To find the equilibrium price I understand you set $$Q^s = Q^d$$ and then solve for p. But as P is not indpendently labeled in $$Q^d$$ I am slightly confused how you would go about writing this equation? Thanks!

So you want to find $\partial p / \partial k$

By implicit differentiation what they mean is let $p=p(k)$ so p is a function of k.

Take your equilibrium condition $Q_s-Q_d=0$ and now differentiate with respect to k.

• @BNA You were able to solve it? – VCG Sep 5 '16 at 18:49

By the implicit function theorem, when we have an equilibrium equation $F$

$$F \equiv Q^s - Q^d = 0 \implies F\equiv kp^2-D(p)=0$$

the equilibrium change of, in this case, $p$ when $k$ changes is given by

$$\frac {dp}{dk} = -\frac {\partial F/\partial k}{\partial F/ \partial p}$$

Since $D(p)$ is not given explicitly, you won't get a fully parametric answer of course, but the sign of $D'(p)$ will help you determine the direction of movement.