Question

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)
	Felix	Larry	Raphael	Alex
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 movie   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)
Felix
Larry
Raphael
Alex		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 Felix is asked his willingness to pay, he will have an incentive to tell the truth. True False

Answer 1

Within the dorm room showing a movie is a public good.

Cost of renting a movie - $8

For the first film total willingness to pay is- $7+$5+$3+$2= $17 which is greater than renting this movie which is $8

For the second film total willingness to pay is= $6+$4+$2+$1= $13 which is greater than the cost of renting this movie which is $8

For the third film total willingness to pay is= $5+$3+$1+$0= $9 which is greater than the cost of renting this movie which is $8

For the fourth film total willingness to pay is= $4+$2+$0+$0= $6 which is less than the cost of renting this movie which is $8

For the fourth film total willingness to pay is= $3+$1+$0+$0= $4 which is less than the cost of renting this movie which is $8

So we can conclude that the roommates should rent three films as for the other two movies willingness to pay for the movie is less than the cost of renting the movie.

Now each movie costs $8. So renting 3 movies will cost $8*3= $24

Now if all the four roommates split the cost of renting the movies equally then each roommate will pay

$24/ 4 = $6

Now for Felix

Total willingness to pay for the three movies are = $7+$6+$5= $18

He will pay $6 for renting 3 movies

So consumer surplus will be = willingness to pay- cost of renting movies = $18-$6 = $12

For Larry

Total willingness to pay = $5+$4+$3 = $12

He will pay $6 to rent these movies

So consumer surplus = $12 - $ 6 = $6

For Raphael

Total willingness to pay for three movies = $3+ $2 +$1= $6

He will pay $ 6 to rent these movies

So consumer surplus is = $6 - $6 = 0

For Alex

Total willingness to pay for three movies

= $2+$1+$0= $3

He will pay $6 to rent these movies

So consumer surplus is = $3- $6 = -$3

As the roommates split the cost of the movies equally Felix has an incentive, to tell the truth about his willingness to pay because his cost per movie is $6/3 = $2 which is less than his willingness ness to pay for each of three movies.

That is $7 > $2

$6 > $2

$5> $2

So the statement is true.