Exercise 3:

Exercise 3. (30 points) Consider two rms that produce a homogeneous good. Firm '5 = 1,2 has the following total cost function: 0012') = 20'11: + ((102- The market demand for this good is given by the following inverse demand function: P(q) = 200 2q, where q = q1 + (12 is the total production. (1) Suppose that rms choose quantities, and they are maximizing prots taking as given the production decision by the other (i.e., they compete a la Cournot). Find the equilib rium price, quantities and prots. (2) How do these results change if rm 1 is able to choose its production level rst? (3) The managers of these two rms nd out that they could be better off by xing production jointly. Suppose now that the two rms collude. Find the equilibrium price, quantities and prots in this case. (4) Now the managers are told that explicit agreements on collusion are illegal. Therefore, each rm will have to decide individually whether to produce at the Cournot equilibrium or at the collusive level. Represent this situation as a simultaneous game using the normal form representation. Find the Nash equilibrium in pure strategies of the game