We can use the Cournot model to derive an equilibrium industry structure. For this pur- pose, we will define an equilibrium as that structure in which no firm has an incentive to leave or enter the industry. If a firm leaves the industry, it enters an alternative com- petitive market in which case it earns zero (economic) profit. If an additional firm enters the industry when there are already n firms in it, the new firm's profit is determined by the Cournot equilibrium with + 1 firms. For this problem, assume that each firm has the cost function: C(g) = 256 + 20g. Assume further that market demand is described by: P =100- Q. a. Find the long-run equilibrium number of firms in this industry. b. What industry output, price, and firm profit levels will characterize the long- run equilibrium? b. What will be increase in per-firm profit, if all the firms (from your answer in (a)) joined a cartel (and the cartel's production was evenly split among the firms)? c. If one of the firms (from the cartel in (b)) wanted to deviate from the cartel arrangement, i. what output should it set? ii. what will be the increase/decrease in its profits as a result of the deviation