Aggregate supply and the AS curve

From the relationship between L and P we can derive the relationship between Y_S and P as Y_S is concluded by L by the production function (the higher L, the higher the). 

Figure: The relationship between YS and P

Between points A and B prices are constant and firms produce an amount exactly equal to aggregate demand. Here reversed Say's Law and IS-LM model apply. In this interval, AS-AD model is redundant. Between points B and C we have a positive relation between P and Y_S. Neither reversed Say's Law nor IS-LM model apply. 

It is, though, unreasonable to believe that there would be a 'sharp edge' in the relationship between L and P and between Y_S and P in real economy. Schedules are drawn this way to simplify the explanation. A more reasonable assumption would be that relationships are smooth curves.

Figure: More realistic relationships between L and P and between YS and P