Q. Explain the long-run Phillips curve?

The long-run Phillips curve

The augmented Phillips curve has an important consequence: the long-run Phillips curve must be vertical.

Figure: The long-term Phillips curve

To realize this, start by drawing a Phillips curve for Π^e = 3%. Only point on this curve that may apply in long run is Π_W = 3% (point A). For illustration Π_W = 2% and Π^e = 3% isn't consistent with equilibrium in the long run since there is no level of inflation which is consistent with these values. p = 3% isn't possible as real wages would go to zero. p = 2% isn't possible as it would be unreasonable to continue to expect 3% inflation if inflation every year was 2%. 

According to neo-classical synthesis, we may temporarily be anywhere on lower Phillips curve when Π^e = 3% however economy should ultimately return to point A (as long Π^e = 3%) 

Now draw a Phillips curve for p^e = 6%. Again, on this curve there is just one point is consistent with equilibrium in the long run and it is the point where Π_W = 6% (point B). This point should be exactly above A as new curve should be exactly three units above the first curve. 

If we draw all possible Phillips curves, we see that all points consistent with long run equilibrium should lie on a vertical curve and this curve is known as long-run Phillips curve. In the long run, economy should return to this curve. This means that in long run, there is no relation between unemployment andinflation. In the long term, economy returns to natural unemployment rate as in the classical model.