explain why it is not a sustainable policy to attempt to keep unemploymment below its natural level according to the augmented Phillips Curve model.
The augmented Phillips Curve allows for shifts in the tradeoff between inflation and unemployment as the core-rate of inflation changes. According to this model we can have an unemployment rate below the natural rate of unemployment (assuming away the complication of supply shocks) if our actual rate of inflation is above the core of inflation. The fundamental reason for the nonsustainability of such a low rate of unemployment comes from the fact that the core rate of inflation is based upon expectations of future inflation and these expectations are related to historical experience. Eventually after a string of quarters where the actual rate of inflation has exceeded the core rate of inflation, the core rate of inflation would begin to ratchet upwards with rising inflationary expectations. That means the Phillips Curve tradeoff would shift upwards and the lower rate of unemployment would require a rate of inflation even higher than before. Core-inflation would follow (or even anticipate) this acceleration of inflation rates.