Question

4. Suppose in the previous problem that Gaston can produce souffles at a constant marginal cost of $5,but Pierre produces souffles for $7. Together, they collude to produce 3 units each.

   1. How much profit will each producer earn? What will be the total profit of the cartel?

   2. Gaston observes that he is a more efficient pro- ducer than Pierre, and suggests that if they are going to produce 6 units, the cartel's interests are better served if Gaston produces all of the souffles.

      1. I f Gaston produces and sells all o f the souf- fles and Pierre produces nothing, what hap- pens to the profit of the cartel?

      2. ls Pierre likely to agree not to produce any souffles?

      3. Suppose Gaston offers to pay Pierre not to produce any souffles. How much would Gaston potentially be willing to offer? What is the minimum offer that Pierre should accept?

      4. 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 agree- ment with Gaston and increases his output from zero souffles to one? What happens to Gaston's profit?

      5. 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 produc- ing 3 units to the potentially more profit- able method of having Gaston produce everything?

(previous question):   3. Because cooking souffles is incredibly difficult, the supply of souffles in a small French town is controlled by two bakers, Gaston and Pierre. The demand for souffles is given by P = 30 - 2Q, and the marginal and average total cost o f producing souffles is $6. Because baking a souffle requires a great deal of work and preparation, each morning Gaston and Pierre make a binding decision about how many souffles to bake.

Answer 1

Part A

Gaston's profit is,

Pierre's profit is,

So the total profit from the cartel is,

Part B

If Gaston produces and sells all souffles, then cartel profit is,

Part C

If pierre agree the cartel only the condition where Gaston should compensate with what he earns before cartel. That is $33. So the Gaston 's profit will become,

Part D

In this case, Gaston profit will become,