The rest of the world in the cross model

In the classical model, imports doesn't depend on Y. The discussion whether imports relies on Y or not is the same as for consumption. Though in the cross model, it's always presumed that when Y increases, consumption will increase by more than imports. This makes sense because C is generally larger than Y. For instance, Assume that C is 1000 whereas Im is 100 and that Y increases by 10%. If C and Im increase by 5% each, C will increase by 50 whereas Im will increases by only 5. 

Net exports NX = X - Im will depend negatively on Y and rest of the world savings S_R = Im - X relies positively on Y in cross model. If we want to be explicit about these dependences we write: 

NX(Y) = X - Im(Y)

S_R(Y) = Im(Y) - X