Two towns, each with three residents, are deciding
whether to put on a fireworks display to celebrate the
New Year. Fireworks cost $360. In each town, some
people enjoy fireworks more than others.
a. In the town of Bayport, each of the residents
values the public good as follows:
Frank $50
Joe $100
Callie $300
Would fireworks pass a cost–benefit analysis?
Explain.
b. The mayor of Bayport proposes to decide by
majority rule and, if the fireworks referendum
passes, to split the cost equally among all
residents. Who would vote in favor, and who
would vote against? Would the vote yield the
same answer as the cost–benefit analysis?
c. In the town of River Heights, each of the residents
values the public good as follows:
Nancy $20
Bess $140
Ned $160
Would fireworks pass a cost–benefit analysis?
Explain.
d. The mayor of River Heights also proposes to
decide by majority rule and, if the fireworks
referendum passes, to split the cost equally
among all residents. Who would vote in favor,
and who would vote against? Would the vote
yield the same answer as the cost–benefit
analysis?
e. What do you think these examples say about the
optimal provision of public goods?

Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

Public goods are those goods that are non-rival and non-excludable in consumption and examples of public goods are national defense, basic research, etc. One of the biggest problems with the provision of public goods is the free-rider problem an individual is called a free-rider who enjoys the benefit of a good but always avoid paying for it. The cost-benefit analysis is used in the case of the provision of public goods. The cost-benefit analysis refers to the study of the cost and benefits of providing a public good to the society by the government.

a) The cost of putting the firework display for the celebration of the new year is $360 and as there are three individuals in the town of Bayport Frank, Joe, and Callie and in this town, Frank is willing to pay $50 for the fireworks, Joe is willing to pay $100 for the fireworks, and Callie is willing to pay $300 for the fireworks so the 3 town members are willing to pay a total of $450 for the fireworks which are greater than the cost of putting the fireworks which are only $360 so in this town fireworks pass the cost-benefit analysis.

b) If the cost of putting up the fireworks is split equally among all three residents then each resident is required to pay $120. In this situation, Frank is going to vote against the referendum because his willingness to pay is only $50 which is less than his required share of $120 also Joe is also going to vote against the referendum because his willingness to pay is only $100 and it is less than the required share of $120 so Frank and Joe both are going to vote against the referendum. 

Carrie is going to vote in favor of the referendum because his willingness to pay is $300 which is way more than his required share of $120. So according to majority rule voting there will not be any fireworks.

The majority rule voting is not going to yield the same answer as the cost-benefit analaysis

c) The cost of putting the firework display for the celebration of the new year is $360 and as there are three individuals in the town of River Heights Nancy, Bess, and Ned and in this town, Nancy is willing to pay $20 for the fireworks, Bess is willing to pay $140 for the fireworks, and Ned is willing to pay $160 for the fireworks so the 3 town members are willing to pay a total of $320 for the fireworks which is less than the cost of putting the fireworks which is $360 so in this town fireworks does not pass the cost-benefit analysis.

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