Suppose that an industry for a single product consists of N symmetric firms (1, 2, ..., N ) that produce the product at a per-unit cost equal to c. The inverse demand for the product is linear and given by p = aQ, where a > c and Q = q1 +...+qN . Firms are Cournot competitors, that is, they simultaneously and independently select their productions (q1,...,qN ) and the market price of the product is determined by the inverse demand function.

Suppose that a = 60 and c = 20 and there are 4 firms in the industry.

Suppose now that all firms compete repeatedly and forever (i.e., infinite horizon) by se- lecting how much to produce (repeated Cournot oligopoly). All firms have discount fac- tor equal to 0 < < 1.

1) If all firms play trigger strategies, find the threshold in the discount factor that allows firms to cooperate (i.e., collude) and produce the collusive output. (hint: find F1's discounted profit if both firms cooperate every period and F1's discounted profit if it selects its optimal defection output in one period and the Cournot equilibrium profit ever after) (3p)

2) Assume that the number of firms (N) is not equal to 4 and can be anything. Find the threshold in the discount factor that allows the firms to cooperate (i.e., collude) and produce the collusive output. What happens to the threshold discount factor as N grows. What would you say is the possibility of collusion in industries in which there is free entry? (1p)