QUESTION $4$

Consider a market with a demand curve given $($in inverse form$)$ by $P(Q)=60-\frac{Q}{4},$ where $Q$ is total market output and $P$ is the price of the good. Two firms compete in this market by sequentially choosing quantities $q_1$ and $q_2($where $q_1+q_2=Q).$

What type of oligopolistic competition does this exercise describe? How does the setup of the game differ from another oligopolistic interaction we have analysed in class? $($please discuss briefly$)$

$,$ Suppose the cost of production is constant at $30$ per unit, and that it is the same for both firms. If the two firms are maximizing profit, what would be the quantity produced by the leader? What is the quantity produced by the follower? Finally, what is the price of the good produced? Please include a graphical analysis that depicts the equilibrium outcome of this game and compares it graphically to that of simultaneous quantity competition.

Does the leader always produce more than the follower in this type of setup? Comment on whether being a leader is beneficial for the profits of the firm compared to the simultaneous game, and also briefly comment on the $($implicit$)$ assumptions on which this is based.