I'm looking at Greg Mankiw's Macroeconomics (7th edition), at the model presented in chapter 3:
$Y = C + I + G,$
where $Y$ is total output, $C = C(Y-T)$ is consumption, $T$ are net taxes (fixed by policy), $I = I(r)$ is investment, $r$ is the interest rate, and $G$ are government purchases (fixed by policy). The model further makes the assumption that
$Y = F(K,L),$
where $K,L$ are the factors of production, capital and labor, and are assumed to be fixed, so that $Y$ is therefore fixed as well. Using the fact that $Y,T,G$ are fixed, it follows that $C$ is also fixed and thus saving,
$S = Y-C-G,$
is fixed. But the model entails that $S = I(r)$ and therefore any movement in saving translates into a movement in investment (and thus the interest rate). How is it possible that investment is considered variable, if investment is the purchase of new capital goods and capital is taken as fixed? If investment increases, then so should capital.