tragedy of the commons property rights l.
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A safe stock that always sells for $20 in equilibrium. Pays $1 per year every year forever ... An optimal investor (with property rights) will invest to maximize ...

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tragedy of the commons property rights
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
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
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%
what will happen 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
what will happen w o property rights7
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
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
Income from calves with property rights

Invest as long as marginal income is at least $5

income from calves with property rights10
Income from calves with property rights

>$5  INVEST

>$5  INVEST

<$5  STOP!

Invest as long as marginal income is at least $5

what is the commons worth as a private good
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
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

Investment decision for the commons owner
summary tragedy of the commons
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