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Yuppietown has two food stores, La Boulangerie, which sells bread, and La Fromagerie, which sells cheese. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If La Boulangerie's price is P1 dollars per loaf of bread and La Fromagerie's price is P2 dollars per pound of cheese, their respective weekly sales, Q1 thousand loaves of bread and Q2 thousand pounds of cheese, are given by the following equations:
Q1 = 10-P1 -0.5P2, Q2 = 12-0.5P1 -P2.
(a) Find the two stores' best-response rules, illustrate the best-response curves, and find the Nash equilibrium prices in this game.
(b) Suppose that the two stores collude and set prices jointly to maximize the sum of their profits. Find the joint profit-maximizing prices for the stores.
(c) Provide a short intuitive explanation for the differences between the Nash equilibrium prices and those that maximize joint profit. Why is joint profit maximization not a Nash equilibrium?
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