5 . Problems and Applications Q5

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:

	Willingness to Pay
(Dollars)
Darnell	Jacques	Musashi	Sean
First film	10	9	6	3
Second film	9	7	4	2
Third film	8	5	2	1
Fourth film	7	3	0	0
Fifth film	6	1	0	0

Within the dorm room, the showing of a movieis not a public good.

If it costs $8 to rent a movie, the roommates should rent

movies 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

.

Complete the following table with each roommate's total willingness to pay for this many movies and the surplus each person obtains from watching the movies.

Roommate	Total Willingness to Pay	Consumer Surplus
(Dollars)	(Dollars)
Darnell
Jacques
Musashi
Sean

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 roommate has an incentive tounderstate 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 understate the value of the movies to him.

True

False

This examples teaches you that the optimal provision of a public good will occur if individuals an incentive to hide their valuation of the good.