042613

Tragedy of the Commons

April 26, 2013

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.

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).

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

Learning Goals for Today

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?

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.

Property Rights & Tragedy of the CommonsNumber 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



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



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



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



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.


• 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.


• 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?

Property Rights and theTragedy of the Commons

Government Bond

Graze on the Common Land

Expenses $100 Steer: $100Land Use: X

Loan: X*(.13)Value at Year End $113 $126+X

Net Income $13 $126+X-100-X-X(.13)

=26-X(.13)


• 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: $100Land: $100Loan: $13

Value at Year End $113 $226

Net Income $13 $13

Property Rights and theTragedy 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.

Documents

042613