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mmons/ Property rights

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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mmons/ Property rights

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  1. 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

  2. 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

  3. 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%

  4. Income from calves:

  5. 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

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

  7. 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

  8. 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

  9. Income from calves with property rights Invest as long as marginal income is at least $5

  10. Income from calves with property rights >$5  INVEST >$5  INVEST <$5  STOP! Invest as long as marginal income is at least $5

  11. 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?

  12. 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

  13. 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

  14. 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

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