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 .

Consider the general symmetric Cournot model with 10 firms and linear demand given above.

1. Find the (i.e., collusive) output that maximises the firms' joint profit. Suppose that each firm produces 0.1 of this output. Find each firm's profit.

2. Find each firm's BR function and the (static) Cournot equilibrium.

3. Suppose that all firms but Firm 1 produce the output that maximises the firms' joint profit (found in Part 1 of this exercise). Find the optimal defection output for Firm 1.

4. Suppose now that all firms compete repeatedly and forever (i.e., infinite horizon) by selecting how much to produce (repeated Cournot oligopoly). All firms have the same discount factor that is equal to = 0.75. If all firms play trigger strategies, can they cooperate on the optimal collusive output? (3p)

5.Suppose now that the firms continue to compete repeatedly and forever by selecting how much to produce. Nonetheless, in every period, there is a probability 1 x, where 0 < x < 1, that the industry seizes to exist. Suppose that all firms have discount factor equal to 0 < < 1. 5. If all firms play trigger strategies, find the discount factor that allows firms to cooperate (i.e., collude) and produce the collusive output. How does this depend on x. Explain. (2p)