Two firms (Firm 1 and Firm 2) are in a market where demand is given by P = 120-(q1 + q2). The firms' marginal cost of production is 60.

(a) Suppose both firms compete by setting their quantities simultaneously and that the game is played only once. Find the best response functions of the firms and draw them.

(b) Find the Nash Equilibrium of the game in part (a). What are the equilibrium profits of the firms?

(c) Now suppose that instead of setting quantities simultaneously, the firms set their quantities sequentially. Specifically, Firm 1 moves first and chooses its quantity (q1). After observing the quantity choice of Firm 1, Firm 2 moves second and chooses its quantity (q2). Find the Subgame Perfect Nash equilibrium of this game. Explain why the quantities in the sequential-move game differ from those in the simultaneous-move game.

(d) Consider the sequential-move game specified in part (c). Suppose that the firms play the Nash Equilibrium strategies you identified in part (b). That is, Firm1 produces q1*, and Firm 2 produces q2* no matter what Firm 1 produces, where q1* and q2* are the Nash Equilibrium quantities you found in part (b). Show that although these strategies constitute a Nash Equilibrium of the game in part (c), they are not subgame perfect.

(e) Now suppose that the two firms play the following game. In stage 1, they simultaneously decide whether to enter or not. Each firm that decides to enter has to paya fixed cost of entry, F. In stage 2, if both firms enter, they play the simultaneous-move game in part (a). That is, they choose simultaneously how many units to produce. If only one firm enters, it becomes a monopolist. Find the Subgame Perfect Nash equilibrium of this game if F < 400.

(f) Now suppose 400 < F < 900. Find the Subgame Perfect Nash Equilibrium of the game in part (e).