Clarke Tax

To determine the true willingness to pay for public goods is difficult. The Clarke tax seeks to solve this problem.

Let’s consider an example.

A group of students living in a shared apartment wants to buy a new TV. The TV costs 600 EUR. They agree that the costs should be distributed evenly among the students. The question now is if they should buy the TV. They could ask everyone to reveal his willingness to pay. But someone who really wants to have this device would state a very high amount and someone who doesn’t want it replies a very low amount. There is an incentive to lie about the willingness to pay in both cases.

The willingness to pay is given in the table.

Student	Willingness to pay	Net WTP	Claimed WTP
1	100	100 – 200 = -100	-100
2	150	150 – 200 = -50	-50
3	500	500 – 200 = 300	300

For that reason, they agree on the following mechanism.

They buy the TV if the total net willingness to pay is higher than zero.

Therefore, they add the net wtps:

-100 -50 +300 = 150 > 0

As a consequence, they would buy the TV. But as we said, they have to check whether the wtps were revealed truthfully.

Now they check what student is pivotal. That means what individual wtp would make a difference if it was not considered.

Without student 1:

-50 +300 = 250 > 0 => Buy TV, student 1 is not pivotal (he doesn’t influence the decision)

Without student 2:

-100 + 300 = 200 > 0 => Buy TV, student 2 is not pivotal

Without student 3:

-100 – 50 = -150 < 0 => Don’t buy TV, student 3 is pivotal.

Student 3 has to pay the Clarke tax of 150.

This mechanism makes it unprofitable to lie about one’s willingness to pay.

Let’s consider a situation where student 1 lies about his wtp.

Student	Willingness to pay	Net WTP	Claimed WTP
1	100	100 – 200 = -100	-300
2	150	150 – 200 = -50	-50
3	500	500 – 200 = 300	300

-300 -50 + 300 = -50 < 0

The students don’t buy the TV.

Without student 1. -50 + 300 = 250 > 0 => Buy TV. Student 1 is pivotal. He would have to pay the Clarke tax of 250. The problem with this mechanism is that it is not resistant to collusion. It is also unclear whether people would agree on such a mechanism that forces them to pay a certain amount on top of the contribution to the public good.