Common Property and Public Goods

1. Common Property and Public Goods

2. Overview This chapter is an extension of the chapter on externalities. Common property has no owner and there is no restriction on its use. The result is dissipation of rents, or no net surplus values. This notion has been called the tragedy of the commons. Let’s turn to an example of a town that has an aquarium. Initially we will assume there is no fee to enter the aquarium. This assumption makes the aquarium common property.

3. example - aquarium The following table will be explained as we proceed. crowd value of total value social marginal size a visit of visits benefit 1 $10/visitor $10 $10/visitor 2 9 18 8 3 8 24 6 4 7 28 4 5 6 30 2 6 5 30 0 7 4 28 -2 8 3 24 -4 9 2 18 -6 10 1 10 -8

4. example - aquarium On the previous screen we have an example of an aquarium. In the first column we show various crowd sizes at the aquarium. In the second column we show the value of a visit for the nth visitor, given other visitors are present. For example, the 1st visitor values the visit at $10. The second visitor, with one person already there, values the visit at $9. But, due to the presence of the second visitor, the first visitor also now only values the visit at $9. The second person creates a negative externality for the first person, reducing the value of the visit for the first person.

5. note a difference Last chapter we saw that an externality could be thought of as an addition to cost, although not paid by the producer(s). In this chapter we see that an external cost can also be viewed as a reduction in benefit. The author wants us to see many points of view. Treat the externality as an added cost OR a reduction in benefit.

6. example - aquarium The second column could be called the private marginal benefit that each new visitor gains from going to the aquarium. In the third column we see the total value of visits at each crowd size. Just multiple column one and two together. In column four we see the social marginal benefit due to each new visitor. Note the fourth visitor results in a value of 4, but the fourth visitor values the visit at 7. But, while the fourth visitor values the visit at 7, their presence reduces the value to the other three by 1 each and thus society has a net of 4.

7. example - aquarium Now, in order to talk about the value of the aquarium we have to think about what people give up if they go to the aquarium. Let’s imagine that people would just go to the park and they would value the visit to the park at $2. This means people would go to the aquarium as long as the value of the aquarium trip is of greater, or equal, value. What this means is that the cost of going to the aquarium is the value of the park visit forgone. Let’s put all of this info. in a graph.

8. example - aquarium $ per visit MBp MCp crowd size 9 MBs

9. example - no admission fee solution In the absence of an admission fee people will visit the aquarium as long as the private marginal benefit is greater than or equal to the private marginal cost. Thus 9 people visit the aquarium. Now, with 9 visitors, each visitor only receives $2 worth of benefits from the aquarium. But, this is as much as they received at the park. The net surplus is zero. There is nothing gained in the town by having an aquarium.

10. social optimum You will note that with 9 visitors the marginal social benefit is a minus 6 and the marginal cost is 2. Some visitors reduce the social benefit below cost because of the externality they cause. Societies optimum is reached where the social marginal benefit is equal to the marginal cost. We saw in the section on externalities a way to get to the social optimum was through a tax on the externality causing entity. The entity here is the visitors to the aquarium. The externality is the disruption they cause to other visitors in the normal course of viewing the aquarium. Some visitors could bribe others not to come, but here the tax will take the form of an admission fee to the aquarium.

11. $1 admission fee $ per visit MBp MCp crowd size 8 9 MBs

12. $1 admission fee A $1 admission fee would make the MC of visiting the aquarium $3 ($2 in giving up the park and the $1 fee). So only 8 visitors have enough benefit to overcome the cost of visiting the aquarium. Now here is how we would measure the social gain. 1) 8 visitors have a private benefit of $3 each, a + $24. 2) 8 visitors have cost of not visiting the park of $2 each, a - $16. 3) The visitors pay the fee if $1, a minus for surplus, but the city receives the revenue, a benefit. Thus the fee is a net wash. Welfare gain = $8 when the fee is $1.

13. $2 admission fee A $2 admission fee would make the MC of visiting the aquarium $4 ($2 in giving up the park and the $2 fee). So only 7 visitors have enough benefit to overcome the cost of visiting the aquarium. Now here is how we would measure the social gain. 1) 7 visitors have a private benefit of $4 each, a + $28. 2) 7 visitors have cost of not visiting the park of $2 each, a - $14. 3) The visitors pay the fee if $2, a minus for surplus, but the city receives the revenue, a benefit. Thus the fee is a net wash. Welfare gain = $14 when the fee is $2.

14. $4 admission fee. We could continue the process of checking higher fees and we would see the fee that leaves society the best off is a $4 fee. NOTE, this occurs where the social marginal benefit equals the original marginal cost of $2. The fee is $4 because that raises the marginal cost enough to equal the value of a visit for the visitors. What is the social gain here?

15. generalize We see here when no one owns, or has a property right to the common property, the property gets overused from a social point of view. A well defined property right, here the ability to charge an entrance fee, can move society to the optimum. We have an optimum in the sense that the social gain is the largest it can be.