# Problem set 2 of Economic Theory I

Nir Dagan, Esther Hauk, and Albrecht Ritschl

Due Monday, 27 April, 1998

1. Montse and Meritxell are friends, but Montse is considered to be more attractive. The boys interested in them are Paco, Joan, and Enric (who all prefer attractive women and go for less attractive girls only after having lost the competition for the attractive ones). Meritxell, the less pretty one, cares more for the emotional qualities of her future boyfriend: above all, she wants him to be very sensitive, although she does care a bit whether he is also guapo and charming. Good-looking Montse, on the other hand, wants her boyfriend to be very guapo and very charming. Being so focused on his visible qualities, she does not care whether he is also very sensitive.

Of the three boys in their party, Paco is muy mono but neither very charming nor very sensitive. Joan is very charming and very sensitive but not very guapo. Enric is neither very good-looking nor very charming but as sensitive as Joan.

1.1 Is there a match between boys and girls, and if so, which one? (We exclude the possibility of having more than one boy-friend or girl-friend at a time).

1.2 Assume that on Saturday night, the whole group goes out to the discotheque "La bella y la bestia", where they meet Jordi who looks very good and turns out to be very charming, however without being a very sensitive mind. Will the match change, and if so, how? (We assume that his preferences are just the same as those of the other boys).

1.3 After three months of disappointment, Montse realizes that it is as important for boys to be sensitive as it is for them to be charming, and she now cares much less about them being mono than about any of the other two qualities. At the same time, Meritxell finds Montse's preferences for the visible qualities in boys somewhat more understandable than before. Assuming that the two girls in fact have identical preferences now, do you know to say what the new match will be? (We assume that all four boys are still available.)

2. Draw indifference curves that correspond to the following statements. In addition, for statements a and b propose utility functions that represent those preferences. For statement d:
What is the marginal rate of substitution between Coca Cola and Pepsi?

1. I don't really mind drinking Pepsi or Coca Cola, I can't tell the difference.
2. I am nuts about Coca Cola, but can't stand Pepsi.
3. I like studying economic theory and mathematics up to a few hours a day. More than that gets boring.
4. I like Coca Cola very much, but I am indifferent about Pepsi.