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Question 15) Ana and Ben each own a pizza store in Frostbite Falls, Minnesota. Demand for pizza is given by q = 320-40p. Having the only two pizza stores in Frostbite Falls, Ana and Ben try to profitably split the market without violating the Sherman Antitrust Act. Each of them has the cost function c(q) = 50+2q. Ana and Ben choose quantities they produce simultaneously and independently of each other. (a) How many pizzas will each of them sell? What will be the market price? What profits will Ana and Ben make? (b) Suppose that Ana and Ben decide to violate the Sherman Antitrust Act. They secretly agree to collude and act as the monopolist. Doing this, they split equally the output. How many pizzas will be sold in Frostbite Falls? What will be the price? What profits will Ana and Ben make? (c) Show that collusion cannot be supported as a Nash equilibrium. (d) Suppose now that Ana was the first to open a pizza store in Frost- bite Falls, and Ben followed her. Ana was aware of the fact that Ben would open his pizza store. How many pizzas will each of them sell in this case? At what price? What will be Ana's and Ben's profits