2. (30 points) Gulliver's Cruises is the only line operating cruises between the islands of Lilliput and Blefuscu, in the South Indian Ocean. Twenty percent of Gulliver's potential customers are high-end passengers, who really value good service and are willing to pay a substantial premium for it. The other 80 percent are regular passengers. The cruise line can offer two types of cabin to its passengers: first-class or economy. The table below describes the willingness to pay for each category of cabin by each type of passenger. The table also presents the marginal costs of each type of cabin for the cruise line. Throughout this question, ignore any sort of capacity constraints faced by Gulliver's-that is, assume that Gulliver's can offer as many cabins of each category as it wants. Also, for simplicity, assume that all cabins are individual, so (i) each passenger buys at most one cabin, and (ii) two or more passengers cannot divide the same cabin. All figures are in dollars. Cabin Costs Willingness to pay Regular passenger High-end First-class 80 100 160 Economy 40 80 90 Each type of passenger calculates the net payoff (benefits minus price) that she would get from each cabin and buys the one that would give the higher net payoff, provided that this payoff is non-negative. If both categories of cabin give equal, non-negative net payoffs for a passenger, she buys first-class; if both cabins have strictly negative net payoff for a passenger, she does not buy any of them. Assume that Gulliver's wants to maximize its expected profits. (a) (5 points) Suppose that the cruise line is able to identify the type (high-end or reg- ular) of every potential passenger in the market. Then, the cruise line can choose which category of cabin to offer to each passenger, and at what price. Which cate- gory of cabin would Gulliver's offer to regular passengers, and what price would it charge for that cabin? What about the high-end passengers? (b) (5 points) More realistically, Gulliver's cannot tell one type of passenger apart from the other in advance. It just sets the prices of first-class and economy cabins, and lets each customer decide which category to buy. First, suppose that Gulliver's decides to offer only economy cabins, charging pp per passenger. What value of pp would maximize profits? (c) (5 points) Next, suppose that Gulliver's offers only first-class cabins on its cruises and charges pp per passenger. What value of pp would maximize profits? (d) (5 points) Finally, suppose that Gulliver's offers both categories of cabin, charging PR for economy and pp for first-class. What incentive-compatibility constraints and par- ficipation constraints on pe and pp must the cruise line satisfy if it wants the regular passengers to travel economy and the high-end ones to buy first-class cabins? (e) (5 points) What values of pg and pp will maximize the expected profit when Gul- liver's offers both cabin categories? What are the expected profits? (f) (5 points) Putting it all together, decide which categories of cabin the cruise line should offer, and what price it should charge for each one of them