Answer
a) Yes, the movie showing is a public good since nobody is excluded from watching the movie.
b) Three movies should be rented.
c) Judd has 12 dollars surplus, Joel has 6 dollars surplus, Gus has no surplus, and Tim has -3 dollars surplus.
d) A larger share of the cost of the films could be borne by Judd (since Judd has the highest surplus).
e) Judd does have an incentive to tell the truth since the group has the greatest surplus when the group rents exactly three movies.
f) This example shows that the optimal provision of public goods will happen if all interested parties (in the public goods) don't have any incentives to hide how they value the good.
Work Step by Step
b)
First movie: $7+5+3+2-8=9$
Second movie: $6+4+2+1-8=5$
Third movie: $5+3+1+0-8=1$
Fourth movie: $4+2+0+0-8=-2$
c)
Three movies rented cost 24 dollars, and an equal share of renting the movies for each person is 6 dollars.
Judd: $7+6+5-6=12$
Joel: $5+4+3-6=6$
Gus: $3+2+1-6=0$
Tim: $2+1+0-6=-3$
d) However, this could lead to everyone else undervaluing the value of the movies. (This would shift even more of the cost to Judd, and eventually, Judd would have a negative surplus, so no movies would be watched.)
