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 .

Reconsider the general symmetric Cournot model with 10 firms

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.