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: # of calves on the commons Price per 2- year-old cow sold ($) Income per cow ($ per year) 113030 212020 311414 411111 51088 61055 71022

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% # of calves on the commons Price per 2- year-old cow sold ($) Income per cow ($ per year) 113030 212020 311414 411111 51088 61055 71022 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 $5 # of calves on the commons Price per 2- year-old cow sold ($) Income per cow ($ per year) Total calf income ($ per year) Marginal income ($ per year) 30 113030 10 21202040 2 31141442 2 41111144

10. 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 113030 10 21202040 2 31141442 2 41111144 >$5  INVEST

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 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

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