Suppose in the previous problem that Gaston can produce souffls at a constant marginal cost of $5,

Suppose in the previous problem that Gaston can produce soufflés at a constant marginal cost of $5, but Pierre produces soufflés for $7. Together, they collude to produce three units each.
a. How much profit will each producer earn? What will be the total profit of the cartel?
b. Gaston observes that he is a more efficient producer than Pierre, and suggests that if they are going to produce six units, the cartel's interests are better served if Gaston produces all of the soufflés.
i. If Gaston produces and sells all of the soufflés and Pierre produces nothing, what happens to the profit of the cartel?
ii. Is Pierre likely to agree not to produce any soufflés?
iii. Suppose Gaston offers to pay Pierre not to produce any soufflés. How much would Gaston potentially be willing to offer? What is the minimum offer that Pierre should accept?
iv. Suppose that the deal in part (iii) is reached for Pierre's minimum price. What happens to Pierre's profit if he cheats on his agreement with Gaston and increases his output from zero soufflés to one? What happens to Gaston's profit?
v. Compare Pierre's incentive to cheat under this arrangement with the incentive that exists when they split production equally. Also compare Gaston's vulnerability to Pierre's cheating under both arrangements. Why might this cartel choose to use the less-profitable method of each member producing three units to the potentially more-profitable method of having Gaston produce everything?