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A town has a bakery that sells bread and a cheese shop. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If the bakery's price for a loaf of bread is p1 and the cheese shop's price for a pound of cheese is p2, then the number of loaves of bread sold q1 and the number of pounds of cheese sold q2 are given by the following demand functions:
q1 = 14 - p1 - .5p2
q2 = 19 - .5p1 - p2
(a) Are bread and cheese complements or substitutes in this problem? Defend your answer.
(b) Suppose the firms choose prices simultaneously. Derive each store's best reply function. Graph the best reply functions and find the Nash equilibrium.
(c) Now suppose the two stores collude and set prices so as to maximize their joint profits. Find the prices that maximize joint profits.
(d) Are the prices in part (b) higher, lower, or equal to the prices in part (c)? What is the intuition behind this result?
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