- There are two goods, $1$ and $2$ produced by two firms at zero marginal costs. The goods are perfect complements. The demand for each goods is: $Q_1=Q_2=a-(p_1+p_2)$. The prices are set sequentially, with the leader firm ($1$) credibly committing to a price which the follower takes as given. Determine the equilibrium prices, quantities and profits.
I understand that in standard Stackelberg games of prices, the follower has a second mover advantage. For the above question, I found that the reaction curves turned out to be downward sloping, i.e. prices are strategic substitutes. $(p^*_1,p^*_2)=(\frac{a}{2},\frac{a}{4})$. Would the second mover advantage still hold? Evaluating the leader's profit function at Bertrand prices would show that the leader has an incentive to set a price above $p^B_1$ since prices are strategic substitutes and goods are perfect complements (evaluating $\frac{\partial\pi_1^L}{\partial p_1}$ at bertrand prices). Is this the correct method to evaluate second mover/first mover advantage?