Question

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)
	Tim	Brian	Edison	Kevin
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 movie (is/is 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)
Tim
Brian
Edison
Kevin

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 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 Tim 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.

Answer 1

Within the dorm room, the showing of a movie is a public good.Any of the roommates cannot be excluded from watching the movie.

The roommates should rent four movies because the value of the fourth film ($7) would be less than the cost ($8).

The total cost would be $8 × 4 = $32. If the cost were divided evenly among the roommates, each would pay $8. Tim values four movies at $34 so his surplus would be $26. Brian values four movies at $24 so his surplus would be $16. Edison values four movies at $12, so his surplus would be $4. Kevin values four movies at $6 so his surplus is -$2. Total surplus among the four roommates would be $44

Roommate	Total Willingness to Pay	Consumer Surplus
Tim	$34	$26
Brian	$24	$16
Edison	$12	$4
Kevin	$6	$-2

The costs could be divided up by the roommates based on the benefits they receive. Because Tim values the movies the most, he would pay the largest share. The practical problem with this solution is that each roommate has an incentive to understate the value of the movies to him.

Because they split the cost of the movies equally, Tim has an incentive to tell the truth about the value he places on movies to ensure that the group rents four movies. He values each of the movies more than his cost per movie. So the given statement is false.

This example teaches you that the optimal provision of a public good will occur if individuals do not have an incentive to hide their valuation of a good. This means that the cost of each individual can't be related to his valuation.