1. The inverse demand curve of an homogeneous product is p = 50 Q /2 . There are two firms and each firm has a unit cost of production equal to 5, and they compete in the markets in quantities. That is, they can choose any quantity to produce, and they make their quantity choices simultaneously.

(a) Show how to derive the Cournot-Nash equilibrium to this game. What are the firms'profits in equilibrium?

(b) Suppose that firm 1 has a cost advantage. Its units cost is constant and equal to 5, whereas the firm 2 has the higher unit cost of 10. What is the Cournot outcome now?

2. The inverse demand function of wheels is given by p(Q) = 100 2Q, and the cost function for any firm operating in this industry is C(Q) = 4qi . (a) Which is the marginal cost of the firms in the industry? If the wheel industry were a perfectly competitive industry, which would its production level? which would be the price of the wheels?

(b) Let us assume that there are only two firms in the industry and they compete "a la Cournot". Work out the reaction functions for both firms. Which are the equilibrium price and production levels? Which is the profit of both firms?

(c) Draw (in a figure) the reaction functions of both firms and indicate the Cournot equilibrium.

(d) If both firms reach a collusive agreement. Which will be production and market price?

(e) Let us assume that both firms behave "a la Stackelberg" being firm 1 the leader and firm 2 the follower. Which will be production and market price? Which will be the production of firms 1 and 2? Which will be the profit of each one of the firms?