(Cartel stability) [6 points each]

Suppose there are 4 firms forming a cartel. The CEOs have a meeting to decide the quantities each firm should produce. The overall market demand isP= 18Q. All firms' marginal cost of production is the same and constant. i.e.MC= 2.

1. The optimal quantity each firm should produce if they collude and act as one entity.
2. Can the quantities you solve for the previous question sustain as an equilibrium? (i.e., does either firm has an incentive to deviate from it?)
3. Suppose all four firms agree that they need to have a plan to prevent any one of them to deviate from their agreement. Their plan is to produce some extra quantities and keep those quantities in their storage. They will dump this quantity into the market if they find any deviation. Figure out this extra quantity.