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:

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.

Answer 1

Public goods has two characteristic which is non excludable and non-rival. In this case watching movie in a dorm room is a public good because if other roommates of that dorm room watch that movie these 3 friends would not leave the room. Watching movie by other roommates will not affect other utility. Hence, both of these traits state that watching movie in dorm room is a public good. The given table shows the willingness to pay of each roommate for watching a movie. Summation of willingness to pay gives the total willingness of the roommates to pay for a movie Judd Joe Gus Tim S2 First Film Second film Third film Fourth film Fifth film S7 $6 $5 $4 $3 Total willingness for watching a move (Marginal benefit $17(= $7 +55 +$3+S2) $136=$6+S4+$2+$1) $9(= $5+3+1+SO) $6(= $4+S2 + S0+S0) $4(=$3+S1+SO+SO) SO S1 SO S O The total cost for renting a movie is $8. Therefore, the number of movies that will be watched are equal to the number of movies for which the total willingness to pay exceeds the cost of renting the movie. Marginal cost Difference First Film Second film Third film Fourth film | Fifth film Total willingness for watching a move (Marginal benefit) $17(= $7 +55 +53 +$2) $13(=$6+S4 +$2+S1) $9(=$5+$3+S1+SO) $6(=$4+$2+S0+S0) $4=$3+S1+S0+S0) $8 $8 $8 $8 S8 -$2 -54 Since the difference is positive till third film. Thus for 3 movies marginal benefit of watching a movie is more than the cost incurred on renting those movies. Therefore, roommates should rent 3 movies to maximize total surplus.

if they are choose to watch 3 movies, they have to pat $24(= $8x3). Now, calculate the surplus Surplus = Total willingness to pay - Cost for renting 3 movies First Film Second film Third film Total willingness Splitted cost to pay $6(24/4) 18 Surplus Judd Joe Gus Tim Therefore, Judd has a surplus of $12. Joe has surplus of $6 Gus gets no surplus and Tim gets a negative surplus of $3. This is difficult because everyone would have the incentive to lie about how much they willingness to pay for watching a movie. For example, Joe's total willingness to pay off is $12, however, by splitting the cast, Joe is only paying $6. Thus, there is no way to split the cost to ensure that everyone benefits. Judd would have the incentive to tell the truth about how much he would be willing to pay to ensure that the group rents three movies. As they already agreed to rent three movies then Judd have an incentive to tell the truth. To calculate the efficient amount, one can't rely on the reported valuation of participants and It is very difficult to achieve the optimal division of public goods because people do not have the incentive to pay the amount, they actually value the good because such goods are not excludable. The provision of public goods is more difficult than provision of private goods. There are no price signals sent from the user of public goods.