Tragedy of the Commons/ Property rights

Property rights are important in order for a person or firm to efficiently use its resources

Classic example Lack of property rights in a grassy

field Total benefit of the grassy field is zero

without property rights

Our example today

Two investment options A safe stock that always sells for $20

in equilibrium Pays $1 per year every year forever

Buy a 1-year-old calf today for $100 Able to sell at two years old The more calves on the grassy field, the

less each will be worth at two years old

What is the return on the safe stock?

Recall Chapter 8 The present value of a permanent

annual payment PV = M / r PV = $20 M = 1 This implies that r = 0.05, or 5%

Income from calves:# of

calves on the

commons

Price per 2-year-old cow sold

($)

Income per cow ($ per year)

1 130 30

2 120 20

3 114 14

4 111 11

5 108 8

6 105 5

7 102 2

What will happen w/o property rights?

People will buy calves as long as the return on the commons is at least 5% $5 return for the $100 investment

Income from calves w/o property rights: Rate of return of 5%

# of calves on

the commons

Price per 2-year-old cow sold

($)

Income per cow ($ per year)

1 130 30

2 120 20

3 114 14

4 111 11

5 108 8

6 105 5

7 102 2Equilibrium w/o property rights

What will happen w/o property rights?

People will buy calves as long as the return on the commons is at least 5% $5 return for the $100 investment

This is not efficient, however No gain versus the safe stock investment Similar to the no-toll situation on

congestible routes

What is efficient?

We need marginal analysis Find marginal income of each calf If marginal income is at least $5

invest in another calf If marginal income is less than $5

stop investing

Income from calves with property rights

Invest as long as marginal income is at least $5

# of calves on

the commons

Price per 2-year-old cow sold

($)

Income per cow ($ per year)

Total calf income ($ per year)

Marginal income ($ per year)

30

1 130 30 30  

        10

2 120 20 40  

        2

3 114 14 42

        2

4 111 11 44  

Income from calves with property rights

Invest as long as marginal income is at least $5

>$5 INVEST

<$5 STOP!

# of calves on the

commons

Price per 2-year-old

cow sold ($)

Income per cow ($ per

year)

Total calf income ($ per year)

Marginal income ($ per year)

30

1 130 30 30  

        10

2 120 20 40  

        2

3 114 14 42

        2

4 111 11 44  

>$5 INVEST

What is the commons worth as a private good? An optimal investor (with property

rights) will invest to maximize the value of commons Suppose that someone has $1000 to

invest What is each person’s willingness to

pay for the commons? How much will be invested in:

Stocks? Calves?

Investment analysis A person that owns the commons will

buy 2 calves $200 invested $40 return

Could get $10 return on the safe stock instead

$30 extra in return Willing to pay $600 to purchase the

commons

Investment decision for the commons owner Investment decision

of the person buying the commons

$600 to buy commons $200 to buy two

calves $200 in safe stocks

Total returns: $50 Commons

$40 for two calves Stock returns

$10 in payments

This is equilibrium, since any person will be indifferent between investing in the commons and in stocks

Summary: Tragedy of the Commons

Without private ownership, use of commons leads to no gain to society, relative to safe investments

With private ownership, the land has a positive value