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:

Orson Alfred Woody Ingmar
Frist 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

b. If it costs $8 to rent a video, how many videos should the roommates rent to
maximize total surplus?
c. If they choose the optimal number from part (b) and then split the cost of
renting the videos equally, how much surplus does each person obtain from
watching the movies?
f. What does this example teach you about optimal provision of public goods?

I would really appreciate the help. :)

Jeff (below) posted this same question. See my response.

To determine the optimal number of videos to rent, we need to analyze the willingness to pay for each roommate for each film.

First, let's calculate the total willingness to pay for each film by summing up the willingness to pay of all four roommates.

For the first film:
- Total willingness to pay = 7 + 5 + 3 + 2 = 17

For the second film:
- Total willingness to pay = 6 + 4 + 2 + 1 = 13

For the third film:
- Total willingness to pay = 5 + 3 + 1 + 0 = 9

For the fourth film:
- Total willingness to pay = 4 + 2 + 0 + 0 = 6

For the fifth film:
- Total willingness to pay = 3 + 1 + 0 + 0 = 4

Now, let's calculate the total surplus for each film by subtracting the cost of renting the film ($8) from the total willingness to pay.

For the first film:
- Total surplus = Total willingness to pay - Cost = 17 - 8 = 9

For the second film:
- Total surplus = Total willingness to pay - Cost = 13 - 8 = 5

For the third film:
- Total surplus = Total willingness to pay - Cost = 9 - 8 = 1

For the fourth film:
- Total surplus = Total willingness to pay - Cost = 6 - 8 = -2 (negative surplus means it's not worth renting)

For the fifth film:
- Total surplus = Total willingness to pay - Cost = 4 - 8 = -4 (negative surplus means it's not worth renting)

From these calculations, we can see that the first three films have positive total surplus, while the last two films have negative total surplus.

To maximize total surplus, we should rent the first three films since they have positive total surplus. Therefore, the roommates should rent three videos.

To find the surplus for each person, we need to divide the total surplus of the rented films by the number of roommates (four in this case) and the total surplus will be divided equally among them.

For the optimal number of three films, the total surplus is 9 + 5 + 1 = 15.

Each person's surplus = Total surplus / Number of roommates = 15 / 4 = 3.75.

Therefore, each person obtains a surplus of $3.75 from watching the movies.

This example teaches us that the optimal provision of public goods, in this case, the movies, is to rent the films that have a positive surplus and maximize the total surplus. By doing so, each person can benefit equally from the public good and maximize their individual surplus.