(See Problem 2.) A small community has 40 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $400 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is b times the total amount of money contributed by individuals in the community. A) This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment. B) If 40b 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 40b 1, there is a dominant strategy equilibrium in which everybody contributes. D) Everybody is worse off if all contribute than if nobody contributes if b 1, but if b 40.

Question

(See Problem 2.) A small community has 40 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $400 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is b times the total amount of money contributed by individuals in the community. A) This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment. B) If 40b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 40b < 1, everybody is better off if nobody contributes than if all contribute. C) If 40b > 1, there is a dominant strategy equilibrium in which everybody contributes. D) Everybody is worse off if all contribute than if nobody contributes if b > 1, but if b < 1, everybody is better off if nobody contributes. E) In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 40.

Quizplus · Accepted Answer

If 40b > 1, then the total benefit for the entire community is greater than the cost of contributing ($400) for each person, so everybody is better off contributing to the public entertainment fund. This creates a Nash equilibrium where all 40 individuals contribute. 
On the other hand, if 40b < 1, the total benefit is less than the cost of contributing, so nobody will want to contribute. This also creates a Nash equilibrium where nobody contributes. Therefore, choice B is the correct answer.