Game Theory.

1. Yuppie town 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 P 1 dollars per loaf of bread and La Fromagerie's price is P 2 dollars per pound of cheese, their respective weekly sales, Q 1 thousand loaves of bread and Q 2 thousand pounds of cheese, are given by the following equations:

a) For each store, write its profits as a function of P 1 and P 2 , 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 an explanation for the differences between the Nash equilibrium prices and those that maximize joint profits.