Dr. Shishkin
ECON 2106
Assignment #15
Fall 2010
ANSWERS
Common Resources and Public Goods
Number
of boats
(1)
0
100
200
300
400
500
600
Total catch
(tons per
month)
(2)
0
7,000
12,000
15,000
16,000
15,000
12,000
MB = Total Catch/ Marginal Cost (the MSB per boat
Number of Boats cost of adding one when adding
more boat)
100 boats
(3)
(4)
(5)
n/a
n/a
n/a
70
25
70
60
25
50
50
25
30
40
25
10
30
25
-10
20
25
-30
The table above shows how the sustainable catch of fish in the Mediterranean Sea
depends on the number of boats that go fishing. The marginal cost of operating a fishing
boat is the same for all producers , the equivalent of 25 tons of fish a month.
1) What is the equilibrium number of boats in the Mediterranean Sea in this case?
Explain how you can find this answer using the concept of marginal private
benefit from adding one more additional boat.
The equilibrium number of boats will be achieved at the number of boats where MB=MC
(marginal private benefit = marginal private cost). The private benefit per boat can be
found as the average catch per boat when the boat is added. For example, where there are
100 boats are fishing, 7,000 tons of fish per month are caught, which is 70 tons per boat.
Thus, when someone adds an additional boat, he will be getting 70 tons per month from
his boat (technically, it will be a tiny bit less, but one additional boat does not change
much, so this number is accurate enough for our purposes). This is what individual
fishermen will be looking at when deciding whether to put their boats on the water or not.
As long, as MB>MC, there will be an inflow of boats to the fishing area because the
difference between MB and MC is the net catch (which could be considered as the profit
per boat). When MB=MC, an equilibrium is achieved because everyone is breaking even,
just covering their cost of maintaining their boats (it would be more intuitive, if you
realize that so-called “normal profit” is included in the cost – something that people
expect to earn on the top of their basic expenses in any kind of business).
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1
Dr. Shishkin
ECON 2106
Fall 2010
Column (4) has the number for MB. There is not exact match for MB and MC, so we can
not really find the exact number of boats for which MB=MC. All we know is that it’s
between 500 and 600. To resolve this ambiguity, lets assume that boats go in groups of
100 (e.g. for safety reasons - there might be pirates around!). In such a case, the
equilibrium number of boats will be at 500 boats. If another group of 100 boats takes off,
it will be losing money because with 600 boats out there the average catch will be 20 tons
per boat, which is less than 25, which is the cost per boat.
2) If an extra hundred boats getting into fishing while there are 300 boats currently
fishing, what would be the marginal social benefit from this increase in the
number of boats fishing?
As we add 100 extra boats to 300, the total catch changes from 15,000 to 16,000 tons of
fish per month: 1000 tons/100 bots = 10 tons per boat.
3) What is the efficient number of fishing boats in the Mediterranean Sea, if boats
can only be added in groups of 100? Explain how you can find this answer using
the marginal analysis approach.
The marginal analysis approach tells us that we should keep extending a particular
activity in small increments as long as each additional steps gives us more in benefit than
takes away in cost (MB>MC). As soon as we achieved the level of output (or
consumption) where MB=MC, we should stop. This is what we have in theory. In real
life we can not usually get exactly to the point where MB=MC (it can only be done when
moving in very small steps, which is not always possible), so a more practical rule is to
stop right before MB becomes smaller than MC, i.e. make the last step for which
MB>MC and don’t go any further. If we follow this rule, we should stop at 300 boats
because adding another hundred will cost 25 tons of fish per boat, and will only add 20
tons of fish per boat in benefit.
Email me at [email protected], and text at (678) 524-5535 if I don’t respond
2
Dr. Shishkin
ECON 2106
Fall 2010
4) Explain how you can double check the answer looking at the net catch (i.e. the
total catch minus cost of maintaining the boats) from the Mediterranean Sea.
Number
Total catch
of boats (tons per month)
(1)
0
100
200
300
400
500
600
(2)
0
7,000
12,000
15,000
16,000
15,000
12,000
Total Cost,
tons of fish
25 x #of Boats)
(6)
0
2,500
5,000
7,500
10,000
12,500
15,000
Net Catch,
tons per
month
(7)
0
4,500
7,000
7,500
6,000
2,500
-3,000
7,500 is the largest net catch (profit) that we can get, which corresponds to 300 boats –
exactly the number that we got when using the marginal analysis approach.
5) If individual transferable quotas (ITQs) are issued to fishing boats to limit the catch in
the Mediterranean Sea to the efficient quantity, what would be the price of an ITQ if
measured in tons of fish per month? Use the following template to build a diagram
that will help you to answer this question:
The price of ITQ will be equal to the net catch per boat, or 50-25=25 tons of fish per
month.
6)
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3
Dr. Shishkin
ECON 2106
Fall 2010
What does it mean for a good to be "nonexcludable"? Are private goods
nonexcludable? Are public goods nonexcludable? Are common resources
nonexcludable?
Nonexcludabe goods are goods for which it is very difficult or impossible to prevent
someone from consuming them.
Private goods are excludable.
Public goods and common resources are nonexcludable.
7) When describing goods and services, what is meant by the terms "rival" and
"nonrival?" Are private goods rival or nonrival? Are public goods rival or
nonrival? Are common resources rival or nonrival?
A good is rival if its use by one person decreases the quantity available to someone else.
Private goods and common resources are rival.
Public goods are not rival.
8) Paul and Paula are the only members of society. The table above gives their
marginal benefits from missile gunboats, a public good. Suppose the marginal
cost of a missile gunboat is $7 million. What is the efficient quantity of missile
gunboats? Explain how you should apply the marginal analysis approach to
answer this question.
As usual, we have to compare marginal benefit and marginal cost for each increase in
quantity of the good. For a public good, the MSB is the sum of MB from this good to
everyone in the society. Thus, MSB=MBpaul + MBpaula. They should produce up to
the point where the last gunboat produced generates larger MSB than MC, which the
3rd boat.
Number
of missile
boats
1
2
3
4
MB
MC
16
12
8
4
7
7
7
7
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