Assume Iberia is a monopoly in the market of flights Madrid-Menorca. Iberia can

choose the quality /service it will offer in its flights at a constant marginal cost of

production of quality/service c=1. There are only two types of consumers that flight to Menorca. One type is rich tourists that travel to Menorca to fish red tuna and play golf.

This type of consumers value a lot the quality of the service during the flight and they have a utility function equal to:

U =3log(q+1)-p, where q is quality/service, log represents the natural log function and p is the price paid by the ticket. There is other type of customers that are poorer tourists that it is just the first time they go to Minorca and they do not value quality of the service as much. Their utility function is U=2log(q+1)-p where as before p is ticket price and q is the level of quality during the flight. If a tourist does not fly then its utility is zero. There is an equal number of consumers of both types. Iberia can not distinguish which type of tourist is flying when he/she buys the ticket and is thinking in designing two class of tickets, one designed for rich tourists with a price ph, and one designed for poor tourists with price pl. Each class of ticket will be

assigned a seat with different quality/service. qh for rich tourist and ql for poor tourists. Assume that Iberia wants to have both types of tourists in its flights.

1. Write the profits of Iberia as a function of ph , qh , pl , and ql .

2- Prove that at least one type of customer will have utility equal to zero if Iberia is

maximizing profits.

3- Prove that it has to be the case that rich tourists are indifferent between

choosing any of the two ticket classes.

4. Prove that it has to be the case that poor tourists will never choose the more

expensive class of tickets.

5. Using the insights of above, solve the maximization problem of Iberia and find the optimal ph ,pl , qh and ql . Explain the intuition of your findings.

Would Iberia provide better quality/services to rich tourists if there were none poor

tourists? Would Iberia provide better quality to poor tourists if there were no rich

tourists?