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Yuppietown's demand for bread and cheese has decreased, and the town's two food stores, La Boulangerie (Firm/Division 1) and La Fromagerie...
Yuppietown's demand for bread and cheese has decreased, and the town's two food stores, La Boulangerie (Firm/Division 1) and La Fromagerie (Firm/Division 2), 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:
Q1 = 8 − P1 − 0.5P2
Q2 = 16 − 0.5P1 − P2 .
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-Epicerie runs La Boulangerie and La Fromagerie as if they were separate firms, with independent manager who each try to maximize their own profit. What are the Nash Equilibrium quantities, prices, and profits for the two divisions of L'Epicerie, given the new quantity equations?
(b) The owners of L'Epicerie 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 chese 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 rational of loss leaders, using your answer from part (b) as an illustration.
