Common Property and Public Goods

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Chapter 14

• Common Property and Public Goods

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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. Lets 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.
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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
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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.
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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.
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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.
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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. Lets 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. Lets put all of this info. in a
graph.
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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.
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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.
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1 admission fee
per visit
MBp
MCp
crowd size
9
8
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.
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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.
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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?
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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.