Question on shifts in Supply and Demand Curves
Write $i=I(y,a)$ for the IS function (expressed as some function of $y$). Likewise, let $i=L(y)$ be the LM function. Assume the following properties:


$\frac{\partial I(y,a)}{\partial a}&gt;0$ : $a$ is a parameter that causes the IS curve to shift up.
$\frac{\partial I(y,a)}{\partial y}&lt;0$: the IS function slopes downwards
$\frac{\partial L(y)}{\partial y}&gt;0$ : the LM function slopes upwards


For any $a$, we find the equilibrium $y^*(a)$ at the intersection of the two functions:
$$I(y^*(a),a)- L(y^*(a))=0.$$
Applying the implicit function theorem:
$$\frac{\partial I}{\partial a}+\frac{\partial y^*}{\partial a}\left(\frac{\partial I}{\partial y^*}-\frac{\partial L}{\partial y^*}\right)=0,$$
which implies
$$\frac{\partial y^*}{\partial a}=-\frac{\frac{\partial I}{\partial a}}{\frac{\partial I}{\partial y^*}-\frac{\partial L}{\partial y^*}}.$$

The numerator is positive by hypothesis. Thus, for $y^*$ to increase with $a$ we require that the denominator be negative: $\frac{\partial I}{\partial y^*}&lt;\frac{\partial L}{\partial y^*}$. This is clearly true because $I$ slopes downward and $L$ slopes upward. But $y^*$ would also increase even if $I$ sloped upward—provided itdoes so more gradually than $L$.