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042613

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  • 1. Tragedy of the CommonsApril 26, 2013
  • 2. Announcements• Practice questions for the midterm (weekfrom today!) are now posted on website.• TAs will go over half of the questions in theirregularly scheduled discussion sections.• Jake will do a midterm review Thursday nightand go over other half– I’ll post on website when we find out where andwhen this will be. Around 6-8 pm.
  • 3. OMG midterm?• All topics from day 1 through today• Next week we’ll spend time pulling everything togetherWarnings:(1) You must be on-time to exam. Friday, May 3, 3pmsharp.-10% Deduction if you are 1 second late.-100% deduction if you arrive after someone elsefinishes and leaves room.(2) No leaving room during exam (it’s less than an hour).
  • 4. Last Class• Continued discussing externalities• Focused on when the Coase theoremapplies, and when it doesn’t– when it doesn’t, policy must be introduced
  • 5. Learning Goals for Today
  • 6. Property Rights and theTragedy of the Commons• The tragedy of the commons: the tendency for a resource thathas no price to be used until it’s marginal benefit=0.• Question: Do you have an incentive to go fill up that horriblepothole on your street?
  • 7. 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 of13%.– A $100 steer to send out onto the commons to graze for ayear.• The price at which they can sell the steer at the end of theyear depends on how much weight it gains, which in turndepends on how many other steers are sent out to graze inthe commons.
  • 8. Property Rights&Tragedy of the CommonsNumber ofSteers onCommonsPrice Per2-Year OldSteerIncomePer SteerTotalCattleIncomeMarginalIncome1 126 262 119 193 116 164 113 135 111 11The village has $500 total. What is the optimum amount of steersfor the entire village to choose (the rest buys 13% yield bonds)?ABCDE
  • 9. Property Rights&Tragedy of the CommonsNumber ofSteers onCommonsPrice Per2-Year OldSteerIncomePer SteerTotalCattleIncomeMarginalIncome1 126 262 119 193 116 164 113 135 111 11The village has $500 total. What is the optimum amount of steersfor the entire village to choose (the rest buys 13% yield bonds)?263848525526121043ABCDE
  • 10. Property Rights&Tragedy of the CommonsNumber ofSteers onCommonsPrice Per2-Year OldSteerIncomePer SteerTotalCattleIncomeMarginalIncome1 126 262 119 193 116 164 113 135 111 11If the villagers act independently, how many steers will be sentinto the commons?ABCDE
  • 11. Property Rights&Tragedy of the CommonsNumber ofSteers onCommonsPrice Per2-Year OldSteerIncomePer SteerTotalCattleIncomeMarginalIncome1 126 262 119 193 116 164 113 135 111 11If the villagers act independently, how many steers will be sentinto the commons?26384852552612104326/1=2638/2=1948/3=1652/4=1355/5=11Each!ABCDE
  • 12. Property Rights&Tragedy of the CommonsNumber ofSteers onCommonsPrice Per2-Year OldSteerIncomePer SteerTotalCattleIncomeMarginalIncome1 126 262 119 193 116 164 113 135 111 11What is the difference in incomes, Together – Separate?26384852552612104326/1=2638/2=1948/3=1652/4=1355/5=11Each!A) 17B) 15C) 13D) 11E) 9Together: 1 steer, 4 13% bonds.Separate: 4 steer, 1 13% bond.
  • 13. Property Rights and theTragedy of the Commons• Why the difference?– When the villagers act independently, they don’t considerthat when they send a steer out into the commons, itnegatively impacts how much weight the other steers willgain.– In a sense, you have a negative externality andoverproduction.– When the villagers act collectively, they internalize thisexternality.
  • 14. Property Rights and theTragedy of the Commons• Solving problems collectively is not always practical– If the villagers collectively agree to send 1 steer into thecommons, 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 thecommons.– Suppose that the villagers face the same investment options asbefore, but decide to auction off the rights to use the commonland to one of the villagers.– Assume the villagers can borrow at an interest rate of 13%.– What will happen?
  • 15. Property Rights and theTragedy of the CommonsGovernmentBondGraze on theCommon LandExpenses $100 Steer: $100Land Use: XLoan:X*(.13)Value at Year End $113 $126+XNet Income $13 $126+X-100-X-X(.13)=26-X(.13)
  • 16. Property Rights and theTragedy of the Commons• 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 theyreceived for the land and earn $13.• So total village income=$78 (same as if they act collectively).GovernmentBondGraze on theCommon LandExpenses $100 Steer: $100Land: $100Loan: $13Value at Year End $113 $226Net Income $13 $13
  • 17. Property Rights and theTragedy of the Commons• When property rights can be clearly defined, the tragedy ofthe 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.

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