Now assume that there are three types of potential passenger: 20 % are high-end, 60% are upper-regular and 20% are regular. Also, the company can offer three categories of cabin: first-class, business and economy. The table describes the willingness to pay for each category of cabin by each type of passenger. Again, all figures are in dollars.

Cabin	Costs	Willingness to pay
		Regular passenger	Upper-regular	High end
First-class	70	90	110	150
Business	40	75	90	100
Economy	30	70	75	80

g) Suppose that the cruise line is able to identify the type (high-end, upper regular or regular) of every potential passenger in the market. Then the cruise line can choose which category of cabin to offer to each passenger, and at which price. What category of cabin would Gulliver's offer to regular passengers, and what price would it charge for that cabin? What about upper-regular passengers? What about the high-end passengers?

More realistically, Gulliver's cannot tell one type of passenger apart from the other in advance. It just sets the prices of first-class, business and economy cabins, and lets each customer decide which category to buy.

h) I will not ask you find the optimal prices for the cruise line, as this would probably take too much time. Instead, I would like you to consider the scenario in which Gulliver's wants to offer the three categories of cabin, charging PE for economy, PB for business and PF for first-class. What incentive compatibility constraints and participation constraints on PE, PB, and PF must the cruise line satisfy if it wants to ensure the following outcomes: (1) the regular passengers travel economy; (2) the upper regular passengers buy business; and (3) the high-end passengers purchase first-class cabins?