Question

# Homework 11 3. Voluntary contributions toward a public good Musashi and Sean are considering contributing toward...

Homework 11

3. Voluntary contributions toward a public good

Musashi and Sean are considering contributing toward the creation of a water fountain. Each can choose whether to contribute \$400 to the water fountain or to keep that \$400 for a pool table.

Since a water fountain is a public good, both Musashi and Sean will benefit from any contributions made by the other person. Specifically, every dollar that either one of them contributes will bring each of them \$0.80 of benefit. For example, if both Musashi and Sean choose to contribute, then a total of \$800 would be contributed to the water fountain. So, Musashi and Sean would each receive \$640 of benefit from the water fountain, and their combined benefit would be \$1,280. This is shown in the upper left cell of the first table.

Since a pool table is a private good, if Musashi chooses to spend \$400 on a pool table, Musashi would get \$400 of benefit from the pool table and Sean wouldn't receive any benefit from Musashi's choice. If Musashi still spends \$400 on a pool table and Sean chooses to contribute \$400 to the water fountain, Musashi would still receive the \$320 of benefit from Sean's generosity. In other words, if Musashi decides to keep the \$400 for a pool table and Sean decides to contribute the \$400 to the public project, then Musashi would receive a total benefit of \$400+\$320=\$720\$400+\$320=\$720, Sean would receive a total benefit of \$320, and their combined benefit would be \$1,040. This is shown in the lower left cell of the first table.

Complete the following table, which shows the combined benefits of Musashi and Sean as previously described.

 Sean Contributes Doesn't contribute Musashi Contributes \$1,280 Doesn't contribute \$1,040

Of the four cells of the table, which gives the greatest combined benefits to Musashi and Sean?

When both Musashi and Sean contribute to the water fountain

When neither Musashi nor Sean contributes to the water fountain

When Musashi contributes to the water fountain and Sean doesn't, or vice versa

Now, consider the incentive facing Musashi individually. The following table looks similar to the previous one, but this time, it is partially completed with the individual benefit data for Musashi. As shown previously, if both Musashi and Sean contribute to a public good, Musashi receives a benefit of \$640. On the other hand, if Sean contributes to the water fountain and Musashi does not, Musashi receives a benefit of \$720.

Complete the right-hand column of the following table, which shows the individual benefits of Musashi.

Hint: You are not required to consider the benefit of Sean.

 Sean Contribute Doesn't contribute Musashi Contribute \$640, -- , -- Doesn't contribute \$720, -- , --

If Sean decides to contribute to the water fountain, Musashi would maximize his benefit by choosing (Contribute OR Not to contribute)   to the water fountain. On the other hand, if Sean decides not to contribute to the water fountain, Musashi would maximize his benefit by choosing (Contribute OR Not to contribute) to the water fountain.

These results illustrate .(Why markets are efficient, The creation of positive externality, The tragedy of the common OR The free-rider problem)

6. Common resources and the tragedy of the commons

Andrew, Darnell, and Jacques are lumberjacks who live next to a forest that is open to logging; in other words, anyone is free to use the forest for logging. Assume that these men are the only three lumberjacks who log in this forest and that the forest is large enough for all three lumberjacks to log intensively at the same time.

Each year, the lumberjacks choose independently how many acres of trees to cut down; specifically, they choose whether to log intensively (that is, to clear-cut a section of the forest, which hurts the sustainability of the forest if enough people do it) or to log nonintensively (which does not hurt the sustainability of the forest). None of them has the ability to control how much the others log, and each lumberjack cares only about his own profitability and not about the state of the forest.

Assume that as long as no more than one lumberjack logs intensively, there are enough trees to regrow the forest. However, if two or more log intensively, the forest will become useless in the future. Of course, logging intensively earns a lumberjack more money and greater profit because he can sell more trees.

The forest is an example of (A club good, Public good, Private Good OR Common Resources) because the trees in the forest are (nonexcludate OR Excludable)   and .

Depending on whether Darnell and Jacques both choose to log either nonintensively or intensively, fill in Andrew's profit-maximizing response in the following table, given Darnell and Jacques's actions.

Darnell and Jacques's Actions

Andrew's Profit-Maximizing Response (Log Nonintensively OR log Intensively)

Which of the following solutions could ensure that the forest is sustainable in the long run, assuming that the regulation is enforceable? Check all that apply.

Develop a program that entices more lumberjacks to move to the area.

Convert the forest to private property, and allow the owner to sell logging rights.

Outlaw intensive logging.

1)

.

 Sean Contributes Doesn't contribute Musashi Contributes \$1,280 400+320+320 = 1040 Doesn't contribute \$1,040 400+400 = 800

Of the four cells of the table, which gives the greatest combined benefits to Musashi and Sean?

When both Musashi and Sean contribute to the water fountain

.

 Sean Contribute Doesn't contribute Musashi Contribute \$640, -- 320, -- Doesn't contribute \$720, -- 400, --

If Sean decides to contribute to the water fountain, Musashi would maximize his benefit by choosing (Not to contribute)   to the water fountain. On the other hand, if Sean decides not to contribute to the water fountain, Musashi would maximize his benefit by choosing (Not to contribute) to the water fountain.

These results illustrate (The free-rider problem)

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