Fast forward a decade beyond the situation in Exercise S3. Yuppietown’s demand for bread and cheese.

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:

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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.

 

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