Two towns, each with three members, are deciding whether to put on a fireworks display to celebrate the new year. fireworks cost $300. in each town, some people enjoy fireworks more than others. in the town of bayport, each of the residents values the public good as follows:

1) Town of Bayport:

We have that the residents value the fireworks at a total of 50+100+300=450$. That is the utility they gain. But they would also have to pay 360$ for the fireworks. The total outcome is 450$ + (-360$) = 90$. Hence, the outcome is positive and the fireworks pass the cost benefit analysis.

If the fireworks' cost is to be split equally, we have that each of the 3 residents has to pay 360/3=120$. Let us now do the cost-benefit analysis for everyone.

Jacques stands to gain 50$ from the fireworks but would have to pay 120$. He will vote against it.

Also, Kyoko will gain 100$ but would have to pay 120$. He will lose utility/money from this so he will vote against.

Musashi on the other hand, would gain 300$ and only pay 120$. He is largely benefitted by this measure. Only he would

We have that 2 out of the 3 would vote against the fireworks, so that the fireworks will not be bought. The vote does not yield the same answer as the benefit-cost analysis.

2) Town of River Heights:

We have that the total value of the fireworks to the community is 20+140+160=320$. The total value of the fireworks is lower than their cost so their cost benefit analysis yields that they should not be bought.

However, let's see what each resident says. The cost to each resident is 360/3=120$. Rina is against the fireworks since she will only gain 20$. Sean and Yvette are for the fireworks since they gain 140$ and 160$ respectively, which are larger than the cost of the fireworks to each of them (120$). Hence, 2 will vote for the fireworks and one will vote against and fireworks will be bought.

Again, the vote clashes with the cost-benefit analysis.

3) The first choice is wrong. It is very difficult for a government to provide the exact types of public goods that everyone wants because that would be too costly; one cannot have a public good that everyone pays for so that only a couple of people enjoy it. In our example, we saw that in every case, a public good and its production would have sime supporters and some adversaries.

Majority rule is not always the most efficient way to decide public goods; as we have seen in the second case, the cost-benefit analysis yields that the fireworks are not worth it but they are approved by the majority nonetheless.

The final sentence is correct. The differing preferences of the people make a clearcut choice impossible and the government has to take into account various tradeoffs and compromises in order to determine which public goods to provide.