Q. Consumption function in the IS-LM model?
The consumption function will be the same as in cross model, consumption will depend positively on Y. In the classical model, consumption relies negatively on the real interest rate. You can allow consumption to depend negatively on interest rates in the IS-LM as well. You should then write C = C(Y, R). In the literature, both variants are found but then since the results will be largely the same so we choose to let C depend on Y only, C = C(Y). We will also, for the same reason, model imports as a function of Y only albeit it may depend on R as well.