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)
	Charles	Gilberto	Lorenzo	Sam
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

Within the dorm room, the showing of a movieis   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)
Charles
Gilberto
Lorenzo
Sam

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 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 Charles 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. Once the movie is purchased, everyone can see the movie (non-excludable) and watching of the movie by one person does not mean that less of the movie is available for anyone else to watch (non-rivalry).

We can find out the total willingness to pay for all the movies by adding the willingness to pay of every individual for each movie. Example for the first movie, Charles' willingness to pay is $7, Gilberto's willingness to pay is $5, Lorenzo's willingness to pay is $3 and Sam's willingness to pay is $2. This makes the total willingness to pay for first movie = $(7+5+3+2) = $17.

Similarly, do for the remaining movies as well.

If it costs $8 to rent a movie, the roommates should rent 3 movies in order to maximize the total surplus (because only first three movies have a lower cost of renting than the willingness to pay, so they should rent the first three movies).

Cost of renting 3 movies = $8*3 =$24

If the cost gets equally divided between four of them, then each of them has to pay = $24/4 = $6.

Charles' willingness to pay for the first three movies = Charles' willingness to pay for the first movie + Charles' willingness to pay for the second movie+ Charles' willingness to pay for the third movie

= $7 + $6 +$5

= $18

Since all of the pay $6 for the movies, Charle's consumer surplus can be found out by subtracting the amount he has to pay from his total willingness to pay

=$(18-6)

=$12

A similar process can be used to find out the total willingness to pay and the consumer surplus of the remaining three individuals. This has been summarised in the table given below:

The practical problem with this solution is that each roommate has an incentive to understate the value of the movies to him (because that way he can pay a lesser cost).

When Charles is asked his willingness to pay, he will have an incentive to understate the value of the movies to him. This statement is true.

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