Aggregate demand with inflation

In previous versions of Keynesian model, Components of aggregate demand did not depend on P. In IS-LM and in AS-AD models, investments depended on nominal interest rate R.

We argued that investment in fact relies on the real interest rate r but as R = r when π^e = 0, we could make it a function of R.  

When π^e no longer is zero and real interest rate r = R - π^e, we must write I(r) or I(R - π^e). We must also write YD(Y, r) or YD(Y, R - π^e). As inflation expectations are exogenous (given), it's still the case that YD relies negatively on R. Please note that if there is an equal increase in expected inflation and in nominal interest rate, real interest rate is unaffected and so is aggregate demand andinvestments.