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)
Van Carlos Felix Larry
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 moviea public good.
If it costs $8 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.
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.
Total Willingness to Pay Consumer Surplus
Roommate (Dollars) (Dollars)
Carlos
Felix
Larry
Raphael
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 tothe 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.

Since their dormitory room is the 'cinema', meaning that it's just going to be 4 of them and a private good that they'll pay for; then the showing of a movie is not a public good!

Public goods are those general utilities usually provided by governments, for their citizens; e.g. public defense, clean drinking water, good roads, etcetera.

PART (B)

Given the 'willingness to pay' constraint, we need to find the optimal number of movies they can watch. It costs $8 to rent a movie, no matter how interesting it is or how much satisfaction the viewers derive from it. So the cost of the 1st film = the cost of the 2nd film = the cost of the 3rd film = the cost of the 4th film = the cost of the 5th film.

To get the total amount they're willing to pay for all 5 movies, sum up!

(10+9+6+3) + (9+7+4+2) + (8+5+2+1) + (7+3+0+0) + (6+1+0+0)

KEY: This arrangement should remind you of the law of diminishing marginal utility. The more movies they watch in one sitting or over a weekend, the less satisfaction they derive from the intangible commodity. Hence, the less they are willing to pay for more of the commodity.

So the sum is 28 + 22 + 16 + 10 + 7 = 83

Now to get the number of movies they should rent if they wish to maximize their total spending, divide the total willingness to pay by the cost for a movie:

83/8 = 10.375

Rounding up to the nearest whole number or in reality, that's 10 movies.

PART (C)

Suppose the roommates choose to rent this optimal number of movies - which is higher than the intended number of movies - and then split the cost equally, what will each roommate pay?

Here, we will use the approximated value 10.

10movies x $8 = $80

Splitting the cost equally, divide by 4

$80 ÷ 4 = $20

This figure is just in obedience to the question's requirements which says the bill must be shared equally. In actual fact, some of the four roommates don't have a purchasing power or willingness that is up to $20! That's Felix and Larry.

PART (D)

Complete the given table by inputing each roommate's total willingness to pay for the 5 movies and the surplus each person obtains from watching the movies. Remember to assume that Van is the same person as Raphael.

Also, total cost for 5 movies is 8 x 5 = $40

Dividing this by 4, you have $10 per roommate. So a surplus would be the excess of each roommate's TWTP over $10.

TWTP($) CS($)

VAN 40 30

CARLOS 25 15

FELIX 12 2

LARRY 6 -4

PART (E)

If the cost is divided up based on the benefits (remember how the price for movie was static despite the movie and satisfaction received by each viewer? That's about to change) or satisfaction each roommate receives, the practical problem with this 'solution' is that each roommate has an incentive to reduce the value of the movies to him; and this can only be measured by the efficient number (the number that rates the value each roommate derives from each movie). In this case, the incentive is the window given to each roommate to 'not tell the truth' about their level of satisfaction from watching each movie, because that would mean a higher bill for the individual.

KUDOS!