The problem with the Keynesian model
We can classify two problems with the Keynesian model as developed so far:
1. Π is exogenous. Although inflation may temporarily deviate from wage inflation, this deviation can't be too large and it can't last for too long (since real wages would become unreasonable low or unreasonable high). This model has no determination of Πw and hence no complete determination of Π. A model which predicts an inflation of around 6% by presuming a wage inflation of 6% isn't very useful. Keynesian model with inflation is hence incomplete.
2. It is quite unreasonable to presume that Πw would be independent of Y. More reasonable would be to model Π Was a positive function of Y. If we are in a boom, L would be above its average and unemployment below its average. In such a situation, it's reasonable to expect wage inflation to increase.
To solve these problems, we have to make Πw endogenous. We do this by Keynesian model adding the Phillips curve.