Fast forward a decade beyond the situation in Exercise S3. Yuppietown’s demand for bread and cheese has decreased, and the town’s two food stores, La Boulangerie and La Fromagerie, have been bought...

Fast forward a decade beyond the situation in Exercise S3. Yuppietown’s demand for bread and cheese has decreased, and the town’s two food stores, La Boulangerie and La Fromagerie, have been bought out by a third company: L’Épicerie. It still costs $1 to make a loaf of bread and $2 to make a pound of cheese, but the quantities of bread and cheese sold (Q₁
and Q₂
respectively, measured in thousands) are now given by the equations:

Again, P1 is the price in dollars of a loaf of bread, and P₂
is the price in dollars of a pound of cheese.

(a) Initially, L’Épicerie runs La Boulangerie and La Fromagerie as if they were separate firms, with independent managers who each try to maximize their own profit. What are the Nash equilibrium quantities, prices, and profits for the two divisions of L’Épicerie, given the new quantity equations?

(b) The owners of L’Épicerie think that they can make more total profit by coordinating the pricing strategies of the two Yuppietown divisions of their company. What are the joint-profit-maximizing prices for bread and cheese under collusion? What quantities do La Boulangerie and La Fromagerie sell of each good, and what is the profit that each division earns separately?

(c) In general, why might companies sell some of their goods at prices below cost? That is, explain a rationale of loss leaders, using your answer from part (b) as an illustration.