Question

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:

First film Second film Third film Fourth film Fifth film Willingness to Pay (Dollars) Darnell Jacques Musashi Sean 10 3 2

Within the dorm room, the showing of a movie (is not or is) a public good.

If it costs $12 to rent a movie, the roommates should rentmovies in order to maximize the total surplus.

Suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally.

This means that each roommate will pay ____

In order to split the cost in a way that ensures that everyone benefits, the cost could be divided up based on the benefits each roommate receives.

The practical problem with this solution is that each roommates has an incentive (overstate or understate) to the value of the movies to him.

Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally.

True or False: When Darnell is asked his willingness to pay, he will have an incentive to tell the truth.

True

False

This examples teaches you that the optimal provision of a public good will occur if individuals (do have or do not have) an incentive to hide their valuation of the good.

Answer 1

In dorm, showing of a movie is public good since it is non-excludable and non-rival.

At optimal, total willingness to pay should be greater than or equal to rent of movie. This is true at the third film. Hence, they should rent 3 movies.

If 3 movies are rented, total cost is 36. So each will pay $9.

If splitting of costs is according to beneifts, each will have incentive to understate true value.

Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally.

When Darnell is asked his willingness to pay, he will have an incentive to tell the truth. True

This examples teaches you that the optimal provision of a public good will occur if individuals do not have an incentive to hide their valuation of the good.