6. {This is Problem 14U4 in the textbook) Cheapskates is a very minor-league professional hockey team. Its facility is large enough to accommodate all of the 1000 fans who might want to watch its home games. It can provide two types of seats- ordinary and luxury. There are also two sorts of fans: 60% of the fans are blue-collar fans, and the rest are white-collar fans. The costs of providing each type of seat and the fans' willingness to pay for each type of seat are given in the following table (measured in dollars): Willingness to Pay Cost Blue-Collar White-Collar Ordinary 4 12 14 Seating Luxury 8 15 22 Each fan will buy at most one seat, depending on the consumer surplus he would get (maximum willingness to pay minus the actual price paid) from the two kinds. If the surplus for both is negative, then he won't buy any. If at least one kind gives him non- negative surplus, then he will buy the kind that gives him the larger surplus. lfthe two kinds give him equal non-negative surplus, then the blue-collar fan will buy the ordinary kind of seat, and the withe-collar fan will buy the luxury kind. The team owners provide and price their seating to maximize profit., measured in thousands of dollars per game. They set prices for each kind of seats, sell as many tickets as are demanded at these prices and then provide the numbers and types of seats of each kind for tickets have sold. (a) First, suppose that the team owners can identify the type of each individial fan who arrives at the ticket window (presumably bythe color of his collar) and can offer him just one type of seat at a stated price on a take-it-orIeave-it basis. What is the owners' maximum prot 7r\" under this system? (b) Now suppose that the owners cannot identify any individual fan, but they still know the proportion of blue-collar fans. Let the price of an ordinary seat beX and the price of a luxury seat be Y. What are the incentive compatibility constraints that will ensure the blue-collar fans buy the ordinary seats and the white-collar fans buy the luxury seats? Graph these constraints on an (X, Y)coordinate plane. (c) What are the fans' participation constraints for the fans' decisions on whether to buy tickets at all? Add these constraints to the grap in part (b). (d) Given the constraints in (b) and (c), what prices X and Y maximize the owners' prot n2 under this price system? What is the value of 712? (e) The owners are considering whether to set prices so that only the white-collar fans will buy tickets. What is theor prot J'Tw if they decide to cater to only white-collar fans? (f) Comparing It; and nw, determine the pricing policy that the owners will set. How does their prot achieved from this policy compare with the case of full information, where they earn rr' ? (g) What is the cost of coping with the information asymmetry in part 1'\"? Who bears this cost? Why