Question

Nick and Tim are considering contributing toward the creation of a water fountain. Each can choose whether to contribute $300 to the water fountain or to keep that $300 for a pool table.

Since a water fountain is a public good, both Nick and Tim will benefit from any contributions made by the other person. Specifically, every dollar that either one of them contributes will bring each of them $0.70 of benefit. For example, if both Nick and Tim choose to contribute, then a total of $600 would be contributed to the water fountain. So, Nick and Tim would each receive $420 of benefit from the water fountain, and their combined benefit would be $840. This is shown in the upper left cell of the first table.

Since a pool table is a private good, if Nick chooses to spend $300 on a pool table, Nick would get $300 of benefit from the pool table and Tim wouldn't receive any benefit from Nick's choice. If Nick still spends $300 on a pool table and Tim chooses to contribute $300 to the water fountain, Nick would still receive the $210 of benefit from Tim's generosity. In other words, if Nick decides to keep the $300 for a pool table and Tim decides to contribute the $300 to the public project, then Nick would receive a total benefit of $300+$210=$510$300+$210=$510, Tim would receive a total benefit of $210, and their combined benefit would be $720. This is shown in the lower left cell of the first table.

Complete the following table, which shows the combined benefits of Nick and Tim as previously described.

		Tim
		Contributes	Doesn't contribute
Nick	Contributes	$840
	Doesn't contribute	$720

Of the four cells of the table, which gives the greatest combined benefits to Nick and Tim?

When both Nick and Tim contribute to the water fountain

When neither Nick nor Tim contributes to the water fountain

When Nick contributes to the water fountain and Tim doesn't, or vice versa

Now, consider the incentive facing Nick individually. The following table looks similar to the previous one, but this time, it is partially completed with the individual benefit data for Nick. As shown previously, if both Nick and Tim contribute to a public good, Nick receives a benefit of $420. On the other hand, if Tim contributes to the water fountain and Nick does not, Nick receives a benefit of $510.

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

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

		Tim
		Contribute	Doesn't contribute
Nick	Contribute	$420, --	, --
	Doesn't contribute	$510, --	, --

If Tim decides to contribute to the water fountain, Nick would maximize his benefit by choosing   to the water fountain. On the other hand, if Tim decides not to contribute to the water fountain, Nick would maximize his benefit by choosing   to the water fountain.

These results illustrate   .

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Answer 1

	Tim: Contributes	Doesn't contribute
Nick: Contributes	840	720
Doesn't contribute	720	600

(When Tim contributes and Nick doesn't, their combined benefit is 720. Similarly, when Nick contributes and Tim doesn't, their comined benefit would be 720. When neither of them contributes, each inidvidual's benefit = 300 from pool. So, combined benefit = 300 + 300 = 600)

When both Nick and Tim contribute to the water fountain
(Combined benefit is highest at $840 when they both contribute.)

	Tim: Contributes	Doesn't contribute
Nick: Contributes	420	210
Doesn't contribute	510	300

(When Nick contributes and Tim doesn't contribute, Nick's benefit is 0.7*300 = 210
When both doesn't contribute, Nick's benefit = 300)

If Tim decides to contribute to the water fountain, Nick would maximize his benefit by choosing to not contribute to the water fountain. On the other hand, if Tim decides not to contribute to the water fountain, Nick would maximize his benefit by choosing not contribute to the water fountain.
(As 510 > 420 and 300 > 210.)