This is perhaps because in the long run the rate of unemployment it becomes equal to its natural rate. This assumption is based on the fact that a long run is a time period in which all the adjustment has taken place and the economy has returned to its full employment level. This means in the long run there will be no deviation of the civilian unemployment rate from its natural level and that any change in the inflation is not going to change the unemployment rate. this makes the Phillips curve perfectly inelastic to inflation and therefore it is vertical.
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