1. Tragedy of the Commons
April 26, 2013

2. Announcements
• Practice questions for the midterm (week
from today!) are now posted on website.
• TAs will go over half of the questions in their
regularly scheduled discussion sections.
• Jake will do a midterm review Thursday night
and go over other half
– I’ll post on website when we find out where and
when this will be. Around 6-8 pm.

3. OMG midterm?
• All topics from day 1 through today
• Next week we’ll spend time pulling everything together
Warnings:
(1) You must be on-time to exam. Friday, May 3, 3pm
sharp.
-10% Deduction if you are 1 second late.
-100% deduction if you arrive after someone else
finishes and leaves room.
(2) No leaving room during exam (it’s less than an hour).

4. Last Class
• Continued discussing externalities
• Focused on when the Coase theorem
applies, and when it doesn’t
– when it doesn’t, policy must be introduced

5. Learning Goals for Today

6. Property Rights and the
Tragedy of the Commons
• The tragedy of the commons: the tendency for a resource that
has no price to be used until it’s marginal benefit=0.
• Question: Do you have an incentive to go fill up that horrible
pothole on your street?

7. Problem Setup
• Village with 5 residents.
• Each with $100 in savings.
• They can each either buy
– A $100 government bond with an annual interest rate of
13%.
– A $100 steer to send out onto the commons to graze for a
year.
• The price at which they can sell the steer at the end of the
year depends on how much weight it gains, which in turn
depends on how many other steers are sent out to graze in
the commons.

8. Property Rights&Tragedy of the Commons
Number of
Steers on
Commons
Price Per
2-Year Old
Steer
Income
Per Steer
Total
Cattle
Income
Marginal
Income
1 126 26
2 119 19
3 116 16
4 113 13
5 111 11
The village has $500 total. What is the optimum amount of steers
for the entire village to choose (the rest buys 13% yield bonds)?
A
B
C
D
E

9. Property Rights&Tragedy of the Commons
Number of
Steers on
Commons
Price Per
2-Year Old
Steer
Income
Per Steer
Total
Cattle
Income
Marginal
Income
1 126 26
2 119 19
3 116 16
4 113 13
5 111 11
The village has $500 total. What is the optimum amount of steers
for the entire village to choose (the rest buys 13% yield bonds)?
26
38
48
52
55
26
12
10
4
3
A
B
C
D
E

10. Property Rights&Tragedy of the Commons
Number of
Steers on
Commons
Price Per
2-Year Old
Steer
Income
Per Steer
Total
Cattle
Income
Marginal
Income
1 126 26
2 119 19
3 116 16
4 113 13
5 111 11
If the villagers act independently, how many steers will be sent
into the commons?
A
B
C
D
E

11. Property Rights&Tragedy of the Commons
Number of
Steers on
Commons
Price Per
2-Year Old
Steer
Income
Per Steer
Total
Cattle
Income
Marginal
Income
1 126 26
2 119 19
3 116 16
4 113 13
5 111 11
If the villagers act independently, how many steers will be sent
into the commons?
26
38
48
52
55
26
12
10
4
3
26/1=26
38/2=19
48/3=16
52/4=13
55/5=11
Each!
A
B
C
D
E

12. Property Rights&Tragedy of the Commons
Number of
Steers on
Commons
Price Per
2-Year Old
Steer
Income
Per Steer
Total
Cattle
Income
Marginal
Income
1 126 26
2 119 19
3 116 16
4 113 13
5 111 11
What is the difference in incomes, Together – Separate?
26
38
48
52
55
26
12
10
4
3
26/1=26
38/2=19
48/3=16
52/4=13
55/5=11
Each!
A) 17
B) 15
C) 13
D) 11
E) 9
Together: 1 steer, 4 13% bonds.
Separate: 4 steer, 1 13% bond.

13. Property Rights and the
Tragedy of the Commons
• Why the difference?
– When the villagers act independently, they don’t consider
that when they send a steer out into the commons, it
negatively impacts how much weight the other steers will
gain.
– In a sense, you have a negative externality and
overproduction.
– When the villagers act collectively, they internalize this
externality.

14. Property Rights and the
Tragedy of the Commons
• Solving problems collectively is not always practical
– If the villagers collectively agree to send 1 steer into the
commons, each will get an income of $15.60.
– If one of the villagers cheats, the villager could get $19.
• Private ownership can provide a solution to the tragedy of the
commons.
– Suppose that the villagers face the same investment options as
before, but decide to auction off the rights to use the common
land to one of the villagers.
– Assume the villagers can borrow at an interest rate of 13%.
– What will happen?

15. Property Rights and the
Tragedy of the Commons
Government
Bond
Graze on the
Common Land
Expenses $100 Steer: $100
Land Use: X
Loan:X*(.13)
Value at Year End $113 $126+X
Net Income $13 $126+X
-100-X-X(.13)
=26-X(.13)

16. Property Rights and the
Tragedy of the Commons
• Socially optimal: 1 steer, 4 government bonds
• Looks like total village income is $65 ($13x5).
• BUT: If the village has any sense, they’ll invest the $100 they
received for the land and earn $13.
• So total village income=$78 (same as if they act collectively).
Government
Bond
Graze on the
Common Land
Expenses $100 Steer: $100
Land: $100
Loan: $13
Value at Year End $113 $226
Net Income $13 $13

17. Property Rights and the
Tragedy of the Commons
• When property rights can be clearly defined, the tragedy of
the commons can be solved through private ownership.
– We achieve the efficient outcome.
• BUT private ownership isn’t always practical
– Harvesting whales in international waters.
– Berries in public parks.
– Splitting a dessert.
– Global warming.