Question

2.   Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film:

           

Judd Joel Gus Tim

first film $ 7 $ 5 $ 3 $ 2

second film 6 4 2 1

Third film 5 3 1 0

Fourth film 4 2 0 0

fifth film 3 1 0 0

d. Is there any way to split the cost to ensure that everyone benefits? What practical problems does this solution raise?

e. Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally. When Judd is asked his willingness to pay, will he have an incentive to tell the truth? If so, why? If not, what will he be tempted to say?

f. What does this example teach you about the optimal provision of public goods?

Answer 1

d) Is there any way to split the cost to ensure that everyone benefits? What practical problems does this solution raise?

Judd – $18; Joel – 12; Gus – 6; Tim – 3 (Amount each roommate would be willing to pay for 3 movies)

The three movies together cost a total of $24. Tim should pay $2, Gus should pay $4, Joel should pay $8, and Judd should pay $10. Tim, Gus, and Joel each pay only 2/3 of what they are willing to pay, and Judd pays only 5/9 of what he is willing to pay. The problem with this idea is that it would seem very unfair, as all the roommates are charged different prices when they are all going to watch the movies.

e) Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally. When Judd is asked his willingness to pay, will he have an incentive to tell the truth? If so, why? If not, what will he be tempted to say?

Judd will have an incentive to lie and say he is only willing to pay the $6 he would have to if the cost were divided equally; essentially, he would try to portray his willingness to pay as no more than the person who values the movies the least. That way, he can be sure not to have to pay a larger portion of the price than his roommates.

f) What does this example teach you about the optimal provision of public goods?

It is very difficult to achieve the optimal division of public goods because people do not have the incentive to pay the amount they actually value the good because such goods are not excludable; they see other people who value the good less paying less for the same thing, and become unwilling to pay the full value they place on the good.