflation in the long run

C. the long-run Phillips curve is vertical because any level of inflation can occur at the full-employment rate of unemployment in the long run

In the long run, the economy will always return to its natural rate of unemployment, also known as the full-employment rate of unemployment. This means that regardless of the level of inflation, the economy will eventually adjust back to this natural rate of unemployment. As a result, the long-run Phillips curve is vertical, indicating that there is no trade-off between inflation and unemployment in the long run.