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Homework answers / question archive / Tim and Brian are considering contributing to the creation of a botanical garden
Tim and Brian are considering contributing to the creation of a botanical garden. Each can choose whether to contribute $300 to the botanical garden or to keep that $300 for a weekend getaway.
Since a botanical garden is a public good, both Tim and Brian will benefit from any contributions made by the other person. Specifically, every dollar that either one of them contributes will bring each of them $0.90 of benefit.
Since a weekend getaway is a private good, if Tim chooses to spend $300 on a weekend getaway, Tim would get $300 of benefit from the weekend getaway and Brian wouldn't receive any benefit from Tim's choice. If Tim still spends $300 on a weekend getaway and Brian chooses to contribute $300 to the botanical garden, Tim would still receive the $270 of benefit from Brian's generosity. In other words, if Tim decides to keep the $300 for a weekend getaway and Brian decides to contribute the $300 to the public project, then Tim would receive a total benefit of $570, Brian would receive a total benefit of $270, and their combined benefit would be $840. This is shown in the lower left cell of the first table.
Complete the following table, which shows the combined benefits of Tim and Brian as previously described.
| Brian | |||
|---|---|---|---|
| Contributes | Doesn't Contributes | ||
| Tim | Contributes | $1,080 | |
| Doesn't contribute | $840 | ||
Of the four cells of the table, which gives the greatest combined benefits to Tim and Brian?
When both Tim and Brian contribute to the botanical garden
When neither Tim nor Brian contributes to the botanical garden
When Tim contributes to the botanical garden and Brian doesn't, or vice versa
Now, consider the incentive facing Tim individually. The following table looks similar to the previous one, but this time, it is partially completed with theindividual benefit data for Tim. As shown previously, if both Tim and Brian contribute to a public good, Tim receives a benefit of $540. On the other hand, if Brian contributes to the botanical garden and Tim does not, Tim receives a benefit of $570.
Complete the right-hand column of the following table which shows the individual benefits of Tim.
Hint: You are not required to consider the benefit of Brian.
| Brian | |||
|---|---|---|---|
| Contributes | Doesn't Contributes | ||
| Tim | Contributes | $540 | |
| Doesn't contribute | $570 | ||
If Brian decides to contribute to the botanical garden, Tim would maximize his benefit by choosing to to the botanical garden. On the other hand, if Brian decides not to contribute to the botanical garden, Tim would maximize his benefit by choosing to to the botanical garden.
These results illustrate .
a) If Tim contributes but Brian does not. The combined benefit would be 300*0.9*2 (Tim's contribution benefiting the two)+ 300 (Brian's getaway to his own benefit)= $840.
If neither contributes, the total benefit would be 300 (Tim's getaway to his own benefit)+300 (Brian's getaway to his own benefit)= $600
See the complete table below for total benefit:
| Brian | |||
|---|---|---|---|
| Contributes | Doesn't Contribute | ||
| Tim | Contributes | $1,080 | $840 |
| Doesn't contribute | $840 | $600 |
As we can see, of the four cells of the table, (Contributes, Contributes) gives the greatest combined benefits to Tim and Brian.
b) When Brian does not contribute,
If Tim contributes, Tim receives 300*0.9 (Tim benefiting from his contribution) =$270
If Tim does not contribute, Tim receives $300, his getaway benefit.
See the table below for Tim's benefit:
| Brian | |||
|---|---|---|---|
| Contributes | Doesn't Contribute | ||
| Tim | Contributes | $540 | $270 |
| Doesn't contribute | $570 | $300 |
As can be seen, regardless of Brian's choice, Tim is better off sticking to the "Does not contribute" action, and this is a typical result of a public good- people end up not contributing to the good for self interest protection.
