Q. What is IS-LM model with inflation?

The IS-LM model with inflation 

The basic assumption

We developed IS-LM model with constant wages and prices. We can now extend this model to allow for inflation. Rather than constant wages and prices, we should presume that π = π_W = π^e. In the same that we dropped assumption of constant P when we went on to AS-AD model to allow for changes in real wages, we will drop assumption that π = π_W to allow for inflation and changing real wages. 

Let's briefly justify the assumption π = π_W = π^e. π_W = π^e may be illustrated by realizing that if workers expect 6% inflation, they will demand 6% wage increases to sustain the same real wage (they typically require more than 6% and an increase in real wages though this is since the growth of the economy will allow for this - always think of these models as if there is no growth). 

Assumption π = π_W means that we have a balanced inflation. Since in IS-LM model, the real wage is then constant. This is a reasonable assumption if economy is in a state where aggregate demand is inadequate and L is lower than profit-maximizing level.