<Dd> π t = β E t (π t + 1) + κ y t (\ displaystyle \ pi _ (t) = \ beta E_ (t) (\ pi _ (t + 1)) + \ kappa y_ (t)) </Dd> <P> where κ = α (1 − (1 − α) β) φ 1 − α (\ displaystyle \ kappa = (\ frac (\ alpha (1 - (1 - \ alpha) \ beta) \ phi) (1 - \ alpha))). The current expectations of next period's inflation are incorporated as β E t (π t + 1) (\ displaystyle \ beta E_ (t) (\ pi _ (t + 1))) </P> <P> In the 1970s, new theories, such as rational expectations and the NAIRU (non-accelerating inflation rate of unemployment) arose to explain how stagflation could occur . The latter theory, also known as the "natural rate of unemployment", distinguished between the "short - term" Phillips curve and the "long - term" one . The short - term Phillips Curve looked like a normal Phillips Curve, but shifted in the long run as expectations changed . In the long run, only a single rate of unemployment (the NAIRU or "natural" rate) was consistent with a stable inflation rate . The long - run Phillips Curve was thus vertical, so there was no trade - off between inflation and unemployment . Edmund Phelps won the Nobel Prize in Economics in 2006 in part for this work . However, the expectations argument was in fact very widely understood (albeit not formally) before Phelps' work on it . </P> <P> In the diagram, the long - run Phillips curve is the vertical red line . The NAIRU theory says that when unemployment is at the rate defined by this line, inflation will be stable . However, in the short - run policymakers will face an inflation - unemployment rate tradeoff marked by the "Initial Short - Run Phillips Curve" in the graph . Policymakers can therefore reduce the unemployment rate temporarily, moving from point A to point B through expansionary policy . However, according to the NAIRU, exploiting this short - run tradeoff will raise inflation expectations, shifting the short - run curve rightward to the "New Short - Run Phillips Curve" and moving the point of equilibrium from B to C. Thus the reduction in unemployment below the "Natural Rate" will be temporary, and lead only to higher inflation in the long run . </P>

Why is the long run philips curve vertical
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