Lecture 11 The Tragedy of the Commons

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Lecture 11The Tragedy of the Commons

• AEDE/NR 531
• Spring Quarter, 2006

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Tragedy of the Commons

• A tragedy of the commons occurs with so-called
  open-access resources.
• When there is no ownership of a resource
• No restrictions to access of the resource
• Result An inefficient allocation of the
  resource.
• TOTC first coined in a parable written in 1833 by
  William Forster Lloyd.
• Repopularized by Garrett Hardin in 1963 Science
  essay.

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Tragedy of the Commons

• If everyone has access to the resource, what rule
  will each person use for deciding how many units
  to extract?
• Answer Continue to extract until cost of
  extracting the last unit is greater than the
  benefit.
• No individual has to pay the scarcity costs they
  are imposing on the other person.
• For now, only consider the one-period case of
  resource extraction. This means there is no
  future to conserve for. Will look at
  intertemporal allocation later.

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Definitions

• Marginal Cost
• Def Cost of extracting each additional unit.
• Marginal Benefit
• Def Benefit of each additional unit. Likely, the
  price the good sells for on the market.
• Marginal Net Benefit
• Def Benefit Cost of last unit, or marg benefit
  marg cost.
• Aggregate Marginal Net Benefit
• Horizontal addition of each persons MNB.

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2-User Static Allocation

• AMNB is the market demand for the resource
• If price is below PA then AMNB is the sum of the
  two MNBs.

PA
P
AMNB
MNBA
MNBB
Q
QA
QB
QAQB
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2-User Static Allocation

• Say there is a scarce amount of water Qt for
  the current period.
• Efficient price if total supply is Qt would be
  P
• Extraction for both A and B are shown
  accordingly with P

P
AMNB
MNBA
MNBB
Q
QA
QB
Qt
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2-User Static Allocation if Supply is Restricted

• With open access, both will extract until MB
  MC. This occurs at QA and QB.
• QAQB is greater than the current supply, so
  both will race to extract as fast as possible.

AMNB
MNBA
MNBB
Q
Qt
QA
QB
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2-User Static Allocation if Supply is Restricted

• If they can extract at the same rate, they will
  split the available water.
• This occurs at Qt/2. This is how much each will
  get.

AMNB
MNBA
MNBB
Q
Qt
QA
QB
Qt/2
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2-User Allocation

• Aggregate Marginal Net Benefit shows the market
  demand for the resource.
• Inefficiency results because total demand exceeds
  supply.
• Efficiency here depends on allocating more of the
  resource to the person who has the higher
  marginal net benefit.

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Redraw diagram by flipping the direction of
person Bs MNB schedule
MNBB
MNBA
P
0
A
Qt
Qt
0
B
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Redraw diagram by flipping the direction of
person Bs MNB schedule
Efficient allocation equates marginal net
benefits.


MNBB
MNBA
P
0
Qt
QA
Qt
QB
0
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Redraw diagram by flipping the direction of
person Bs MNB schedule

• Net Benefit for A is area below MNB and up to QA
• Net Benfit for B is area below MNB and up to QB

MNBB
MNBA
NBA
NBB
P
0
Qt
QA
Qt
QB
0
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Redraw diagram by flipping the direction of
person Bs MNB schedule

• Net Benefit for A increases under even split.
• Net Benfit for B decreases under even split.
• Total Net Benefits decrease by triangle Z.

MNBB
MNBA
NBA
NBB
P
Z
0
Qt
QA
Qt
QB
0
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Efficient Allocation

• Imagine giving complete ownership of the resource
  to either person A or B. What would the
  allocation of resources be?
• If you give ownership to A, how much will they
  extract?
• If you give ownership to B, how much will they
  extract?
• Allow the person with ownership to sell the
  rights to extract to the other person. What price
  will they charge?

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Efficient Allocation Under Ownership


MNBB
MNBA
P
0
Qt
QA
Qt
QB
0
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Giving Ownership

• Person A would be willing to sell the right to
  extract to B if B is willing to pay more than the
  benefit A would receive from extracting it
  themselves.
• Person A would charge P to B for the right to
  extract each unit
• Marginal User Cost
• Def Scarcity cost imposed on others by
  extracting a scarce resource. In the diagram on
  the previous page it is equal to P.

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Giving Ownership

• If A charged an amount above P, A would extract
  more units themselves than would be efficient.
• If A charged an amount below P, B would pay to
  extract more units than would be efficient.
• Efficient allocation is achieved by having the
  person with the higher MNB curve extracting more.
  
• A higher MNB curve means society receives greater
  benefit from that persons use of the extracted
  resource than the other person.

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Ownership and Conservation

• Can imagine giving complete ownership to either
  the government or to a firm.
• If the government is person A who has complete
  ownership, the MNB for A may be the benefit from
  recreational use and non-use values of the
  public.
• Person B then is a natural resource extraction
  firm that pays P to buy the right to extract
  each unit of the resource.