Question

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?

Answer 1

G) Gulliver's aim would be Maximizing the profit.

The regular type passenger is Willing to pay 90 $ for first class but it cost 70 so profit would be 20$ per passenger.

For business class regular passenger is willing to pay 75 but it cost 40 ,so profit would be 35 per passenger.

For economy class , regular passenger is willing to pay 70 but it cost only 30 ,so profit would be 40 $ per passenger so to maximize its profit Gulliver will sell economy class to regular passenger at price of 70$

The same reasoing we used for regular passenger ,we would use for upper regular passenger and high end passenger too.

The upper regular passenger is willing to pay 110 ,90, 75 for first class, business class , economy class and profit would be 40, 50,45 respectively.

So to maximize per upper regular passenger profit , Gulliver would offer upper regular passenger, business class at 90$.

And by same reasoing ,he will offer high end passenger ,first class at 150$.

H) participation constraints tells ,the conditions that make all participants to participate in the game or in our case all three type of passenger to travel.

Participation constraint:

PE≤70

PB≤90

PF≤150

Incentive compatibility constraint tells, condition that leads to each type of passenger to choose naturally what Gulliver wants.

Incentive compatibility constraint:

PE=70

75<PB<85

110<PF≤125

Given incentive compatibility constraint , regular would choose economy class, upper regular would choose business class and high end would choose first class.{ Upper regular would choose business class because he is getting surplus of 5 by choosing economy class but getting surplus more than 5 by choosing business class and same reasoing while high end choose between economy, business and first class,, he would choose first class as he is getting highest surplus from chosing this}