Suppose that there are only two firms that produce widgets, Firm 1 and Firm 2. The two firms face the following inverse market demand curve for widgets:

P = 90 2Q.

Both firms have a constant marginal cost of $10, and no fixed costs.

(a) Suppose Firms 1 and 2 act as Cournot duopolists. Derive each firm's reaction function. What output level will each firm produce in the long run? Given these output levels, what will be the equilibrium price in the widget market? What level of profit will each producer make?

(b) Find the Stackelberg equilibrium quantity, price, and profits for each firm, assuming that firm 1 is the leader and firm 2 is the follower.

(c) Find the Bertrand equilibrium quantity, price and profits for each firm.

(d) Now say that Firms 1 and 2 figure out that by cooperating, they can each make more profit. They decide to collude and act as a monopolist, each producing the same amount and splitting monopoly profits evenly. How much will each firm produce? What is the equilibrium price? What is the profit of each firm?

(e) Soon after their meeting, Firm 1 decides to go out on her own. Given that Firm 2 will produce the collusive quantity from above (i.e. half the total monopoly quantity), Firm1 will produce whatever level of output is best for her. How much will Firm 1 produce? What is the new equilibrium market price? Calculate the profits for each firm.