Problem 3. Four roommates are planning to spend the weekend in their dorm room w

Question

Problem 3. 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 (in dollars): Allan Bob Cris Dave 1st film 7 532 2nd film 6 42 rd film5 4h film 4 | 5th film I 3 (a) If it costs $8 to rent a movie, how many movies should the roommates rent to maximize total surplus? (b) If they choose the optimal number from part (a) and then split the cost of renting the movies equally, how much surplus does each person obtain from watching the movies?

Explanation / Answer

a) The rent to watch movie is given as $8.

For finding the optimal number of movies watched by the roommates , the total willingness for each movie should be calculated .

so we have for movies 1 = $7+$5+$3+$2 =$17

movie 2 = $ (6+4+2+1) = $13

movie 3= $(5+3+1+0)= $9

movie 4= $(4+2)= $6
movie 5 = $(3+1)= $4

The following table is showing the marginal benefit and amrginal cost of each movie

So three movies should be watched because in the fourth movie the marginal cost is more than the marginal benefit .

b)Total cost for 3 movies is $8*3= $24/4= $6

for each of the roommate will pay $ 6

Adding the willingness to pay for 3 movies of 4 roommates individually we get

Allan = $(7+6+5) = $18

Bob = $(5+4+3) = $ 12

Cris= $(3+2+1)= $6

Dave = $(2+1)= $3

Surplus would be

Allan = $18- $6= $12

Bob = $ 12- 6= $6

Cris = $(6-6) = 0

Dave = $3-$6= - $3

c) There is a solution which is when all of them reveal their preferences or willingness to pay and the amount or costs can be split according to the proportion of their willingness to pay .

The practical problem arising would be that it is not always necessary that the roommates will reveal their preferences honestly. If they do then everyone can be benefitted from it though the amounts would be different from the current method .

d) Allan may have an incentive to pay if only he feels that the others will reveal their preferences honestly .

He would be tempted not to reveal his actual preferences . There can be a problem of free rider ie he under reveal his willingness to pay so that others end up paying the amount and the movie is rented . This way he will free ride and his surplus will increase. . But if everyone does it , it might even lead to not watching the movie.

movie Marginal cost Marginal benefit 1 $8 $17 2 $8 $13 3 $8 $9 4 $8 $6 5 $8 $4

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