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:
(a) For each store, write its profit as a function of P1 and P2 (in the exercises that follow, we will call this “the profit function” for brevity). Then find their respective best-response rules. Graph 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?
(d) In this problem, bread and cheese are mutual complements. They are often consumed together; that is why a drop in the price of one increases the sales of the other. The products in our bistro example in Section 1.A are substitutes for each other. How does this difference explain the differences among your findings for the best-response rules, the Nash equilibrium prices, and the joint profit-maximizing prices in this question, and the corresponding entities in the bistro example in the text?