Answer
a) 3 films
b) 2 films
c) 2 films
d) Quentin and Spike would each vote for three films, while Ridley, Martin, and Steven would each vote for two films. The majority would be with two films.
e) No, the proposal would lose.
f) We cannot count on majority rule to reach efficient outcomes regarding public goods.
Work Step by Step
a)
$14+10+8+4+2=38$ (first film)
$12+8+4+2=26$ (second film)
$10+6+2=18$ (third film)
$6+2=8$ (fourth film)
$2=2$ (fifth film)
Total surplus is maximized with three films, as the total surplus for the fourth film is 8 dollars (compared to the cost of 15 dollars of the film).
b)
Quentin's net surplus (after paying for the movie) is positive for the first four films. Spike's net surplus is positive for the first three films. Ridley's net surplus is positive for the first two films. Martin's net surplus is positive for the first movie, and Steven's net surplus is positive for no films.
If we add up how many films have a positive surplus for each person, we have 10 films ($4+3+2+1+0=10$). However, since there are 5 roommates, $10/5=2$, so two films are the median and average voter's preferred number of movies.
c) $0, 1, 2, 3, 4$
Of this set of numbers, the median number is 2.
d) Quentin and Spike would each vote for three films, while Ridley, Martin, and Steven would each vote for two films.
e) If someone wanted one film (or no films at all), three people would want to watch at least two films. If someone wanted to watch three (or more) films, three people would want to watch no more than two films.
